Particle size effect on diffusion in tubes with dead ends: Nonmonotonic size dependence of effective diffusion constant

Diffusion of a spherical particle of radius r in a tube with identical periodic dead ends is analyzed. It is shown that the effective diffusion constant follows the Stokes-Einstein relation, D-eff(r)proportional to 1/r, only when r is larger or much smaller than the radius of the dead end entrance. In between, D-eff(r) not only deviates from the 1/r behavior but may also even become a nonmonotonic function, which increases with the particle radius for a certain range of r.