Hydromechanics of Low-Reynolds-Number FLow. Part 3. Motion of a Spheroidal Particle in Quandratic flows.

摘要

Exact solutions in closed form have been found using the singularity method for various quadartic flows of an unbounded incompressible viscous fluid at low Reynolds numbers past a prolate spheroid. The motion of a force-free spheroidal particle in a paraboloidal flow has been determined. It is shown that the spheroid rotates about three principal axes with angular velocities governed by a set of Jeffery orbital equations with the rate of shear evaluated at the centre of the spheroid. The spheroid also translates at a variable speed, depending on its orientation relative to the surrounding fluid, along a straight path parallel to the main flow direction without any side drift or migration. (Author)