Kinetic theory of dense fluids of rigid biaxial ellipsoids

The transport equation for a one-particle distribution function f of a pure and dense fluid composed of hard biaxial ellipsoids has been derived by the Enskog method through a modification of the Taxman equation which describes the corresponding low-density fluid. The equation for f has been utilized in obtaining approximate equations of continuity, linear momentum, and energy of the dense fluid, and has then been solved through the Enskog infinite series expansion technique, and a second-order approximate formula for f has been achieved. Using this, results are derived for the hydrodynamic pressure, shear and bulk viscosity coefficients, and heat conductivity of the fluid. Fast exchange of energy between the translational and rotational motions is assumed throughout the calculation. The quantities ultimately appearing in the results, which cannot further be reduced analytically and require numerical evaluation, are the four-dimensional quadratures over the orientational coordinates of two interacting rigid ellipsoidal molecules. In the appropriate limit, all results reduce to those obtained by Enskog for a dense fluid of hard spheres, and a first-order modified Eucken-type formula for the dense fluid emerges.