Thierry Biben

Dynamics and rheology of a dilute suspension of vesicles: higher-order theory.

Vesicles under shear flow exhibit various dynamics: tank treading (TT), tumbling (TB), and vacillating breathing (VB). The VB mode consists in a motion where the long axis of the vesicle oscillates about the flow direction, while the shape undergoes a breathing dynamics. We extend here the original small deformation theory [C. Misbah, Phys. Rev. Lett. 96, 028104 (2006)] to the next order in a consistent manner. The consistent higher order theory reveals a direct bifurcation from TT to TB if Ca identical with taugamma is small enough-typically below 0.5, but this value is sensitive to the available excess area from a sphere (tau=vesicle relaxation time towards equilibrium shape, gamma=shear rate). At larger Ca the TB is preceded by the VB mode. For Ca1 we recover the leading order original calculation, where the VB mode coexists with TB. The consistent calculation reveals several quantitative discrepancies with recent works, and points to new features. We briefly analyze rheology and find that the effective viscosity exhibits a minimum in the vicinity of the TT-TB and TT-VB bifurcation points. At small Ca the minimum corresponds to a cusp singularity and is at the TT-TB threshold, while at high enough Ca the cusp is smeared out, and is located in the vicinity of the VB mode but in the TT regime.

Phase-field models for free-boundary problems

Phase-field models are very attractive in view of their numerical simplicity. With only a few lines of code, one can model complex physical situations such as dendritic growth. From this point of view, they constitute very interesting tools for teaching purposes at graduate level. The main difficulty with these models is in their formulation, which incorporates the physical ingredients in a subtle way. We discuss these approaches on the basis of two examples: dendritic growth and multiphase flows.

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 <pi/4 with respect to the shear stress if the viscosity contrast between the interior and the exterior is not large enough. Above a certain viscosity contrast, the vesicle undergoes a tumbling bifurcation, a bifurcation which is known for red blood cells. We have recently presented the full numerical analysis of this transition. In this paper, we introduce an analytical model that has the advantage of being both simple enough and capturing the essential features found numerically. The model is based on general considerations and does not resort to the explicit computation of the full hydrodynamic field inside and outside the vesicle.

Stationary state of thermostated inelastic hard spheres

We consider a fluid composed of inelastic hard spheres moving in a thermostat modelled by a hard sphere gas. The losses of energy due to inelastic collisions are balanced by the energy transfer via elastic collisions from the thermostat particles. The resulting stationary state is analysed within the Boltzmann kinetic theory. A numerical iterative method permits to study the nature of deviations from the Gaussian state. Some analytic results are obtained for a one-dimensional system.

Dynamics of Bio-Polymeric Brushes Growing from a Cellular Membrane: Tentative Modelling of the Actin Turnover within an Adhesion Unit; the Podosome

Podosomes are involved in the adhesion process of various cells to a solid substrate. They have been proven to consist of a dense actin core surrounded by an actin cloud. The podosomes, which nucleate when the cell comes in the vicinity of a substrate, contribute to link the membrane to the solid surface, but rather than frozen links, collective dynamical behaviors are experimentally observed. Depending on the differentiation stage, podosomes assemble and form clusters, rings or belts. Considering the dynamics of a polymeric brush, we design a simple model aiming at the description of a single podosome, the basic unit of these complex adhesion-structures and compare our theoretical conclusions to recent experimental results. Particularly, we explain, by solving the diffusion problem around the podosome, why the structure is likely to have a finite life-span.

Stress induced topological fluctuations in confined lamellar systems

We investigate the role of defects in a model order-disorder transition, the lamellar-microemulsion transition. We focus on the effect of an applied external stress on the transition mechanism. We first analyse the thermodynamical consistency of the usual Landau-Ginzburg modelling of these systems, and show that thermodynamical, mechanical and structural quantities can all be probed at the same time, which allows for a deeper understanding of the transition mechanisms. We apply this formalism to the case of a lamellar system confined between two plates, the model geometry for a surface force apparatus.