Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, 09340 Mexico City, Mexico.
J Chem Phys. 2012 Jul 14;137(2):024107. doi: 10.1063/1.4733394.
This study focuses on the derivation of a general effective diffusion coefficient to describe the two-dimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width, in the simple diffusional motion of noninteracting pointlike particles under no external field. We present a generalization to the case of an asymmetric channel using the projection method introduced earlier by Kalinay and Percus [J. Chem. Phys. 122, 204701 (2005); and Phys. Rev. E 74, 041203 (2006)] to project the 2D diffusion equation into an effective one-dimensional generalized Fick-Jacobs equation. The expression for the diffusion coefficient given in Eq. (23) is our main result. This expression is a more general effective diffusion coefficient for narrow channels in 2D, which contains the well-known previous results as special cases, namely, those obtained by Bradley [Phys. Rev. E 80, 061142 (2009)], and more recently by Berezhkovskii and Szabo [J. Chem. Phys. 135, 074108 (2011)]. Finally, we study some specific 2D asymmetric channel configurations to test and show the broader applicability of Eq. (23).
本研究专注于推导一个通用的有效扩散系数，以描述在无外场作用下，非相互作用点状粒子的简单扩散运动中，变窄且平滑不对称通道内的二维（2D）扩散。我们使用 Kalinay 和 Percus [J. Chem. Phys. 122, 204701 (2005); and Phys. Rev. E 74, 041203 (2006)] 之前引入的投影方法，将 2D 扩散方程推广到不对称通道的情况，将其投影到有效一维广义 Fick-Jacobs 方程中。方程（23）给出的扩散系数表达式是我们的主要结果。这个表达式是 2D 窄通道更通用的有效扩散系数，它包含了先前已知的特殊情况，即 Bradley [Phys. Rev. E 80, 061142 (2009)] 以及 Berezhkovskii 和 Szabo [J. Chem. Phys. 135, 074108 (2011)] 最近获得的结果。最后，我们研究了一些特定的 2D 不对称通道配置，以测试和展示方程（23）更广泛的适用性。
