Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane

The dynamics of a liquid capsule enclosed by an elastic membrane in a shear flow is investigated using a front tracking finite difference method. We compute deformation, orientation and tank-treading of the capsule, as functions of the forcing (capillary number) and the viscosity ratio for two different membrane constitutive equations – Neo-Hookean and Skalak. The computed results compare very well with those obtained by high-order boundary element methods as well as the small deformation perturbation analysis. The simulation shows that a drop and a capsule, even under those circumstances that result in the same Taylor deformation criterion for both, attain very different shapes. The tank-treading period even for different capillary numbers as well as capsules with different constitutive laws, is primarily determined by the deformation and the viscosity ratio. At low capillary numbers the simulation predicts buckling due to large compressive stresses on the membrane. However, we show that in shear, unlike in extension, the tank-treading motion can inhibit the buckling instability and gives rise to a stable evolution even in presence of membrane compressive stresses. At large capillary numbers the capsule experiences large bounded shape followed by tip buckling indicating possible membrane breakup.