Novel Kinetic Theory of the Classical Isotropic Oscillator Gas, the Flexible Shell Model

Ever since Chapman and Enskog first used the hard sphere model to evaluate the collision integral in the Boltzmann equation, more sophisticated models for molecular encounters have been sought. Rotation of molecules in kinetic theory has been pursued with a number of models, such as the spherocylinder or loaded sphere, to account for that aspect. As these efforts continued, more workers started to incorporate quantum mechanics methods in pursuit of solutions to the Boltzmann equation. Progress there with both rotational and vibrational features of molecules has been attained. Until now though, there has been no classical vibration model for molecules in kinetic theory. Far from standard kinetic theory, here a simple classical mechanics isotropic oscillator is combined, through a flexible shell, with the hard sphere model in a full Chapman Enskog procedure. The intent here has been to introduce the model, so items like translational-vibrational coupling have not been included. Still, the results compliment literature.