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The instability of uniform viscous flow under rollers and spreaders

Published online by Cambridge University Press:  28 March 2006

J. R. A. Pearson
Affiliation:
Imperial Chemical Industries Limited, Akers Research Laboratories, The Frythe, Welwyn, Herts.
Now at The Metal Box Co. Ltd., Technical Engineering Division, Borehamwood, Herts.

Abstract

When a thin film of viscous fluid is produced by passing it through a small gap between a roller or spreader and a flat plate, it often presents a waved, or ribbed, surface. An analysis is given here in terms of lubrication theory to show why in many cases flow leading to a uniform film is unstable. Account is taken of surface tension which proves to be a stabilizing factor. The most unstable values of the wave-number, n (characterizing the disturbance), are calculated as functions of the dimensionless variable TU0, and of the geometry of the system; T is the surface tension, μ the viscosity and U0 a representative velocity of the fluid. For the particular case of a spreader in the form of a wide-angled wedge, these predictions are compared with experimental observations. Agreement is obtained for values of TU0 between about 10 and 0.1, but for smaller values of TU0 it is clear that other considerations, involving only viscous and pressure forces, determine the nature of the secondary flow.

Type
Research Article
Copyright
© 1960 Cambridge University Press

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