Relaxation in a binary gaseous mixture of Maxwell molecules

Over the years, much work has been done in developing sets of equations describing the physical properties of gaseous mixtures. One person to do such work was Walker1, who developed a set of equations for a gaseous mixture of Maxwell molecules. His theory is valid for gases having arbitrary velocity and temperature differences but small stresses and heat fluxes. Since the proposal of his equations, there has been no attempt made to solve these equations numerically. One purpose, then, of this paper is to offer numerical solutions to a dimensionless form of Walker's equations for the case of a binary gas mixture. Another purpose is to verify a qualitative prediction by Morse2 as to what a solution of this type might reveal. His prediction is that when a gaseous mixture of a light and heavy gas is initially far from equilibrium, it will relax in three stages. In the first stage, the lighter gas molecules will relax with one another. In the second stage, the heavier molecules will equilibrate, and in the third stage, through cross-collisions, the lighter molecules and the heavier molecules will reach equilibrium with one another. This is because the relaxation time is directly proportional to the square root of the mass of the molecules in the gas