Harmonic modes in binary monatomic gas mixtures.

The dispersion and absorption coefficient of sound is calculated using the linearized thirteen-moment equations for binary monatomic gas mixtures. By extending the formal results of Huck and Johnson to include general interatomic force laws it is confirmed that the dispersion law for acoustic modes is influenced by the presence of other harmonic modes in the gas. Specific predictions are made for He-Xe since interference between modes occurs at lower frequencies in disparate mass mixtures. It is shown that either the diffusion mode or the thermal mode has a major influence on the behaviour of the acoustic mode, depending on the interatomic force law. The interference is strongest in a critical region where the mole fraction of helium is roughly 0. 45 and the effective frequency is approximately 75 MHz. Atm We have reformulated the application of perturbation theory for the calculation of harmonic solutions of the coupled Boltzmann equations for a mixture at low frequencies. For higher frequencies, including the critical region, a different perturbation expansion is shown to be necessary for disparate mass mixtures. Such an expansion is given and formal results are obtained which validate the thirteen moment theory for the critical region and define the accuracy of its predictions. Experimental apparatus has been designed and built to measure sound absorption and dispersion in He-Xe mixtures. Data were obtained for effective frequencies of up to 100 MHz. Atm The results corroborate the thirteen moment theory and suggest that the acoustic mode and at least one other mode were excited