Papers and Publications
Selected publications. Full list also on ORCID and Google Scholar.
Highlights
Four most-cited papers from the group, by Web of Science Core citation count.
2023
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Magnetic nanorods driven by rotating fields in water can be rapidly steered along any direction while generating strong and localized hydrodynamic flow fields. Here we show that, when raising the frequency of the rotating field, these nanopropellers undergo a dynamic transition from a rolling to a kayak-like motion due to the increase in viscous drag and acquire a finite inclination angle with respect to the plane perpendicular to the bottom surface. We explain these experimental observations with a theoretical model which considers the nanorod as a pair of ferromagnetic particles hydrodynamically interacting with a close stationary surface. Further, we quantify how efficiently microscopic cargoes can be trapped or expelled from the moving nanorod and use numerical simulations to unveil the generated hydrodynamic flow field. These propulsion regimes can be implemented in microfluidic devices to perform precise operations based on the selective sorting of microscopic cargoes.
2022
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We introduce a novel mesoscopic computational model based on a multiphase-multicomponent lattice Boltzmann method for the simulation of self-phoretic particles in the presence of liquid-liquid interfaces. Our model features fully resolved solvent hydrodynamics, and, thanks to its versatility, it can handle important aspects of the multiphysics of the problem, including particle wettability and differential solubility of the product in the two liquid phases. The method is extensively validated in simple numerical experiments, whose outcome is theoretically predictable, and then applied to the study of the behavior of active particles next to and trapped at interfaces. We show that their motion can be variously steered by tuning relevant control parameters, such as the phoretic mobilities, the contact angle, and the product solubility. Published under an exclusive license by AIP Publishing.
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Hypothesis: The dynamics of colloidal suspension confined within porous materials strongly differs from that in the bulk. In particular, within porous materials, the presence of boundaries with complex shapes entangles the longitudinal and transverse degrees of freedom inducing a coupling between the transport of the suspension and the density inhomogeneities induced by the walls. Method: Colloidal suspension confined within model porous media are characterized by means of active microrheology where a net force is applied on a single colloid (tracer particle) whose transport properties are then studied. The trajectories provided by active microrheology are exploited to determine the local transport coefficients. In order to asses the role of the colloid-colloid interactions we compare the case of a tracer embedded in a colloidal suspension to the case of a tracer suspended in an ideal bath. Finding: Our results show that the friction coefficient increases and the passage time distribution widens upon increasing the corrugation of the channel. These features are obtained for a tracer suspended in a (thermalized) colloidal bath as well as for the case of an ideal thermal bath. These results highlight the relevance of the confinement on the transport and show a mild dependence on the colloidal/thermal bath. Finally, we rationalize our numerical results with a semi-analytical model. Interestingly, the predictions of the model are quantitatively reliable for mild external forces, hence providing a reliable tool for predicting the transport across porous materials. (c) 2021 Elsevier Inc. All rights reserved.
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The homogeneous covering of amphiphillic polymer molecules onto metallic surfaces is of great importance for corrosion inhibitor applications. Lyophillic side chains grafted onto a lyophobic backbone act as anchors that allow the molecule to absorb at the metallic surface preventing the exposure with the solvent. Coarse-grained simulations are used to study the sorption and conformation behaviour of amphiphillic grafted polymers for corrosion inhibition. The backbone insolubility is found to play a key role in the sorption and conformation behaviour in the dilute limit. For finite concentrations, moderate backbone solubility and moderate molecule concentrations achieve optimal surface coverage, while highly a lyophobic backbone leads to bulk-like structures as a consequence of aggregation.
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Artificial active particles are autonomous agents able to convert energy from the environment into net propulsion, breaking detailed balance and the action-reaction law, clear signatures of their out-of-equilibrium nature. Here we investigate the emergence of directed motion in clusters composed of passive and catalytically active apolar colloids. We use a light-induced chemophoretic flow to rapidly assemble hybrid self-propelling clusters composed of hematite particles and passive silica spheres. By increasing the size of the passive cargo, we observe a reversal in the transport direction of the pair. We explain this complex yet rich phenomenon using a theoretical model which accounts for the generated chemical field and its coupling with the surrounding medium. We exploit further our technique to build up more complex, chemically driven, architectures capable of carrying several passive or active species, that quickly assemble and disassemble under light control.
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In active nematic liquid crystals, activity is able to drive chaotic spatiotemporal flows referred to as active turbulence. Active turbulence has been characterized through theoretical and experimental work as a low Reynolds number phenomenon. We show that, in two dimensions, the active forcing alone is able to trigger hydrodynamic turbulence leading to the coexistence of active and inertial turbulence. This type of flow develops for sufficiently active and extensile flow-aligning nematics. We observe that the combined effect of an extensile nematic and large values of the flow-aligning parameter leads to a broadening of the elastic energy spectrum that promotes a growth of kinetic energy able to trigger an inverse energy cascade.
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In viscous fluids, motile microentities such as bacteria or artificial swimmers often display different transport modes than macroscopic ones. A current challenge in the field aims at using friction asymmetry to steer the motion of microscopic particles. Here we show that lithographically shaped magnetic microtriangles undergo a series of complex transport modes when driven by a precessing magnetic field, including a surfing-like drift close to the bottom plane. In this regime, we exploit the triangle asymmetric shape to obtain a transversal drift which is later used to transport the microtriangle in any direction along the plane. We explain this friction-induced anisotropic sliding with a minimal numerical model capable to reproduce the experimental results. Due to the flexibility offered by soft-lithographic sculpturing, our method to guide anisotropic-shaped magnetic microcomposites can be potentially extended to many other field responsive structures operating in fluid media.
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Emergent behavior of dense living materials shows coexistence of both equilibrium and non-equilibrium features, such as glassy states and motility-induced phase separation. Here, the authors study transition between these two phases in a model of dense, disordered, soft active materials and find that the mechanism leading to fluidization from the glassy phase do not have an equilibrium counterpart.Dense active systems are widespread in nature, examples range from bacterial colonies to biological tissues. Dense clusters of active particles can be obtained by increasing the packing fraction of the system or taking advantage of a peculiar phenomenon named motility-induced phase separation (MIPS). In this work, we explore the phase diagram of a two-dimensional model of active glass and show that disordered active materials develop a rich collective behaviour encompassing both MIPS and glassiness. We find that, although the glassy state is almost indistinguishable from that of equilibrium glasses, the mechanisms leading to its fluidization do not have any equilibrium counterpart. Our results can be rationalized in terms of a crossover between a low-activity regime, where glassy dynamics is controlled by an effective temperature, and a high-activity regime, which drives the system towards MIPS.
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Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer-particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg-Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg-Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg-Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles.
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The sedimentation process in an active suspension is the result of the competition between gravity and the autonomous motion of particles. We carry out simulations of run-and-tumble squirmers that move in a fluid medium, focusing on the dependence of the non-equilibrium steady state on the swimming properties. We find that for large enough activity, the density profiles are no longer simple exponentials; we recover the numerical results through the introduction of a local effective temperature, suggesting that the breakdown of the Perrin-like exponential form is a collective effect due to fluid-mediated dynamic correlations among particles. We show that analogous concepts can also fit the case of active non-motile particles, for which we report the first study of this kind. Moreover, we provide evidence of scenarios where the solvent hydrodynamics induces non-local effects which require the full three-dimensional dynamics to be taken into account in order to understand sedimentation in active suspensions. Finally, analyzing the statistics of the orientations of microswimmers, the emergence of a height-dependent polar order in the system is discussed.
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Ratchet transport systems are widespread in physics and biology; however, the effect of the dispersing medium in the collective dynamics of these out-of-equilibrium systems has been often overlooked. We show that, in a traveling wave magnetic ratchet, long-range hydrodynamic interactions (His) produce a series of remarkable phenomena on the transport and assembly of interacting Brownian particles. We demonstrate that His induce the resynchronization with the traveling wave that emerges as a speed-up effect, characterized by a net raise of the translational speed, which doubles that of single particles. When competing with dipolar forces and the underlying substrate symmetry, His promote the formation of clusters that grow perpendicular to the driving direction. We support our findings both with Langevin dynamics and with a theoretical model that accounts for the fluid-mediated interactions. Our work illustrates the role of the dispersing medium on the dynamics of driven colloidal matter and unveils the growing process and cluster morphologies above a periodic substrate.
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We present a hydrodynamic theory for systems of dipolar active Brownian particles which, in the regime of weak dipolar coupling, predicts the onset of motility-induced phase separation (MIPS), consistent with Brownian dynamics (BD) simulations. The hydrodynamic equations are derived by explicitly coarse-graining the microscopic Langevin dynamics, thus allowing for a mapping of the coarse-grained model and particle-resolved simulations. Performing BD simulations at fixed density, we find that dipolar interactions tend to hinder MIPS, as first reported in [Liao et al., Soft Matter, 2020, 16, 2208]. Here we demonstrate that the theoretical approach indeed captures the suppression of MIPS. Moreover, the analysis of the numerically obtained, angle-dependent correlation functions sheds light into the underlying microscopic mechanisms leading to the destabilization of the homogeneous phase.
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In the nanoscale regime, flow behaviors for liquids show qualitative deviations from bulk expectations. In this work, we reveal by molecular dynamics simulations that plug flow down to nanoscale induces molecular friction that leads to a new flow structure due to the molecular clogging of the encaged liquid. This plug-like nanoscale liquid flow shows several features differ from the macroscopic plug flow and Poiseuille flow: It leads to enhanced liquid/solid friction, producing a friction of several order of magnitude larger than that of Couette flow; the friction enhancement is sensitively dependent of the liquid column length and the wettability of the solid substrates; it leads to the local compaction of liquid molecules that may induce solidification phenomenon for a long liquid column.
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In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes' characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.
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We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We perform a linear stability analysis of the homogeneous solution of the field equations and find both long-wavelength and short-wavelength instabilities. The former signals the emergence of a macroscopic structure, which we associate with motility-induced phase separation, while the second one signals the growth of a finite structure with a characteristic size. Intrinsic torques hinder phase separation, pushing the onset of the long-wavelength instability to higher activities. Furthermore, they generate finite-sized structures with a characteristic size proportional to both the self-propulsion velocity and the inverse of the self-rotation frequency. Our results show that a general mechanism might explain why chirality tends to suppress motility-induced phase separation but instead promotes the formation of non-equilibrium patterns. Published under an exclusive license by AIP Publishing.
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Block copolymer nanocomposites including anisotropic nanoparticles have been previously found to co-assemble into complex structures with nanoparticle alignment. Anisotropic nanoparticles with large aspect ratios are found to modify the morphology of block copolymers at modest concentrations, inducing a sphere-to-cylinder phase transition by breaking the local symmetry in the vicinity of a solid particle. This transition takes place over a wide range of NP lengths comparable with the BCP spacing. Controlling the orientation of uniaxial nanoparticles provides additional control over the global orientation of the block copolymer, as previously reported by experiments.
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Block copolymer melts have been previously used to control the position and alignment of anisotropic nanoparticles. In this work, 2D and 3D mesoscopic simulations are used to explore the phase behavior of block copolymer/nanoparticle systems. The method combines a time-dependent Ginzburg-Landau for the polymer and Brownian dynamics for the anisotropic nanoparticles. Rhomboidal and spheroidal shaped particles are simulated in two and three dimensions, respectively. It is found that the nanoparticle nematic order aligned by the block copolymer domains enhances the lamellar phase of the block copolymer, due to an anisotropy-driven phase transition. Additionally, anisotropic nanoparticles within circular-forming block copolymer leads to a competition between the nematic colloidal ordering and the hexagonally ordered mesophase. At large concentrations, the nematic order dominates, deforming the block copolymer mesophase.
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Similar to cells, bacteria, and other micro-organisms, synthetic chemically active colloids can harness the energy from their environment through a surface chemical reaction and use the energy to self-propel in fluidic environments. In this paper, we study the chemo-mechanical coupling that leads to the self-propulsion of chemically active colloids. The coupling between chemical reactions and momentum transport is a consequence of Onsager reciprocal relations. They state that the velocity and the surface reaction rate are related to mechanical and chemical affinities through a symmetric matrix. A consequence of Onsager reciprocal relations is that if a chemical reaction drives the motion of the colloid, then an external force generates a reaction rate. Here, we investigate Onsager reciprocal relations for a spherical active colloid that catalyzes a reversible surface chemical reaction between two species. We solve the relevant transport equations using a perturbation expansion and numerical simulations to demonstrate the validity of reciprocal relations around the equilibrium. Our results are consistent with previous studies and highlight the key role of solute advection in preserving the symmetry of the Onsager matrix. Finally, we show that Onsager reciprocal relations break down around a nonequilibrium steady state, which has implications for the thermal fluctuations of the active colloids used in experiments. Published under an exclusive license by AIP Publishing.
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In this work we study microwimmers, whether colloids or polymers, embedded in bulk or in confinement. We explicitly consider hydrodynamic interactions and simulate the swimmers via an implementation inspired by the squirmer model. Concerning the surrounding fluid, we employ a Dissipative Particle Dynamics scheme. Differently from the Lattice-Boltzmann technique, on the one side this approach allows us to properly deal not only with hydrodynamics but also with thermal fluctuations. On the other side, this approach enables us to study microwimmers with complex shapes, ranging from spherical colloids to polymers. To start with, we study a simple spherical colloid. We analyze the features of the velocity fields of the surrounding solvent, when the colloid is a pusher, a puller or a neutral swimmer either in bulk or confined in a cylindrical channel. Next, we characterise its dynamical behaviour by computing the mean square displacement and the long time diffusion when the active colloid is in bulk or in a channel (varying its radius) and analyze the orientation autocorrelation function in the latter case. While the three studied squirmer types are characterised by the same bulk diffusion, the cylindrical confinement considerably modulates the diffusion and the orientation autocorrelation function. Finally, we focus our attention on a more complex shape: an active polymer. We first characterise the structural features computing its radius of gyration when in bulk or in cylindrical confinement, and compare to known results obtained without hydrodynamics. Next, we characterise the dynamical behaviour of the active polymer by computing its mean square displacement and the long time diffusion. On the one hand, both diffusion and radius of gyration decrease due to the hydrodynamic interaction when the system is in bulk. On the other hand, the effect of confinement is to decrease the radius of gyration, disturbing the motion of the polymer and thus reducing its diffusion.
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We show that arbitrarily large polar flocks are susceptible to the presence of a single small obstacle. In a wide region of parameter space, the obstacle triggers counterpropagating dense bands leading to reversals of the flow. In very large systems, these bands interact, yielding a never-ending chaotic dynamics that constitutes a new disordered phase of the system. While most of these results were obtained using simulations of aligning self-propelled particles, we find similar phenomena at the continuous level, not when considering the basic Toner-Tu hydrodynamic theory, but in simulations of truncations of the relevant Boltzmann equation.
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Spontaneous capillary imbibition is a classical problem in interfacial fluid dynamics with a broad range of applications, from microfluidics to agriculture. Here we study the duration of the cross-over between an initial linear growth of the imbibition front to the diffusive-like growth limit of Washburn's law. We show that local-resistance sources, such as the inertial resistance and the friction caused by the advancing meniscus, always limit the motion of an imbibing front. Both effects give rise to a cross-over of the growth exponent between the linear and the diffusive-like regimes. We show how this cross-over is much longer than previously thought - even longer than the time it takes the liquid to fill the porous medium. Such slowly slowing-down dynamics is likely to cause similar long cross-over phenomena in processes governed by wetting.
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We provide a comprehensive quantitative analysis of localized and extended topological defects in the steady state of 2D passive and active repulsive Brownian disk systems. We show that, both in and out-of-equilibrium, the passage from the solid to the hexatic is driven by the unbinding of dislocations, in quantitative agreement with the KTHNY singularity. Instead, extended clusters of defects largely dominate below the solid-hexatic critical line. The latter percolate in the liquid phase very close to the hexatic-liquid transition, both for continuous and discontinuous transitions, in the homogeneous liquid regime. At critical percolation the clusters of defects are fractal with statistical and geometric properties that are independent of the activity and compatible with the universality class of uncorrelated critical percolation. We also characterize the spatial organization of point-like defects and we show that the disclinations are not free, but rather always very near more complex defect structures. At high activity, the bulk of the dense phase generated by Motility-Induced Phase Separation is characterized by a density of point-like defects, and statistics and morphology of defect clusters, set by the amount of activity and not the packing fraction. Hexatic domains within the dense phase are separated by grain-boundaries along which a finite network of topological defects resides, interrupted by gas bubbles in cavitation. This structure is dynamic in the sense that the defect network allows for an unzipping mechanism that leaves free space for gas bubbles to appear, close, and even be released into the dilute phase.
2021
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Active nematic fluids confined in narrow channels are known to generate spontaneous flows when the activity is sufficiently intense. Recently, it was demonstrated [R. Green, J. Toner, and V. Vitelli, Phys. Rev. Fluids 2, 104201 (2017)] that if the molecular anchoring at the channel walls is conflicting, i.e., perpendicular on one plate and parallel on the other, flows are initiated even in the zero activity limit. An analytical laminar velocity profile for this specific configuration was derived within a simplified nematohydrodynamic model in which the nematic order parameter is a fixed-magnitude unit vector n. The solution holds in a regime where the flow does not perturb the nematic order imposed by the walls. In this study, we explore systematically active flows in this confined geometry with a more general theoretical model that uses a second-rank tensor order parameter Q to express both the magnitude and orientation of the nematic phase. The Q-model allows for the presence of defects and biaxial, in addition to uniaxial, molecular arrangements. Our aim is to provide a unified picture, beyond the limiting regime explored previously, to serve as a guide for potential microfluidic applications that exploit the coupling between the orientational order of the molecules and the velocity field to finely control the flow and overcome the intrinsic difficulties of directing and pumping fluids at the microscale. We reveal how the nematic-flow coupling is not only dependent on geometrical constraints, but is also highly sensitive to material and flow parameters. We specifically stress the key role played by the activity and the flow aligning parameter, and we show that solutions mostly depend on two dimensionless parameters. We find that for large values of the activity parameter, the flow is suppressed for contractile particles while it is either sustained or suppressed for extensile particles depending on whether they tend to align or tumble when subject to shear. We explain these distinct behaviors by an argument based on the results of the stability analysis applied to two simpler configurations: active flows confined between parallel plates with either orthogonal or perpendicular alignment at both walls. We show that the analytical laminar solution derived for the n model in the low activity limit is found also in the Q model, both analytically and numerically. This result is valid for both contractile and extensile particles and for a flow-tumbling as well as aligning nematics. We remark that this velocity profile can be derived for generic boundary conditions. To stress the more general nature of the Q model, we conclude by providing a numerical example of a biaxial three-dimensional thresholdless active flow for which we show that biaxiality is especially relevant for a weakly first-order isotropic-nematic phase transition.
