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Thermal instabilities in two-fluid horizontal layers

Published online by Cambridge University Press:  29 March 2006

Richard W. Zeren  and
William C. Reynolds
Richard W. Zeren
Affiliation:
Department of Mechanical Engeering, Michigan state university
William C. Reynolds
Affiliation:
Department of mechanical engineering, state university
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Abstract

An analytical and experimental study of thermally induced instability in horizontal two-fluid layers is reported. A liner stability analysis for two initially motionless, viscous immiscible fluids confined between horizontal isothermal solid surface and subject to both density (Bénard) and surface-tension-grandient (Marangoni) drving mechanisms is presented. Calculations for the labortory configuaration reported below predict instability for heating from above or below. Response is strongly department on the ratios of the properties of the fluids, the total depth of the layer and the depth fraction of one fluid. Three different response modes occur(interfacial-tension-gradient dominated, buoyancy dominated and surface-deflexion dominated) depending on the fluid depth fractions when the heating is from above, the buoyanvy mechanism is stabilizing for most wavenumbers, including the xritical one. Heating from below lowere the critical Marangoni number and adds a buoyancy driven response mode. Results of experimental measurement of the critical Marangoni number exceeds the predicted critical value by as much as five times. The critical Rayleigh number observe for heating from below fallos between the critical values predicted with and without the Marangoni effect. The presence of surface contamination is belived to be responsible for the apparent lack of convection when heating is from above and for the different between the predicted and measured critical Rayleigh number when heating is from below.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 2 , 23 May 1972 , pp. 305 - 327
Copyright
© 1972 Cambridge University Press

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