Fluid Vesicles in Shear Flow.

The shape dynamics of fluid vesicles is governed by the coupling of the flow within the two-dimensional membrane to the hydrodynamics of the surrounding bulk fluid. We present a numerical scheme which is capable of solving this flow problem for arbitrarily shaped vesicles using the Oseen tensor formalism. For the particular problem of simple shear flow, stationary shapes are found for a large range of parameters. The dependence of the orientation of the vesicle and the membrane velocity on shear rate and vesicle volume can be understood from a simplified model. PACS numbers: 47.55.-Dz, 68.10.-m, 87.45.-k Vesicles are closed lipid membranes suspended in aqueous solution. If the composition of this solution inside and outside the vesicle is identical, it affects the equilibrium properties of the vesicle only by osmotically fixing the enclosed volume. Minimizing the bending energy of the membrane under the constraints of fixed enclosed volume and membrane area then yields the equilibrium vesicle shape at rest[1]. The dynamics of this shape, however, is governed by the coupling of the flow within the two-dimensional incompressible fluid membrane to the hydrodynamics of the bulk fluid. Any theory of vesicle dynamics is complicated by the fact, that the boundary conditions for the three-dimensional Navier-Stokes equations have to be evaluated at the vesicle surface, which is moving with the fluid and whose shape is not known a priori.