Ultrasonic dispersion in mixtures

Experimental observation of relaxation phenomena in binary mixtures of polyatomic gases affords much more information about vibration-vibration transfer. The nature of the vibrational relaxation process for a mixture of a relaxing gas, A, with a non-relaxing gas, B, has been discussed in Section 4.3. It involves two collision processes 

If both A and B are polyatomic relaxing gases, there will also be two collision processes, corresponding to (1) and (2), for vibration-translation energy transfer from B in homomolecular and heteromolecular collisions. In addition there can be a vibration-vibration transfer between A and B, making five transfer processes in all 

If process (3), vibration-vibration transfer, does not occur, the mixture will show a double relaxation phenomenon, characterized by two relaxation times, / A and / B which will both be related to molar composition by equations of type (20), each giving a linear plot of 1 // against composition. If vibration-vibration transfer does occur, the picture is completely altered. Supposing, for convenience, that pure A relaxes slowly, and pure B rapidly, so that processes (4) and (5) are both much faster than processes (1) and (2), there are now two alternative possibilities for the overall relaxation process. 

Alternatively, when process (3) is slower than (4) or (5), but faster than (1) or (2), A will again relax by the route (3) followed by (4) or (5), but now (3) will be rate determining. This will give a linear variation of 1// A with x. B will relax independently, and more rapidly, via (4) and (3), with linear dependence of 1// B on x. There will thus be a double relaxation phenomenon with two relaxation times, PA involving only the vibrational heat capacity of A, and / B only that of B, both showing linear concentration dependence. This mechanism is analogous to the relaxation behaviour discussed in Section 3.1 for pure polyatomic gases, which show double dispersion because vibration-vibration transfer between modes is slower than vibration-translation transfer from the lowest mode. 

EXPERIMENTAL COLLISION NUMBBRS FOR INTBRMOLBCULAR VIBRATIONAL ENERGY 

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