Kinetic Model for Gases with Internal Degrees of Freedom

A new model equation has been obtained which permits a kinetic description of gases possessing internal degrees of freedom. The collision term of the model equation is related to the Wang-Chang and Uhlenbeck results for polyatomic gases much in the same manner as the Bhatnagar, Gross, and Krook model is related to the Boltzmann collision integral. A modified perturbation technique utilizing the various time scales of the flow situation has been employed in closing the equations of change. (This has been shown to be asymptotically equivalent to the Chapman-Enskog expansion of the time derivative.) From the model equation and its moments, depending upon the ratio of a ``flow through'' time to the inelastic relaxation time, one directly obtains either the bulk viscosity as a term modifying the pressure tensor, or a relaxation equation for the internal temperature. The model also accounts for the contribution to the heat transfer vector due to the presence of internal degrees of freedom. In this theory, the inelastic relaxation time appears as a parameter of the system. It is hoped that this model may serve the same function for aerodynamic and kinetic boundary value problems for gases with internal degrees of freedom that the Bhatnagar, Gross, and Krook model has for the simple gas.