Analogy between soap film and gas dynamics. I. Equations and shock jump conditions

Abstract

The governing equations of compressible flows in soap films are formulated based on the very specific property equations of soap films. The basic normal shock relations and the Rankine–Hugoniot equation are derived for steady one-dimensional flows in soap films. The results are similar to those of compressible gases. The analogy between compressible flows in soap films and that in gases is discussed. On short time scales, the dynamic response of the film is characterized by the Marangoni elasticity, and soap films are shown to be analogous to compressible gases with a specific heat ratio of γ=1.0. Results for Gibbs elasticity are also presented for reference, and no clear analogy to compressible gases is obtained.