On the formulation of boundary conditions for rigid nonspherical Brownian particles near solid walls: Applications to orientation-specific reactions with immobilized enzymes

Transport processes involving the motion of rigid nonspherical Brownian particles within porous media and, more generally, proximate to solid surfaces, arise in a multitude of natural and engineered contexts. Detailed modeling proceeds via solution of the microscale convective-diffusion equation in the six-dimensional configuration space composed of particle positions and orientations, subject to boundary conditions accounting for either impenetrability (inertness) or catalytic activity of the bounding surfaces. Owing to the geometrical complexity associated with even simple particle-wall combinations, the construction of such conditions has long been the source of ambiguities in the literature. We present a rigorous, general analysis of issues arising from particle-wall contact within the context of Brownian transport. Abstract configuration-space flux conditions are shown to possess a physically transparent interpretation in terms of rigid-body kinematics. As a specific application of our general theory, explicit asymptotic results are derived for a model problem pertaining to orientation-specific reactions of macromolecular substrates with immobilized enzymes. In the course of the analysis, a robust numerical technique is developed for the solution of configuration-space diffusion problems, the general utility of which transcends its application to the specific physical system considered here.