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Steady rimming flows with surface tension

Published online by Cambridge University Press:  01 February 2008

E. S. BENILOV ,
M. S. BENILOV  and
N. KOPTEVA
E. S. BENILOV
Affiliation:
Department of Mathematics, University of Limerick, Ireland
M. S. BENILOV
Affiliation:
Department of Physics, University of Madeira, Portugal
N. KOPTEVA
Affiliation:
Department of Mathematics, University of Limerick, Ireland
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Abstract

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder's bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 91 - 118
Copyright
Copyright © Cambridge University Press 2008

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References

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