On the interpretation of measured rotational and vibrational relaxation times. III. Failure of the mixture rule for non-dilute gases

The rotation–vibration relaxation of a mixture of a diatomic gas (approximately simulating hydrogen) with an inert gas is studied both by direct integration, and by an approximate linearised normal-mode method. It is shown that although the linearised normal-mode approximation is a powerful aid to understanding these processes, its numerical accuracy is limited to high dilutions (e.g. 1% of X 2 in M) and to times shorter than the final relaxation time.Direct numerical integration of the relaxation equations for various mixture ratios shows that the plot of vibrational relaxation rate constant vs. mole fraction x is non-linear, and that the slope of this plot near x = 0 can be correlated with the rates of the R–R processes, not the V–V processes as is normally assumed. A brief discussion is presented of the conditions under which the linear mixture rule for relaxation is rigorously obeyed: as is the case for chemical reaction, these conditions are impossibly stringent.An appendix presents a comparison of the transition probabilities used in this series of papers with those recently obtained by Tarr and Rabitz for the relaxation of hydrogen in argon.