Modified rough sphere models, with application to sound absorption in gas mixtures

Conservation laws for a pair of colliding rough spheres are newly formulated, introducing the relative velocity g measured in a reference point Y outside the point of contact and the total angular momentum (spin plus orbital about Y) transferred between the spheres. Rules for rough sphere dynamics are reviewed. From equations for temperature relaxation in a binary mixture, the rotational relaxation number Zrot is obtained. Sound absorption data for pure methanes and methane-inert gas mixtures are interpreted on the assumption that most collisions follow a two-deflection dynamics, a small fraction being governed by direct energy transfer between the components of g. The rotational temperature appears to relax against one fixed translational temperature. Attractive forces should be included in the dynamical model. Assuming that the model parameters are connected to a coefficient of non-sphericity, Zrot from theory is fitted to the experimental data with a standard deviation Δ = 17.2%.