Diffusion in a tube consisting of alternating wide and narrow sections

The problem of the diffusion of particles in a tube consisting of identical units, each composed of a wide and narrow section is solved. With an approach based on reducing the problem to a one-dimensional, the statistics of times of particle transition between adjacent sections is determined, which is a detailed characteristic of the diffusion process. An expression for the effective diffusion coefficient D (ef) , defining the slow-down of transport due to variations of the tube profile, is derived. It is shown that D (ef) behaves monotonically with increasing length of both the narrow and wide sections. The predictions of analytical formulas are in good agreement with the results of computer simulation performed by the Brownian dynamics method.