Diffusional description of vibrational relaxation in a binary mixture of diatomic molecules — quantum oscillators Original Research Article

The finite-difference equations of diffusional type for the vibrational relaxation process in a binary gas mixture of diatomic molecules - quantum oscillators are derived. The derivation begins with the corresponding complete (with allowance for multiquantum transitions) population balance equations and uses techniques of the finite-difference analysis. The kinetic equations obtained approximately take account of multiquantum transitions and are exact in the case of the one-quantum energy transfer; in the classical limit, these equations are transformed into equations of the classical (or continual) diffusional theory of vibrational relaxation. The time-dependent isothermal problem of vibrational relaxation in a binary mixture of anharmonic oscillators is numerically solved. The results presented illustrate the effect of multi-quantum vibration exchange processes for components with essentially different fundamental vibrational frequencies in various concentrations and initial conditions. A comparison of micro- and macroscopic vibration kinetic descriptions is carried out.