Effect of slip-induced fluid inertial torque on the angular dynamics of spheroids in a linear shear flow

Abstract

The angular dynamics of tiny spheroidal particles in shear flows have been widely investigated, but most of the studies mainly focus on the effect of strong shear, while the combined effect of both shear and slip velocity at the center of the particle has been less considered. Actually, the fluid inertial torque induced by the slip velocity between particle and fluid plays a significant role in spheroid angular dynamics. However, it is difficult to investigate these dynamics theoretically until the analytical expression of the fluid inertial torque at a small Reynolds number was derived by Dabade et al. [J. Fluid Mech. 778, 133–188 (2015)]. In this study, the effect of the fluid inertial torque on the particle rotations is considered in a linear shear flow with a small streamwise slip velocity at the center of the particle. We find that as the fluid inertial torque dominates, the prolate spheroids tend to logroll while oblate ones have a tendency to tumble or align to a direction with a relative angle to the streamwise direction. These results are opposite to the earlier results in the absence of the fluid inertial torque. Different ultimate rotation modes of spheroids are dependent on the relative importance between the fluid inertial torque and the particle inertia, as well as the initial orientations. This reflects a non-trivial effect of fluid inertial torque on the angular dynamics of inertial spheroidal particles.