A COMPARISON BETWEEN KINETIC-THEORY AND AFFINE TRANSFORMATION THEORY FOR SELF-DIFFUSION IN A FLUID OF ALIGNED HARD SPHEROIDS

The Lorentz-Boltzmann kinetic equation is analysed to obtain the diffu sion tenser describing the motion of a tagged particle in a fluid of ( partially) aligned hard spheroids. The calculation is carried out to t he first Sonine polynomial approximation with regard to velocity and a ngular velocity but, within this approximation, the shape dependence o f the friction and mobility tensors are treated essentially exactly. T hus, the solutions are believed to be accurate to within a few percent of the exact Lorentz-Boltzmann solution. On comparing our analysis wi th the recent work of S. Tang and G. T. Evans (1993, J. chem. Phys., 9 8, 7281), it is concluded that the approximations they make in treatin g the shape dependence of the friction tenser are very good. Our resul ts are also compared with the affine transformation theory due to S. H ess, D. Frenkel and M. P. Alien (1991, Molec. Phys., 74, 765). Even fo r perfect alignment this theory is not exact. Numerically, the compone nts of the diffusion tenser differ from kinetic theory predictions by up to 40%. Despite this, the anisotropy of the diffusion tensor, (D-zz - Dxx)/(D-zz + 2D(xx)), where D-xx and D-zz are, respectively, the di ffusion constants perpendicular to and parallel to the axis of alignme nt, is predicted extremely accurately by the affine transformation the ory.