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Depletion interactions between colloids of discoidal shape can induce their self-assembly into columnar aggregates. This is an effect of entropic origin with important implications in a range of colloidal systems, particularly in the clustering of erythrocytes that determine the rheological properties of blood. Here, we investigate the equilibrium state reached by discoidal colloids in a solution of smaller depletant particles. We develop a thermodynamic model of depletion-induced aggregation based on self-assembly theory and solve it analytically. We test the validity of the model by using Langevin simulations of a system of discs and depletant particles in which the depletion interaction emerges naturally. In addition, we consider the effect of an attractive interaction between depletant and discoidal particles, which we show induces a re-entrant dependence of aggregation with temperature.
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Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a nonequilibrium phase transition into a quasihexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.
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We investigate phase separation in a chiral fluid, made of spinning ferromagnetic colloids that interact both via hydrodynamic and dipolar forces and collectively organize into separated circulating clusters. We show that, at high spinning frequency, hydrodynamics dominate over attractive magnetic interactions and impede coarsening, forcing the particles to assemble into a collection of finite rotating clusters of controllable size. We introduce a minimal particle-based model that unveils the fundamental role of hydrodynamics and the boundary plane in the self-organization process of the colloidal spinners. Our results shed light on the control of coarsening and dynamic self-assembly in chiral active systems and the key role played by fluid mediated long-range interactions.
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Active matter deals with systems whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures, several models have been suggested, such as the on-lattice model of run-and-tumble particles implemented via the persistent exclusion process (PEP). In our work, we study a one-dimensional system of run-and-tumble repulsive or attractive particles, both on-lattice and off-lattice. Additionally, we implement cluster motility dynamics in the on-lattice case (since in the off-lattice case, cluster motility arises from the individual particle dynamics). While we observe important differences between discrete and continuous dynamics, few common features are of particular importance. Increasing particle density drives aggregation across all different systems explored. For non-attractive particles, the effects of particle activity on aggregation are largely independent of the details of the dynamics. In contrast, once attractive interactions are introduced, the steady-state, which is completely determined by the interplay between these and the particles' activity, becomes highly dependent on the details of the dynamics.
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We present a comprehensive study about the relationship between the way detailed balance is broken in non-equilibrium systems and the resulting violations of the fluctuation-dissipation theorem. Starting from stochastic dynamics with both odd and even variables under time-reversal, we derive an explicit expression for the time-reversal operator, i.e. the Markovian operator which generates the time-reversed trajectories. We then exploit the relation between entropy production and the breakdown of detailed balance to establish general constraints on the non-equilibrium steady-states (NESS), which relate the non-equilibrium character of the dynamics with symmetry properties of the NESS distribution. This provides a direct route to derive extended fluctuation-dissipation relations, expressing the linear response function in terms of NESS correlations. Such framework provides a unified way to understand the departure from equilibrium of active systems and its linear response. We then consider two paradigmatic models of interacting self-propelled particles, namely active Brownian particles and active Ornstein-Uhlenbeck particles. We analyze the non-equilibrium character of these systems (also within a Markov and a Chapman-Enskog approximation) and derive extended fluctuation-dissipation relations for them, clarifying which features of these active model systems are genuinely non-equilibrium.
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Collective guidance of out-of-equilibrium systems without using external fields is a challenge of paramount importance in active matter, ranging from bacterial colonies to swarms of self-propelled particles. Designing strategies to guide active matter and exploiting enhanced diffusion associated to its motion will provide insights for application from sensing, drug delivery to water remediation. However, achieving directed motion without breaking detailed balance, for example by asymmetric topographical patterning, is challenging. Here we engineer a two-dimensional periodic topographical design with detailed balance in its unit cell where we observe spontaneous particle edge guidance and corner accumulation of self-propelled particles. This emergent behaviour is guaranteed by a second-order non-Hermitian skin effect, a topologically robust non-equilibrium phenomenon, that we use to dynamically break detailed balance. Our stochastic circuit model predicts, without fitting parameters, how guidance and accumulation can be controlled and enhanced by design: a device guides particles more efficiently if the topological invariant characterizing it is non-zero. Our work establishes a fruitful bridge between active and topological matter, and our design principles offer a blueprint to design devices that display spontaneous, robust and predictable guided motion and accumulation, guaranteed by out-of-equilibrium topology.
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Generation of mechanical oscillations is ubiquitous to a wide variety of intracellular processes, ranging from activity of muscle fibers to oscillations of the mitotic spindle. The activity of motors plays a vital role in maintaining the integrity of the mitotic spindle structure and generating spontaneous oscillations. Although the structural features and properties of the individual motors are well characterized, their implications on the functional behavior of motor-filament complexes are more involved. We show that force-induced allosteric deformations in dynein, which result in catchbonding behavior, provide a generic mechanism to generate spontaneous oscillations in motor-cytoskeletal filament complexes. The resultant phase diagram of such motor-filament systems-characterized by force-induced allosteric deformations-exhibits bistability and sustained limit-cycle oscillations in biologically relevant regimes, such as for catchbonded dynein. The results reported here elucidate the central role of this mechanism in fashioning a distinctive stability behavior and oscillations in motor-filament complexes such as mitotic spindles.
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Computer simulations of experimentally comparable system sizes in soft matter often require considerable elapsed times. The use of many cores can reduce the needed time, ideally proportionally to the number of processors. In this paper a parallel computational method using coarray Fortran is implemented and tested for large systems of purely block copolymer melts, as well as block copolymer nanocomposites. A satisfactory strong scaling is shown up to 512 cores while a weak scaling with a drop in performance is achieved up to 4096 cores. The scaling of the parallel cell dynamic simulations scheme displays no drawbacks over MPI and provides an example of the simplicity of the coarray approach. The code has been tested on several architectures and compilers. The hybrid block copolymer/nanoparticle algorithm can achieve previously unavailable system sizes.
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We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.
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Polar active particles constitute a wide class of active matter that is able to propel along a preferential direction, given by their polar axis. Here, we demonstrate a generic active mechanism that leads to their spontaneous chiralization through a symmetry-breaking instability. We find that the transition of an active particle from a polar to a chiral symmetry is characterized by the emergence of active rotation and of circular trajectories. The instability is driven by the advection of a solute that interacts differently with the two portions of the particle surface and it occurs through a supercritical pitchfork bifurcation.
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Magnetic colloids adsorbed at a fluid interface are unique model systems to understand self-assembly in confined environments, both in equilibrium and out of equilibrium, with important potential applications. In this work the pearl-chain-like self-assembled structures of superparamagnetic colloids confined to a fluid-fluid interface under static and time-dependent actuations are investigated. On the one hand, it is found that the structures generated by static fields transform as the tilt angle of the field with the interface is increased, from 2D crystals to separated pearl-chains in a process that occurs through a controllable and reversible zip-like thermally activated mechanism. On the other hand, the actuation with precessing fields about the axis perpendicular to the interface induces dynamic self-assembled structures with no counterpart in non-confined systems, generated by the interplay of averaged magnetic interactions, interfacial forces, and hydrodynamics. Finally, how these dynamic structures can be used as remotely activated roller conveyors, able to transport passive colloidal cargos at fluid interfaces and generate parallel viscous flows is shown. The latter can be used in the mixture of adsorbed molecules and the acceleration of surface-chemical reactions, overcoming diffusion limitations.
2020
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Simulations and experiments of nanorods (NRs) show that co-assembly with block copolymer (BCP) melts leads to the formation of a superstructure of side-to-side NRs perpendicular to the lamellar axis. A mesoscopic model is validated against scanning electron microscopy (SEM) images of CdSe NRs mixed with polystyrene-block-poly(methyl methacrylate). It is then used to study the co-assembly of anisotropic nanoparticles (NPs) with a length in the same order of magnitude as the lamellar spacing. The phase diagram of BCP/NP is explored as well as the time evolution of the NR. NRs that are slightly larger than the lamellar spacing are found to rotate and organize side-to-side with a tilted orientation with respect to the interface. Strongly interacting NPs are found to dominate the co-assembly, while weakly interacting nanoparticles are less prone to form aggregates and tend to form well-ordered configurations.
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Binary fluids are present in a wide variety of systems at microscales, such as microfluidic devices containing drops, fluids with air bubbles trapped in them, and devices designed to mix fluids or to make two fluid substances react. Microfluidics devices are often, intentionally or unintentionally, subject to pulsatile forces due to the passing of drops. We demonstrate that when a binary fluid is subject to a pulsatile forcing, the compressibility of the lower viscosity phase is so important that it is able to generate resonances in the dynamic permeability of the whole system. This implies that the flow amplitude of a binary-fluid system in a zero-mean flow could be optimized at certain frequencies. The dynamic permeability is a powerful concept to describe the dynamics of the system, in the regime where the flow and the pressure gradient are related linearly in the frequency domain. We find two regimes for the frequency at which the resonance occurs: one dominated by a characteristic frequency of the system, related to the compressibility of the lower viscosity phase; and another one dominated by a more complex frequency, involving both the characteristic viscous frequency of the lower viscosity phase and a characteristic frequency related to the compressibility. In order to guide potential experiments, we calculate relevant quantities for two sets of binary fluids in standard microfluidic setups. Our calculations imply that for systems of typical microfluidic dimensions, involving a compressible fluid, the existence of the compressibility-induced resonance has to be contemplated for a correct description of the dynamics.
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We combine experiments and numerical simulations to investigate the emergence of clogging in a system of interacting paramagnetic colloidal particles driven against a disordered landscape of larger obstacles. We consider a single aperture in a landscape of immobile silica particles which are irreversibly attached to the substrate. We use an external rotating magnetic field to generate a traveling wave potential which drives the magnetic particles against these obstacles at a constant and frequency tunable speed. Experimentally we find that the particles display an intermittent dynamics with power law distributions at high frequencies. We reproduce these results by using numerical simulations and show that clogging in our system arises at large frequency, when the particles desynchronize with the moving landscape. Further, we use the model to explore the hidden role of flexibility in the obstacle displacements and the effect of hydrodynamic interactions between the particles. We also consider numerically the situation of a straight wall and investigate the range of parameters where clogging emerges in such case. Our work provides a soft matter test-bed system to investigate the effect of clogging in driven microscale matter.
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Populations of mobile agents-animal groups, robot swarms, or crowds of people-self-organize into a large diversity of states as a result of information exchanges with their surroundings. While in many situations of interest the motion of the agents is driven by the transmission of information from neighboring peers, previous modeling efforts have overlooked the feedback between motion and information spreading. Here we show that such a feedback results in contagion enhanced by flocking. We introduce a reference model in which agents carry an internal state whose dynamics is governed by the susceptible-infected-susceptible (SIS) epidemic process, characterizing the spread of information in the population and affecting the way they move in space. This feedback triggers flocking, which is able to foster social contagion by reducing the epidemic threshold with respect to the limit in which agents interact globally. The velocity of the agents controls both the epidemic threshold and the emergence of complex spatial structures, or swarms. By bridging together soft active matter physics and modeling of social dynamics, we shed light upon a positive feedback mechanism driving the self-organization of mobile agents in complex systems.
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Droplets made of a water/ethanol mixture spontaneously self-propel in an oil/surfactant solution and, depending on the initial ethanol concentration at the time of production, may evolve in up to three stages. Upon self-propulsion the droplets absorb surfactant molecules during their continuous motion in the oily phase. In combination with the continuous loss of ethanol this mass exchange with the ambient phase may lead to a spontaneous phase separation of the water/ethanol mixture, and eventually to the formation of characteristic Janus droplets. Supported by experimental evidence, we propose a simple model that is able to explain the propulsion velocity and its scaling with the droplet radius in the last stage of the droplet evolution.
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Changes in membrane deformation and compressibility, induced by an external electric field, are investigated using coarse-grained MARTINI force field simulations in a salt-free environment. We observe changes in the area of the membrane above a critical electric field. Below this value, the membrane compressibility modulus is found to decrease monotonically. For higher electric fields, the membrane projected area remains constant while the net interfacial area increases, with the corresponding compressibility moduli, show the opposite behavior. We find that the mechanical parameters, surface tension and bending modulus, of a freely floating membrane in the absence of explicit ions, are unaffected by the presence of the electric field. We believe these results have a bearing on our understanding of the electroformation of uncharged lipids in a salt-free environment.
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In this manuscript we describe the realization of a minimal hybrid microswimmer, composed of a ferromagnetic nanorod and a paramagnetic microsphere. The unbounded pair is propelled in water upon application of a swinging magnetic field that induces a periodic relative movement of the two composing elements, where the nanorod rotates and slides on the surface of the paramagnetic sphere. When taken together, the processes of rotation and sliding describe a finite area in the parameter space, which increases with the frequency of the applied field. We develop a theoretical approach and combine it with numerical simulations, which allow us to understand the dynamics of the propeller and explain the experimental observations. Furthermore, we demonstrate a reversal of the microswimmer velocity by varying the length of the nanorod, as predicted by the model. Finally, we determine theoretically and in experiments the Lighthill's energetic efficiency of this minimal magnetic microswimmer.
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In this article, using numerical simulations we investigate the self-assembly of rod-like particles in suspension due to depletion forces which naturally emerge due to the presence of smaller spherical depletant particles. We characterize the type of clusters that are formed and the evolution of aggregation departing from a random initial configuration. We show that eventually the system reaches a thermodynamic equilibrium state in which the aggregates break and reform dynamically. We investigate the equilibrium state of aggregation, which exhibits a strong dependence on depletant concentration. In addition, we provide a simple thermodynamic model inspired on the theory of self-assembly of amphiphilic molecules which allows us to understand qualitatively the equilibrium aggregate size distributions that we obtain in simulation.
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We study the self-propulsion of a charged colloidal particle that releases ionic species using theory and experiments. We relax the assumptions of thin Debye length and weak nonequilibrium effects assumed in classical phoretic models. This leads to a number of unexpected features that cannot be rationalized considering the classic phoretic framework: an active particle can reverse the direction of motion by increasing the rate of ion release and can propel even with zero surface charge. Our theory predicts that there are optimal conditions for self-propulsion and a novel regime in which the velocity is insensitive to the background electrolyte concentration. The theoretical results quantitatively capture the salt-dependent velocity measured in our experiments using active colloids that propel by decomposing urea via a surface enzymatic reaction.
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We examine a mechanism of locomotion of active particles whose surface is uniformly coated with mobile enzymes. The enzymes catalyze a reaction that drives phoretic flows but their homogeneous distribution forbids locomotion by symmetry. We find that the ability of the enzymes to migrate over the surface combined with self-phoresis can lead to a spontaneous symmetry-breaking instability whereby the homogeneous distribution of enzymes polarizes and the particle propels. The instability is driven by the advection of enzymes by the phoretic flows and occurs above a critical Peclet number. The transition to polarized motile states occurs via a supercritical or subcritical pitchfork bifurcations, the latter of which enables hysteresis and coexistence of uniform and polarized states.
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In this perspective communication, we briefly sketch the current state of computational (bio)material research and discuss possible solutions for the four challenges that have been increasingly identified within this community: (i) the desire to develop a unified framework for testing the consistency of implementation and physical accuracy for newly developed methodologies, (ii) the selection of a standard format that can deal with the diversity of simulation data and at the same time simplifies data storage, data exchange, and data reproduction, (iii) how to deal with the generation, storage, and analysis of massive data, and (iv) the benefits of efficient core engines. Expressed viewpoints are the result of discussions between computational stakeholders during a Lorentz center workshop with the prosaic title Workshop on Multi-scale Modeling and are aimed at (i) improving validation, reporting and reproducibility of computational results, (ii) improving data migration between simulation packages and with analysis tools, (iii) popularizing the use of coarse-grained and multi-scale computational tools among non-experts and opening up these modern computational developments to an extended user community.
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Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external force. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically the suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamically resolved solute-mediated phoretic interactions and solvent-mediated hydrodynamic interactions. Our results show that the system displays different scenarios at changing the colloid-solute affinity and it develops a cluster phase in the chemoattractive case. We study the statistics of cluster sizes and cluster morphologies for different magnitudes of colloidal activity. Finally, we provide evidences that hydrodynamics plays a relevant role in the aggregation kinetics and cluster morphology, significantly hindering cluster growth.
2019
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Recently, we characterized the complete phase transition diagram in the phi-Pe parameter space for two models of active brownian particles in two dimensions. These models are composed of hard disks and dumbbells, respectively, the former being isotropic and the latter anisotropic. Here, we want to outline all the most significant features of these two paradigmatic models and compare them.Remarkably, the phase diagrams of the two models are affected differently by the introduction of activity. Disks present a two-stage melting scenario from Pe=0 to about Pe=3, with a first order phase transition between liquid and hexatic and a Berezinskii-Kosterlitz-Thouless transition between hexatic and solid. At higher activities, the three phases are still observed, but the transition between liquid and hexatic becomes a BKT transitions without a distinguishable coexistence region. Dumbbells, instead, present a macroscopic coexistence between hexatically ordered regions and disordered ones, over a finite interval of packing fractions, for all activities, included Pe=0, without any observable discontinuity in the behavior upon increasing Pe.
