title: Assessing corrections to the Fick-Jacobs equation.
abstract: We utilize macrotransport theory to compute the effective diffusion coefficient of a point-sized particle in a periodic channel of slowly varying cross-section to the second order in the long-wavelength limit. This asymptotic result serves as a benchmark test for the respective modifications of the Fick-Jacobs equation proposed by Zwanzig [J. Phys. Chem. 96, 3926 (1992)], Reguera and Rubi [Phys. Rev. E 64, 061106 (2001)], and Kalinay and Percus [Phys. Rev. E 74, 041203 (2006)]. While all three modifications result in an identical effective diffusivity at first order, only the model proposed by Kalinay and Percus agrees at second order with our asymptotic result.
authors.affiliation: Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, USA.
authors.forename: Kevin D
authors.initials: KD
authors.lastname: Dorfman
authors.affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Ehud
authors.initials: E
authors.lastname: Yariv