Fokker-Planck equation and the grand molecular friction tensor for coupled rotational and translational motions of structured Brownian particles near structured surfaces

The Fokker-Planck equation and molecular-based grand friction tensor are derived for the problem of rotational and translational motions of a structured Brownian particle, including the presence of a structured wall. Using the method of multiple time scales, it is shown that the time independent, grand friction tensor for the Brownian particle includes, in a general way, terms that account for the fluid molecular mediated interactions with the wall. The resulting Fokker-Planck equation has important applications in processes involving site-specific adsorption of macromolecules, such as affinity chromotography, biological separations, and numerous cellular processes involving attachment of macromolecules.