We study steady-state properties of a bath of active Brownian particles (ABPs) in two dimensions in the presence of two fixed, permeable (hollow) disklike inclusions, whose interior and exterior regions can exhibit mismatching motility (self-propulsion) strengths for the ABPs. We show that such a discontinuous motility field strongly affects spatial distribution of ABPs and thus also the effective interaction mediated between the inclusions through the active bath. Such net interactions arise from soft interfacial repulsions between ABPs that sterically interact with and/or pass through permeable membranes assumed to enclose the inclusions. Both regimes of repulsion and attractive (albeit with different mechanisms) are reported and summarized in overall phase diagrams.
The initiation of fluid-induced fracture in formations of permeable geomaterials subjected to quasi-stationary flow processes (drained response) can be strongly affected by Biot's coefficient and the size of the formation. The aim of this paper is to analyse the influence of these parameters on the initial fracture process of a thick-walled hollow permeable sphere subjected to fluid injection in the hole. Assuming that fracture patterns are distributed uniformly during the hardening stage of the fracture initiation process, the coupled fluid-solid problem is described by a nonlinear ordinary d…
Flow-induced failure of granular materials is relevant to a broad range of geomechanical applications. Plasticity, which is the inherent failure mechanism of most granular materials, enables large deformations that can invalidate linearised models. Motivated by fluid injection into a borehole, we develop a steady-state model for the large deformation of a thick-walled, partially-permeable, elastic--perfectly-plastic annulus with a pressurised inner cavity. We account for pre-existing compressive stresses, as would be present in the subsurface, by subtracting a compressed initial state from our…
Using Gibbs ensemble Monte Carlo simulations and density functional theory we investigate the fluid-fluid demixing transition in inhomogeneous colloid-polymer mixtures confined between two parallel plates with separation distances between one and ten colloid diameters covering the complete range from quasi two-dimensional to bulk-like behavior. We use the Asakura-Oosawa-Vrij model in which colloid-colloid and colloid-polymer interactions are hard-sphere like, whilst the pair potential between polymers vanishes. Two different types of confinement induced by a pair of parallel walls are consider…
Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a `bridging' transition as the wetting films join to form a fluid bridge. The potential between the two big particles becomes lon…
Taking into account simultaneously the Vicsek short range ordering and also the far-field hydrodynamic interactions mediated by the ambient fluid, we investigate the role of long range interactions in the ordering phenomena in a quasi 2-dimensional active suspension. By studying the number fluctuations, the velocity correlation functions and cluster size distribution function, we observe that depending on the number density of swimmers and the strength of noise, the hydrodynamic interactions affect the ordering in a suspension. For a fixed value of noise, at large density of particles, long ra…
Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified during the past. Prime example systems are given by functionalized elastic composite materials or fluid colloidal suspensions. Here, we address the significantly less frequently studied situation of rigid inclusions in two-dimensional elastic or low-Reynolds-number fluid films. We concentrate on the situation in which disk-like inclusions remain well separated from each other and do not get into contact. Specifically, we demonstrate a…
We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modeling the neighbor-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration-velocity distribution function $P\left(v^{\prime},a^{\prime};t\right)$. Quadrant-conditioned covariance integrals of $P\left(v^{\prime},a^{\prime};t\right)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature. Analytical predictions are in agreement with…
We consider binary liquid mixtures close to their critical points confined by two parallel, geometrically flat but chemically structured, substrates. Universal order parameters profiles are calculated within mean field theory for periodic patterns of stripes with alternating preferences for the two species of the mixture and with different relative positions of the two substrates. From the order parameters profiles the effective forces between the two plates are derived. The tuning of Casimir amplitudes is discussed.
