Red blood cell: from its mechanics to its motion in shear flow.

There is a number of publications on red blood cell deformability, that is, on the remarkable cell ability to change its shape in response to an external force and to pass through the narrowest blood capillaries and splenic sinuses. Cell deformability is postulated to be a major determinant of impaired perfusion, increase of blood viscosity, and occlusion in microvessels. Current deformability tests like ektacytometry measure global parameters, related to shape changes at the whole cell scale. Despite strong advances in our understanding of the molecular organization of red blood cells, the relationships between the rheology of each element of the cell composite structure, the global deformability tests, and the cell behavior in microflows are still not elucidated. This review describes recent advances in the description of the dynamics of red blood cells in shear flow and in the mechanistic understanding of this dynamics at the scale of the constitutive rheological and structural elements of the cell. These developments could open up new horizons for the determination of red blood cell mechanical parameters by analyzing their motion under low shear flows.

Microscopic mechanisms of the brittleness of viscoelastic fluids.

We show that a large class of viscoelastic fluids, i.e., transient networks, are brittle according to the Griffith's theory of solid fracture. However, contrary to solids, cracks are intrinsic to the material arising from the equilibrium nature of the fluid microstructure. The brittleness of these fluids comes from thermal fluctuations of bonds distribution. In this approach, the rupture stress is predicted to be on the order of the Young modulus, in very good agreement with experimental values.

Dynamics of viscous vesicles in shear flow.

The dynamics of giant lipid vesicles under shear flow is experimentally investigated. Consistent with previous theoretical and numerical studies, two flow regimes are identified depending on the viscosity ratio between the interior and the exterior of the vesicle, and its reduced volume or excess surface. At low viscosity ratios, a tank-treading motion of the membrane takes place, the vesicle assuming a constant orientation with respect to the flow direction. At higher viscosity ratios, a tumbling motion is observed in which the whole vesicle rotates with a periodically modulated velocity. When the shear rate increases, this tumbling motion becomes increasingly sensitive to vesicle deformation due to the elongational component of the flow and significant deviations from simpler models are observed. A good characterization of these various flow regimes is essential for the validation of analytical and numerical models, and to relate microscopic dynamics to macroscopic rheology of suspensions of deformable particles, such as blood.

Dynamics of vesicles in a wall-bounded shear flow.

We report a detailed study of the behavior (shapes, experienced forces, velocities) of giant lipid vesicles subjected to a shear flow close to a wall. Vesicle buoyancy, size, and reduced volume were separately varied. We show that vesicles are deformed by the flow and exhibit a tank-treading motion with steady orientation. Their shapes are characterized by two nondimensional parameters: the reduced volume and the ratio of the shear stress with the hydrostatic pressure. We confirm the existence of a force, able to lift away nonspherical buoyant vesicles from the substrate. We give the functional variation and the value of this lift force (up to 150 pN in our experimental conditions) as a function of the relevant physical parameters: vesicle-substrate distance, wall shear rate, viscosity of the solution, vesicle size, and reduced volume. Circulating deformable cells disclosing a nonspherical shape also experience this force of viscous origin, which contributes to take them away from the endothelium and should be taken into account in studies on cell adhesion in flow chambers, where cells membrane and the adhesive substrate are in relative motion. Finally, the kinematics of vesicles along the flow direction can be described in a first approximation with a model of rigid spheres.

Giant lipid vesicles filled with a gel: shape instability induced by osmotic shrinkage.

We report the properties of giant lipid vesicles enclosing an agarose gel. In this system, the lipid bilayer retains some basic properties of biological membranes and the internal fluid exhibits viscoelastic properties, thus permitting us to address the question of the deformation of a cell membrane in relation to the mechanical properties of its cytoskeleton. The agarose gel (concentration c0gel = 0.07%, 0.18%, 0.36%, and 1% w/w), likely not anchored to the membrane, confers to the internal volume elastic moduli in the range of 10-10(4) Pa. Shapes and kinetics of de-swelling of gel-filled and aqueous solution-filled vesicles are compared upon either a progressive or a fast osmotic shrinkage. Both systems exhibit similar kinetics. Shapes of solution-filled vesicles are well described using the area difference elasticity model, whereas gel-filled vesicles present original patterns: facets, bumps, spikes (c0gel < 0.36%), or wrinkles (c0gel > or = 0.36%). These shapes partially vanish upon re-swelling, and some of them are reminiscent of echinocytic shapes of erythrocytes. Their characteristic size (microns) decreases upon increasing c0gel. A possible origin of these patterns, relying on the formation of a dense impermeable gel layer at the vesicle surface and associated with a transition toward a collapsed gel phase, is advanced.

Motion of phospholipidic vesicles along an inclined plane: sliding and rolling.

The migration of giant phospholipidic vesicles along an inclined plane in a quiescent fluid was observed as a function of the mass and the radius R of the vesicles, and as a function of the angle of inclination of the plane. Vesicles were swollen, and did not adhere to the substrate surface. It was observed from a side-view chamber that they have quasispherical shapes. The vesicles mainly slide along the plane, but also roll. The ratio omegaR/v of rotational to translational velocities is of the order of 0.15 for vesicles of radius ranging from 10 to 30 microm. Values of this ratio, and variations of v versus R, are well described by Goldman et al.'s model developed for the motion of rigid spheres close to a wall [Chem. Eng. Sci. 22, 637 (1967)]. In this framework, the thickness of the fluid film between the vesicle and the substrate derived from fitting experimental data was found to be equal to 48 nm.