Hindered diffusion in slit pores: An analytical result

An analytical result for the hindered diffusional mobility of a spherical particle in a slit pore is derived using an asymptotic matching technique and published expressions for the enhanced viscous drag on the particle caused by the flat walls. A hard sphere-hard wall potential is assumed for the interaction between the particle and pore wall. The mobility is presented as a regular expansion in the parameter λ and is correct to O(λ3), where λ is the ratio of particle radius to half-width of the pore. Our result agrees quantitatively with published numerical evaluations of the mobility up to λ0.5. The derivation is sufficiently general that it allows for inclusion of nonsteric interactions between the particle and the pore wall.