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

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 1970-04, Vol.41 (3), p.619-625
Main Author: Goren, Simon L.
Format: Article
Language:English
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112070000782