Coupled translational and rotational diffusion in liquids

The equations for coupled translational and rotational diffusion of asymmetric molecules immersed in a fluid are obtained. The method used begins with the Kramers–Liouville equation and leads to the generalized Smoluchowski equation for diffusion in the presence of potentials. Both external potentials and intermolecular potentials are considered. The contraction of the description from the Kramers–Liouville equation to the Smoluchowski equation is achieved by using a combination of operator calculus and cumulants. Explicit solutions to these equations are obtained for the two-dimensional case. Comparison of our results with earlier literature is also presented.