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The Rayleigh–Taylor instability of a viscous liquid layer resting on a plane wall

Published online by Cambridge University Press:  26 April 2006

Lori A. Newhouse  and
C. Pozrikidis
Lori A. Newhouse
Affiliation:
Department of Applied Mechanics and Engineering Sciences, R-011, University of California, San Diego, La Jolla, CA 92093, USA
C. Pozrikidis
Affiliation:
Department of Applied Mechanics and Engineering Sciences, R-011, University of California, San Diego, La Jolla, CA 92093, USA
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Abstract

The nonlinear Rayleigh–Taylor instability of a liquid layer resting on a plane wall below a second liquid of higher density is considered. Under the assumption of creeping flow, the motion is studied as a function of surface tension and the ratio of the viscosities of the two fluids. The flow induced by the deformation of the layer is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind is derived for the density of the distribution, and is solved by successive iteration. The results show that for small and moderate surface tension, the instability of the layer leads to the formation of a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of these plumes strongly depends upon the viscosity ratio and surface tension. When the viscosity of the overlying fluid is comparable with or larger than that of the layer, the plumes are composed of a well-defined leading drop on top of a narrow stem. When the viscosity of the overlying fluid is smaller than that of the layer, the plumes take the form of a compact column of rising fluid. The size of the drop leading a plume is roughly proportional to the initial thickness of the layer. When surface tension is sufficiently small, ambient fluid is entrained into the leading drop and circulates in a spiral pattern. Convection currents generated by the rising plumes are visualized with streamline patterns, and the rate of thinning of the remnant layer, as well as the speed of the rising drop or plumes, are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 615 - 638
Copyright
© 1990 Cambridge University Press

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