Off-plane motion of a prolate capsule in shear flow

The objective is to study the motion of an ellipsoidal capsule in a simple shear flow when its revolution axis is initially placed off the shear plane. We consider prolate capsules with an aspect ratio of 2 or 3 enclosed by a membrane, which is either strain-hardening or strain-softening. We seek the equilibrium motion of the capsule as we increase the capillary number Ca, which measures the ratio between the viscous and elastic forces. The three-dimensional fluid-structure interaction problem is solved numerically by coupling a boundary integral method (for the internal and external flows) with a finite element method (for the wall deformation). For any initial inclination with the flow vorticity axis, a given capsule converges towards a unique equilibrium configuration which depends on Ca. At low capillary number, the stable equilibrium motion is the rolling regime: the capsule aligns its long axis with the vorticity axis, while the membrane tank-treads entrained by the shear flow. As Ca increases, the capsule takes a complex wobbling motion at equilibrium, precessing around the vorticity axis. As Ca is further increased, the capsule long axis oscillates about the shear plane, while the membrane rotates around a capsule cross-section that also oscillates over time (oscillating-swinging regime). The amplitude of the oscillations about the shear plane decreases as Ca increases and the capsule finally takes a swinging motion in the shear plane. It is found that the transitions from rolling to wobbling and from wobbling to oscillating-swinging depend on the mean energy stored in the membrane.