Vesicle dynamics under weak flows: Application to large excess area

Abstract

Dynamics of a vesicle under simple shear flow is studied in the limit of small capillary number. A perturbative approach is used to derive the equation of vesicle dynamics. The expansions are shown to converge for significantly deflated vesicles (with excess area from the sphere as high as 2). In particular, we provide an explicit analytical expression for the tank-treading to tumbling bifurcation point. This expression is valid for excess areas up to 2.5. The results are compared with full 3D numerical simulations. The proposed method can be used for analytical or numerical solution of vesicle dynamics under weak flow of general form.