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Synchronization, the temporal coordination of coupled oscillators, allows fireflies to flash in unison, neurons to fire collectively, and human crowds to fall in step on the London millenium bridge. Here, we interpret active (or self-propelled) chiral microswimmers with a distribution of intrinsic frequencies as motile oscillators and show that they can synchronize over very large distances, even for local coupling in two dimensions (2D). This opposes canonical nonactive oscillators on static or time-dependent networks, leading to synchronized domains only. A consequence of this activity-induced synchronization is the emergence of a mutual flocking phase, where particles of opposite chirality cooperate to form superimposed flocks moving at a relative angle to each other, providing a chiral active matter analogue to the celebrated Toner-Tu phase. The underlying mechanism employs a positive feedback loop involving the two-way coupling between oscillators' phase and self-propulsion and could be exploited as a design principle for synthetic active materials and chiral self-sorting techniques.
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We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, the amplitude, and the packing density of grains. We determine the local density and kinetic energy profiles of granular particles along the axis of the dimer to find no gradients in the density fields and additive gradients in the kinetic energies. Published under license by AIP Publishing.
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Block copolymer are ideal matrices to control the localisation of colloids. Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an additional orientational degree of freedom that can play a crucial role in the formation of highly ordered materials made of block copolymers. This work presents a mesoscopic simulation method to assert the co-assembly of Janus nanoparticles in a block copolymer mixture, finding numerous instances of aggregation and formation of ordered configurations. Comparison with chemically homogeneous neutral nanoparticles shows that Janus nanoparticles are less prone to induce bridging along lamellar domains, thus being a less destructive way to segregate nanoparticles at interfaces. The combination of asymmetric block copolymer and asymmetric Janus nanoparticles can result in assembly of colloids with an even number of layers within the minority domain.
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We study the flow properties of red blood cells in confined channels, when the channel width is comparable to the cell size. We focus on the case of intermediate concentrations when hydrodynamic interactions between cells play a dominant role. This regime is different to the case of low concentration in which the cells behave as hydrodynamically isolated. In this last case, the dynamic behavior is entirely controlled by the interplay between the interaction with the wall and the elastic response of the cell membrane. Our results highlight the different fluid properties when collective flow is present. The cells acquire a characteristic slipper shape, and parachute shapes are only observed at very large capillary numbers. We have characterized the spatial ordering and the layering by means of a pairwise correlation function. Focusing effects are observed at the core of the channel instead of at the lateral position typical of the single-train case. These results indicate that at these intermediate concentrations we observed at the microscale the first steps of the well-known macroscopic Fahraeus-Lindqvist effect. The rheological properties of the suspension are studied by means of the effective viscosity, with an expected shear-thinning behavior. Two main differences are obtained with respect to the single-train case. First, a large magnitude of the viscosity is obtained indicating a high resistance to flow. Secondly, the shear-thinning behavior is obtained at larger values of the capillary number respect to the single-train case. These results suggest that the phenomena of ordering in space and orientation occur at higher values of the capillary number.
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Recent experiments with electrolytes driven through conical nanopores give evidence of strong rectified current response. In such devices, the asymmetry in the confinement is responsible for the non-Ohmic response, suggesting that the interplay of entropic and enthalpic forces plays a major role. Here, we propose a theoretical model to shed light on the physical mechanism underlying ionic current rectification. By use of an effective description of the ionic dynamics, we explore the system's response in different electrostatic regimes. We show that the rectification efficiency, as well as the channel selectivity, is driven by the surface-to-bulk conductivity ratio Dukhin length rather than the electrical double layer overlap.
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The realization of artificial microscopic swimmers able to propel in viscous fluids is an emergent research field of fundamental interest and vast technological applications. For certain functionalities, the efficiency of the microswimmer in converting the input power provided through an external actuation into propulsive power output can be critical. Here we use a microswimmer composed by a self-assembled ferromagnetic rod and a paramagnetic sphere and directly determine its swimming efficiency when it is actuated by a swinging magnetic field. Using fast video recording and numerical simulations we fully characterize the dynamics of the propeller and identify the two independent degrees of freedom which allow its propulsion. We then obtain experimentally the Lighthill's energetic efficiency of the swimmer by measuring the power consumed during propulsion and the energy required to translate the propeller at the same speed. Finally, we discuss how the efficiency of our microswimmer could be increased upon suitable tuning of the different experimental parameters.
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We characterize the dynamics of a z - z electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated with externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We show here that the linear transport coefficients are particularly sensitive to the geometry and the conductive properties of the channel walls when the Debye length is comparable to the channel width. In this regime, we found that one pair of off-diagonal Onsager matrix elements increases with the corrugation of the channel transport, in contrast to all other elements which are either unaffected by or decrease with increasing corrugation. Our results have a possible impact on the design of blue-energy devices as well as on the understanding of biological ion channels through membranes. Published under license by AIP Publishing.
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Artificial microswimmers have the potential for applications in many fields, ranging from targeted cargo delivery and mobile sensing to environmental remediation. In many of these applications, the artificial swimmers will operate in complex media necessarily involving liquid-liquid interfaces. Here, we experimentally study the motion of chemically powered phoretic active colloids close to liquid-liquid interfaces while swimming next to a solid substrate. In a system involving this complex geometry, we find that the active particles have an alignment interaction with both the neighbouring solid and liquid interfaces, allowing for a robust guiding mechanism along the liquid interface. We compare with minimal active Brownian simulations to show that these phoretically active particles stay along the interfaces for much longer times and lengths than expected for standard active Brownian particles. We also track the propulsion speeds of these particles and find a reduced speed close to the liquid-liquid interface. We report an interesting non-linear dependence of this reduction on the particle's bulk speed.
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Block copolymer melts self-assemble in the bulk into a variety of nanostructures, making them perfect candidates to template the position of nanoparticles. The morphological changes of block copolymers are studied in the presence of a considerable filling fraction of colloids. Furthermore, colloids can be found to assemble into ordered hexagonally close-packed structures in a defined number of layers when softly confined within the phase-separated block copolymer. A high concentration of interface-compatible nanoparticles leads to complex long-lived block copolymer morphologies depending on the polymeric composition. Macrophase separation between the colloids and the block copolymer can be induced if colloids are unsolvable within the matrix. This leads to the formation of ellipsoid-shaped polymer-rich domains elongated along the direction perpendicular to the interface between block copolymer domains.
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In this article, we combine experiments and theory to investigate the transport properties of anisotropic hematite colloidal rotors that dynam ically assemble into translating clusters upon application of a rotating magnetic field. The applied field exerts a torque to the particles forcing rotation close to a surface and thus a net translational motion at a frequency tunable speed. When approaching, pairs of particles are observed to assemble into stable three-dimensional clusters that perform a periodic leap-frog type dynamics and propel at a faster speed. We analyze the cluster formation and its lifetime and investigate the role of particle shape in the propulsion speed and stability. We show that the dynamics of the system results from a delicate balance between magnetic dipolar interactions and hydrodynamics, and we introduce a theoretical model that qualitatively explains the observed phenomena.
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We address the question of how interacting active systems in a nonequilibrium steady state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for active Brownian particles (ABP), which highlights the role played by the local violation of detailed balance due to activity. By making use of a Markovian approximation we derive closed Green-Kubo expressions for the diffusivity and mobility of ABP and quantify the deviations from the Stokes-Einstein relation. We compute the linear response function to an external force using unperturbed simulations of ABP and compare the results with the analytical predictions of the transport coefficients. Our results show the importance of the interplay between activity and interactions in the departure from equilibrium linear response.
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Self-propulsion of magneto-elastic composite microswimmers is demonstrated under a uniaxial field at both the air-water and the water-substrate interfaces. The microswimmers are made of elastically linked magnetically hard Co-Ni-P and soft Co ferromagnets, fabricated using standard photolithography and electrodeposition. Swimming speed and direction are dependent on the field frequency and amplitude, reaching a maximum of 95.1 mu m/s on the substrate surface. Fastest motion occurs at low frequencies via a spinning (air-water interface) or tumbling (water-substrate interface) mode that induces transient inertial motion. Higher frequencies result in low Reynolds number propagation at both interfaces via a rocking mode. Therefore, the same microswimmer can be operated as either a high or a low Reynolds number swimmer. Swimmer pairs agglomerate to form a faster superstructure that propels via spinning and rocking modes analogous to those seen in isolated swimmers. Microswimmer propulsion is driven by a combination of dipolar interactions between the Co and Co-Ni-P magnets and rotational torque due to the applied field, combined with elastic deformation and hydrodynamic interactions between different parts of the swimmer, in agreement with previous models.
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A hybrid two-dimensional block copolymer (BCP) nanocomposite computational model is proposed to study nanoparticles (NPs) with a generalized shape including square, rectangle, and rhombus. Simulations are used to study the role of anisotropy in the assembly of colloids within BCPs, ranging from NPs that are compatible with one phase to neutral NPs. The ordering of squarelike NPs into grid configurations within a minority BCP domain was investigated, as well as the alignment of nanorods in a lamellar-forming BCP, comparing the simulation results with experiments of mixtures of nanoplates and polystyrene-b-poly(methyl methacrylate) BCP. The assembly of rectangular NPs at the interface between domains resulted in alignment along the interface. The aspect ratio is found to play a key role in the aggregation of colloids at the interface, which leads to a distinct co-assembly behavior for low- and high-aspect-ratio NPs.
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Due to the combined effect of anisotropic interactions and activity, Janus swimmers are capable to self-assemble in a wide variety of structures, many more than their equilibrium counterpart. This might lead to the development of novel active materials capable of performing tasks without any central control. Their potential application in designing such materials endows trying to understand the fundamental mechanism in which these swimmers self-assemble. In the present work, we study a quasi-two-dimensional semidilute suspensions of two classes of amphiphilic spherical swimmers whose direction of motion can be tuned: either swimmers propelling in the direction of the hydrophobic patch or swimmers propelling in the opposite direction (toward the hydrophilic side). In both systems we have systematically tuned swimmers' hydrophobic strength and signature and observed that the anisotropic interactions, characterized by the angular attractive potential and its interaction range, in competition with the active stress, pointing toward or against the attractive patch gives rise to a rich aggregation phenomenology.
2018
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We use the dynamic length and time scale separation in suspensions to formulate a general description of colloidal thermophoresis. Our approach allows an unambiguous definition of separate contributions to the colloidal flux and clarifies the physical mechanisms behind non-equilibrium motion of colloids. In particular, we derive an expression for the interfacial force density that drives single-particle thermophoresis in non-ideal fluids. The issuing relations for the transport coefficients explicitly show that interfacial thermophoresis has a hydrodynamic character that cannot be explained by a purely thermodynamic consideration. Our treatment generalises the results from other existing approaches, giving them a clear interpretation within the framework of non-equilibrium thermodynamics.
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Collections of interacting active particles, self-propelling or not, have shown remarkable phenomena including the emergence of dynamic patterns across different length scales, from animal groups to vibrated grains, microtubules, bacteria, and chemicalor field-driven colloids. Burgeoning experimental and simulation activities are now exploring the possibility of realizing solid and stable structures from passive elements that are assembled by a few active dopants. Here we show that such an elusive task may be accomplished by using a small amount of apolar dopants, namely synthetic active but not self-propelling units. We use blue light to rapidly assemble 2D colloidal clusters and gels via nonequilibrium diffusiophoresis, where microscopic hematite dockers form long-living interstitial bonds that strongly glue passive silica microspheres. By varying the relative fraction of doping, we uncover a rich phase diagram including ordered and disordered clusters, space-filling gels, and bicontinuous structures formed by filamentary dockers percolating through a solid network of silica spheres. We characterize the slow relaxation and dynamic arrest of the different phases via correlation and scattering functions. Our findings provide a pathway toward the rapid engineering of mesoscopic gels and clusters via active colloidal doping.
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We analyze the dynamics of a tracer particle embedded in a bath of hard spheres confined in a channel of varying section. By means of Brownian dynamics simulations, we apply a constant force on the tracer particle and discuss the dependence of its mobility on the relative magnitude of the external force with respect to the entropic force induced by the confinement. A simple theoretical one-dimensional model is also derived, where the contribution from particle-particle and particle-wall interactions is taken from simulations with no external force. Our results show that the mobility of the tracer is strongly affected by the confinement. The tracer velocity in the force direction has a maximum close to the neck of the channel, in agreement with the theory for small forces. Upon increasing the external force, the tracer is effectively confined to the central part of the channel and the velocity modulation decreases, which cannot be reproduced by the theory. This deviation marks the regime of validity of linear response. Surprisingly, when the channel section is not constant, the effective friction coefficient is reduced as compared to the case of a plane channel. The transversal velocity, which cannot be studied with our model, follows qualitatively the derivative of the channel section, in agreement with previous theoretical calculations for the tracer diffusivity in equilibrium. Published by AIP Publishing.
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We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.
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In this study, the phase diagram of Pluronic L64 and water is simulated via dissipative particle dynamics (DPD). The peculiar structures that form when the concentration varies from dilute to dense (i.e., spherical and rod-like micelles, hexagonal and lamellar phases, as well as reverse micelles) are recognized, and predictions are found to be in good agreement with experiments. A novel clustering algorithm is used to identify the structures formed, characterize them in terms of radius of gyration and aggregation number and cluster mass distributions. Non-equilibrium simulations are also performed, in order to predict how structures are affected by shear, both via qualitative and quantitative analyses. Despite the well-known scaling problem that results in unrealistic shear rates in real units, results show that non-Newtonian behaviors can be predicted by DPD and associated with variations of the observed microstructures. Published by AIP Publishing.
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Hydrodynamic interactions (HIs), namely, solvent-mediated long-range interactions between dispersed particles, play a crucial role in the assembly and dynamics of many active systems, from swimming bacteria to swarms of propelling microrobots. We experimentally demonstrate the emergence of long-living hydrodynamic bound states between model microswimmers at low Reynolds numbers. A rotating magnetic field forces colloidal hematite microparticles to translate at a constant and frequency-tunable speed close to a bounding plane in a viscous fluid. At high driving frequency, HIs dominate over magnetic dipolar ones, and close propelling particles couple into bound states by adjusting their translational speed to optimize the transport of the pair. The physical system is described by considering the HIs with the boundary surface and the effect of gravity, providing an excellent agreement with the experimental data for all the range of parameters explored. Moreover, we show that in dense suspensions, these bound states can be extended to one-dimensional arrays of particles assembled by the sole HIs. Our results manifest the importance of the boundary surface in the interaction and dynamics of confined propelling microswimmers.
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In this work, we numerically study a dense colloidal suspension flowing through a small outlet driven by a pressure drop using lattice-Boltzmann methods. This system shows intermittent flow regimes that precede clogging events. Several pieces of evidence suggest that the temperature controls the dynamic state of the system when the driving force and the aperture size are fixed. When the temperature is low, the suspension's flow can be interrupted during long time periods, which can be even two orders of magnitude larger than the system's characteristic time (Stokes). We also find that strong thermal noise does not allowthe formation of stable aggregate structures avoiding extreme clogging events, but, at the same time, it randomizes the particle trajectories and disturbs the advective particle flow through the aperture. Moreover, examining the particle velocity statistics, we obtain that in the plane normal to the pressure drop the colloids always move as free particles regardless of the temperature value. In the pressure drop direction, at high temperature the colloids experience a simple balance between advective and diffusive transport, but at low temperature the nature of the flow is much more complex, correlating with the occurrence of very long clogging events.
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We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with coexistence between active liquid and hexatic order, followed by a proper hexatic phase, and a further transition to an active solid. As activity increases, the emergence of hexatic and solid order is shifted towards higher densities. Above a critical activity and for a certain range of packing fractions, the system undergoes motility-induced phase separation and demixes into low and high density phases; the latter can be either disordered (liquid) or ordered (hexatic or solid) depending on the activity.
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Field-driven direct assembly of nanoscale matter has impact in disparate fields of science. In microscale systems, such concept has been recently exploited to optimize propulsion in viscous fluids. Despite the great potential offered by miniaturization, using self-assembly to achieve transport at the nanoscale remains an elusive task. Here we show that a hybrid propeller, composed by a ferromagnetic nanorod and a paramagnetic microsphere, can be steered in a fluid in a variety of modes, from pusher to puller, when the pair is dynamically actuated by a simple oscillating magnetic field. We exploit this unique design to build more complex structures capable of carrying several colloidal cargos as microscopic trains that quickly disassemble at will under magnetic command. In addition, our prototype can be extended to smaller nanorods below the diffraction limit, but still dynamically reconfigurable by the applied magnetic field.
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A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces. Published by AIP Publishing.
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Nanocomposite materials made of block copolymer (BCP) and nanoparticles display properties which can be different from the purely polymeric matrix. The resulting material is a crossover of the original properties of the BCP and the presence of the assembled nanoparticles. A mesoscopic study using cell dynamic simulations is reported, to quantitatively describe the structural properties of such hybrid materials. The most relevant parameters are identified to be the fraction of nanoparticles in the system and its chemical affinity, while the nanoparticle size with respect to the BCP length scales plays a role in the assembly. The morphological phase diagram of the BCP is constructed for nanoparticles with chemical affinity ranging from A-compatible to B-compatible for a symmetric A-B diblock copolymer. Block-compatible nanoparticles are found to induce a phase transition due to changes in the effective concentration of the hosting phase, while interface-compatible particles induce the appearance of two new phases due to the saturation of the diblock copolymer interface.
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In this work, we study the constitutive behavior of interacting colloidal suspensions for moderate and high concentrations. Specifically, using a lattice Boltzmann solver, we numerically examine suspensions flowing through narrow channels, and explore the significance of the interaction potential strength on the system's macroscopic response. When only a short-range interaction potential is considered, a Newtonian behavior is always recovered and the system's effective viscosity mostly depends on the suspension concentration. However, when using a Lennard-Jones potential we identify two rheological responses depending on the interaction strength, the volume fraction, and the pressure drop. Exploiting a model proposed in the literature we rationalize the simulation data and propose scaling relations to identify the relevant energy scales involved in these transport processes. Moreover, we find that the spatial distribution of colloids in layers parallel to the flow direction does not correlate with changes in the system macroscopic response; but, interestingly, the rheology changes do correlate with the spatial distribution of colloids within individual layers. Namely, suspensions characterized by a Newtonian response display a cubiclike structure of the colloids within individual layers, whereas for suspensions with non-Newtonian response colloids organize in a hexagonal structure.
