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The normal force exerted by creeping flow on a small sphere touching a plane

Published online by Cambridge University Press:  29 March 2006

Simon L. Goren
Simon L. Goren
Affiliation:
Department of Chemical Engineering, University of California, Berkeley
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Abstract

The hydrodynamic force experienced by a small solid sphere of radius ap resting on a solid plane wall in axisymmetric stagnation flow, ${\bf v}_{\infty} = \Omega(- z^2{\bf i}_z + z\tilde{\omega}{\bf i}_{\tilde{\omega}})$, or in planar stagnation flow, v∞ = Ω(−z2iz + 2zxix), is computed on the basis of Stokes’ creeping flow equations. In both cases, as well as for any flow whose z component of velocity is −Ωz2, this force is found to be Fz = − 60·87μΩap3, where μ is the viscosity of the fluid. The uniform flow parallel to the line of centres of two touching spheres of arbitrary radii is also solved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 3 , 29 April 1970 , pp. 619 - 625
Copyright
© 1970 Cambridge University Press

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References

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