Modeling of spinning sphere motion in shear flow of viscous fluid

Abstract

Modeling the motion of a small rigid spinning spherical particle in viscous Navier—Stokes fluid, we generalize the Rubinow—Keller and Maxey—Riley method of estimating the force and the torque acting on the particle to the case of shear flow and arbitrary Reynolds number. We represent the velocity of the flow near the particle as solid body part and small perturbation. As for the velocity far from the particle, it includes a steady external shear flow part and again small perturbation. We use the simplest quadratic polynomial approximation for the small velocity parts and insert it in matching condition at some intermediate spherical surface. It appears that the force parallel to the angular velocity of the particle proves to contain the oscillatory part, with the frequency being proportional to the gradient of the external steady velocity.