The effects of density difference and surface tension on the development of Rayleigh-Taylor instability of an interface between fluid media

Abstract

To describe the evolution of an interface between two immiscible media, an equation for a volume fraction function is derived, with the interface curvature effect being described by a “continuum model” of a surface tension force. A numerical study of the Rayleigh-Taylor instability problem is performed for different density ratios ρ1/ρ2 on the interface, including the real cases corresponding to available experimental data. At the initial stage, the instability development is independent of ρ1/ρ2 and consistent with the Taylor linear theory, then (for ρ1/ρ2 < 5) a spiral-like Kelvin-Helmholtz instability structure is observed. For ρ1/ρ2 < 2, the instability development pattern remains symmetric until large times when (same as for large ρ1/ρ2) an asymmetry appears. The surface tension and the viscosity result in the suppression of the Rayleigh-Taylor instability disturbances and secondary small-scale irregularities of the interface.