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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
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.
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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 T/μU0, 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 T/μU0 between about 10 and 0.1, but for smaller values of T/μU0 it is clear that other considerations, involving only viscous and pressure forces, determine the nature of the secondary flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 4 , April 1960 , pp. 481 - 500
Copyright
© 1960 Cambridge University Press

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References

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