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Sliding sheets: lubrication with comparable viscous and inertia forces

Published online by Cambridge University Press:  20 April 2006

E. O. Tuck  and
M. Bentwich
E. O. Tuck
Affiliation:
Applied Mathematics Department, University of Adelaide
M. Bentwich
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel Aviv University
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Abstract

A rigid plane thin sheet is sliding steadily at speed U close to a plane wall, in a fluid of kinematic viscosity v. The sheet is infinitely wide and is of length L in the direction of motion, and its leading edge is a distance h0 [Lt ] L from the wall. A solution is sought for arbitrary finite values of R = Uh20/νL. In the limit as ε = h0/L→0, the problem reduces to that of solving the boundary-layer equation in the gap region between sheet and wall, and this is done here both by an empirical linearization, and by direct numerical methods. The solutions have the property that they reduce to those predicted by lubrication theory when R is small, and to those predicted by an inviscid small-gap theory when R is large. Special attention is paid to the correct entrance and exit conditions, and to the location of the centre of pressure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 51 - 69
Copyright
© 1983 Cambridge University Press

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