Two-fluid Euler theory of sound dispersion in gas mixtures of disparate masses

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Abstract
The suitability of an Euler-level two-fluid theory to describe the behaviour of gas mixtures with disparate masses is explored for the problem of sound propagation at frequencies high enough that dispersion effects are important. The determination of the speed of propagation is reduced to solving a quadratic equation in the complex plane. The model leads to small errors of the order of the molecular mass ratio M when the molar fraction xp of the heavy gas is small (xp = O(M)), becoming increasingly inaccurate at larger values of xp. Yet agreement with He-Xe experiments is excellent for the whole range of frequencies tested, up to values of xp = 0.4. For values of xp above 0.5 our quantitative results become poorer but they still agree qualitatively with experiments, predicting small and negative dispersion coefficients and the presence of a bifurcation at critical values of the frequency and the composition. It is concluded that this generalized Euler theory provides an excellent framework within which to develop a two-fluid boundary-layer description of the peculiar dynamics of disparate-mass mixtures in the region of parameters of greatest industrial interest.