Relaxation by Vibration–Vibration Exchange Processes. Part II. Binary Mixtures

Abstract

A previous paper on vibration processes in a pure gas is extended to the case of binary mixtures of gases. Through numerical integration of the master equation for vibrational relaxation, three distinct time scales to the relaxation processes are identified. The first time scale characterizes the pure-gas vibrational exchange reactions, the second relaxation time describes the coupling between species, while vibration–translation processes are characterized by a third time scale. Depending on the relative vibrational spacing and vibration–translation rates of the components in the mixture, vibrational distributions consistent with each of these time scales may be evident during the relaxation process. Through a steady-state analysis to the vibrational exchange terms in the master equation, it is demonstrated that large differences can exist between population factors (or vibrational temperatures in the harmonic model) for each species at steady state. Only at high kinetic temperatures (i.e., >1000°K) or for equilibrium conditions does vibrational coupling between the species in a mixture give rise to equal vibrational temperatures. In a binary mixture with T(vib) > T(trans), the species having the smallest vibrational spacing is described by higher vibrational temperatures than the second species, and this difference in vibrational temperatures increases with both decreasing kinetic temperature and mole fraction of the component with the smaller spacing. Non-Boltzmann distributions are predicted in the anharmonic model at steady state. However, it is shown that the harmonic treatment to the mixture coupling gives a reasonable zeroth-order solution. Comparison of the results with recent discharge flow data verify the mixture analysis and are consistent with the presence of non-Boltzmann distributions at steady state. More complete agreement must await better kinetic temperature measurements in the discharge flow environment.