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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

REFERENCES

Ashmore, J., Hosoi, A. E. & Stone, H. A. 2003 The effect of surface tension on rimming flows in a partially filled rotating cylinder. J. Fluid Mech. 479, 65–98.CrossRefGoogle Scholar
Benilov, E. S. & O'Brien, S. B. G. 2005 Inertial instability of a liquid film inside a rotating horizontal cylinder. Phys. Fluids 17, 052106.CrossRefGoogle Scholar
Benjamin, T. B., Pritchard, W. G. & Tavener, S. J. 1993 Steady and unsteady flows of a highly viscous liquid inside a rotating horizontal cylinder. Unpublished manuscript.Google Scholar
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.CrossRefGoogle Scholar
Jeong, J.-T. & Moffatt, H. K. 1992 Free-surface cusps associated with a flow at low Reynolds number. J. Fluid Mech. 241, 1–22.CrossRefGoogle Scholar
Johnson, R. E. 1990 Coating flow stability in rotating molding. In Engineering Science, Fluid Dynamics: A Symposium to Honor T.Y. Wu (ed. Yates, G. T.), pp. 435–449. World Scientific.Google Scholar
Landau, L. & Levich, B. 1942 Dragging of liquid by a plate. Acta Physiochim. USSR 17, 42–54.Google Scholar
Moffatt, H. K. 1977 Behaviour of a viscous film on the outer surface of a rotating cylinder. J. Fluid Mech. 16, 651–574.Google Scholar
O'Brien, S. B. G. 2002 Linear stability of rimming flows. Q. Appl. Maths. 60, 201–212.CrossRefGoogle Scholar
O'Brien, S. B. G. & Gath, E. G. 1998 The location of a shock in rimming flow. Phys. Fluids 10, 1040–1042.CrossRefGoogle Scholar
Press, W. H., Teulkolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes, 2nd Edn. Cambridge University Press.Google Scholar
Wilson, S. D. R. 1982 The drag-out problem in film coating theory. J. Engng Maths 16, 209–221.CrossRefGoogle Scholar
Wilson, S. D. R. & Jones, A. F. 1983 The entry of a falling film into a pool and the air-entrainment problem. J. Fluid Mech. 128, 219–230.CrossRefGoogle Scholar