"Theoretical investigations of the rheology of fluid membranes" by George Biros
October 27, 2010 - 11:00am
Fluid membranes (vesicles) are area-preserving interfaces that resist bending. They are models of cell membranes, intracellular organelles, and viral particles. We are interested in developing simulation tools for dilute suspensions of deformable vesicles. These tools should be computationally efficient, that is, they should scale well as the number of vesicles increases. For very low Reynolds numbers, as it is often the case in mesoscopic length scales, the Stokes approximation can be used for the background fluid. We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the nonlocal hydrodynamic forces with the elastic forces due to bending and tension. We report results from numerical experiments that have produced new results regarding the rheology. In particular, we consider various viscoelastic effects: shape equilibria in shear flows, migration on flows with ``curvature'', and pattern formation in confined flows.