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Title: Projection of two-dimensional diffusion in narrow asymmetric channels onto the longitudinal direction

Diffusive transport of particles is a ubiquitous feature of physical, chemical and biological systems. Typical structures like pores, tubes or fibers, are quasi one-dimensional, such that we need to solve 2+1 or 3+1 dimensional differential equations to describe correctly transport along them. The so-called Fick-Jacobs approach dramatically simplifies the problem if one assumes that a solute distribution in any cross-section of the channel is uniform at equilibrium. That study focuses on the mapping of the diffusion equation in a two-dimensional narrow asymmetric channel of varying cross section onto the longitudinal coordinate. We present a generalization to the case of an asymmetric channel using the projection method introduced earlier by Kalinay and Percus. We derive an expansion of the effective diffusion coefficient, which represents corrections to the Fick-Jacobs equation and contains the well-known previous results as special cases. Finally, we study numerically some specific two-dimensional asymmetric channel configurations to test and show the broader applicability of this effective diffusion coefficient formula.
Authors:
;  [1]
  1. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México Distrito Federal (Mexico)
Publication Date:
OSTI Identifier:
22264071
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1579; Journal Issue: 1; Conference: 5. Leopoldo Garcia-Colin Mexican meeting on mathematical and experimental physics, Mexico City (Mexico), 9-13 Sep 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CROSS SECTIONS; DIFFUSION; DIFFUSION EQUATIONS; EQUILIBRIUM; EXPANSION; ONE-DIMENSIONAL CALCULATIONS; PARTICLES; TWO-DIMENSIONAL CALCULATIONS