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

Author:

Goren Simon L.

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.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference6 articles.

1. Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics .Englewood Cliffs, N.J.:Prentice-Hall.

2. Spielman, L. A. & Goren, S. L. 1970 Particle capture by London forces from low speed flows. Submitted toEnviron. Sci. & Tech.

3. Erdelyi, A. , Magnus, W. , Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms , vol. 11. Bateman Manuscript Project.New York:McGraw-Hill.

4. Goldman, A. J. , Cox, R. G. & Brenner, H. 1967 Slow viscous motion of a sphere parallel to a plane wall. Part I. Motion through a quiescent liquid. Part II. Couette flow.Chem. Engng Sci. 22,637,653.

5. Stimson, M. & Jeffery, G. B. 1926 The motion of two spheres in a viscous fluid.Proc. Roy. Soc. A111,110.

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