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

By A. M. Ardekani1, R. H. Rangel1 and D. D. Joseph2.

1Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
2Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA

(Posted 27 March 2008)


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-order fluid. 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 equations when \alpha_1 + \alpha_2 = 0. In addition, a perturbation method has been utilized for a sphere very close to a wall and the effect of a non-zero \alpha_1 + \alpha_2 is discussed. Finally, viscoelastic potential flow is used and the results are compared with the other methods.