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Self-propelled droplets capable of transporting cargo to specific target locations are desired tools for many future applications. Here we propose a class of active droplets with programmable delivery time that are attracted or repelled by certain obstacle geometries. These droplets consist of a water/ethanol mixture and are dispersed in an oil/surfactant solution. Owing to a mass exchange between fluid phases during self-propulsion, the initially homogeneous droplets spontaneously de-mix and evolve into characteristic Janus droplets. Cargo molecules, like DNA, can be separated into the trailing ethanol-rich droplet and are carried to their target location like in a backpack. The delayed onset of phase separation provides a handle to control the time frame of delivery, while long-ranged hydrodynamic interactions and short-ranged wetting forces are exploited to achieve the desired spatial specificity with respect to obstacle geometry and surface chemistry.
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The formation, maintenance and reorganization of the cytoskeletal filament network is essential for a number of cellular processes. While the crucial role played by active forces generated by motor proteins has been studied extensively, only recently the importance of passive forces exerted by non-enzymatic crosslinkers has been realized. The interplay between active and passive proteins manifests itself, e.g., during cell division, where the spindle structure formed by overlapping microtubules is subject to both active sliding forces generated by crosslinking motor proteins and passive forces exerted by passive crosslinkers, such as Ase1 and PRC1. We propose a minimal model to describe the stability behaviour of a pair of anti-parallel overlapping microtubules resulting from the competition between active motors and passive crosslinkers. We obtain the stability diagram which characterizes the formation of stable overlap of the microtubule pair, identify the controlling biological parameters which determine their stability, and study the impact of mutual interactions between motors and passive crosslinkers on the stability of these overlapping filaments. Copyright (C) EPLA, 2019
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We study the phase behavior of polar active Brownian particles moving in two-spatial dimensions and interacting through volume exclusion and velocity alignment. We combine particle-based simulations of the microscopic model with a simple mean-field kinetic model to understand the impact of velocity alignment on the motility-induced phase separation of self-propelled disks. We show that, as the alignment strength is increased, approaching the onset of collective motion from below, orientational correlations grow, rendering the diffusive reorientation dynamics slower. As a consequence, the tendency of particles to aggregate into isotropic clusters is enhanced, favoring the complete de-mixing of the system into a low and high-density phase. Copyright (C) EPLA, 2018
2017
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As a result of the competition between self-propulsion and excluded volume interactions, purely repulsive self-propelled spherical particles undergo a motility-induced phase separation (MIPS). We carry out a systematic computational study, considering several interaction potentials, systems confined by hard walls or with periodic boundary conditions, and different initial conditions. This approach allows us to identify that, despite its non-equilibrium nature, the equations of state of Active Brownian Particles (ABP) across MIPS verify the characteristic properties of first-order liquid-gas phase transitions, meaning, equality of pressure of the coexisting phases once a nucleation barrier has been overcome and, in the opposite case, hysteresis around the transition as long as the system remains in the metastable region. Our results show that the equations of state of ABPs account for their phase behaviour, providing a firm basis to describe MIPS as an equilibrium-like phase transition.
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In eukaryotic cells, motor proteins (MPs) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules forms whose stability and dynamics under the influence of MPs have been studied extensively. Although passive cross linkers (PCLs) are known to provide structural stability to a filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on filamentous overlap remain largely unexplored. Here, we formulate and characterize a model to study this, using linear stability analysis and numerical integration. In the presence of PCLs, we find dynamic phase transitions with changing activity exhibiting regimes of stable partial overlap with or without oscillations, instability towards complete overlap, and stable limit cycle oscillations that emerge via a supercritical Hopf bifurcation characterized by an oscillation frequency determined by the MP and PCL parameters. We show that the overlap dynamics and stability depend crucially on whether both the filaments of an overlapping pair are movable or one is immobilized, having potential implications for in vivo and in vitro studies.
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We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motor displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean-field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynamic coupling as well as on system size. We quantify the phase diagram for the different phases that characterize the collective motion of hydrodynamically coupled motors and show that sustained oscillations can be reached for biologically relevant parameters, hence, demonstrating the relevance of hydrodynamic interactions in intracellular transport.
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The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studied in this work. A continuum description for the polymer is used, while colloids are individually resolved. The method allows for a variable preference of the colloids, which can have different sizes, to the different components the block copolymer is made of. The impact that the nanoparticle preference for either, both, or none of the blocks has on the collective properties of nanoparticle-block copolymer composites can be analyzed. Several experimental results are reproduced covering colloid-induced phase transition, particles' placement within the matrix, and the role of incompatibilities between colloids and monomers.
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We study a two-filament driven lattice gas model with oppositely directed species of particles moving on two parallel filaments with filament-switching processes and particle inflow and outflow at filament ends. The filament-switching process is correlated with the occupation number of the adjacent site such that particles switch filaments with finite probability only when oppositely directed particles meet on the same filament. This model mimics some of the coarse-grained features observed in context of microtubule-(MT) based intracellular transport, wherein cellular cargo loaded and off-loaded at filament ends are transported on multiple parallel MT filaments and can switch between the parallel microtubule filaments. We focus on a regime where the filaments are weakly coupled, such that filament-switching rate of particles scale inversely as the length of the filament. We find that the interplay of (off-) loading processes at the boundaries and the filament-switching process of particles leads to some distinctive features of the system. These features includes occurrence of a variety of phases in the system with inhomogeneous density profiles including localized density shocks, density difference across the filaments, and bidirectional current flows in the system. We analyze the system by developing a mean field (MF) theory and comparing the results obtained from the MF theory with the Monte Carlo (MC) simulations of the dynamics of the system. We find that the steady-state density and current profiles of particles and the phase diagram obtained within the MF picture matches quite well with MC simulation results. These findings maybe useful for studying multifilament intracellular transport.
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Phase-field models have been extensively used to study interfacial phenomena, from solidification to vesicle dynamics. In this article, we analyze a phase-field model that captures the relevant physical features that characterize biological membranes. We show that the Helfrich theory of elasticity of membranes can be applied to phase-field models, allowing to derive the expressions of the stress tensor, lateral stress profile and elastic moduli. We discuss the relevance and interpretations of these magnitudes from a phase-field perspective. Taking the sharp-interface limit we show that the membrane macroscopic equilibrium equation can be derived from the equilibrium condition of the phase-field interface. We also study two dynamic models that describe the behaviour of a membrane. From the study of the relaxational behaviour of the membrane we characterize the relevant dynamics of each model, and discuss their applications.
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Flowing Matter 2017
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In order to assess the effect of hydrodynamics in the assembly of active attractive spheres, we simulate a semi-dilute suspension of attractive self-propelled spherical particles in a quasi-two dimensional geometry comparing the case with and without hydrodynamics interactions. To start with, independent of the presence of hydrodynamics, we observe that depending on the ratio between attraction and propulsion, particles either coarsen or aggregate forming finite-size clusters. Focusing on the clustering regime, we characterize two different cluster parameters, i.e. their morphology and orientational order, and compare the case when active particles behave either as pushers or pullers (always in the regime where inter-particle attractions compete with self-propulsion). Studying cluster phases for squirmers with respect to those obtained for active Brownian disks (indicated as ABPs), we have shown that hydrodynamics alone can sustain a cluster phase of active swimmers (pullers), while ABPs form cluster phases due to the competition between attraction and self-propulsion. The structural properties of the cluster phases of squirmers and ABPs are similar, although squirmers show sensitivity to active stresses. Active Brownian disks resemble weakly pusher squirmer suspensions in terms of cluster size distribution, structure of the radius of gyration on the cluster size and degree of cluster polarity.
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The principles underlying the biomechanics of morphogenesis are largely unknown. Epiboly is an essential embryonic event in which three tissues coordinate to direct the expansion of the blastoderm. How and where forces are generated during epiboly, and how these are globally coupled remains elusive. Here we developed a method, hydrodynamic regression (HR), to infer 3D pressure fields, mechanical power, and cortical surface tension profiles. HR is based on velocity measurements retrieved from 2D+T microscopy and their hydrodynamic modeling. We applied HR to identify biomechanically active structures and changes in cortex local tension during epiboly in zebrafish. Based on our results, we propose a novel physical description for epiboly, where tissue movements are directed by a polarized gradient of cortical tension. We found that this gradient relies on local contractile forces at the cortex, differences in elastic properties between cortex components and the passive transmission of forces within the yolk cell. All in all, our work identifies a novel way to physically regulate concerted cellular movements that might be instrumental for the mechanical control of many morphogenetic processes.
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We describe a method to trap, transport and release microscopic particles in a viscous fluid using the hydrodynamic flow field generated by a magnetically propelled colloidal ribbon. The ribbon is composed of ferromagnetic microellipsoids that arrange with their long axis parallel to each other, a configuration that is energetically favorable due to their permanent magnetic moments. We use an external precessing magnetic field to torque the anisotropic particles forming the ribbon, and to induce propulsion of the entire structure due to the hydrodynamic coupling with the close substrate. The propulsion speed of the ribbon can be controlled by varying the driving frequency, or the amplitude of the precessing field. The latter parameter is also used to reduce the average inter particle distance and to induce the twisting of the ribbon due to the increase in the attraction between the rotating ellipsoids. Furthermore, non magnetic particles are attracted or repelled with the hydrodynamic flow field generated by the propelling ribbon. The proposed method may be used in channel free microfluidic applications, where the precise trapping and transport of functionalized particles via non invasive magnetic fields is required.
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We analyze the dynamic behavior of Newtonian fluids in elastic tubes subject to pulsatile pressure gradients and show that the interplay between the viscosity of the fluid, the elasticity of the wall, and the characteristic size of the confining media gives rise to a rich phenomenology that includes resonances. We find that these resonances are relevant for small confining geometries with low Young's moduli, typical of elastomeric materials in microfluidics. These resonances disappear beyond a certain tube radius, a certain Young's modulus, and below a certain fluid viscosity. In order to guide potential experiments, we present results for mineral oil flowing through polydimethylsiloxane microtubes and find resonances of the order of few tens of kHz. Published by AIP Publishing.
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The emergent cooperative behavior of mobile physical entities exchanging information with their neighborhood has become an important problem across disciplines, thus requiring a general framework to describe such a variety of situations. We introduce a generic model to tackle this problem by considering the synchronization in time-evolving networks generated by the stochastic motion of self-propelled physical interacting units. This framework generalizes previous approaches and brings a unified picture to understand the role played by the network topology, the motion of the agents, and their mutual interaction. This allows us to identify different dynamic regimes where synchronization can be understood from theoretical considerations. While for noninteracting particles, self-propulsion accelerates synchronization, the presence of excluded volume interactions gives rise to a richer scenario, where self-propulsion has a nonmonotonic impact on synchronization. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening, verifying the dynamic scaling hypothesis, with the same scaling laws as the 2D XY model following a quench. Our results shed light into the generic nature of synchronization in time-dependent networks, providing an efficient way to understand more specific situations involving interacting mobile agents.
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Redundancy constitutes a fundamental and intrinsic aspect of healthy vasculatures. Built-in redundancy might also be a desirable feature in man-made microfluidic devices. We show that redundant and non-redundant networks, built to have identical resistances to flow when unobstructed, allow for very different flows when they are occluded; redundant ones -densely occluded at a certain bifurcation level-allowing for larger flows than non-redundant ones-obstructed above relatively small thresholds. We also show that redundancy protects vessels against the large shear-rate gradients that occlusions would cause if it were not present. Our study allows one to quantify a network tolerance against blockage, provides guidance in the tailoring of microfluidic devices, and offers novel insights into why nature has selected intrinsic redundancy over thicker vessels to assure blood supply at key places of the organisms. Copyright (C) EPLA, 2017
2016
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Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. The interplay between cell softness, cell-cell adhesion, and contact inhibition of locomotion (CIL) yields structures and collective dynamics observed in several existing tissue phenotypes. These include regular distributions of cells, dynamic cell clusters, gel-like networks, collectively migrating monolayers, and 3D aggregates. We give analytical predictions for transitions between noncohesive, cohesive, and 3D cell arrangements. We explicitly show how CIL yields an effective repulsion that promotes cell dispersal, thereby hindering the formation of cohesive tissues. Yet, in continuous monolayers, CIL leads to collective cell motion, ensures tensile intercellular stresses, and opposes cell extrusion. Thus, our work highlights the prominent role of CIL in determining the emergent structures and dynamics of cell colonies.
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Coarse-graining (CG) of complex molecules is a method to reach time scales that would be impossible to access through brute force molecular simulations. In this paper, we formulate a coarse-grained model for complex molecules using first principles caculations that ensures energy conservation. Each molecule is described in a coarse way by a thermal blob characterized by the position and momentum of the center of mass of the molecule, together with its internal energy as an additional degree of freedom. This level of description gives rise to an entropy-based framework instead of the usual one based on the configurational free energy (i.e. potential of mean force). The resulting dynamic equations, which account for an appropriate description of heat transfer at the coarse-grained level, have the structure of the dissipative particle dynamics with energy conservation (DPDE) model but with a clear microscopic underpinning. Under suitable approximations, we provide explicit microscopic expressions for each component (entropy, mean force, friction and conductivity coefficients) appearing in the coarse-grained model. These quantities can be computed directly using MD simulations. The proposed non-isothermal coarse-grained model is thermodynamically consistent and opens up a first principles CG strategy for the study of energy transport issues that are not accessible using current isothermal models.
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We analyze the diffusion of charged and neutral tracers suspended in an electrolyte embedded in a channel of varying cross section. Making use of systematic approximations, the diffusion equation governing the motion of tracers is mapped into an effective 1D equation describing the dynamics along the longitudinal axis of the channel where its varying-section is encoded as an effective entropic potential. This simplified approach allows us to characterize tracer diffusion under generic confinement by measuring their mean first passage time (MFPT). In particular, we show that the interplay between geometrical confinement and electrostatic interactions strongly affect the MFTP of tracers across corrugated channels hence leading to alternative means to control tracers translocation across charged pores. Finally, our results show that the MFPTs of a charged tracer in opposite directions along an asymmetric channel may differ We expect our results to be relevant for biological as well synthetic devices whose dynamics is controlled by the detection of diluted tracers. (C) 2016 AIP Publishing LLC.
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Mesoscopic Non-equilibrium Thermodynamics
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We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and backward probabilities depend on the nature of the host medium, on local forces, and also on time. We have applied our results to two situations: diffusion in a disordered medium, and diffusion in a confined system. For such scenarios, we have shown that our theoretical predictions are in very good agreement with numerical results. Moreover, we have shown that the deviations from the Gaussian solution lead to the onset of rectification. Our predictions could be used to detect the presence of local forces and to characterize the intrinsic short-scale properties of the host mediuma problem of current interest in the study of micro- and nano-systems.
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The rate of spreading or retraction of a drop on a flat substrate is determined through a balance of surface tension and hydrodynamic flow. While asymptotic regimes are known, no general rate equation has hitherto been available. Here, we revisit this classic problem, in a regime governed by capillary and viscous forces, by performing an exhaustive numerical study of drop evolution as a function of the contact angle with the substrate. Our study reveals a universal evolution of the drop radius parameterised only by the substrate wettability. Two limits of this evolution recover the familiar exponential and algebraic regimes. Our results show quantitative comparison with the evolution derived from lubrication theory, indicating that dissipation at the contact line is the key determinant in drop evolution. Our work, both numerical and theoretical, provides a foundation for studying the full temporal dynamics of droplet evolution under the influence of external fields and thermal fluctuations, which are of importance in nanofluidics.
2015
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We demonstrate that migration away from self-produced chemicals (chemorepulsion) generates a generic route to clustering and pattern formation among self-propelled colloids. The clustering instability can be caused either by anisotropic chemical production, or by a delayed orientational response to changes of the chemical environment. In each case, chemorepulsion creates clusters of a self-limiting area which grows linearly with self-propulsion speed. This agrees with recent observations of dynamic clusters in Janus colloids (albeit not yet known to be chemorepulsive). More generally, our results could inform design principles for the self-assembly of chemorepulsive synthetic swimmers and/or bacteria into nonequilibrium patterns.
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We study propulsion arising from microscopic colloidal rotors dynamically assembled and driven in a viscous fluid upon application of an elliptically polarized rotating magnetic field. Close to a confining plate, the motion of this self-assembled microscopic worm results from the cooperative flow generated by the spinning particles which act as a hydrodynamic conveyor belt. Chains of rotors propel faster than individual ones, until reaching a saturation speed at distances where induced-flow additivity vanishes. By combining experiments and theoretical arguments, we elucidate the mechanism of motion and fully characterize the propulsion speed in terms of the field parameters.
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We characterize the motion of charged as well as neutral tracers, in an electrolyte embedded in a varying section channel. We exploit a set of systematic approximations that allows us to simplify the problem, yet capturing the essential of the interplay between the geometrical confinement provided by the corrugated channel walls and the electrolyte properties. Our simplified approach allows us to characterize the transport properties of corrugated channels when a net flux of tracers is obtained by keeping the extrema of the channel at different chemical potentials. For highly diluted tracer suspensions, we have characterized tracers currents and we have estimated the net electric current which occurs when both positively and negatively charged tracers are considered.
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The cell contains highly dynamic structures exploiting physical principles of self-organisation at the mesoscale (100 nm to 10 mu m). Examples include non-membrane bound cytoplasmic bodies, cytoskeleton-based motor networks and multi-scale chromatin organisation. The challenges of mesoscale self-organisation were discussed at a CECAM workshop in July 2014. Biologists need approaches to observe highly dynamic, low affinity, low specificity associations and to perturb single structures, while biological physicists and biomathematicians need to work closely with biologists to build and validate quantitative models. A table of terminology is included to facilitate multidisciplinary efforts to reveal the richness and diversity of mesoscale cell biology.
