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Stokes problems for moving half-planes

Published online by Cambridge University Press:  26 April 2006

Y. Zeng  and
S. Weinbaum
Y. Zeng
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, NY 10031, USA
S. Weinbaum
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, NY 10031, USA
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Abstract

New exact solutions of the Navier–Stokes equations are obtained for the unbounded and bounded oscillatory and impulsive tangential edgewise motion of touching half-infinite plates in their own plane. In contrast to Stokes classical solutions for the harmonic and impulsive motion of an infinite plane wall, where the solutions are separable or have a simple similarity form, the present solutions have a two-dimensional structure in the near region of the contact between the half-infinite plates. Nevertheless, it is possible to obtain relatively simple closed-form solutions for the flow field in each case by defining new variables which greatly simplify the r- and θ-dependence of the solutions in the vicinity of the contact region. These solutions for flow in a half-infinite space are then extended to bounded flows in a channel using an image superposition technique. The impulsive motion has application to the motion near geophysical faults, whereas the oscillatory motion has arisen in the design of a novel oscillating half-plate flow chamber for examining the effect of fluid shear stress on cultured cell monolayers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 59 - 74
Copyright
© 1995 Cambridge University Press

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