Shock-Wave Study of Vibrational Energy Exchange between Diatomic Molecules

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Abstract
The relaxation equation of the vibrational energy for a mixture of two diatomic gases is solved under the condition of Landau–Teller, considering the translation–vibration energy transfer (T–V) processes as well as the vibrational energy exchange (V–V) process. The solution shows that the relaxation of each of the component molecules proceeds as if it has two relaxation times. At the starting point of the relaxation process, both of the components begin to relax with their respective T–V relaxation rates, and then, the relaxation rate of one component, which has a smaller T–V relaxation time, decreases gradually, while the rate of the other component increases. Finally, both the components relax with the same rate toward their equilibrium states. The extent of coupling between the T–V processes of the two components is determined by the rate of the V–V process and by the concentration of two species in the mixture. Based on the preceding analysis, the vibrational relaxations of CO in CO–N2, CO–C2, CO–D2, and CO–H2 mixtures diluted in Ar are observed by the infrared emission of the CO fundamental behind shock waves, and the V–V collision probabilities are determined. The results agree with the SSH theory except in the case of CO–H2 collision. Theoretical calculation using the Morse‐type potential is also discussed for the near‐resonant V–V process between CO and N2.