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The contribution of fiber dynamics and clustering to the effective permeability in hierarchical fibrous media is poorly understood, due to the complex fluid structure interactions taking place across fiber, yarn and textile scales. In this work, a two-dimensional model for fiber deformation subject to out movement restrictions is derived for creeping flow conditions by analogy with non-Brownian suspensions of particles with confining potentials. This leads to a homogeneous Fokker-Planck equation in a phase space of fiber configurations, for the probability density function of the fiber displacements. A fiber clustering criterion is then defined using autoconvoluiion functions of the local probability densities, which yields the local change in fiber scale permeability according to a topological description of the porous media instead of the typical geometric description. The resulting multi-scale hydrodynamic system is numerically solved by a coupled method, where the Stokes flow at yarn-scale is solved with a finite volume method and the mesoscopic model that recovers information from the fiber-scale is solved by a lattice Boltzmann method. The fiber-scale permeability is characterized in terms of porosity, dimensionless shear rate and dimensionless out-of-plane forces. When assessed in terms of a reduced viscosity related to Brinkman's closure for porous media, the mesoscopic model shows that deformable fibrous porous media qualitatively behave like dense particle suspensions. For low volume fractions a non-Newtonian reduced viscosity exhibiting shear-thinning and low- and high-shear plateaux is obtained. For high volume fractions and high shear rates the out-of-plane forces lead to shear thickening. The results on steady fiber-scale permeability are presented in the form of phase diagrams which show that in the typical range of parameters for textiles, the effective permeability of the deformable case can be up 60% lower than that of the rigid case due to the formation of fiber clusters. (C) 2015 Elsevier Ltd. All rights reserved.
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We relate vascular network structure to hemodynamics after vessel obstructions. We consider tree-like networks with a viscoelastic fluid with the rheological characteristics of blood. We analyze the network hemodynamic response, which is a function of the frequencies involved in the driving, and a measurement of the resistance to flow. This response function allows the study of the hemodynamics of the system, without the knowledge of a particular pressure gradient. We find analytical expressions for the network response, which explicitly show the roles played by the network structure, the degree of obstruction, and the geometrical place in which obstructions occur. Notably, we find that the sequence of resistances of the network without occlusions strongly determines the tendencies that the response function has with the anatomical place where obstructions are located. We identify anatomical sites in a network that are critical for its overall capacity to supply blood to a tissue after obstructions. We demonstrate that relatively small obstructions in such critical sites are able to cause a much larger decrease on flow than larger obstructions placed in non-critical sites. Our results indicate that, to a large extent, the response of the network is determined locally. That is, it depends on the structure that the vasculature has around the place where occlusions are found. This result is manifest in a network that follows Murray's law, which is in reasonable agreement with several mammalian vasculatures. For this one, occlusions in early generation vessels have a radically different effect than occlusions in late generation vessels occluding the same percentage of area available to flow. This locality implies that whenever there is a tissue irrigated by a tree-like in vivo vasculature, our model is able to interpret how important obstructions are for the irrigation of such tissue.
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Biological membranes are complex structures whose mechanics are usually described at a mesoscopic level, such as the Helfrich bending theory. In this article, we present the phase-field methods, a useful tool for studying complex membrane problems which can be applied to very different phenomena. We start with an overview of the general theory of elasticity, paying special attention to its derivation from a molecular scale. We then study the particular case of membrane elasticity, explicitly obtaining the Helfrich bending energy. Within the framework of this theory, we derive a phase-field model for biological membranes and explore its physical basis and interpretation in terms of membrane elasticity. We finally explain three examples of applications of these methods to membrane related problems. First, the case of vesicle pearling and tubulation, when lipidic vesicles are exposed to the presence of hydrophobic polymers that anchor to the membrane, inducing a shape instability. Finally, we study the behavior of red blood cells while flowing in narrow microchannels, focusing on the importance of membrane elasticity to the cell flow capabilities. (C) 2014 Elsevier Ireland Ltd. All rights reserved.
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Understanding fluid dynamics under extreme confinement, where device and intrinsic fluid length scales become comparable, is essential to successfully develop the coming generations of fluidic devices. Here we report measurements of advancing fluid fronts in such a regime, which we dub superconfinement. We find that the strong coupling between contact-line friction and geometric confinement gives rise to a new stability regime where the maximum speed for a stable moving front exhibits a distinctive response to changes in the bounding geometry. Unstable fronts develop into drop-emitting jets controlled by thermal fluctuations. Numerical simulations reveal that the dynamics in superconfined systems is dominated by interfacial forces. Henceforth, we present a theory that quantifies our experiments in terms of the relevant interfacial length scale, which in our system is the intrinsic contact-line slip length. Our findings show that length-scale overlap can be used as a new fluid-control mechanism in strongly confined systems.
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The physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial applications. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape. (C) 2015 AIP Publishing LLC.
2014
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When a large set of discrete bodies passes through a bottleneck, the flow may become intermittent due to the development of clogs that obstruct the constriction. Clogging is observed, for instance, in colloidal suspensions, granular materials and crowd swarming, where consequences may be dramatic. Despite its ubiquity, a general framework embracing research in such a wide variety of scenarios is still lacking. We show that in systems of very different nature and scale -including sheep herds, pedestrian crowds, assemblies of grains, and colloids- the probability distribution of time lapses between the passages of consecutive bodies exhibits a power-law tail with an exponent that depends on the system condition. Consequently, we identify the transition to clogging in terms of the divergence of the average time lapse. Such a unified description allows us to put forward a qualitative clogging state diagram whose most conspicuous feature is the presence of a length scale qualitatively related to the presence of a finite size orifice. This approach helps to understand paradoxical phenomena, such as the faster-is-slower effect predicted for pedestrians evacuating a room and might become a starting point for researchers working in a wide variety of situations where clogging represents a hindrance.
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We show that when particles are suspended in an electrolyte confined between corrugated charged surfaces, electrokinetic flows lead to a new set of phenomena such as particle separation, mixing for low-Reynolds micro- and nanometric devices, and negative mobility. Our analysis shows that such phenomena arise, for incompressible fluids, due to the interplay between the electrostatic double layer and the corrugated geometrical confinement and that they are magnified when the width of the channel is comparable to the Debye length. Our characterization allows us to understand the physical origin of such phenomena, therefore, shedding light on their possible relevance in a wide variety of situations ranging from nano- and microfluidic devices to biological systems.
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Polydisperse systems are commonly encountered when dealing with soft matter in general or any non-simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially devised for simple-non-fully polydisperse-systems. In this paper, we address the issue of defining a non-ambiguous combinatorial entropy for these systems. We do so by focusing on the general property of extensivity of the thermodynamic potentials and discussing a specific mixing experiment. This leads us to introduce the new concept of composition entropy for single phase systems that we do not assimilate to a mixing entropy. We then show that they do not contribute to the thermodynamics of the system at a fixed composition and prescribe to subtract ln N! from the free energy characterizing a system however polydisperse it can be. We then re-derive general expressions for the mixing entropy between any two polydisperse systems and interpret them in term of distances between probability distributions, showing that one of these metrics relates naturally to a recent extension of Landauer's principle. We then propose limiting expressions for the mixing entropy in the case of mixing with equal proportions in the original compositions and finally address the challenging problem of chemical reactions.
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We study the focusing of red blood cells and vesicles in pressure-driven flows in highly confined microchannels (10-30 mm), identifying the control parameters that dictate the cell distribution along the channel. Our results show that an increase in the flow velocity leads to a sharper cell distribution in a lateral position of the channel. This position depends on the channel width, with cells flowing at outer (closer to the walls) positions in thicker channels. We also study the relevance of the object shape, exploring the different behaviour of red blood cells and different vesicles. We also analyze the implications of these phenomena in the cell suspension rheology, highlighting the crucial role of the wall confinement in the rheological properties of the suspension.
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We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high confinement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.
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We present experimental and numerical results for particle alignment and stress distribution in packings of faceted particles deposited in a small-scale bi-dimensional silo. First, we experimentally characterize the deposits' morphology in terms of the particles' aspect ratio and feeding rate. Then we use the experimental results to validate our discrete element method (DEM) based on spheropolygons. After achieving excellent agreement, we use contact forces and fabric provided by the simulations to calculate the coarse-grained stress tensor. For low feeding rates, square particles display a strong tendency to align downwards, i.e., with a diagonal parallel to gravity. This morphology leads to stress transmission towards the walls, implying a quick development of pressure saturation, in agreement with the Janssen effect. When the feed rate is increased, both the disorder and the number of horizontal squares in the silo increase, hindering the Janssen effect. Conversely, for elongated particles the feed rate has a weak effect on the final deposit properties. Indeed, we always observe highly ordered structures of horizontal rods where the stress is transmitted mainly in the vertical direction.
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We analyze the performance of a Brownian ratchet in the presence of geometrical constraints. A two-state model that describes the kinetics of molecular motors is used to characterize the energetic cost when the motor proceeds under confinement, in the presence of an external force. We show that the presence of geometrical constraints has a strong effect on the performance of the motor. In particular, we show that it is possible to enhance the ratchet performance by a proper tuning of the parameters characterizing the environment. These results open the possibility of engineering entropically-optimized transport devices.
2013
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We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e. g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.
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We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0 <= alpha <= 1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition alpha(c) which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above alpha(c), however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent mu = 2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent mu = 9/2. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.
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Chemical cycle kinetics is customarily analyzed by means of the law of mass action which describes how the concentrations of the substances vary with time. The connection of this approach with non-equilibrium thermodynamics (NET) has traditionally been restricted to the linear domain close to equilibrium in which the reaction rates are linear functions of the affinities. We show, by a pertinent formulation of the concept of local equilibrium in the mesoscopic description along the reaction coordinates, that the connection between kinetic and thermodynamic approaches is deeper than thought and holds in the nonlinear domain far from equilibrium, for higher values of the affinity. This new perspective indicates how to overcome the inherent limitation of classical NET in treating cyclic reactions, providing a description of closed and open cycles operating far from equilibrium, in accordance with thermodynamic principles. We propose that the new set of equations are tested and used for data reduction in chemical reaction kinetics.
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We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale. (C) 2013 AIP Publishing LLC.
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We examine the phenomenon of hydrodynamic-induced cooperativity for pairs of flagellated micro-organism swimmers, of which spermatozoa cells are an example. We consider semiflexible swimmers, where inextensible filaments are driven by an internal intrinsic force and torque-free mechanism (intrinsic swimmers). The velocity gain for swimming cooperatively, which depends on both the geometry and the driving, develops as a result of the near-field coupling of bending and hydrodynamic stresses. We identify the regimes where hydrodynamic cooperativity is advantageous and quantify the change in efficiency. When the filaments' axes are parallel, hydrodynamic interaction induces a directional instability that causes semiflexible swimmers that profit from swimming together to move apart from each other. Biologically, this implies that flagella need to select different synchronized collective states and to compensate for directional instabilities (e. g., by binding) in order to profit from swimming together. By analyzing the cooperative motion of pairs of externally actuated filaments, we assess the impact that stress distribution along the filaments has on their collective displacements. DOI: 10.1103/PhysRevE.87.032720
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We derive a one-dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non-trivial fashion. We consider two kinds of non-uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one-and three-dimensional solutions of the electrokinetic equations. (C) 2013 AIP Publishing LLC.
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Red blood cells are highly sensitive to changes in the relative areas of the two lipid leaflets of the cell membrane. Expansion of the outer leaflet forces the membrane to bend, leading to the deformation of the biconcave discocyte into increasingly spiculated shapes, in a well-defined series of cell shapes known as the discoechinocyte transition. We explore the first stages of this transition by means of an elastic membrane energy model that accounts for the bilayer and cytoskeleton contributions. The morphological evolution is explained in terms of the elastic response of these membrane components. Our results highlight the importance of the cytoskeleton as a stabilizing component and how it determines the strong sequential character of the development of different morphologies. In general, cells develop undulations around the cell contour prior to the growth of out-of-plane bumps; this was found to be due to the high energetic penalty relative to a limited area-difference benefit.
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Electrokinetic effects, i.e. the coupled hydrodynamic and electric phenomena which occur near charged interfaces, constitute a challenge to theorists due to the variety of length and time scales involved. We discuss recent advances in the modelling of these phenomena, emphasising the interplay between the molecular specificity and the collective induced flows that emerge. We discuss the complementary simulation methodologies that have been developed either to focus on the molecular aspects of electrokinetics or on their effective properties on larger scales, as well as the proposed hybrid schemes that can incorporate both aspects. We highlight the insights that molecular studies have brought on the nature of interfacial charges and their implications for kinetic phenomena in confined fluids and also discuss advances in a number of relevant contexts.
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A method for particle hydrodynamics based on an hybrid Eulerian-Lagrangian approach is presented. Particle dynamics are solved in continuum space while the fluid equations are solved in an Eulerian mesh, and described by finite volume fluctuating hydrodynamics. This set-up is particularly suited for micron-size devices where the Reynolds number is small but thermal fluctuations are important. The particle-fluid coupling force is obtained by imposing zero relative (particle-fluid) velocity at a local average over the particle volume. In doing so the momentum exchanged between fluid and particle is transferred instantaneously ensuring a correct treatment of inertia and correct particle velocity fluctuations uniquely driven by fluid thermal forces. Consistency between the Eulerian and Lagrangian momentum balance is shown to be essential. The scheme is applied to compressible fluids at low Mach number and moderate Reynolds number. A series of tests show that the near velocity field around the particle is correctly captured up to distances of about one particle hydrodynamic diameter. Also, acoustic forces measured under ultrasound waves are in excellent agreement with the theoretical expressions. (C) 2012 Elsevier Inc. All rights reserved.
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The effect of the filling mechanism on the packing of faceted particles with different aspect ratios has been examined. We have experimentally measured the particle angular distribution and the packing fraction of ensembles of faceted particles deposited in a bidimensional box. The granular system has been numerically simulated using a two-dimensional model of faceted particles. We found that increasing the feeding rate results in an enhancement of the disorder in the final deposit and, consequently, in a reduction of the number of particles oriented in their most stable configuration. In this regime, the final packing fraction monotonically decreases as the feeding rate increases. The correlations between the final packing morphology and the stress transmission were examined by describing the micromechanical properties of the deposits. For the case of elongated particles, increasing the feeding rate leads to an enhancement of the stress transmission towards the sides of the box. On the contrary, for the case of square particles, increasing the feeding rate promotes vertical transmission of the stress.
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In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ. DOI: 10.1103/PhysRevE.87.012202
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We show that the kinetics of a molecular motor fueled by ATP and operating between a deactivated and an activated state can be derived from the principles of non-equilibrium thermodynamics applied to the mesoscopic domain. The activation by ATP, the possible slip of the motor, as well as the forward stepping carrying a load are viewed as slow diffusion along a reaction coordinate. Local equilibrium is assumed in the reaction coordinate spaces, making it possible to derive the non-equilibrium thermodynamic description. Using this scheme, we find expressions for the velocity of the motor, in terms of the driving force along the spacial coordinate, and for the chemical reaction that brings about activation, in terms of the chemical potentials of the reactants and products which maintain the cycle. The second law efficiency is defined, and the velocity corresponding to maximum power is obtained for myosin movement on actin. Experimental results fitting with the description are reviewed, giving a maximum efficiency of 0.45 at a myosin headgroup velocity of 5 x 10(-7) m s(-1). The formalism allows the introduction and test of meso-level models, which may be needed to explain experiments.
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We have developed numerical simulations of three dimensional suspensions of active particles to characterize the capabilities of the hydrodynamic stresses induced by active swimmers to promote global order and emergent structures in active suspensions. We have considered squirmer suspensions embedded in a fluid modeled under a Lattice Boltzmann scheme. We have found that active stresses play a central role to decorrelate the collective motion of squirmers and that contractile squirmers develop significant aggregates. (C) 2012 Elsevier B.V. All rights reserved.
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A general thermodynamic analysis is given of dissipative self-assembly (DSA). Subsequently, the analysis is used to quantify the lost work in a recently published chemical realization of DSA (Boekhoven et al., Angew Chem Int Ed 49:4825, 2010) where a formation reaction produces the monomers that subsequently self-assemble and are finally annihilated by means of a destruction reaction. For this example, the work lost in self-assembly itself is found to be negligibly small compared to the work lost in the reactions driving the non-spontaneous formation reaction and the kinetically hindered destruction reaction.
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We analyze the rheological response of a suspension of simple model swimmers subject to a steady Couette flow. We consider the squirmer model as a means to control systematically the interplay between self-propulsion and active stress generation and analyze their relative impact both on the effective viscosity of a suspension and the microstructure the squirmers develop. We show how self-propulsion introduces an intrinsic contribution to the effective viscosity of the active suspension. Accordingly, apolar squirmers show shear thickening while polar ones develop a shear thinning response to the applied shear. We show that the detailed coupling of the squirmers to the bounding walls has a strong influence on the structure of the suspension and the development of shear bands.
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We report on the onset of fluid entrainment when a contact line is forced to advance over a dry solid of arbitrary wettability. We show that entrainment occurs at a critical advancing speed beyond which the balance between capillary, viscous, and contact-line forces sustaining the shape of the interface is no longer satisfied. Wetting couples to the hydrodynamics by setting both the morphology of the interface at small scales and the viscous friction of the front. We find that the critical deformation that the interface can sustain is controlled by the friction at the contact line and the viscosity contrast between the displacing and displaced fluids, leading to a rich variety of wetting-entrainment regimes. We discuss the potential use of our theory to measure contact-line forces using atomic force microscopy and to study entrainment under microfluidic conditions exploiting colloid-polymer fluids of ultralow surface tension.
