Interaction of Rotational and Translational Diffusion

The Brownian motion of cylindrically symmetric particles is discussed, taking into account the unequal rates of diffusion parallel and perpendicular to the unique axis, as well as rotational diffusion. The problem is solved analytically for the case where the diffusing particles are initially distributed uniformly and with random orientation over a given plane. It is shown that the distribution at a later time is not strictly Gaussian, as is the case with spherically symmetric particles. On a macroscopic scale the effect is a small one.