Effect of fluid viscosities onthe deformation of liquidcapsules enclosed by thin shellin shear flow

Abstract

The deformation of liquid capsules enclosed by thin shell immersedin a simple shear flow is studied numerically using an implicit immersed boundarymethod. The membrane structure of the capsule is described by a thin-shell model which computes the forces acting on the shell middle surface within the framework of the Kirchhoff-Love theory of thin shell. The middle surface is discretized into triangular elements, each of which has three nodes at the vertices and anotherthree along the edges. The implicit immersed boundary method is employed for computing the hydradynamics and fluid-structure interation and the advancing of the membrane over time. Our numerical simulation has good agreement with analytical and numerical results in the literature. Results show that at low viscosity ratio between the internal and surrounding fluids, the liquid capsule keeps a steady tank-treading motion. As the viscosity ratio increases, transition from tumbling to tank-treading is observed. For large viscosity ratios, the motion has changed to periodic tumbling.