Orbital drift of capsules and red blood cells in shear flow

Many numerical studies have considered the dynamics of capsules and red blood cells in shear flow under the condition that the axis of revolution of such bodies remained aligned in the shear plane. In contrast, several experimental studies have shown that the axis of revolution of red blood cells could drift away from the shear plane in a certain range of controlling parameters. In this article, we present three-dimensional numerical simulations on the orientation dynamics of capsules in simple shear flow with different initial undeformed shapes, namely, prolate, oblate, and biconcave disk. It is observed that unlike rigid ellipsoids in Stokes flow, capsules reorient their axis of revolution either towards the vorticity axis while undergoing a precessing motion or towards the shear plane while undergoing a kayaking-type motion. The specific dynamics are observed to depend on initial shape, capillary number, and the ratio of the internal to external fluid viscosity. Near the physiological values of the viscosity ratio, the biconcave shape performs a rolling motion like a wheel. If the viscosity ratio is reduced below the physiological range, a transition to the kayaking dynamics is observed with increasing capillary number. The critical shear stress at which the rolling-to-kayaking transition occurs is found to be dependent on the viscosity ratio. (C) 2013 AIP Publishing LLC.