We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real and reciprocal space data, a picture of a two-step crystallization process is supported: First dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of meta…
Here we compare two extreme regimes of non-suspended fluid-mediated particle transport, transport in light and heavy fluids ("saltation" and "bedload", respectively), regarding their particle fluctuation energy balance. From direct numerical simulations, we surprisingly find that the ratio between collisional and fluid drag dissipation of fluctuation energy is significantly larger in saltation than in bedload, even though the contribution of interparticle collisions to transport of momentum and energy is much smaller in saltation due to the low concentration of particles in the transport layer…
We investigate the solvent mediated interactions between nanoparticles adsorbed at a liquid-vapor interface in comparison to the solvent mediated interactions in the bulk liquid and vapor phases of a Lennard-Jones solvent. Molecular dynamics simulation data for the latter are in good agreement with results from integral equations in the reference functional approximation and a simple geometric approximation. Simulation results for the solvent mediated interactions at the interface differ markedly from the interactions of the particles in the corresponding bulk phases. We find that at short int…
The effective interaction between two planar walls immersed in a fluid is investigated by use of Density Functional Theory in the super-critical region of the phase diagram. A hard core Yukawa model of fluid is studied with special attention to the critical region. To achieve this goal a new formulation of the Weighted Density Approximation coupled with the Hierarchical Reference Theory, able to deal with critical long wavelength fluctuations, is put forward and compared with other approaches. The effective interaction between the walls is seen to change character on lowering the temperature: …
We study the hydrodynamic interactions between colloids suspended in a compressible fluid inside a rigid channel. Using lattice-Boltzmann simulations and a simplified hydrodynamic theory, we find that the diffusive dynamics of density perturbations (sound) in the confined fluid give rise to particle correlations of exceptionally long spatial range and algebraic temporal decay. We examine the effect of these sound-mediated correlations on two-particle dynamics and on the collective dynamics of a quasi-one-dimensional suspension.
We propose a continuum theory of the liquid-liquid phase separation in an elastic network where phase-separated microscopic droplets rich in one fluid component can form as an interplay of fluids mixing, droplet nucleation, network deformation, thermodynamic fluctuation, \emph{etc}. We find that the size of the phase separated droplets decreases with the shear modulus of the elastic network in the form of $\sim[\mathrm{modulus}]^{-1/3}$ and the number density of the droplet increases almost linearly with the shear modulus $\sim[\mathrm{modulus}]$, which are verified by the experimental observa…
A theoretical model is developed for predicting dynamic polymer depletion effects under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform fluid flow across a slit containing a solution with polymer chains. The two parallel and infinitely long walls are permeable to solvent only and the polymers do not adsorb to these walls. For a weak flow and a narrow slit in Theta-solvent conditions, an analytic expression is derived to describe the steady state polymer concentration profiles. In both Theta- a…
To describe many-particle systems suspended in incompressible low-Reynolds-number fluids, effective hydrodynamic interactions can be introduced. Here, we consider particles embedded in elastic media. The effective elastic interactions between spherical particles are calculated analytically, inspired by the approach in the fluid case. Our experiments on interacting magnetic particles confirm the theory. In view of the huge success of the method in hydrodynamics, we similarly expect many future applications in the elastic case, e.g. for elastic composite materials.
We present a single, unified, multi-scale model to study the attachment\detachment dynamics of two deforming, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous fluid medium. The binding ligands on the surface of the cells experience attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The macroscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previousl…
Motion of an object near a soft wall with intervening fluid is a canonical problem in elastohydrodynamics, finding presence in subjects spanning biology to tribology. Particularly, motion of a sphere towards a soft substrate with intervening fluid is often encountered in the context of scanning probe microscopy. While there have been fundamental theoretical studies on this setup, they have focussed on specific applications and thus enforced suitable simplifications. Here we present a versatile semi-analytical framework for studying the elastohydrodynamics of axisymmetric loading of a rigid sph…
We study the interaction between two neutral plane-parallel dielectric bodies in the presence of a highly asymmetric ionic fluid, containing multivalent as well as monovalent (salt) ions. Image charge interactions, due to dielectric discontinuities at the boundaries, as well as effects from ion confinement in the slit region between the surfaces are taken fully into account, leading to image-generated depletion attraction, ion correlation attraction and steric-like repulsive interactions. We investigate these effects by employing a combination of methods including explicit-ion and implicit-ion…
The phase behavior of hydrocarbon fluids confined in porous media has been reported to deviate significantly from that in the bulk environment due to the existence of sub-10nm pores. Though experiments and simulations have measured the bubble/dew points and sorption isotherms of hydrocarbons confined in both natural and synthetic nanopores, the confinement effects in terms of the strength of fluid-pore interactions tuned by surface wettability and chemistry have received comparably less discussion. More importantly, the underlying physics of confinement-induced phenomena remain obfuscated. In …
We determine the solvent mediated contribution to the effective potentials for model colloidal or nano- particles dispersed in a binary solvent that exhibits fluid-fluid phase separation. Using a simple density functional theory we calculate the density profiles of both solvent species in the presence of the `colloids', which are treated as external potentials, and determine the solvent mediated (SM) potentials. Specifically, we calculate SM potentials between (i) two colloids, (ii) a colloid and a planar fluid-fluid interface, and (iii) a colloid and a planar wall with an adsorbed wetting fil…
Characterizing the softness of deformable materials having partial elastic and partial viscous behaviour via soft lubrication experiments has emerged as a versatile and robust methodology in recent times. However, a straightforward extension of the classical elastohydrodynamic lubrication theory that is commonly employed for characterizing elastic materials turns out to be rather inadequate in explaining the response of such viscoelastic materials subjected to dynamic loading conditions, despite adhering to a mathematically acceptable framework via the complex Young's modulus as a material pro…
We show that a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones can describe systems that exhibit fluid-fluid phase separation: the theory captures effects of strong adsorption (wetting) and of critical fluctuations in the solvent. We illustrate the approach for the Gaussian core model, a simple model of a polymer mixture in solution and find extremely attractive, long ranged solvent mediated potentials between the big particles for state points lying close to the binodal, on the side where the solvent is poor in the …
Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.
