Effective diffusion coefficient of a Brownian particle in a periodically expanded conical tube.

Diffusion in a tube of periodically varying diameter occurs slower than that in a cylindrical tube because diffusing particles get trapped in wells of the periodic entropy potential which is due to variation of the tube cross-section area. To quantify the slowdown one has to establish a relation between the effective diffusion coefficient of the particle and the tube geometry, which is a very complicated problem. Here we show how to overcome the difficulties in the case of a periodically expanded conical tube, where we find an approximate solution for the effective diffusion coefficient as a function of the parameters determining the tube geometry.