Analytical analysis of a vesicle tumbling under a shear flow.

Vesicles under a shear flow exhibit a tank-treading motion of their membrane, while their long axis points with an angle

Steady to unsteady dynamics of a vesicle in a flow.

We investigate the dynamics of a vesicle in a shear flow on the basis of the newly proposed advected field (AF) method [T. Biben and C. Misbah, Eur. Phys. J. E 67, 031908 (2003)]. We also solve the same problem with the boundary integral formulation for the sake of comparison. We find that the AF results presented previously overestimated the tumbling threshold due to the finite size of the membrane, inherent to the AF model. A comparison between the two methods shows that only in the sharp interface limit (extrapolating the results to a vanishing width) the AF method leads to accurate quantitative results. We extensively investigate the tank-treading to tumbling transition, and compare our numerical results to the theory of Keller and Skalak which assumes a fixed ellipsoidal shape for the vesicle. We show that this theory describes correctly the two regimes, at least in two dimensions, even for the quite elongated non-convex shapes corresponding to red blood cells (and therefore far from ellipsoidal), This theory is, however, not fully quantitative. Finally we investigate the effect of a confinement on the tank-treading to tumbling transition, and show that the tumbling regime becomes unfavorable in a capillary vessel, which should have strong effects on blood rheology in confined geometries.

Experimental study of the collision process of a grain on a two-dimensional granular bed

We report an experimental study on the collision of a bead on a two-dimensional hexagonal granular packing. This collision process is of crucial importance in aeolian transport of grains. We have investigated the kinematic properties of the incident bead before and after the collision, and the resulting deformation of the packing. A typical collision is characterized by the rebound of the impacting bead and the ejection of a few beads of the packing. We have shown that the properties of the rebound bead depend weakly on the impact speed and that the rebound process involves only a few bead layers of the packing. On the contrary, the ejection mechanism depends strongly on the impact speed. In particular, it is found that the number of ejected grains increases with the impact speed whereas the most likely value of their energy is practically independent of the impact speed. Furthermore, we have given evidences that the ejection process involves a great number of packing layers and therefore is extremely sensitive to the height of the packing. For small packing heights, one observes additional ejected grains which can be interpreted as being produced by the reflection of the shock wave on the bottom of the pile.