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

TL;DR

This paper develops a formalism for the dynamics of fluid membranes in flow fields, applying it to fluctuating quasi-spherical vesicles in shear flow, revealing their shape dynamics and stability characteristics.

Contribution

It introduces a comprehensive theoretical framework for fluid membrane dynamics in flow fields, including thermal fluctuations and compares results with experiments.

Findings

Vesicles exhibit overdamped oscillatory approach to steady tanktreading shape.

Inclination angle and ellipticity depend on excess area and shear rate.

Theoretical predictions align with numerical simulations and experimental data.

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.