Gravity-driven soap film dynamics in subcritical regimes

Abstract

We undertake the analysis of soap-film dynamics with the classical approach of asymptotic expansions.We focus our analysis in vertical soap film tunnels operating in subcritical regimes with elastic Mach numbersMe = O(10−1). Considering the associated set of nondimensional numbers that characterize this flow, we show thatthe flow behaves as a two-dimensional (2D) divergence free flow with variable mass density. When the soap filmdynamics agrees with that of a 2D and almost constant mass density flow, the regions where the second invariant ofthe velocity gradient is non-null correspond to regions where the rate of change of film thickness is non-negligible.