Subdivision elements for large deformation of liquid capsules enclosed by thin shells

This paper presents a numerical method for studying the large deformation of a liquid capsule enclosed by a thin shell in a simple shear flow. An implicit immersed boundary method is employed for calculating the hydrodynamics and fluid–structure interaction effects. A thin-shell model for computing the forces acting on the shell middle surface during the deformation is described within the framework of the Kirchhoff–Love theory of thin shells. This thin-shell model takes full account of finite-deformation kinematics which allows thickness stretching as well as large deflections and bending strains. The interpolation of the reference and deformed surfaces of the shell is accomplished through the use of Loop's subdivision surfaces. The resulting limit surface is C1-continuous which significantly improves the ability of the method in simulating capsules enclosed by hyperelastic thin shells with different physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, oblate spheroidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, tumbling and transition from tumbling to tank-treading have been studied over a range of shear rates and viscosity ratios.