In steady sediment transport, sediment deposition is balanced by entrainment of bed particles by fluid forces or particle-bed impacts. Here we propose a proxy to determine the role of impact entrainment relative to entrainment by the mean turbulent flow: the "bed velocity" $V_b$, which is an effective near-bed-surface value of the average horizontal particle velocity that generalizes the classical slip velocity, used in studies of aeolian saltation transport, to sediment transport in an arbitrary Newtonian fluid. We study $V_b$ for a wide range of the particle-fluid-density ratio $s$, Galileo …
The force between two approaching solids in a liquid medium becomes increasingly large with decreasing separation, a phenomenon that prevents contact between the two solids. This growth in force occurs because of the intervening liquid, and, studies of such physical systems constitute the classical discipline of lubrication. Furthermore, when the solid(s) are soft, there are quantitative as well as qualitative alterations in the force interaction due to the solids' deformation. The underlying physics as well as resultant system behaviour are even more complex when forces of non-hydrodynamic or…
We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between cha…
The interaction of bodies in a fluid, mediated by hydrodynamic fluctuations and proposed by Dzyaloshinskii, Lifshitz, and Pitaevskii, is calculated exactly for parallel infinite planes and is shown to be attractive. The second mechanism of fluctuation interaction, proposed in the present work, is due to fluctuations of linear and angular velocities of bodies in a hydrodynamic medium and leads to a repulsion. The both mechanisms provide an interaction energy of two particles in a fluid of the order of temperature for the inter-particle distance of the micron scale, where the interaction mediate…
The basic ingredients of osmotic pressure are a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van't Hoff Law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length-scale associated with the sol…
In a bilayered system of particles with wake-mediated interactions, the action-reaction symmetry for the effective forces between particles of different layers is broken. Under quite general conditions we show that, if the interaction nonreciprocity exceeds a certain threshold, this creates an active dispersion of self-propelled clusters of Brownian particles. The emerging activity promotes unusual melting scenarios and an enormous diffusivity in the dense fluid. Our results are obtained by computer simulation and analytical theory, and can be verified in experiments with colloidal dispersions…
Many practically relevant materials combine properties of viscous fluids and elastic solids to viscoelastic behavior. Our focus is on the induced dynamic behavior of damped finite-sized particulate inclusions in such substances. We explicitly describe history-dependent interactions that emerge between the embedded particles. These interactions are mediated by the viscoelastic surroundings. They result from the flows and distortions of the viscoelastic medium when induced by the rigid inclusions. Both, viscoelastic environments of terminal fluid-like flow or of completely reversible damped elas…
Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered micro-crystallites, time-periodic structures, and chaotic fluctuating patterns with complex dynamics. A model based on streaming flow gives a good quantitative account of the attractive part of the interaction.
We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes.
