Viscous torque on a sphere under arbitrary rotation

Abstract

The viscous torque on a sphere was derived when the sphere is rotating with an arbitrary time varying angular velocity about a given diameter under the low Reynolds number assumption. The torque is composed of a quasisteady torque and an acceleration torque, which is an integral expression depending on the acceleration history. The acceleration torque can be neglected when the acceleration time scale is sufficiently greater than the viscous time scale, which is appropriate for particles with micron size subject to electrokinetic manipulation.