Understanding why red blood cells (RBCs) move with an asymmetric shape (slipperlike shape) in small blood vessels is a long-standing puzzle in blood circulatory research. By considering a vesicle (a model system for RBCs), we discovered that the slipper shape results from a loss in stability of the symmetric shape. It is shown that the adoption of a slipper shape causes a significant decrease in the velocity difference between the cell and the imposed flow, thus providing higher flow efficiency for RBCs. Higher membrane rigidity leads to a dramatic change in the slipper morphology, thus offering a potential diagnostic tool for cell pathologies.

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles towards the center of the Poiseuille flow. This is in a marked contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12, 435 (1980)] according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation towards its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.

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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 (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<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 ϕ0, 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.

This study focuses numerically on dynamics in two dimensions of vesicles in microcirculation. The method used is based on boundary integral formulation. This study is inspired by the behavior of red blood cells (RBCs) in the microvasculature. Red RBCs carry oxygen from the lungs and deliver it through the microvasculature. The shape adopted by RBCs can affect blood flow and influence oxygen delivery. Our simulation using vesicles (a simple model for RBC) reveals unexpected complexity as compared to the case where a purely unbounded Poiseuille flow is considered [Kaoui, Biros, and Misbah, Phys. Rev. Lett. 103, 188101 (2009)]. In sufficiently large channels (in the range of 100 μm; the vesicle size and its reduced volume are taken in the range of those of a human RBC), such as arterioles, a slipperlike (asymmetric) shape prevails. A parachutelike (symmetric) shape is adopted in smaller channels (in the range of 20 μm, as in venules), but this shape loses stability and again changes to a pronounced slipperlike morphology in channels having a size typical of capillaries (5-10 μm). Stiff membranes, mimicking malaria infection, for example, adopt a centered or off-centered snakelike locomotion instead (the denomination snaking is used for this regime). A general scenario of how and why vesicles adopt their morphologies and dynamics among several distinct possibilities is provided. This finding potentially points to nontrivial RBCs dynamics in the microvasculature.

Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.

The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing and only a limited number of experimental and theoretical studies is available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that the Segré-Silberberg effect is suppressed with respect to the particle deformability. Depending on the deformability and strength of inertial effects, inward or outward lateral migration of the particles takes place. In particular, for increasing Reynolds numbers and strongly deformable particles, a hitherto unreported distinct flow focusing effect emerges which is accompanied by a non-monotonic behaviour of the apparent suspension viscosity and thickness of the particle-free layer close to the channel walls. This effect can be explained by the behaviour of a single particle and the change of the particle collision mechanism when both deformability and inertia effects are relevant. †

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.