Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the con figuration is derived taking into account both viscous dissipation in the s urrounding liquid and local incompressibility of the membrane. For quasi sp herical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The sol ution to this equation shows an overdamped oscillatory approach to a statio nary tanktreading shape. Inclination angle and ellipticity of the contour a re determined as a function of excess area and shear rate. Comparisons to n umerical results and experiments are discussed.