A general, rotating, hard sphere model applied to the transport properties of a low density gas

A general, spherical, rigid model is introduced for describing rotating and translating particles. The model contains a parameter, which we label γ, that smoothly interpolates between the smooth hard sphere (γ = 0) and rough hard sphere (γ = 1) limits. Analytic expressions for transport coefficients are determined for the general model in the low density limit and compared with those for the smooth and rough hard sphere cases. While the diffusion constant decreases monotonically on moving from the smooth to the rough sphere limits, both the viscosity and thermal conductivity first decrease and then increase, thereby producing a minimum between the two limits. This qualitative change in behaviour is new and suggests translational-rotational coupling acts to decrease the values of the transport coefficients (in contrast to the prediction from the rough sphere model). Although the model still has the (known) deficiencies of rigid models, it is more flexible than either the smooth or rough sphere model and should find use in better representing molecular behaviour. The general model provides a consistent representation of the transport coefficients because it has proper, microscopic collision dynamics obeying conservation laws for total momentum, total angular momentum, and total energy.