Numerical simulation of interfacial resonant Faraday waves between two immiscible liquids

Abstract

An in-house numerical model is extended to study the resonant Faraday waves at the interface between two immiscible liquids with the consideration of surface tension. The surface tension module was first added in this model and validated by two standard tests, i.e., the development of a non-equilibrium liquid droplet with square shape and the development of Rayleigh–Taylor instability on the interface of two fluids with different densities. Two experiments were conducted to investigate the resonant Faraday waves at the interface of two liquids in a tank under vertical excitation. The numerical results are compared with the experimental data in terms of wave profiles, and favorable agreements are obtained. It has been found that only when the surface tension is properly taken into account, the numerical model can describe the resonant Faraday waves satisfactorily, especially for the secondary interfacial instability and the wave breaking between two immiscible liquids. In addition, the comparisons between numerical results for different surface tensions indicate that the surface tension plays an important stabilizing role during the development of interfacial Faraday waves and the subsequent secondary instability, and the existence of surface tension can help prevent the flow structures transforming from two-dimensional to three-dimensional.