Kinetische Theorie des Lorentz-Gases aus rotierenden Molekülen

Abstract

Irreversible processes like diffusion or heat conduction in gases with rotating molecules are accompanied by a partial polarization (or alignment) of molecular axes. In order to calculate these effects, a BOLTZMANN equation is set up for the distribution function containing the molecular angular velocity. The general properties of the BOLTZMANN equation (H-theorem, corresponding collisions, time reversal) are studied. A complete set of orthonormalized tensors is chosen and the distribution function is expanded with respect to these tensors. Inserting into the BOLTZMANN equation yields the system of the transport-relaxation equations for the expansion coefficients. The ONSAGER-CASIMIR relations for the relaxation constants are stated. Some of the expansion coefficients have a familiar physical significance (particle density, temperature, particle flux, heat flux etc.), others are a measure for the mean polarization (or alignment) of the molecules. The diffusion and heat conduction problems are solved formally, giving general expressions for the transport constants and for the mean molecular polarization in terms of the various relaxation constants. Some of these are explicitly calculated for a special model, the rough spheres. These calculations show that taking the polarization into account may decrease the diffusion constant by about 20% and that fast molecules flying perpendicular to the diffusion flux may be polarized by about 30%.