Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow.

The dynamic motion of three-dimensional (3D) capsules in a shear flow is investigated by direct numerical simulation. The capsules are modeled as Newtonian liquid droplets enclosed by elastic membranes, with or without considering the membrane-area incompressibility. The internal liquid of the capsules is the same as that outside. The dynamic motion of capsules with initially spherical and oblate spheroidal unstressed shapes is studied under various shear rates. The results show that spherical capsules deform to stationary configurations and then the membranes rotate around the liquid inside (steady tank-treading motion). Such a steady mode is not observed for oblate spheroidal capsules. It is shown that with the shear rate decreasing, the motion of oblate spheroidal capsules changes from the swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to tumbling mode.