Interplay between microdynamics and macrorheology in vesicle suspensions

The microscopic dynamics of objects suspended in a fluid determines the macroscopic rheology of a suspension. For example, as shown by Danker and Misbah [Phys. Rev. Lett. {\bf 98}, 088104 (2007)], the viscosity of a dilute suspension of fluid-filled vesicles is a non-monotonic function of the viscosity contrast (the ratio between the viscosities of the internal encapsulated and the external suspending fluids) and exhibits a minimum at the critical point of the tank-treading-to-tumbling transition. By performing numerical simulations, we recover this effect and demonstrate that it persists for a wide range of vesicle parameters such as the concentration, membrane deformability, or swelling degree. We also explain why other numerical and experimental studies lead to contradicting results. Furthermore, our simulations show that this effect even persists in non-dilute and confined suspensions, but that it becomes less pronounced at higher concentrations and for more swollen vesicles. For dense suspensions and for spherical (circular in 2D) vesicles, the intrinsic viscosity tends to depend weakly on the viscosity contrast.Comment: 9 pages, 9 figures, to appear in Soft Matter (2014

Axisymmetric flow due to a Stokeslet near a finite-sized elastic membrane

Elastic confinements play an important role in many soft matter systems and affect the transport properties of suspended particles in viscous flow. On the basis of low-Reynolds-number hydrodynamics, we present an analytical theory of the axisymmetric flow induced by a point-force singularity (Stokeslet) directed along the symmetry axis of a finite-sized circular elastic membrane endowed with resistance toward shear and bending. The solution for the viscous incompressible flow surrounding the membrane is formulated as a mixed boundary value problem, which is then reduced into a system of dual integral equations on the inner and outer sides of the domain boundary. We show that the solution of the elastohydrodynamic problem can conveniently be expressed in terms of a set of inhomogeneous Fredholm integral equations of the second kind with logarithmic kernel. Basing on the hydrodynamic flow field, we obtain semi-analytical expressions of the hydrodynamic mobility function for the translational motion perpendicular to a circular membrane. The results are valid to leading-order in the ratio of particle radius to the distance separating the particle from the membrane. In the quasi-steady limit, we find that the particle mobility near a finite-sized membrane is always larger than that predicted near a no-slip disk of the same size. We further show that the bending-related contribution to the hydrodynamic mobility increases monotonically upon decreasing the membrane size, whereas the shear-related contribution displays a minimum value when the particle-membrane distance is equal to the membrane radius. Accordingly, the system behavior may be shear or bending dominated, depending on the geometric and elastic properties of the system. Our results may find applications in the field of nanoparticle-based sensing and drug delivery systems near elastic cell membranes

Two-dimensional lattice Boltzmann simulations of vesicles with viscosity contrast

We present a numerical approach to simulate the dynamics of viscous vesicles (their internal and external fluids have different viscosities). The flow is computed using the lattice Boltzmann method and the fluid-vesicle two-way coupling is achieved using the immersed boundary method. The viscosity contrast (defined as the ratio of the internal to the external viscosities) is included using a geometrical algorithm that detects if a fluid node is either located inside or outside a vesicle. Our two-dimensional simulations successfully reproduce the tank-treading and tumbling dynamical states known for a viscous vesicle when it is subjected to simple shear flow. A good qualitative agreement between our simulation results and literature data is obtained. Moreover, we quantitatively analyze how inertia influences the dynamics of a vesicle and as an outlook we present an application of our method to the flow of multiple viscous vesicles in a microfluidic constriction

Forced transport of deformable containers through narrow constrictions

We study, numerically and analytically, the forced transport of deformable containers through a narrow constriction. Our central aim is to quantify the competition between the constriction geometry and the active forcing, regulating whether and at which speed a container may pass through the constriction and under what conditions it gets stuck. We focus, in particular, on the interrelation between the force that propels the container and the radius of the channel, as these are the external variables that may be directly controlled in both artificial and physiological settings. We present Lattice-Boltzmann simulations that elucidate in detail the various phases of translocation, and present simplified analytical models that treat two limiting types of these membrane containers: deformational energy dominated by the bending or stretching contribution. In either case we find excellent agreement with the full simulations, and our results reveal that not only the radius but also the length of the constriction determines whether or not the container will pass.Comment: 9 pages, 4 figure

Computer simulations of shape deformation and dynamics of biological cells subjected to flow

Sheet presentati

How does confinement affect the dynamics of viscous vesicles and red blood cells?

Despite its significance in microfluidics, the effect of confinement on the transition from the tank-treading (steady motion) to the tumbling (unsteady motion) dynamical state of deformable micro-particles has not been studied in detail. In this paper, we investigate the dynamics of a single viscous vesicle under confining shear as a general model system for red blood cells, capsules, or viscous droplets. The transition from tank-treading to tumbling motion can be triggered by the ratio between internal and external fluid viscosities. Here, we show that the transition can be induced solely by reducing the confinement, keeping the viscosity contrast constant. The observed dynamics results from the variation of the relative importance of viscous-, pressure-, and lubrication-induced torques exerted upon the vesicle. Our findings are of interest for designing future experiments or microfluidic devices: the possibility to trigger the tumbling-to-tank-treading transition either by geometry or viscosity contrast alone opens attractive possibilities for microrheological measurements as well as the detection and diagnosis of diseased red blood cells in confined flow.Comment: 8 pages, 8 figures; Soft Matter 201

A Necklace Model for Vesicles Simulations in 2D

International audienceThe aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles which are maintained in cohesion by using two different type of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force. Numerical simulations of vesicles in shear flow have been run using Finite Element Method and the FreeFem++[1] software. Exploring different ratios of inner and outer viscosities, we recover the well known "Tank-Treading" and "Tumbling" motions predicted by theory and experiments. Moreover, for the first time, 2D simulations of the "Vacillating-Breathing" regime predicted by theory in [2] and observed experimentally in [3] are done without special ingredient like for example thermal fluctuations used in [4]

Study Of Inertia And Stoichiometric Effect On Surface Diffusion By Monte Carlo Method

In this work, we investigate the inertia and stoichiometric effect on surface diffusion of adsorbates particles. The study is done by means of Monte-Carlo simulation in the framework of the lattice gas model. Only first neighboring repulsive pair interaction is considered. We concentrate on the behaviour of the tracer diffusion coefficient Dt(θ), as a function of surface coverage θ in the case where two type of particles A and B are adsorbed. A and B are only different by their mass. The results shows that θt ordering phenomenon is not strongly influenced. However the diffusion process is decreased by inclusion of heavy particles.w.In this work, we investigate the inertia and stoichiometric effect on surface diffusion of adsorbates particles. The study is done by means of Monte-Carlo simulation in the framework of the lattice gas model. Only first neighboring repulsive pair interaction is considered. We concentrate on the behaviour of the tracer diffusion coefficient Dt(θ), as a function of surface coverage θ in the case where two type of particles A and B are adsorbed. A and B are only different by their mass. The results shows that θt ordering phenomenon is not strongly influenced. However the diffusion process is decreased by inclusion of heavy particles.w