Elongated active units cannot spontaneously break rotation symmetry in bulk fluids to form nematic or polar phases. This has led to the image of active suspensions as spontaneously evolving, spatiotemporally chaotic fluids. In contrast, I show that bulk active fluids have stable active nematic and polar states at fluid-fluid or fluid-air interfaces. The active flow-mediated long-range interactions that destroy the ordered phase in bulk, lead to long-range order at the interface. The active fluids have a surface ordering transition and form states with quiescent, ordered surfaces and a chaotic …
Two interaction mechanisms of particles in a fluid are proposed on base of forces, mediated by hydrodynamic thermal fluctuations. The first one is similar to the conventional van der Waals interaction, but instead of been mediated by electromagnetic fluctuations, it is mediated by fluctuations of hydrodynamic sound waves. The second one is due to a thermal drift of particles to the region with a bigger effective mass, which is formed by the involved surrounding fluid and depends on an inter-particle distance. The both mechanisms likely can be relevant in interpretation of the observed long-ran…
Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins influence the membrane shape, the membrane shape affects the interactions between the proteins. To study these membrane-mediated interactions on closed and anisotropically curved membranes, we use colloids adhered to ellipsoidal membrane vesicles as a model system. We find that two particles on a closed system always attract each other, and tend to align with the…
Interactions mediated by the cell membrane between inclusions, such as membrane proteins or antimicrobial peptides, play important roles in their biological activity. They also constitute a fascinating challenge for physicists, since they test the boundaries of our understanding of self-assembled lipid membranes, which are remarkable examples of two-dimensional complex fluids. Inclusions can couple to various degrees of freedom of the membrane, resulting in different types of interactions. In this chapter, we review the membrane-mediated interactions that arise from direct constraints imposed …
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about positional coherence -- i.e., how a hidden dynamic skeleton organizes the underlying chaotic motion -- despite this being one of their most prominent and experimentally accessible features. Using a combination of dynamical systems theory, experiments on two-dimensional mixtures of microtubules and kinesin and hydrodynamic simulations, we characterize positional …
We investigated the X-ray scattering signal of highly aligned multilayers of the zwitterionic lipid 1,2-dilauroyl-sn-glycero-3-phosphatidylcholine containing pores formed by the antimicrobial peptide gramicidin as a function of the peptide/lipid ratio. We are able to obtain information on the structure factor of the pore fluid, which then yields the interaction potential between pores in the plane of the bilayers. Aside from a hard core with a radius close to the geometric radius of the pore, we find a repulsive exponential lipid-mediated interaction with a decay length of 2.5 Å and an amplitu…
Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations. The instability originates from an interplay between the focusing of the elastic forces, mediated …
Electrohydraulic Fields Generated by Active Transport at Tissue Interfaces
University of Warwick（华威大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology（系统生物学中心）；Technische Universit¨at Dresden（德累斯顿工业大学）
In a system of colloidal inclusions suspended in a thermalized bath of smaller particles, the bath engenders an attractive force between the inclusions, arising mainly from entropic origins, known as the depletion force. In the case of active bath particles, the nature of the bath-mediated force changes dramatically from an attractive to a repulsive one, as the strength of particle activity is increased. We study such bath-mediated effective interactions between colloidal inclusions in a bath of self-propelled Brownian particles, being confined in a narrow planar channel. Confinement is found …
We study whether fine discretization (i.e., terracing) of continuous pair interactions, when used in combination with first-order mean-spherical approximation theory, can lead to a simple and general analytical strategy for predicting the equilibrium structure and thermodynamics of complex fluids. Specifically, we implement a version of this approach to predict how screened electrostatic repulsions, solute-mediated depletion attractions, or ramp-shaped repulsions modify the radial distribution function and the potential energy of reference hard-sphere fluids, and we compare the predictions to …
Because active particles break time-reversal symmetry, an active fluid can sustain currents even without an external drive. We show that when a passive body is placed in a fluid of pairwise interacting active particles, it generates long-range currents, corresponding to density and pressure gradients. By using a multipole expansion and a far-field constitutive relation, we show that the leading-order behavior of all three corresponds to a source dipole. Then, when two bodies or more are placed in the active fluid, generic long-range interactions between the bodies occur. We find these to be qu…
Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along any contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the mem…
We adapt the Halperin-Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that $\pm 1/2$ defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it i…
For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface--mediated interactions of capillary and fluctuation--induced type are analyzed. For contact angles different from 90$^o$, static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer--sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluct…
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 forcing. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of the autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamicall…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This contour may be deformed to exploit the symmetries present; for two identical particles, one obtains an exact expression for the force between them in terms of the local surface geometry of their mid-plane; in the case of a fluid membrane the sign of the interaction is often evident. The approach, by construction, is adapted directly to the surface and is indep…
