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Non-isothermal spreading of a thin liquid film on an inclined plane

Published online by Cambridge University Press:  26 April 2006

P. Gilberto López ,
S. George Bankoff  and
Michael J. Miksis
P. Gilberto López
Affiliation:
McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
S. George Bankoff
Affiliation:
McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
Michael J. Miksis
Affiliation:
McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
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Abstract

A thin layer of liquid advancing over a dry, heated, inclined plate is studied. A lubrication model with contact line motion is derived. The plate is at constant temperature, and the surface Biot number is specified. The steady-state solution is obtained numerically. In addition, the steady-state solution is studied analytically in the neighbourhood of the contact line. A linear stability analysis about the steady state is then performed. The effects of gravity, thermocapillarity and contact line motion are discussed. In particular, we determine a band of unstable wavenumbers, and the maximum growth rate as a function of these parameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 324 , 10 October 1996 , pp. 261 - 286
Copyright
© 1996 Cambridge University Press

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