Effects of surface tension on Rayleigh-Taylor instability

Abstract

In this paper, Layzers model which has a simple velocity potential, and Zufirias model are extended to the case of non-ideal fluids, and the effects of surface tension on Rayleigh-Taylor instability are investigated. Firstly, the analytical expressions for the asymptotic bubble velocity and curvature are obtained in the two models. Secondly, the effects of surface tension on Rayleigh-Taylor instability are studied systematically. Finally, the two models are compared with each other and the comparisons with numerical simulation are made as well. The results indicate that the surface tension depresses the bubble velocity, but does not affect the bubble curvature. The Layzers model with the simple velocity potential gives a smaller bubble velocity than that predicted by the Layzers model with a complex velocity potential. But the bubble velocity predicted by the Layzers model with the simple velocity potential is larger than that obtained by Zufirias model. Both Layzers models lead to the same bubble velocity when the Atwood number is A = 1.