2012
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Application of force to echinocytes during atomic force microscopy measurements was shown to be able to convert the cells to stable discocyte shapes. The echinocyte shape is associated with a relative excess of the area of the outer leaflet of the cell membrane; the AFM measurements are therefore associated with a change in the relative areas of the inner and outer membrane leaflets. It was hypothesized that localised damage in the lipid bilayer that is caused by an AFM tip can permit the lipids to flip-flop between the two membrane leaflets, thus changing their relative areas. The conditions in which AFM measurements on cells could induce shape changes were investigated both experimentally and by modelling. The relative area change of the membrane leaflets, attributed here to lipid movement, was characterised in terms of the membrane energy levels; membrane energy was calculated using a version of the area-difference-elasticity model that was applied to predetermined shapes, rather than being used to generate shapes as solutions found at the energy minima. Shapes were generated by rotation of Cassini ovals with a superimposed undulation in order to generate spikes similar to those of the echinocytes. The membrane energy was considered as a function of the membrane curvature, the area difference between the two membrane leaflets, and the deformation of the cytoskeleton. This led to the conclusions that the minimisation of the membrane energy causes the lipid translocation, with the relaxation of the cytoskeleton being a significant driving force.
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We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may develop even in situations where separately the ratchet and the geometric restrictions do not give rise to particle motion. The combined rectification effects can lead to bidirectional transport depending on particle size, resulting in a different route for segregation. The reported mechanism can be used to control transport in mesostructures and nanodevices in which particles move in a reduced space.
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We have derived reaction-dispersal-aggregation equations from Markovian reaction-random walks with density-dependent jump rate or density-dependent dispersal kernels. From the corresponding diffusion limit we recover well-known reaction-diffusion-aggregation and reaction-diffusion-advection-aggregation equations. It is found that the ratio between the reaction and jump rates controls the onset of spatial patterns. We have analyzed the qualitative properties of the emerging spatial patterns. We have compared the conditions for the possibility of spatial instabilities for reaction-dispersal and reaction-diffusion processes with aggregation and have found that dispersal process is more stabilizing than diffusion. We have obtained a general threshold value for dispersal stability and have analyzed specific examples of biological interest. (C) 2012 Elsevier Ltd. All rights reserved.
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We analyze the dynamics of overlapping antiparallel treadmilling microtubules in the presence of crosslinking processive motor proteins that counterbalance an external force. We show that coupling the force-dependent velocity of motors and the kinetics of motor exchange with a bath in the presence of treadmilling leads generically to oscillatory behavior. In addition, we show that coupling the polymerization kinetics to the external force through the kinetics of the crosslinking motors can stabilize the oscillatory instability into finite-amplitude nonlinear oscillations and may lead to other scenarios, including bistability. Copyright (C) EPLA, 2012
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We present simulations that reveal a surprisingly large effect of hydrodynamic coupling on the speed of thermal ratchet motors. The model that we use considers particles performing thermal ratchet motion in a hydrodynamic solvent. Using particle-based, mesoscopic simulations that maintain local momentum conservation, we analyze quantitatively how the coupling to the surrounding fluid affects ratchet motion. We find that coupling can increase the mean velocity of the moving particles by almost 2 orders of magnitude, precisely because ratchet motion has both a diffusive and a deterministic component. The resulting coupling also leads to the formation of aggregates at longer times. The correlated motion that we describe increases the efficiency of motor-delivered cargo transport and we speculate that the mechanism that we have uncovered may play a key role in speeding up molecular motor-driven intracellular transport.
2011
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We study the electrophoretic flow of suspensions of charged colloids with a mesoscopic method that allows us to model generic experimental conditions. We show that for highly charged colloids their electrophoretic mobility increases significantly and displays a mobility maximum on increasing the colloidal charge for all salt concentrations. The electrophoretic mobility of highly charged colloids is also enhanced significantly when ion advection is dominant, leading to a strong heterogeneity in the local electrophoretic response especially at low-salt concentration, when ion diffuse layers overlap.
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In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any chemical instability. This study extends the analysis in our first paper on the subject [J. M. Ortiz de Zarate, J. V. Sengers, D. Bedeaux, and S. Kjelstrup, J. Chem. Phys. 127, 034501 (2007)], where we considered fluctuations in a non-isothermal reaction-diffusion system but still close to equilibrium. The present extension is based on mesoscopic non-equilibrium thermodynamics that we recently developed [D. Bedeaux, I. Pagonabarraga, J. M. Ortiz de Zarate, J. V. Sengers, and S. Kjelstrup, Phys. Chem. Chem. Phys. 12, 12780 (2010)] to derive the law of mass action and fluctuation-dissipation theorems for the random contributions to the dissipative fluxes in the nonlinear macroscopic description. Just as for non-equilibrium fluctuations close to equilibrium, we again find an enhancement of the intensity of the concentration fluctuations in the presence of a temperature gradient. The non-equilibrium concentration fluctuations are in both cases spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a proportional to q(-4) to a proportional to q(-2) behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction experimentally. The important conclusion overall is that non-equilibrium fluctuations in non-isothermal reaction-diffusion systems are always long ranged. (C) 2011 American Institute of Physics. [doi:10.1063/1.3640010]
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The controlled formation of micrometre-sized drops is of great importance to many technological applications(1-5). Here we present a wetting-based destabilization mechanism of forced microfilaments on either hydrophilic or hydrophobic stripes that leads to the periodic emission of droplets. The drop emission mechanism is triggered above the maximum critical forcing at which wetting, capillarity, viscous friction and gravity can balance to sustain a stable driven contact line. The corresponding critical filament velocity is predicted as a function of the static wetting angle, which can be tuned through the substrate behaviour, and shows a strong dependence on the filament size. This sensitivity explains the qualitative difference in the critical velocity between hydrophilic and hydrophobic stripes, and accounts for previous experimental results of splashing solids(6). We demonstrate that this mechanism can be used to control independently the drop size and emission period, opening the possibility of highly monodisperse and flexible drop production techniques in open microfluidic geometries.
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We compute the electrostatic potential at the surface, or zeta potential zeta, of a charged particle embedded in a colloidal suspension using a hybrid mesoscopic model. We show that, for weakly perturbing electric fields, the value of zeta obtained at steady state during electrophoresis is statistically indistinguishable from zeta in thermodynamic equilibrium. We quantify the effect of counter-ion concentration on zeta. We also evaluate the relevance of the lattice resolution for the calculation of zeta and discuss how to identify the effective electrostatic radius.
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Growth saturation of unstable thin films on transverse-striped hydrophilic-hydrophobic micropatterns
Using three-dimensional numerical simulations, we demonstrate the growth saturation of an unstable thin liquid film on micropatterned hydrophilic-hydrophobic substrates. We consider different transverse-striped micropatterns, characterized by the total fraction of hydrophilic coverage and the width of the hydrophilic stripes. We compare the growth of the film on the micropatterns to the steady states observed on homogeneous substrates, which correspond to saturated sawtooth and growing finger configurations for hydrophilic and hydrophobic substrates, respectively. The proposed micropatterns trigger an alternating fingering-spreading dynamics of the film, which leads to a complete suppression of the contact line growth above a critical fraction of hydrophilic stripes. Furthermore, we find that increasing the width of the hydrophilic stripes slows down the advancing front, giving smaller critical fractions the wider the hydrophilic stripes are. Using analytical approximations, we quantitatively predict the growth rate of the contact line as a function of the covering fraction, and predict the threshold fraction for saturation as a function of the stripe width.
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We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.
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The interaction between a diblock copolymer and nanoscopic particles can lead to highly organized hybrid materials. The morphology of such hybrid materials depends on the polymer compositions as well on the shapes, sizes, and surface treatment of the particles. A hybrid mesoscopic approach to study the dynamics of nanocomposites composed from a block copolymer melt and a suspension of colloids is proposed. A collective description of the polymer dynamics is combined with the individual resolution of the colloids. The implementation of the method in two and three dimensions is described and the method is tested for different particle sizes, diblock copolymer compositions and polymer/colloid interactions.
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Recently, we have started to develop mesoscopic nonequilibrium thermodynamics for a reaction far from equilibrium in the presence of a temperature gradient, so that the interplay between the chemical reaction, diffusion and thermal diffusion can be described within the same theoretical framework. In this article we show that the spatial symmetry properties of the deterministic solution, which were so characteristic for conditions close to equilibrium, are no longer valid far from equilibrium. This is expected to have some conceptual consequences for the spatial spectrum of the fluctuations of temperature and concentrations around their local equilibrium values. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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We present a two-channel driven lattice gas model with oppositely directed species moving on two parallel lanes with lane switching processes. We study the correlated lane switching mechanism for particles so that switching may occur with finite probability only when oppositely directed species meet on the same channel. The system is analyzed for a closed ring with conserved total particle number. For asymmetric particle exchange between the lanes, the system exhibits a unique polarization phenomenon with segregation of oppositely directed species between the two lanes. The polarization phenomenon can be understood as a consequence of the existence of an absorbing steady state. For symmetric exchange rate of particles between the lanes, the system remains unpolarized, with equal particle density on both the lanes in the thermodynamic limit of large system size. We study the system using a combination of a mean field (MF) analysis and Monte Carlo simulations. The nature of phase segregation that we see for this system is distinct from driven particle systems which are in contact with the particle reservoir. The features observed for this minimal model will have ramifications for biofilament based intracellular transport, wherein cellular cargoes, e.g. organelles and vesicles, are transported by oppositely directed particles on multiple filament tracks.
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We present experimental and numerical results of the effect that a partial discharge has on the morphological and micro-mechanical properties of non-spherical, convex particles in a silo. The comparison of the particle orientation after filling the silo and its subsequent partial discharge reveals important shear-induced orientation, which affects stress propagation. For elongated particles, the flow induces an increase in the packing disorder which leads to a reduction of the vertical stress propagation developed during the deposit generated prior to the partial discharge. For square particles, the flow favors particle alignment with the lateral walls promoting a behavior opposite to the one of the elongated particles: vertical force transmission, parallel to gravity, is induced. Hence, for elongated particles the flow developed during the partial discharge of the silo leads to force saturation with depth whereas for squares the flow induces hindering of the force saturation observed during the silo filling.
2010
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We present a generic mechanism by which reproducing microorganisms, with a diffusivity that depends on the local population density, can form stable patterns. For instance, it is known that a decrease of bacterial motility with density can promote separation into bulk phases of two coexisting densities; this is opposed by the logistic law for birth and death that allows only a single uniform density to be stable. The result of this contest is an arrested nonequilibrium phase separation in which dense droplets or rings become separated by less dense regions, with a characteristic steady-state length scale. Cell division predominates in the dilute regions and cell death in the dense ones, with a continuous flux between these sustained by the diffusivity gradient. We formulate a mathematical model of this in a case involving run-and-tumble bacteria and make connections with a wider class of mechanisms for density-dependent motility. No chemotaxis is assumed in the model, yet it predicts the formation of patterns strikingly similar to some of those believed to result from chemotactic behavior.
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We present a coarse-grained simulation method for complex charged systems. This mesoscopic model couples a hydrodynamic description to a free energy functional accounting for the interactions between solvent(s) and charged solutes. It is implemented in a hybrid lattice-based algorithm, whereby the evolution of the overall mass and momentum is taken care of via a Lattice Boltzmann scheme, whereas the composition and ionic concentrations are updated using the link-flux method. Several applications illustrate the power of this coarse-grained model for charged heterogeneous media: the transport of charged tracers in charged porous media, the deformation of an oil droplet in water under the effect of an applied electric field, and the distribution of ions at an oil-water interface as a function of their affinity for both solvents.
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We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume v, with the constraint of a fixed total volume V=Sigma(N)(i=1)v(i), N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as v(i)(1/p) and our model thus represents a gas of polydisperse hard rods with variable diameters v(i)(1/p). We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard-rod system, under the constraints of fixed N and V. Complementary approaches (explicit construction of the steady state distribution on the one hand; density functional theory on the other hand) completely and consistently specify the behavior of the system. A real space condensation transition is shown to take place for p>1; beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.
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We study the propulsion of a micron-size paramagnetic colloidal doublet dispersed in water and driven above a surface by an external precessing magnetic field. The applied field forces the doublet to precess around an axis parallel to the plane of motion and the rotation of the colloidal assembly is rectified into translation due to a periodic asymmetry in dissipation close to the bounding plate. These recent experimental findings [P. Tierno, R. Golestanian, I. Pagonabarraga, and F. Sagues, Phys. Rev. Lett. 101, 218304 (2008)] are complemented here with a theoretical analysis of the system and extended to more complex magnetic modulations such as elliptical driving fields. Experimental results show a good agreement with numerical simulations with the aim to find the best conditions toward the optimization of propulsion speed and swimming efficiency.
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The cooling dynamics of a 2D granular gas of elongated particles is analyzed. We perform simulations on the temporal evolution of soft particles, using a molecular dynamics algorithm. For weakly dissipative particles, we found a homogeneous cooling process where the overall translational kinetic energy decreases analogously to viscoelastic circular particles. In contrast, for strongly dissipative particles we observed an inhomogeneous cooling process where the diminishing of translational kinetic energy notably slows down. The rotational kinetic energy, however, always decays in agreement with Haff's prediction for the homogeneous cooling state of inelastic particles. We mainly found that the cooling kinetics of the system is controlled by the mechanisms that determine the local energy dissipation (collisions). However, we detected a strong influence of particle shape and inelasticity on the structure of the clusters which develop in the inhomogeneous cooling regimes. Our numerical outcomes suggest that strong dissipation and particle anisotropy induce the formation of ordered cluster structures that retards the relaxation to the final asymptotic regime.
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We investigate numerically the dynamics of unstable gravity driven three-dimensional thin liquid films on hydrophilic-hydrophobic patterned substrates. We explore longitudinally striped and checkerboard arrangements. Simulations show that for longitudinal stripes, the thin film can be guided preferentially on the hydrophilic stripes, while fingers develop on adjacent hydrophobic stripes if the width of the stripes is large enough. On checkerboard patterns, the film develops as a finger on hydrophobic domains, while it spreads laterally to cover the hydrophilic domains. providing a mechanism to tune the growth rate of the film. By means of kinematical arguments, we quantitatively predict the growth rate of the contact line on checkerboard arrangements, providing a fist step toward potential techniques that control thin film growth in experimental setups.
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We report experimental and theoretical results of the effect that particle shape has on the packing properties of granular materials. We have systematically measured the particle angular distribution, the cluster size distribution and the stress profiles of ensembles of faceted elongated particles deposited in a bidimensional box. Stress transmission through this granular system has been numerically simulated using a two-dimensional model of irregular particles. For grains of maximum symmetry (squares), the stress propagation localizes and forms chain-like forces analogous to those observed for granular materials composed of spheres. For thick layers of grains, a pressure saturation is observed for deposit depths beyond a characteristic length. This scenario correlates with packing morphology and can be understood in terms of stochastic models of aggregation and random multiplicative processes. As grains elongate and lose their symmetry, stress propagation is strongly affected. Lateral force transmission becomes less favored than vertical transfer, and hence, an increase in the pressure develops with depth, hindering force saturation.
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We present a theoretical study of the behaviour of two active particles under the action of harmonic traps kept at a fixed distance away from each other. We classify the steady configurations the squirmers develop as a function of their self-propelling velocity and the active stresses the swimmers induce around them. We have further analyzed the stability of such configurations, and have found that the ratio between their self-propelling velocity and the apolar flow generated through active stresses determines whether collinear parallel squirmers or perpendicularly swimming particles moving away from each other are stable. Therefore, there is a close connection between the stable configurations and the active mechanisms leading to the particle self-propulsion. The trap potential does not affect the stability of the configurations; it only modifies some of their relevant time scales. We have also observed the development of characteristic frequencies which should be observable. Finally, we show that the development of the hydrodynamic flows induced by the active particles may be relevant even when its time scale orders of magnitude smaller than the other present characteristic time scales and may destabilize the stable configurations.
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We analyze the hydrodynamic coupling of pairs of squirmers and the impact it has on their short and long-time behavior. The study combines an analytic analysis of the hydrodynamic interactions between pairs of squirmers with computer simulations to elucidate the quantitative capabilities of the theoretical approach. The numerical study allows us to address the motion of simple geometries of squirmers on long times and perform a complete discussion of the effective repulsive interactions in squirmer ensembles. The contrast between analytic and numerical results identifies the features of active motion responsible for such effective interactions. The framework developed also allows for an analysis of the hydrodynamic coupling between a squirmer and a solid wall and shows the possibility of bounded motion next to a solid wall. (C) 2010 Elsevier B.V. All rights reserved.
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We introduce a multispecies lattice-gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargos being carried by oppositely directed molecular motors, moving on a single biofilament. Building on a totally asymmetric exclusion process to characterize the motion of the interacting cargos, we allow for mass exchange with the environment, input, and output at filament boundaries and focus on the role of interconversion rates and how they affect the directionality of the net cargo transport. We quantify the effect of the various different competing processes in terms of nonequilibrium phase diagrams. The interplay of interconversion rates, which allow for flux reversal and evaporation-deposition processes, introduces qualitatively unique features in the phase diagrams. We observe regimes of three-phase coexistence, the possibility of phase re-entrance, and a significant flexibility in how the different phase boundaries shift in response to changes in control parameters. The moving steady-state solutions of this model allows for different possibilities for the spatial distribution of cargo vesicles, ranging from homogeneous distribution of vesicles to polarized distributions, characterized by inhomogeneities or shocks. Current reversals due to internal regulation emerge naturally within the framework of this model. We believe that this minimal model will clarify the understanding of many features of collective vesicle transport, apart from serving as the basis for building more exact quantitative models for vesicle transport relevant to various in vivo situations.
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We show how the law of mass action can be derived from a thermodynamic basis, in the presence of temperature gradients, chemical potential gradients and hydrodynamic flow. The solution gives the law of mass action for the forward and the reverse contributions to the net chemical reaction. In addition we derive the fluctuation-dissipation theorem for the fluctuating contributions to the reaction rate, heat flux and mass fluxes. All these results arise without any other assumptions than those which are common in mesoscopic non-equilibrium thermodynamics; namely quasi-stationary transport across a high activation energy barrier, and local equilibrium along the reaction coordinate. Arrhenius-type behaviour of the kinetic coefficients is recovered. The thermal conductivity, Soret coefficient and diffusivity are significantly influenced by the presence of a chemical reaction. We thus demonstrate how chemical reactions can be fully reconciled with non-equilibrium thermodynamics.
