Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows

Bees, M.A., Hill, N. and Pedley, T.J. (1998) Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows. Journal of Mathematical Biology, 36(3), pp. 269-298. (doi: 10.1007/s002850050101)

Abstract

Analytic approximations are obtained to solutions of the steady Fokker-Planck equation describing the probability density functions for the orientation of dipolar particles in a steady, low-Reynolds-number shear flow and a uniform external field. Exact computer algebra is used to solve the equation in terms of a truncated spherical harmonic expansion. It is demonstrated that very low orders of approximation are required for spheres but that spheroids introduce resolution problems in certain flow regimes. Moments of the orientation probability density function are derived and applications to swimming cells in bioconvection are discussed. A separate asymptotic expansion is performed for the case in which spherical particles are in a flow with high vorticity, and the results are compared with the truncated spherical harmonic expansion. Agreement between the two methods is excellent.

• Item Type: Articles
• Additional Information: The original publication is available at www.springerlink.com
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Hill, Professor Nicholas and Bees, Dr Martin
• Authors: Bees, M.A., Hill, N., and Pedley, T.J.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Mathematical Biology
• Journal Abbr.: J. math. biol.
• Publisher: Springer
• ISSN: 0303-6812
• ISSN (Online): 1432-1416
• Copyright Holders: Copyright © 1998 Springer
• First Published: First published in Journal of Mathematical Biology 1998 36(3):269-298
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher