Hydrodynamic coupling and nonequilibrium distribution in pore diffusion of nonspherical fine particles

A detailed investigation is presented of a model problem describing diffusion of a thin rod between parallel walls. Analysis proceeds by formulation of the exact diffusion equation in spatial and angular coordinates, and therefore accounts for all translational and rotational modes of transport. It is shown that the presence of a longitudinal concentration gradient produces cross-sectional forcing because of hydrodynamic anisotropy, and thereby leads to a steady-state, configuration-dependent distribution that does not relax to the uniform equilibrium distribution. A general formula derived for the effective dif- fusivity D shows that the configuration-average longitudinal diffusivity is modified by an additive contribution arising from hydrodynamic coupling. Calculation of the latter term requires solution of a translational-rotational diffusion problem. Thus, determination of D cannot generally be achieved by integration alone. Boundary-layer analysis, augmented by a finite-difference calculation, reveals the asymptotic structure of the coupling effect and leads to an explicit expression for D applicable to relatively small particles.