Orbital drift of capsules and red blood cells

Experiments using deformable red blood cells (RBC) in shear flow showed that the cells orient their symmetry axis towards the plane of shear (C = $\infty$ orbit) in a high viscosity medium, and along the vorticity direction (C = 0 orbit) in a low viscosity medium. In contrast, rigid ellipsoids in Stokes flow exhibit degenerate trajectories. The degeneracy can be broken by inertial effects, or, deformability. To explore the orientational drift, we conduct a 3D numerical simulation of prolate and oblate capsules and RBC over a range of capillary number, asphericity, and viscosity ratio. Four types of motion are observed: a stable precessing about C = 0, a stable kayaking about C = $\infty$, an unstable precessing towards C = 0, and a transition from a kayaking to a drifting precession. A prolate capsule with viscosity ratio of one mostly exhibits a kayaking at low asphericity, but mostly a drifting precession at high asphericity. In contrast, an oblate capsule drifts towards C = $\infty$. In agreement with published experiments, we find that the RBC orients its symmetry axis to C = 0 at high viscosity ratio, and C = $\infty$ at low viscosity ratio. We also find that the RBC orientation is dependent on the capillary number, implying the role of deformation.