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The stability of uniformly accelerated flows with application to convection driven by surface tension

Published online by Cambridge University Press:  29 March 2006

Raymond J. Gumerman  and
George M. Homsy
Raymond J. Gumerman
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305 Present address: Chevron Research Corp., Richmond, California.
George M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
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Abstract

The method of energy is used to study the stability of uniformly accelerated flows, i.e. those flows characterized by an impulsive change in boundary temperature or velocity. Two stability criteria are considered: strong stability, in which there is exponential decay of the disturbance energy, and marginal stability, in which the disturbance energy is less than or equal to its initial value. For the important case in which the critical stability parameter (measured by the Marangoni, Rayleigh or Reynolds number) decreases with time, it is proved that an onset time exists. Furthermore, it is shown that the experimental onset time is bounded below by the marginal stability limit, which in turn is bounded below by the strong stability limit.

The method is then applied to the problem of an impulsively cooled liquid layer susceptible to instabilities driven by interfacial-tension gradients. The strong stability and marginal stability boundaries are calculated and bounds on the onset time are given. These results represent the first rigorous bounds for convective instability problems of this class. Comparison with the limited available experimental data shows the calculated results to be lower bounds on the experimental onset times, and hence the theory is in agreement with available experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 1 , 11 March 1975 , pp. 191 - 207
Copyright
© 1975 Cambridge University Press

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