Underdamped capillary wave caused by solutal Marangoni convection in immiscible liquids

Abstract

Using a Cahn–Hilliard–Navier–Stokes model with a capillary tensor to account for solutal Marangoni force, we observe an interfacial wave at the interface of two immiscible liquids. A Fourier analysis shows that the interfacial wave is induced by oscillatory modes of solutal Marangoni convection. A critical Marangoni number is defined above which the oscillatory modes of solutal Marangoni convection are able to occur. This material property is a function of the wave number for different Cahn numbers and is determined from numerical simulations.