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Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers

Published online by Cambridge University Press:  26 April 2006

S. W. Joo ,
S. H. Davis  and
S. G. Bankoff
S. W. Joo
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
S. G. Bankoff
Affiliation:
Department of Chemical Engineering, Northwestern University, Evanston, IL 60208, USA
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Abstract

A layer of volatile viscous liquid drains down a uniformly heated inclined plate. Long-wave instabilities of the uniform film are studied by deriving an evolution equation for two-dimensional disturbances. This equation incorporates viscosity, gravity, surface tension, thermocapillarity, and evaporation eifects. The linear theory derived from this describes the competition among the instabilities. Numerical solution of the evolution equation describes the finite-amplitude behaviour that determines the propensity for dryout of the film. Among the phenomena that appear are the tendency to wave breaking, the creation of secondary structures, and the preemption of dryout by mean flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 117 - 146
Copyright
© 1991 Cambridge University Press

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