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Rimming flow: numerical simulation of steady, viscous, free-surface flow with surface tension

Published online by Cambridge University Press:  12 April 2006

F. M. Orr  and
L. E. Scriven
F. M. Orr
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis Present address: Shell Development Company, P.O. Box 481, Houston, Texas 77001.
L. E. Scriven
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis
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Abstract

Flow in a partly liquid-filled, rotating, horizontal cylinder is analysed by means of finite-element numerical simulation. Of alternative methods for locating the free surface, a boundary collocation scheme with Newton-Raphson iteration converges. This method forces the residual in the normal-stress boundary condition to zero at a finite set of points on the liquid meniscus. Solutions of the steady, two-dimensional, incompressible flow problem show circumferential variation of the liquid-film thickness and corresponding pressure and velocity fields, including recirculation zones. The complications of an unknown meniscus location and a nonlinear normal-stress condition when surface tension is significant are illustrated. The finite-element method proves an effective and convenient tool for such flows, in which inertial, gravitational, pressure, viscous and capillary forces are all important.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 1 , 16 January 1978 , pp. 145 - 165
Copyright
© 1978 Cambridge University Press

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