Hindered Brownian diffusion of spherical solutes within circular cylindrical pores

A detailed asymptotic analysis accounting for wall curvature extends the Brenner-Gaydos formula for the hydrodynamic hindrance factor (J. Colloid Interface Sci. 1977, 58, 312-356) to terms of order λ 2 , yielding a new result of the form D/D∞ = (1-λ) -2 [1+(9/8)λ ln λ - 1.539λ +C 2 λ 2 + o(λ 2 )], with C 2 ≃1.2, where λ denotes the ratio of solute to pore radii. The accuracy of approximate formulas for D is assessed definitively by comparison with recent boundary element calculations and experiments