Off-plane motion of an oblate capsule in a simple shear flow.

We investigate the mechanical equilibrium state of an oblate capsule when its revolution axis is initially off the shear plane. We consider an oblate capsule with an aspect ratio of 0.5 and a strain-hardening membrane. The three-dimensional fluid-structure interaction problem is solved numerically by coupling a finite element method with a boundary integral method. The capsule converges towards the same mechanical equilibrium state whatever the initial orientation. This equilibrium depends on the capillary number Ca, which compares the viscous to the elastic forces and on the viscosity ratio λ between the internal and external fluids. For λ = 1, the tumbling and swinging motions, observed when the revolution axis is initially in the shear plane, are mechanically stable until Ca ∼ 1; when Ca is further increased, the capsule assumes the rolling motion that is observed when its revolution axis is initially aligned with the vorticity axis. When λ is increased, the tumbling-to-swinging transition appears for higher Ca and the swinging-to-rolling transition for lower Ca. For λ ≥ 5, the swinging regime completely disappears: depending on Ca, it is then either the tumbling or the rolling motion that is the mechanical equilibrium state.