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

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

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

Inversion of hematocrit partition at microfluidic bifurcations

Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit ($\phi_0$) partition depends strongly on RBC deformability, as long as $\phi_0 <20$% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough $\phi_0$, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.Comment: 16 page

Coexistence of stable branched patterns in anisotropic inhomogeneous systems

A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class and a model equation, we show that branched stripe patterns emerge, which for a given parameter set are stable within a band of different wavenumbers and different numbers of branching points (defects). Moreover, the branched patterns and unbranched ones (defect-free stripes) coexist over a finite parameter range. We propose two systems where this generic scenario can be found experimentally, surface wrinkling on elastic substrates and electroconvection in nematic liquid crystals, and relate them to the findings from the amplitude equation.Comment: 7 pages, 4 figure

Non-inertial lateral migration of vesicles in bounded Poiseuille flow

Cross-streamline non-inertial migration of a vesicle in a bounded Poiseuille flow is investigated experimentally and numerically. The combined effects of the walls and of the curvature of the velocity profile induce a movement towards the center of the channel. A migration law (as a function of relevant structural and flow parameters) is proposed that is consistent with experimental and numerical results. This similarity law markedly differs from its analogue in unbounded geometry. The dependency on the reduced volume $\nu$ and viscosity ratio $\lambda$ is also discussed. In particular, the migration velocity becomes non monotonous as a function of $\nu$ beyond a certain $\lambda$.Comment: 5 pages, 3 figures. To appear in Phys. Fluid