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Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities

Published online by Cambridge University Press:  20 April 2006

Marc K. Smith  and
Stephen H. Davis
Marc K. Smith
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201 Present address: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201
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Abstract

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 119 - 144
Copyright
© 1983 Cambridge University Press

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