Kinetic Theory of Time-Dependent Correlation Functions in a Binary Gas Mixture

Time-dependent correlation functions in a binary mixture of gases are studied on the basis of kinetic theory. The problem is formulated as an initial-value solution to the linearized Boltzmann equation for the mixture. The analysis is made tractable by the use of an appropriate kinetic model which is developed for Maxwell molecules (1/r4 repulsive potential). The resulting description yields density correlation functions which are valid for arbitrary ratios of wavelength to mean free path. In particular, the results can be used to discuss deviations from hydrodynamic behavior. With the present theory a detailed analysis of the spectral distribution of laser light scattered by dilute binary gas mixtures is made. Explicit results for xenon-helium mixtures are shown to be in very good agreement with the recent measurements of Clark and Benedek.