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The transverse force on a spinning sphere moving in a viscous fluid

Published online by Cambridge University Press:  28 March 2006

S. I. Rubinow  and
Joseph B. Keller
S. I. Rubinow
Affiliation:
Stevens Institute of Technology, Hoboken, New Jersey
Joseph B. Keller
Affiliation:
Institute of Mathematical Sciences, New York University, New York, N.Y.
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Abstract

The flow about a spinning sphere moving in a viscous fluid is calculated for small values of the Reynolds number. With this solution the force and torque on the sphere are computed. It is found that in addition to the drag force determined by Stokes, the sphere experiences a force FL orthogonal to its direction of motion. This force is given by ${\bf F}_L = \pi a^3 \rho \Omega \times {\bf V}[1 + O(R)]$ .

Here a is the radius of the sphere, Ω is its angular velocity, V is its velocity, ρ is the fluid density and R is the Reynolds number, $R = \rho \mu ^{-1} Va$. For small values of R, the transverse force is independent of the viscosity μ. This force is in such a direction as to account for the curving of a pitched baseball, the long range of a spinning golf ball, etc. It is used as a basis for the discussion of the flow of a suspension of spheres through a tube.

The calculation involves the Stokes and Oseen expansions. A representation of solutions of the Oseen equations in terms of two scalar functions is also presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 3 , November 1961 , pp. 447 - 459
Copyright
© 1961 Cambridge University Press

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