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Electrokinetic phenomena are of great practical importance in fields as diverse as micro-fluidics, colloid science and oil exploration. However, the quantitative prediction of electrokinetic effects was until recently limited to relatively simple geometries that allowed the use of analytical theories. In the past decade, there has been a rapid development in the use of numerical methods that can be used to model electrokinetic phenomena in complex geometries or, more generally, under conditions where the existing analytical approaches fail. The present paper discusses these recent developments, with special emphasis on the advent of coarse-grained models that make it possible to bridge the gap between a purely atomistic and macroscopic descriptions.
2009
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Microscopic semiflexible filaments suspended in a viscous fluid are widely encountered in biophysical problems. The classic example is the flagella used by microorganisms to generate propulsion. Simulating the dynamics of these filaments numerically is complicated because of the coupling between the motion of the filament and that of the surrounding fluid. An attractive idea is to simplify this coupling by modeling the fluid motion by using Stokeslets distributed at equal intervals along the model filament. We show that, with an appropriate choice of the hydrodynamic radii, one can recover accurate hydrodynamic behavior of a filament with a finite cross section without requiring an explicit surface. This is true, however, only if the hydrodynamic radii take specific values and that they differ in the parallel and perpendicular directions leading to a caterpillarlike hydrodynamic shape. Having demonstrated this, we use the model to compare with analytic theory of filament deformation and rotation in the small deformation limit. Generalization of the methodology, including application to simulations using the Rotne-Prager tensor, is discussed.
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We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model (CDFBM). Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models.
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We introduce a simple numerical algorithm to describe collision-induced fragmentation. We consider fragmentation induced by collisions between pairs of particles and perform numerical studies for several classes of interaction kernels, and for several types of breaking processes. We validate the algorithm by comparing the results of the kinetic evolution and particle size statistics with previous analytical results for symmetric and asymmetric kernels. The excellent agreement obtained proves the algorithm versatility. The method also allows us to examine generic kernels, for which no exact solutions are known.
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We analyze fluctuation-dissipation relations in the backgammon model: a system that displays glassy behavior at zero temperature due to the existence of entropy barriers. We study local and global fluctuation relations for the different observables in the model. For the case of a global perturbation we find a unique negative fluctuation-dissipation ratio that is independent of the observable and which diverges linearly with the waiting time. This result suggests that a negative effective temperature can be observed in glassy systems even in the absence of thermally activated processes.
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We present an experimental and numerical study on the influence that particle aspect ratio has on the mechanical and structural properties of granular packings. For grains with maximal symmetry (squares), the stress propagation in the packing localizes forming chainlike forces analogous to the ones observed for spherical grains. This scenario can be understood in terms of stochastic models of aggregation and random multiplicative processes. As the grains elongate, the stress propagation is strongly affected. The interparticle normal force distribution tends toward a Gaussian, and, correspondingly, the force chains spread leading to a more uniform stress distribution reminiscent of the hydrostatic profiles known for standard liquids.
2008
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We study a minimal model for bidirectional collective transport of cargo vesicles on a biofilament where the competing motion is characterized by the cargo densities moving toward the opposite filament ends. The model incorporates inter-vesicle interaction (through excluded volume) and active transport as well as motor regulation and environment interactions. From the current profiles we derive the non-equilibrium phase diagram. In terms of the filament end cargo fluxes, the phase diagram allows for re-emergent density shocks. This approach captures qualitatively a number of features of the collective state of the cargoes associated with bidirectional transport: current reversals due to internal regulation, boundary induced phase transitions and domain wall localization in the bulk. Vesicle polarization emerges naturally within the proposed framework. Copyright (C) EPLA, 2008
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We show that DNA-linked anisotropic doublets composed of paramagnetic colloidal particles can be endowed with controlled propulsion when floating above a flat plate and subjected to a magnetic field precessing around an axis parallel to the plate. The propulsion mechanism for this artificial swimmer does not involve deformations, and it makes use of the minimal two degrees of freedom needed to propel it at low Reynolds numbers. We combine experimental observations with a theoretical analysis that fully characterizes the propulsion velocity in terms of the strength and frequency of the actuating magnetic field.
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We analyze the role of hydrodynamic cooperativity in different systems of biological interest. We describe alternative approaches to model the dynamics of suspensions which account for realistic dynamic coupling on the length and time sales in which mesoscopic suspended particles (such as semiflexible filaments and swimmers) evolve. The time evolution and transport of such systems, which are relevant in physical biology, are studied in detail.We consider the interactions in the dynamic response of inextensible semiflexible filaments subject to uniform external drivings and describe the interplay between elastic and hydrodynamic stresses. We analyze how such couplings give rise to a rich phenomenology in their dynamics. Using a complementary mesoscopic approach, we also discuss the dynamic regimes of suspensions of self-propelling particles which interact only through the embedding solvent.
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We describe a simple simulation method that describes the hydrodynamics of semiflexible filaments immersed in a low Reynolds number fluid and analyze how multiple body cooperativity emerges due to the presence of hydrodynamic interactions (HI). We study the sedimentation of ensembles of filaments under an external force and also consider the propulsion of filaments subject to simple periodic driving. In both cases the dynamics shows qualitative differences due to the presence of HI. For sedimentation, the effects include cooperative velocity and instabilities that can be understood from the interplay of deformations due to flexibility and hydrodynamic forces. The motion of swimmers is more complex, and shows both positive and negative cooperation depending on distance, frequency of drive, and flexibility. (C) 2008 Elsevier B.V. All rights reserved.
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We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime t(f) of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tf and the characteristic time t(m) of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of tf from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements.
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We report a lattice-Boltzmann scheme to compute the dispersion of charged tracers in charged porous media under the combined effect of advection, diffusion and electro-migration. To this end, we extend the moment propagation approach, introduced to study the dispersion of neutral tracers (Lowe C. and FRENKEL D., Phys. Rev. Lett., 77 (1996) 4552), to include the effect of electrostatic forces. This method allows us to compute the velocity autocorrelation function of the charged tracers with high accuracy. The algorithm is validated studying the dispersion coefficient in the case of electro-osmotic flow in a slit without added salt. We find excellent agreement between the numerical and analytical results. This method also provides the full time dependence of the diffusion coefficient, including for charged tracers. We illustrate on the slit case how D(t), which is measured by NMR to probe the geometry of porous media, reflects how the porosity explored by tracers depends on their charge. Copyright (C) EPLA, 2008.
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The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the long velocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f(c)similar to exp(-c(n)), with n approximate to 1.2, regarding less the fragmentation mechanisms.
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We analyze the role of the force-dependent kinetics of motor proteins in the stability of antiparallel arrays of polar. laments, such as those in the mitotic spindle. We determine the possible stable structures and show that there exists an instability associated to the collective behavior of motors that leads to the collapse of the structure. The agreement of our results and several experimental observations in eukaryotic cell division suggests an important role of kinesin-5 motors and microtubule bundles in the stability of the mitotic spindle. Copyright (C) EPLA, 2008.
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We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently. (c) American Institute of Physics.
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We propose a simple derivation of the one-dimensional hard-rod equation of state, with and without a Kac tail (a long-range and weak potential). The case of hard spheres in higher dimension is also addressed, and we recover the virial form of the equation of state in a direct way. (c) 2008 American Association of Physics Teachers.
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We analyze the collective motion of suspensions of active rotators at low Reynolds numbers which interact hydrodynamically. We introduce a simple model for a rotator which allows us to classify the relevant dynamical regimes of the suspension. We characterize the collective velocity at which rotators displace and analyze its implications at long times, when these rotator suspensions diffuse. We analyze the differences with respect to diffusion in suspensions of passive particles, and assess the relevance of the Stokes-Einstein relation on rotators' diffusivity.
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To achieve permanent propulsion of micro-objects in confined fluids is an elusive but challenging goal that will foster future development of microfluidics and biotechnology. Recent attempts based on a wide variety of strategies are still far from being able to design simple, versatile, and fully controllable swimming engines on the microscale. Here we show that DNA-linked anisotropic colloidal rotors, composed of paramagnetic colloidal particles with different or similar size, achieve controlled propulsion when subjected to a magnetic field precessing around an axis parallel to the plane of motion. During cycling motion, stronger viscous friction at the bounding plate, as compared to fluid resistance in the bulk, creates an asymmetry in dissipation that rectifies rotation into a net translation of the suspended objects. The potentiality of the method, applicable to any externally rotated micro/nano-object, is finally demonstrated in a microfluidic platform by guiding the colloidal rotors through microscopic-size channels connected in a simple geometry.
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A mesoscopic model for studying capillary phenomena is introduced. The fluid is represented by particles interacting through soft forces that allow condensation. A model for a solid wall is also presented whose affinity for the liquid can be tuned from hydrophilic to superhydrophobic. Regarding the dynamics, the validity of the model was assessed studying the classical drop spreading on a wetting substrate where good agreement was found with the scaling predicted theoretically. We show also how to extend the proposed model to deal with symmetrical binary mixtures. This model opens the way to model capillary phenomena involving complex fluids. (c) 2008 Elsevier B.V.. All rights reserved.
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A description of the steps taken to produce a massively parallel code for particle suspension problems using the lattice Boltzmann method is presented. A number of benchmarks based on a binary fluid lattice Boltzmann model are used to assess the performance of the code in terms of the computational overhead required for the particle problem compared with the fluid-only problem, and for the scaling of the code to large processor numbers. On the Blue Gene/L architecture, the additional computational cost of particle suspensions Of LIP to 40% solid volume fraction (here over a million particles) is negligible compared with the fluid-only code. (c) 2007 Elsevier Ltd. All rights reserved.
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We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0 <= alpha <= 1 of fibers is unbreakable, while the remaining 1-alpha fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components alpha(c) which separates two qualitatively different regimes of the system: below ac the burst size distribution is a power law with the usual exponent tau = 5/2, while above ac the exponent switches to a lower value tau = 9/4 and a cutoff. function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point de. ning a novel universality class of breakdown phenomena. Copyright (c) EPLA, 2008.
2007
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Local density dependent potentials constitute a family of many body potentials which have been recently introduced in mesoscopic modeling of simple and complex fluids. We construct a field theory for these potentials and calculate the structure factor of the fluid through a saddle point expansion. We propose also an integral equation for local density potentials which shows quantitative agreement both for the correlation functions and thermodynamic properties of such potentials, even close to binodals where the simpler saddle point approximation fails. Contrary to the limitations of global density dependent potentials, there is no ambiguity in the expression of thermodynamics quantities such as the pressure.
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We study the dynamics of granular gases which fragment due to their collisions. We have developed a kinetic model that accounts for the correlations between grains' size and velocity at collisions. We analyze how the fragmentation events taking place at collisions affect the growth in the number of grains, and also which distribution of grain' sizes they give rise to. We describe the effects that the mechanisms which control the fragmentation process have on the kinetics of the granular mixture, and have characterized the different kinetic regimes they give rise to, depending on the asymptotic behavior of the fragmentation probability. In these different scenarios the size and velocity distributions display also distinct features, and hence can be used to understand the physical processes in fragmenting systems.
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We develop a simple lattice model to describe the hydrodynamic influence of active mass transport along bio-filaments on freely diffusing mass in the cell. To quantify the overall mass transport we include Brownian motion, excluded volume interactions, active transport along the filaments, and hydrodynamic interactions. The model shows that the hydrodynamic forces induced by molecular motors attached to the. laments give rise to a non-negligible flux close to the filament. This additional flux appears to have two effects. Depending on the degree of filament occupation it can exert a sufficiently large influence on unbound motors and cargo to modify their transport and also regulate the influx of motors bound to the filament. We expect such a mechanism is important in situations found in plant cells, where directional transport spans the entire cell. In particular, it can explain the cytoplasmic streaming observed in plant cells.
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We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.
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We study the kinetics of nonlinear irreversible fragmentation. Here, fragmentation is induced by interactions/collisions between pairs of particles and modelled by general classes of interaction kernels, for several types of breakage models. We construct initial value and scaling solutions of the fragmentation equations, and apply the 'non-vanishing mass flux' criterion for the occurrence of shattering transitions. These properties enable us to determine the phase diagram for the occurrence of shattering states and of scaling states in the phase space of model parameters.
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We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and PEclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal. (C) 2007 American Institute of Physics.
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We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction. (C) 2007 American Institute of Physics.
2006
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We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two dimensions. Active particles with symmetric and asymmetric force distribution on their surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady-state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.
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We present a mesoscopic model for simulating the dynamics of a non-volatile liquid on a solid substrate. The wetting properties of the solid can be tuned from complete wetting to total non-wetting. This model opens the way to study the dynamics of drops and liquid thin films at mesoscopic length scales of the order of the nanometer. As particular applications, we analyze the kinetics of spreading of a liquid drop wetting a solid substrate and the dewetting of a liquid film on a hydrophobic substrate. In all these cases, very good agreement is found between simulations and theoretical predictions.
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We analyze the collective dynamics of self-propelling particles (spps) which move at small Reynolds numbers including the hydrodynamic coupling to the suspending solvent through numerical simulations. The velocity distribution functions show marked deviations from Gaussian behavior at short times, and the mean-square displacement at longtimes shows a transition from diffusive to ballistic motion for appropriate driving mechanism at low concentrations. We discuss the structures the spps form at longtimes and how they correlate to their dynamic behavior.
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We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal surface and charge, we can clarify the effect of the particle shape on the sedimentation process. We find that disks and spheres exhibit a different dependence of the sedimentation velocity on the Debye screening length. An analysis of the behavior of highly charged disks (beyond the scope of the linearized Poisson-Boltzmann equation) shows that, in that regime, the charge dependence of the sedimentation velocity of disks and spheres is similar. This suggests that, at high charge, the effective hydrodynamic shape of the disks becomes more spherical. (c) 2006 American Institute of Physics.
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We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seifert's integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.
2005
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Colloidal particles or nanoparticles, with equal affinity for two fluids, are known to adsorb irreversibly to the fluid-fluid interface. We present large-scale computer simulations of the demixing of a binary solvent containing such particles. The newly formed interface sequesters the colloidal particles; as the interface coarsens, the particles are forced into close contact by interfacial tension. Coarsening is markedly curtailed, and the jammed colloidal layer seemingly enters a glassy state, creating a multiply connected, solidlike film in three dimensions. The resulting gel contains percolating domains of both fluids, with possible uses as, for example, a microreaction medium.
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We describe simulations of an elastic filament immersed in a fluid and subjected to a body force. The coupling between the fluid flow and the friction that the filament experiences induces bending and alignment perpendicular to the force. With increasing force there are four shape regimes, ranging from slight distortion to an unsteady tumbling motion. We also find marginally stable structures. The instability of these shapes and the alignment are explained by induced bending and nonlocal hydrodynamic interactions. These effects are experimentally relevant for stiff microfilaments.
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A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid-fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number of simple benchmark problems involving a single particle at or near a fluid-fluid interface are undertaken and show good agreement with available theoretical or numerical results.
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The development of models for electrolytes is challenging due to the long-range nature of electric interactions. We propose a novel implementation of a lattice Boltzmann model that solves a number of limitations and inconsistencies in previously proposed variants and discuss the range of parameters the model can cover. We show how the relevant electrohydrodynamic couplings are recovered analyzing a particular electrokinetic phenomena. (c) 2005 Elsevier B.V. All rights reserved.
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Dispersed nanoparticles self-assemble into complex structures when segregated from the solvent either by evaporation or precipitation. Thus, different micro- and macroscopic structures (opals, fractals, liquid crystals) formed by nanoparticles are observed as a result of the balance between electrostatic forces, surface tension, volume exclusion, substrate topography and affinity, and size, shape and concentration of the particles. The formation process is close to the hard-sphere case with two special features: nanoparticles are coated with surfactant molecules of roughly 1 nm in length, and nanoparticles are in the nanometric scale resulting in an increased mobility. Moreover, self-assembly does not take place in solution; hence, a minimum concentration is needed in order to start self-assembly. This process occurs in contact with the substrate, when the solvent cannot re-disperse the particles anymore.
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We describe some scaling issues that arise when using lattice Boltzmann (LB) methods to simulate binary fluid mixtures-both in the presence and absence of colloidal particles. Two types of scaling problem arise: physical and computational. Physical scaling concerns how to relate simulation parameters to those of the real world. To do this effectively requires careful physics, because (in common with other methods) LB cannot fully resolve the hierarchy of length, energy and time-scales that arise in typical flows of complex fluids. Care is needed in deciding what physics to resolve and what to leave unresolved, particularly when colloidal particles are present in one or both of two fluid phases. This influences steering of simulation parameters such as fluid viscosity and interfacial tension. When the physics is anisotropic (for example, in systems under shear) careful adaptation of the geometry of the simulation box may be needed, an example of this, relating to our study of the effect of colloidal particles on the Rayleigh-Plateau instability of a fluid cylinder, is described. The second and closely related set of scaling issues are computational in nature: how do you scale-up simulations to very large lattice sizes? The problem is acute for system undergoing shear flow. Here one requires a set of blockwise co-moving frames to the fluid, each connected to the next by a Lees-Edwards like boundary condition. These matching planes lead to small numerical errors whose cumulative effects can become severe; strategies for minimizing such effects are discussed.
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We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analog in the limit of large dimension. Our exact solution shows that, for both models, X-infinity=1/2 if the system is unmagnetized while X-infinity=4/5 if the initial magnetization is nonzero. This indicates that two different classes of critical coarsening dynamics need to be distinguished depending on the initial conditions, each with its own nontrivial FDR. We also analyze the dependence of the FDR on whether local and global observables are used. These results clarify how a proper local FDR (and the corresponding effective temperature) should be defined in long-range models in order to avoid spurious inconsistencies and maintain the expected correspondence between local and global results; global observables turn out to be far more robust tools for detecting nonequilibrium FDRs.
