The transport properties of dense assemblies of rigid spheres

Summary

A general method is described for the calculation of transport coefficients in dense fluids composed of rigid spheres. It is assumed that for uniform concentrations the spatial distribution function has its equilibrium value, but that the velocity distribution is a product of Maxwellian single-particle functions chosen to give correctly the local temperature and hydrodynamic velocity. The following assemblies are investigated: 1) The single-component assembly of smooth rigid spheres for which the shear and bulk viscosities, the thermal conductivity and the self-diffusion coefficient are calculated explicitly. 2) The two-component mixture of spheres of different mass and the same radius; for this assembly the heat and matter transport coefficients are calculated and are found to satisfy Onsager’s theorem. 3) The multicomponent assembly. The diffusion constants are calculated and are also found to satisfy Onsager’s theorem. 4) The one-component assembly of rough spheres. The viscosity and thermal conductivity are found to be greater than in the smooth sphere assembly. 5) A one-component assembly of spheres each of which possesses two internal energy levels, excitable by collision. For this assembly a formula is obtained for the absorption of sound at high frequencies.