Carbon dioxide, the primary constituent of the Martian atmosphere, has low-energy vibrational modes that are significantly populated at typical temperatures on both Mars and Earth. When changes in temperature occur, the relative populations of these modes change correspondingly, but this population redistribution is slow because the probability of transferring energy between the kinetic energy of a carbon dioxide molecule and a vibrational state during a collision is very small. Hence, a large number of collisions, resulting in a long period of vibrational nonequilibrium, may be required to distribute the energy between these states.

Herzfeld and Rice first described vibrational nonequilibrium in 1928 to explain observed sound wave absorption and dispersion effects in various gases. Experimentalists reported, contrary to prediction, that sound waves in many gases showed anomalous frequency-dependent attenuation. Herzfeld and Rice showed that if there was a slow energy exchange between translational and internal degrees of freedom (slow compared to the mean collision time), the experimental results could be explained. Low-frequency sound waves provide enough time for energy equilibrium to be achieved, and hence the waves propagate as predicted by Stokes. However, high-frequency sound waves do not allow energy equilibrium to be achieved. In this case, energy exchange between the translational and internal degrees of freedom is delayed with respect to the traveling sound wave and results in attenuation of the wave.

For several years after Herzfeld and Rice’s paper, gas relaxation effects were treated as separate from the standard continuum mechanics treatment of gas phenomenon. It was not until 1942, in an intriguing paper by Tisza, that a theoretical link between these two fields was proposed. Tisza recalls that there are two viscosity coefficients, a shear viscosity and a bulk viscosity, in the standard continuum mechanics development and that it is normally assumed that the bulk viscosity is small and can be neglected (for an ideal gas the bulk viscosity is equal to zero). He then went on to show that, by including the bulk viscosity term and including it in a description of sound wave propagation, the results of Herzfeld and Rice can be derived. Accepting this result provides a direct process whereby gas relaxation parameters can be merged into the Navier Stokes relation and used to predict aerodynamic effects.

Over the next 20 years, hundreds of papers in this field were published. Researchers realized that, by measuring the sound propagation characteristics of a gas, information on the internal degrees of freedom of that gas could be found. The field flourished and achieved impressive results as described by several review papers and books published in the 1950’s and 1960’s. But, with the advent of more sophisticated and precise methods of examining molecular degrees of freedom, the attractiveness of this field declined. By the 1970’s, the extensive body of information achieved in the field of gas relaxation phenomenon was rarely mentioned in typical graduate or undergraduate sequences. By the 1990’s, few scientists were familiar with this phenomenon and its possible impact on Martian aerodynamics was ignored.