Bérénice Grec

Viscoelastic fluids in thin domains: A mathematical proof

The present paper deals with non-Newtonian viscoelastic flows of Oldroyd-B type in thin domains. Such geometries arise for example in the context of lubrication. More precisely, we justify rigorously the asymptotic model obtained heuristically by proving the mathematical convergence of the Navier-Stokes/Oldroyd-B system towards the asymptotic model.

A 1D model of leukocyte adhesion coupling bond dynamics with blood velocity

Cell adhesion on the vascular wall is a highly coupled process where blood flow and adhesion dynamics are closely linked. Cell dynamics in the vicinity of the vascular wall is driven mechanically by the competition between the drag force of the blood flow and the force exerted by the bonds created between the cell and the wall. Bonds exert a friction force. Here, we propose a mathematical model of such a competitive system, namely leukocytes whose capacity to create bonds with the vascular wall and transmigratory ability are coupled by integrins and chemokines. The model predicts that this coupling gives rise to a dichotomic cell dynamic, whereby cells switch from sliding to firm arrest, through non linear effects. Cells can then transmigrate through the wall. These predicted dynamic regimes are compared to in-vitro trajectories of leukocytes. We expect that competition between friction and drag force in particle dynamics (such as shear stress-controlled nanoparticle capture) can lead to similar dichotomic mode.

An integro-differential equation for 1D cell migration

Cell migration is a fundamental biological phenomenon involved for example in development, wound healing, cancer and immune response. Understanding its key features is therefore a burning issue. In this work, we introduce an integro-differential equation describing 1D cell migration. We show existence and uniqueness of a solution, and in some cases informations about its asymptotic behavior. This model opens the way to a global description of cell trajectories based on microscopic features.