Dorfman Kevin D, Yariv Ehud
Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, USA.
Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel.
J Chem Phys. 2014 Jul 28;141(4):044118. doi: 10.1063/1.4890740.
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.
我们利用宏观输运理论来计算一个点大小的粒子在横截面缓慢变化的周期性通道中的有效扩散系数，该计算是在长波长极限下进行到二阶的。这个渐近结果作为对Zwanzig [《物理化学杂志》96, 3926 (1992)]、Reguera和Rubi [《物理评论E》64, 061106 (2001)]以及Kalinay和Percus [《物理评论E》74, 041203 (2006)]提出的菲克 - 雅各布斯方程各自修正的基准测试。虽然这三种修正在一阶时都导致相同的有效扩散率，但只有Kalinay和Percus提出的模型在二阶时与我们的渐近结果一致。
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