Time Correlation Functions in a Binary Gas Mixture

Abstract

The low density forms of the correlation functions which yield the coefficients of mutual and thermal diffusion in a binary gas mixture are derived and examined from two points of view. One approach uses the binary collision expansion of the existing correlation function expressions, another uses the physical arguments given by Mori to extract these correlation functions from the Boltzmann equation by considering the evolution of the system from an arbitrary initial state. Both approaches indicate that the time correlation functions can be expressed in terms of single momentum averages of two dynamical functions which obey coupled integrodifferential equations of the Boltzmann type. These equations are solved by Sonine polynomial expansion and calculations are performed for a hard-sphere gas mixture in order to illustrate the results. The correlation functions which characterize the thermal diffusion coefficient are discussed in some detail and several interesting aspects of the dynamics are pointed out.