Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasi-spherical vesicles in shear flow

Abstract

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipiticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed.