Effects of surface tension on Rayleigh-Taylor instability

In this paper, Layzer's model which has a simple velocity potential, and Zufiria's 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 Layzer's model with the simple velocity potential gives a smaller bubble velocity than that predicted by the Layzer's model with a complex velocity potential. But the bubble velocity predicted by the Layzer's model with the simple velocity potential is larger than that obtained by Zufiria's model. Both Layzer's models lead to the same bubble velocity when the Atwood number is A = 1.