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Film-splitting flows in forward roll coating

Published online by Cambridge University Press:  21 April 2006

D. J. Coyle ,
C. W. Macosko  and
L. E. Scriven
D. J. Coyle
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Present address: General Electric Company, Corporate Research and Development, Schenectady, NY 12301, USA.
C. W. Macosko
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
L. E. Scriven
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

A model based on the lubrication approximation is put forward for the general case of asymmetric forward roll coating of Newtonian liquids. Two more-rigorous theories are developed, one based on asymptotic expansions for small ratios of gap-to-roll diameter (H0/R), the second on Galerkin/finite-element solutions of the full Navier–Stokes equations over the relevant flow domain. The lubrication model is useful only as an approximation at high capillary numbers $(Ca\equiv \mu\overline{V}/\sigma) $. The asymptotic analysis is accurate when H0/R < 0.001 and Ca > 0.1. The ratio of the film thicknesses on the two rolls is predicted to equal the speed ratio to the 0.65 power, which is confirmed experimentally. The Galerkin/finite-element solutions give full details of the steady two-dimensional free-surface flows including complex recirculation patterns in the film-splitting region, and show how the film-splitting stagnation line becomes a static contact line in the limit as one roll surface becomes stationary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 183 - 207
Copyright
© 1986 Cambridge University Press

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