Inertial torque on a small spheroid in a stationary uniform flow

Abstract

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio λ = 1 / 6 ) to prolate ( λ = 6 ) , and we consider low and moderate particle Reynolds numbers ( Re ≤ 50 ) . We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers, remains qualitatively correct for Reynolds numbers up to Re ∼ 10 . The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as Re increases. For Re larger than 10, the flow past oblate spheroids acquires a more complicated structure, resulting in systematic deviations from the theoretical predictions. Overall, our numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in a turbulent flow.