Stability analysis on the angular dynamics of a spheroid in simple shear flow: influence of slip-induced fluid-inertial torque

We investigate the angular dynamics of a single spheroidal particle with large particle-to-fluid density ratio in simple shear flows, focusing on the influence of the fluid-inertial torque induced by slip velocity. A linear stability analysis is performed to examine how the fluid-inertial torque, viscous shear torque and particle inertia affect the various stable rotation modes, including logrolling, tumbling and aligning modes. As particle inertia increases, bistable or tristable rotation modes emerge depending on initial conditions. For prolate spheroids, three distinct stable-mode regimes are identified, i.e. logrolling, tumbling and tumbling–logrolling (TL). The presence of these modes depends on particle shape and inertia. For oblate spheroids, when the Stokes number is small, we observe monostable modes (logrolling, tumbling and aligning) and bistable modes (TL, aligning–logrolling) varying with different factors. As Stokes number increases, the tristable mode (aligning–tumbling–logrolling) of oblate spheroids appears. These results of the stability analysis further highlight the intricate and significant effect of fluid-inertial torque compared with the results in the absence of fluid-inertial torque. When we apply fluid-inertial torque to the point-particle model, we reproduce the stable rotation modes observed in particle-resolved simulations, which validates the present stability analysis.