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Motion of a Deformed Sphere With Slip in Creeping Flows

[+] Author Affiliations
Liping Jia, André Bénard, Charles A. Petty

Michigan State University, East Lansing, MI

Paper No. FEDSM2005-77187, pp. 929-935; 7 pages
  • ASME 2005 Fluids Engineering Division Summer Meeting
  • Volume 1: Symposia, Parts A and B
  • Houston, Texas, USA, June 19–23, 2005
  • Conference Sponsors: Fluids Engineering Division
  • ISBN: 0-7918-4198-7 | eISBN: 0-7918-3760-2
  • Copyright © 2005 by ASME


The motion of a rigid particle whose surface is a slightly deformed sphere is studied for creeping flows with the assumption of slip on the particle. Expressions are obtained for the hydrodynamic force and torque exerted by the fluid on a deformed sphere using an asymptotic method introduced by H. Brenner, wherein the normalized amplitude of the deviation from sphericity is assumed to be a small parameter. The Stokes’ resistance calculated by this method is validated by comparing with existing solutions the limiting cases of no slip and perfect slip. The equations describing the motion of a deformed sphere with a slip surface in a simple shear flow are also derived and solved. The motion of the deformed sphere is shown to differ significantly from the no-slip case for low values of a dimensionless parameter that incorporates the slip coefficient. The period of rotation of the deformed sphere is longer, and for cases where the slip coefficient is low, the spheroid rotates to a fixed angle and reaches a quasi-steady orientation.

Copyright © 2005 by ASME
Topics: Motion , Creeping flow



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