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The influence of Coriolis force on surface-tension-driven convection

Published online by Cambridge University Press:  28 March 2006

A. Vidal  and
Andreas Acrivos
A. Vidal
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California
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Abstract

The effect of uniform rotation on surface-tension-driven convection in an evaporating fluid layer is considered both theoretically and experimentally. The theoretical analysis follows the usual small-disturbance approach of perturbation theory and leads, at the neutral state, to a functional relation between the Marangoni and Taylor numbers which is then computed numerically. In addition, it is shown analytically that, in the limit of rapid rotation, the velocity and temperature fluctuations are confined to a thin Ekman layer near the surface, and that Mc = 4·42T½ and ac = 0·5T¼, where Mc and ac are, respectively, the critical Marangoni number and the critical wave number for neutral stability, and T is the Taylor number.

The experimental part deals primarily with the flow pattern of a 50% solution of ethyl ether in n-heptane evaporating into still air. In this case, the convective flow is surface-tension-driven and its structure was observed using schlieren optics. In the absence of rotation, the flow shows a remarkable cellular pattern when the layer is shallow, but when the depth of the layer is increased the pattern quickly becomes highly irregular. In contrast, for T > 103, a cellular structure is always observed even for deep layers, a result which is attributable to the stabilizing effect of the Coriolis force. A further increase in T leaves the flow pattern unchanged except that the size of the cells is found to decrease as T−¼ which is in agreement with the results of the linear stability analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 26 , Issue 4 , December 1966 , pp. 807 - 818
Copyright
© 1966 Cambridge University Press

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