Diffusion in two-dimensional conical varying width channels: Comparison of analytical and numerical results

Abstract

This study is devoted to the unbiased motion of a point-like brownian particle in two-dimensional tilted asymmetric channels of varying width formed by straight walls. An effective one-dimensional description in terms of the generalized Fick-Jacobs equation is used to derive formulas that yield the particle's effective diffusion coefficient as a function of the geometric parameters of the channel. To such end, we use the formulas obtained by Bradley [Phys. Rev. E 80, 061142 (2009)] and by Dagdug and Pineda [J. Chem. Phys. 137, 024107 (2012)] to study two-dimensional diffusion in narrow and smoothly asymmetric channels of varying width. Comparison with brownian dynamics simulation results allows us to establish the domain of applicability of both the one-dimensional description and the effective diffusion coefficient formulas.