2004
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We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. The method is based on identifying the elementary fluxes between nodes, which ensures the absence of spurious fluxes in equilibrium. We show how the model is suitable to study electro-osmotic flows. As an illustration, we show that, by introducing appropriate dynamic rules in the presence of solid interfaces, we can compute the sedimentation velocity (and hence the sedimentation potential) of a charged sphere. Our approach does not assume linearization of the Poisson-Boltzmann equation and allows us for a wide variation of the Peclet number. (C) 2004 American Institute of Physics.
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Lattice Boltzmann modeling of complex fluids: Colloidal suspensions and fluid mixtures
The study of complex fluid dynamics requires development of numerical tools that capture the essentials of the dynamic coupling among the different particles that characterize these materials. At the same time these techniques should operate on mesoscopic time and length scales, such that the relevant phenomena can be addressed in detail. Lattice Boltzmann (LB) is a simulation procedure that, although initially introduced to address problems related to fluid flows at high Reynolds numbers, has proven to be a very flexible technique to study complex fluids in generic geometries. I will address the fundamentals of the method and describe in detail two different perspectives to model complex fluids: Colloidal suspensions, where the mesoscopic particles are described in full detail, and non-ideal fluid mixtures, where there exists no clear length scale separation. In this case, a coarse-grained description of the interactions is enough to capture the essentials of the collective dynamics. In both cases I analyze the basic formulation, emphasizing their similarities, and I will afterward discuss new results that have been obtained using LB in these systems.
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The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focused on the local density distribution rho(sigma,z), measuring the number density of particles of diameter sigma at a distance z from the wall. Estimates of rho(sigma,z) are obtained for bulk volume fractions eta(b)=0.2 and eta(b)=0.4, and for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity delta=11.5% and delta=40.4%, and a truncated Schulz form having delta=40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at eta(b)=0.2. A detailed analysis of rho(sigma,z) confirms the presence of oscillatory size segregation effects, as observed in a previous DFT study [I. Pagonabarraga, M. E. Cates, and G. J. Ackland, Phys. Rev. Lett. 84, 911 (2000)]. For large delta, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive sigma-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity delta(z) is suppressed in this region, while further from the wall it exhibits oscillations. (C) 2004 American Institute of Physics.
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We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy.
2003
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We develop a general analysis of the diffusive dynamics of polydisperse polymers in the presence of chemical potential gradients, within the context of the tube model (with all species entangled). We obtain a set of coupled dynamical equations for the time evolution of the polymeric densities in a form proposed phenomenologically in recent work by Clarke, but with explicitly derived coefficients. For the case of chemical polydispersity (a set of chains that are identical except for having a continuous spectrum of enthalpic interaction strengths) the coupled equations can be fully solved in certain cases. For these, we study the linearized mode spectrum following a quench through the spinodal, with and without a passive (polymeric) solvent. We also study the more conventional case of length polydisperse chains in a poor solvent. Here the mode structure is more complicated and exact analysis difficult, but enough progress can still be made to gain some qualitative insight. We briefly discuss the modifications required to allow for the presence of unentangled, low molecular weight species in the system.
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Kinetics of fragmenting freely evolving granular gases
2002
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By performing lattice Boltzmann simulations of a binary mixture, we scrutinize the dynamical scaling hypothesis for the spinodal decomposition of binary mixtures for the crossover region, i.e., the region of parameters in the growth curve where neither inertia nor viscous forces dominate the coarsening process. Our results give no evidence for a breakdown of scaling in this region, as might arise if the process were limited by molecular scale physics at the point of fluid pinch-off between domains. A careful data analysis allows us to refine previous estimates on the width of the crossover region which is somewhat narrower than previously reported.
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Lees-Edwards boundary conditions (LEbc) for Molecular Dynamics simulations((1)) are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be implemented in isothermal lattice Boltzmann simulations and how LEbc can be used to overcome the problem of a maximum shear rate that is limited to less then 1/L-y (with L-y the transverse system size) in traditional lattice Boltzmann implementations of shear flow. The only previous Lattice Boltzmann implementation of LEbc((2)) requires a specific fourth order equilibrium distribution. In this paper we show how LEbc can be implemented with the usual quadratic equilibrium distributions.
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We present a molecular-dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short-distance correlations in the nonequilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e., factorization of the two-particle distribution function, f((2))(x(1), x(2))similar or equal tochif((1))(x(1))f((1))(x(2)) in a product of single-particle ones, where x(i)={r(i), v(i)} with i = 1,2 and chi represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space {x(1), x(2)}, where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle- and noise-induced recollisions magnifies the departure from mean-field behavior. The implications of this breakdown in several physical quantities are explored.
2001
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The Flory-Huggins equation of state for monodisperse polymers can be turned into density functional by adding square gradient term, with coefficient fixed by appeal to RPA (random phase approximation). We present instead model nonlocal functional in which each polymer is replaced by deterministic, penetrable particle of known shape. This reproduces the RPA and square gradient theories in the small deviation and/or weak gradient limits, and can readily be extended to polydisperse chains. The utility of the new functional is shown for the case of polydisperse polymer solution at coexistence in poor solvent.
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We introduce a dissipative particle dynamics scheme for the dynamics of nonideal fluids. Given a free-energy density that determines the thermodynamics of the system, we derive consistent conservative forces. The use of these effective, density dependent forces reduces the local structure as compared to previously proposed models. This is an important feature in mesoscopic modeling, since it ensures a realistic length and time scale separation in coarse-grained models. We consider in detail the behavior of a van der Waals fluid and a binary mixture with a miscibility gap. We discuss the physical implications of having a single length scale characterizing the interaction range, in particular for the interfacial properties. (C) 2001 American Institute of Physics.
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The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamically consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecedented range of length and time scales when expressed in reduced physical units. (These are the length and time units derived from fluid density, viscosity, and interfacial tension.) Using eight large (256(3)) runs, the resulting composite graph of reduced domain size I against reduced time t covers 1 less than or similar to l less than or similar to 10(5), 10(5), 10 less than or similar to t less than or similar to 10(8). Our data are consistent with the dynamical scaling hypothesis that 1(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields. Using the conventional definition of Reynolds number for this problem, Re-phi = l dl/dt, we attain values approaching 350. At Re-phi greater than or equal to 100 (which requires t greater than or equal to 10(6)) we find clear evidence of Furukawa's inertial scaling (l similar to t(2/3)), although the crossover from the viscous regime (l similar to t) is both broad and late (10(2) less than or similar to t less than or similar to 10(6)). Though it cannot be ruled out, we find no indication that Reo is self-limiting (l less than or similar to t(1/2)) at late times, as recently proposed by Grant & Elder. Detailed study of the velocity fields confirms that, for our most inertial runs, the RMS ratio of nonlinear to viscous terms in the Navier-Stokes equation, R-2, is of order 10, with the fluid mixture showing incipient turbulent characteristics. However, we cannot go far enough into the inertial regime to obtain a clear length separation of domain size, Taylor microscale, and Kolmogorov scale, as would be needed to test a recent 'extended' scaling theory of Kendon (in which R2 is self-limiting but Re-phi not). Obtaining our results has required careful steering of several numerical control parameters so as to maintain adequate algorithmic stability, efficiency and isotropy, while eliminating unwanted residual diffusion. (We argue that the latter affects some studies in the literature which report l similar to t(2/3) for t less than or similar to 10(4).) We analyse the various sources of error and find them just within acceptable levels (a few percent each) in most of our datasets. To bring these under significantly better control, or to go much further into the inertial regime, would require much larger computational resources and/or a breakthrough in algorithm design.
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The late-stage phase ordering, in three dimensions, of fully symmetric binary fluid mixtures is studied via a lattice Boltzmann method. We present time-resolved maps of the fluid velocity fields and also animated visualizations of the interfacial motion. These show distinct features corresponding to regimes where viscous, crossover and inertial hydrodynamic scaling have previously been identified. Specifically, while the interface is overdamped in the viscous regime, it exhibits recoil after topological reconnection at intermediate and higher inertia; and in our most inertial runs the interface shows extensive underdamped capillary disturbances not attributable to topological reconnection events. The advantages and practicality of presenting such dynamical data in fully animated form are demonstrated and briefly discussed.This paper's animations are available from the Multimedia Enhancements page as individual files and also packed into archives (two formats).
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This paper describes Ludwig, a versatile code for the simulation of Lattice-Boltzmann (LB) models in 3D on cubic lattices. In fact, Ludwig is not a single code, but a set of codes that share certain common routines, such as I/O and communications. If Ludwig is used as intended, a variety of complex fluid models with different equilibrium free energies are simple to code, so that the user may concentrate on the physics of the problem, rather than on parallel computing issues. Thus far, Ludwig's main application has been to symmetric binary fluid mixtures. We first explain the philosophy and structure of Ludwig which is argued to be a very effective way of developing large codes for academic consortia. Next we elaborate on some parallel implementation issues such as parallel I/O, and the use of MPI to achieve full portability and good efficiency on both MPP and SMP systems. Finally, we describe how to implement generic solid boundaries, and look in detail at the particular case of a symmetric binary fluid mixture near a solid wall. We present a novel scheme for the thermodynamically consistent simulation of wetting phenomena, in the presence of static and moving solid boundaries, and check its performance. (C) 2001 Elsevier Science B.V. All rights reserved.
2000
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The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of density fields. The case of continuous polydispersity thereby becomes tractable. We predict, generically, an oscillatory size segregation close to the wall, and connect this, by a perturbation theory for narrow distributions, with the reversible work for changing the size of one particle in a monodisperse reference fluid.
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We propose a new method for implementing conservative forces in a dissipative particle dynamics (DPD) system. We allow multibody interactions, and use information on the macroscopic equilibrium behaviour of the system. We show that it is then possible to induce a fluid/fluid phase transition, and also that the local structure is then less pronounced than in previous models. This last feature is desirable in the description of fluids at a mesoscopic scale.
1999
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In this article we present a detailed analysis of the kinetics of a class of sequential adsorption models that take into account the effect of externally applied fields las an electric field, or a shear rate) on the adsorption. The excluded volume interactions related to the finite size of the adsorbing particles are modified by the external fields. As a result, new adsorption mechanisms appear with respect to the ones used to describe the kinetics in a quiescent fluid. In particular, if the adsorbing particles are allowed to roll over preadsorbed ones, adsorption becomes non local even in the simplest geometry. An exact analytic theory cannot be developed, but we introduce a self-consistent theory that turns out to agree with the simulation results over all the range of the parameters.
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The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long-range correlations, which behave as similar to 1/r in three and similar to ln(L/r) in two dimensions. We calculate the corresponding structure factors over the whole range of wave numbers, and find good agreement with two-dimensional molecular dynamics simulations. It is also shown by means of a mode coupling calculation, how the mean field values for the steady-state temperature and collision frequency, as obtained from the Enskog-Boltzmann equation, are renormalized by long wavelength hydrodynamic fluctuations.
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We analyze the short-time dynamical behavior of a colloidal suspension in a confined geometry. We analyze the relevant dynamical response of the solvent, and derive the temporal behavior of the velocity autocorrelation function, which exhibits an asymptotic negative algebraic decay. We are able to compare quantitatively with theoretical expressions, and analyze the effects of confinement on the diffusive behavior of the suspension.
1998
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Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the longtime tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available. [S1063-651X(98)00612-6].
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We present a model for treating solid boundaries of a DPD fluid. The basic idea is to model the stick boundary conditions by assuming that a layer of DFD particles is stuck on the boundary. By taking a continuum limit of this layer effective dissipative and stochastic forces on the fluid DPD particles are obtained. The boundary model is tested by a simulation of planar Couette flow which allows the performance of vicosimetric measurements. We analyze the conditions that ensure a proper stick boundary condition for an impenetrable wall, comparing with previous methods used.
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We propose an implementation of dissipative particle dynamics that is free of the inconsistencies that plagued earlier algorithms. The present algorithm satisfies a form of microscopic reversibility. As a consequence, we recover the correct equilibrium properties. Moreover, we can use much larger time steps than previously. We report a detailed comparison between simulated transport properties and the theoretical predictions. We find that the existing theory is only valid under very special conditions. A more general theory is still lacking.
1997
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Computer simulations of a colloidal particle suspended in a fluid confined by rigid walls show that, at long times, the velocity correlation function decays with a negative algebraic tail. The exponent depends on the confining geometry, rather than the spatial dimensionality. We can account for the tail by using a simple mode-coupling theory which exploits the fact that the sound wave generated by a moving particle becomes diffusive.
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For general irreversible deposition processes, a relation between the variance sigma(2) of the number of deposited particles on subsystems out of a large surface and the available surface function Phi is obtained. This relation is based on a mean field assumption and follows the resolution of a master equation system. It is valid at low to intermediate values of the surface coverage theta as shown by comparison with exact results and with numerical simulations for special deposition models. In the low coverage limit, if the available surface function is written as a series expansion of the coverage theta, whose first nontrivial term varies as theta(k), the reduced variance has a similar expansion, However, the prefactor of theta(k) derived in this article is in general different in both series expansions. This result has also been obtained by a rigorous argument based on the evolution of the k-particle distribution function with the coverage. (C) 1997 American Institute of Physics.
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We have used the thermodynamical description of a chemical reaction as a diffusion process along an internal coordinate to analyze fluctuations in the density of the constituents, which are treated under the framework of fluctuating hydrodynamics. We then obtain a Langevin equation for the density, as a function of the internal coordinate, whose stochastic source statisfies a fluctuation-dissipation theorem. After contraction of the description, by means of integration in the internal coordinate, we derive the Langevin equation for the concentration of reactants and products as well as the statistical properties of the random source which agree with the corresponding results obtained by means of Keizer's theory. Application of the formalism is illustrated by considering particular cases. An extension to coupled chemical reactions is also discussed.
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In this paper we consider the influence of hydrodynamic interactions on the irreversible adsorption of hard spheres on a flat surface. Unlike the usual models which take into account the finite size of the adsorbing particles, we have made computer simulations where both the transport and the geometric aspects related to the adsorption problem are taken into account. We are able to compare our data with some recent experimental results, explaining some discrepancies obtained when comparing the experimental data with the appropriate adsorption kinetic model. (C) 1997 Elsevier Science B.V.
1996
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The ballistic deposition of particles by taking hydrodynamic interactions (HI) into account has been studied by means of computer simulations. The radial distribution function of the assembly of particles deposited on a plane has been determined as a function of the coverage and compared to experimental data. It appears that the introduction of HI in the model when compared to the ballistic model (BM) predictions leads to a better agreement between experiment and simulation in particular for the radial distribution function. HI also modify the value of the first non-vanishing term (B-3) in the expansion of the available surface function, Phi, in the coverage. One can estimate the ratio B-3(BHM)/B(3)(BM)similar to 0.5, where B-3(BHM) (resp. B-3(BM)) corresponds to simulations in which HI have been (resp. have not been) taken into account. The introduction of HI, however, leads to small changes in Phi. Finally, we conclude that, as far as average global quantities are concerned, the BM without HI constitutes a good approximation. It is only for the detailed analysis of the structure of the layer of deposited particles that HI play a significant quantitative role. (C) 1996 American Institute of Physics.
1995
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We present a new class of sequential adsorption models in which the adsorbing particles reach the surface following an inclined direction (shadow models). Capillary electrophoresis, adsorption in the presence of a shear, and adsorption on an inclined substrate are physical manifestations of these models. Numerical simulations are carried out to show how the new adsorption mechanisms are responsible for the formation of more ordered adsorbed layers and have important implications in the kinetics, in particular, modifying the jamming limit.
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In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models.
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We have studied the thermocapillary motion of a drop in a fluid under nonequilibrium conditions, in the presence of velocity and temperature gradients, After reformulating the boundary value problem in terms of an induced force and an induced heat source densities, we have derived the Faxen theorem for the drop. The theorem gives the hydrodynamic force exerted on the drop as a function of its velocity and of the unperturbed velocity and temperature fields. From it we infer expressions for the mobility and thermocapillary coefficients. Our general result then permits us to analyze a number of particular situations of interest which have been reported by other authors.
1994
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We have studied the adsorption process of non-Brownian particles on a line. Our work differs from previously proposed models in that we have incorporated hydrodynamic interactions between the incoming particles and the preadsorbed particles as well as the surface. We then numerically analyze the effect of these interactions on quantities related to the adsorption process. Comparing our model to the ballistic deposition model (BM) shows a significant discrepancy in the pair correlation function. These results can explain some differences between recent experiments and BM predictions. Finally, the limitations of the applicability of BM are addressed.
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We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monatomic steps. The validity of the continuum approximation treated by Frank is checked against numerical calculations and simple, qualitative arguments. The continuum approximation is found to suffer from limitations related, in particular, to the existence of angular points. These limitations are often related to the adatom detachment rate which is higher on the lower side of each step than on the upper side ('Schwoebel effect').
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We study the dynamics of density fluctuations in purely diffusive systems away from equilibrium, Under some conditions the static density correlation function becomes long ranged. We then analyze this behavior in the framework of nonequilibrium fluctuating hydrodynamics.
1992
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The Langmuir equation describing the adsorption kinetics of particles on surfaces is obtained from non-equilibrium thermodynamics. For this purpose, we consider that the adsorption phenomenon consists of two different processes, namely, diffusion and transition through a potential barrier. The latter is treated using the theory of internal degrees of freedom.
1991
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We analyze the effect of boundary conditions in the Rayleigh spectrum of a fluid under a temperature gradient. A specific wave vector geometry prevents coupling between temperature and velocity fluctuations and could make boundary effects observable. These effects are introduced by means of dimensionless numbers, which combine both the nature of the contact surfaces and the size of the system. We then show that the height of the peak as well as the total intensity under the Rayleigh line are modified by the presence of the walls.
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