A comparison between kinetic theory and affine transformation theory for self diffusion in a fluid of aligned hard spheroids

Abstract

The Lorentz-Boltzmann kinetic equation is analysed to obtain the diffusion tensor describing the motion of a tagged particle in a fluid of (partially) aligned hard spheroids. The calculation is carried out to the first Sonine polynomial approximation with regard to velocity and angular velocity but, within this approximation, the shape dependence of the friction and mobility tensors are treated essentially exactly. Thus, the solutions are believed to be accurate to within a few percent of the exact Lorentz-Boltzmann solution. On comparing our analysis with the recent work of S. Tang and G. T. Evans (1993, J. chem. Phys., 98, 7281), it is concluded that the approximations they make in treating the shape dependence of the friction tensor are very good. Our results are also compared with the affine transformation theory due to S. Hess, D. Frenkel and M. P. Allen (1991, Molec. Phys., 74, 765). Even for perfect alignment this theory is not exact. Numerically, the components of the diffusion tensor differ from kinetic theory predictions by up to 40%. Despite this, the anisotropy of the diffusion tensor, (D_zz - D_xx )/(D_zz + 2D_xx ), where D_xx and D_zz are, respectively, the diffusion constants perpendicular to and parallel to the axis of alignment, is predicted extremely accurately by the affine transformation theory.