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Motion of a sphere normal to a wall in a second-order fluid

Published online by Cambridge University Press:  31 August 2007

A. M. ARDEKANI ,
R. H. RANGEL  and
D. D. JOSEPH
A. M. ARDEKANI
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA
R. H. RANGEL
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA
D. D. JOSEPH
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA Department of Aerospace Engineering and Mechanics, University of Minnesota, MN 55455, USA
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Abstract

The motion of a sphere normal to a wall is investigated. The normal stress at the surface of the sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analysed. For small separation distances, when the particle is moving away from the wall, a tensile normal stress exists at the trailing edge if the fluid is Newtonian, while for a second-order fluid a larger tensile stress is observed. When the particle is moving towards the wall, the stress is compressive at the leading edge for a Newtonian fluid whereas a large tensile stress is observed for a second-orderfluid. The contribution of the second-order fluid to the overall force applied to the particle is towards the wall in both situations. Results are obtained using Stokes equationswhen α1+α2=0. In addition, a perturbation method has been utilized for a sphere very close to a wall and the effect of non-zero α1+α2 is discussed. Finally, viscoelastic potential flow is used and the results are compared with the other methods.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 163 - 172
Copyright
Copyright © Cambridge University Press 2007

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