External Transverse Field: 2D Narrow Channel

In this chapter, we focus on the derivation of a general position-dependent effective diffusion coefficient to describe two-dimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width under the influence of a transverse gravitational external field. In order to do so, we employ the projection method by Kalinay and Percus (KP) to project the 2D Smoluchowski equation into an effective one-dimensional generalized Fick-Jacobs equation. Then, based on the theoretical effect diffusivity, an equation for the mean first-passage time (MFPT) of a conical 2D channel was obtained. Subsequently, we found the numerical solution of the MFPT and compared such results to the times obtained by means of Brownian Dynamics simulations to validate the range of applicability of these equations.