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Hydromechanics of low-Reynolds-number flow. Part 3. Motion of a spheroidal particle in quadratic flows

Published online by Cambridge University Press:  29 March 2006

Allen T. Chwang
Allen T. Chwang
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Permanent address: Engineering Science Department, California Institute of Technology, Pasadena.
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Abstract

Exact solutions in closed form have been found using the singularity method for various quadratic flows of an unbounded incompressible viscous fluid at low Reynolds numbers past a prolate spheroid with an arbitrary orientation with respect to the fluid. The quadratic flows considered here include unidirectional paraboloidal flows, with either an elliptic or a hyperbolic velocity distribution, and stagnation-like quadratic flows as typical representations. 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. These angular velocities depend on the minor-to-major axis ratio of the spheroid and its instantaneous orientation, but are independent of its actual size. 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. This ‘jerk’ motion obeys a trajectory equation which is size dependent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 1 , 11 November 1975 , pp. 17 - 34
Copyright
© 1975 Cambridge University Press

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