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Steady-state coating flows inside a rotating horizontal cylinder

Published online by Cambridge University Press:  21 April 2006

R. E. Johnson
R. E. Johnson
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA
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Abstract

Thin coating flows inside a rotating circular cylinder are investigated when the axis of rotation is perpendicular to the direction of gravity. Attention is restricted to flows of power-law fluids having negligible inertia. Four distinct steady-state liquid-film profiles are found to be possible. Two of the cases correspond to a continuous coating, i.e. films that cover the entire inner surface of the cylinder. The other two cases involve partial films covering a limited portion of the cylinder surface. Of the two continuous films, one is the expected configuration involving a coating that gradually changes in thickness as one moves around the cylinder, the film being thicker on the ascending portion of the cylinder and thinner on the descending portion. The second continuous-film configuration has regions on the rising side of cylinder where a rapid change in depth is possible. This case also has the potential to have recirculating zones where a portion of the fluid is trapped in either one or two eddies at fixed locations on the rising side of the cylinder. Of the two partial films, one corresponds to a weakly deformed puddle at the bottom of the cylinder and is the appropriate solution at small rotation rates. The second partial film is a film which coats a portion of the ascending side of the cylinder, the extent of which depends on the film volume.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 321 - 342
Copyright
© 1988 Cambridge University Press

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References

Balmer, R. T. 1970 The hygrocyst - a stability phenomenon in continuum mechanics. Nature 227, 600–601.Google Scholar
Davis, S. H. 1983 Contact-line problems in fluid mechanics. Trans. ASME E: J. Appl. Mech. 105, 977–982.Google Scholar
Debler, W. R. & Yih, C. S. 1962 Formation of rings in a liquid film attached to the inside of a rotating cylinder. J. Aero. Sci. 29, 364.Google Scholar
Deiber, J. A. & Cerro, R. L. 1976 Viscous flow with a free surface inside a horizontal rotating drum. I. Hydrodynamics. Ind. Engng Chem. Fundam. 15, 102–110.Google Scholar
Karweit, J. J. & Corssin, S. 1975 Observation of cellular patterns in a partly filled, horizontal, rotating cylinder. Phys. Fluids 18, 111–112.Google Scholar
Orr, F. M. & Scriven, L. E. 1978 Rimming flow: numerical simulation of steady, viscous, free-surface flow with surface tension. J. Fluid Mech. 84, 145–165.Google Scholar
Phillips, O. M. 1960 Centrifugal waves. J. Fluid Mech. 7, 340–352.Google Scholar
Ruschak, K. J. 1985 Coating flows. Ann. Rev. Fluid Mech. 17, 65–89.Google Scholar
Ruschak, K. J. & Scriven, L. E. 1976 Rimming flow of liquid in a rotating horizontal cylinder. J. Fluid Mech. 76, 113–125.Google Scholar
Tuck, E. O. 1983 Continuous coating with gravity and jet stripping. Phys. Fluids 26, 2352–2358.Google Scholar
Van Rossum, J. J. 1958 Viscous lifting and drainage of liquids. Appl. Set. Res. A7, 121–144.Google Scholar
White, R. E. 1956 Residual condensate, condensate behavior, and siphoning in paper driers. Tech. Assoc. Pulp Paper Ind. 39, 228–233.Google Scholar
White, R. E. & Higgins, T. W. 1958 Effect of fluid properties on condensate behavior. Tech. Assoc. Pulp Paper Ind. 41, 71–76.Google Scholar