When is the next extending of Fick-Jacobs equation necessary?

摘要

Applicability of the effective one-dimensional equations, such as Fick-Jacobs equation and its extensions, describing diffusion of particles in 2D or 3D channels with varying cross section A(x) along the longitudinal coordinate x, is studied. The leading nonstationary correction to Zwanzig-Reguera-Rubí equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)10.1021/j100189a004; D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001)10.1103/PhysRevE.64.061106] is derived and tested on the exactly solvable model, diffusion in a 2D linear cone. The effects of such correction are demonstrated and discussed on elementary nonstationary processes, a time dependent perturbation of the stationary flow and calculation of the mean first passage time.