The kinetic theory of sound propagation in binary gaseous mixtures.

We develop a theory for the study of the absorption and dispersion of a sound wave propagating in a binary mixture of gases by using both the 13-moment approximation and the Navier - Stokes theory. This general theory is valid for a mixture of any two monatomic gases, however, we limit our study to the mixture of helium and argon. After lengthy mathematical formulation we obtain a set of linear equations in the general eigenvalue - eigenvector form. Using numerical methods to solve the eigenvalue equation, we compute the absorption and dispersion. We compare the absorption calculated by both the 13-moment approximation and the Navier - Stokes theory with experimental data for mixtures containing 5%, 10%, 25%, 50% and 75% argon. Both theories give values which compare favorably with experiment for low and mid-range values of frequency/pressure. The Navier - Stokes absorption values are consistently closer to experiment for higher values of f/p. For the 50% argon mixture, we find that the 13-moment absorption curve peaks sharply for f/p ˜ 280. The corresponding dispersion curve dips at the same value. The Navier - Stokes theory yields neither of these features. For each of the remaining cases, the dispersion curves for the 13-moment approximation start at ˜ and decrease until leveling off. The Navier - Stokes dispersion curves also start at 1 but decrease steadily, with the final dispersion value being greater than the corresponding absorption by .01