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Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):054101. doi: 10.1103/PhysRevE.88.054101. Epub 2013 Nov 7.
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本文引用的文献

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Diffusion in a tube of alternating diameter.在直径交替变化的管道中的扩散。
Chem Phys. 2010 May 12;370(1-3):238-243. doi: 10.1016/j.chemphys.2010.04.012. Epub 2009 Nov 11.
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Entropic splitter for particle separation.用于粒子分离的熵分离器。
Phys Rev Lett. 2012 Jan 13;108(2):020604. doi: 10.1103/PhysRevLett.108.020604.
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Communication: drift velocity of Brownian particle in a periodically tapered tube induced by a time-periodic force with zero mean: dependence on the force period.通讯：零均值时变周期力作用下布朗粒子在周期性渐缩管中的扩散速度：对力周期的依赖性。
J Chem Phys. 2011 Sep 28;135(12):121102. doi: 10.1063/1.3647873.
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Unbiased diffusion in tubes with corrugated walls.无偏扩散在波纹壁管中。
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One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach.一维描述管中扩散：基于边界均匀化的方法。
J Chem Phys. 2009 Dec 14;131(22):224110. doi: 10.1063/1.3271998.
6
Diffusion in a tube of varying cross section: numerical study of reduction to effective one-dimensional description.变截面管中的扩散：简化为有效一维描述的数值研究。
J Chem Phys. 2007 Apr 7;126(13):134706. doi: 10.1063/1.2719193.
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Corrections to the Fick-Jacobs equation.对菲克-雅各布斯方程的修正。
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Oct;74(4 Pt 1):041203. doi: 10.1103/PhysRevE.74.041203. Epub 2006 Oct 5.
8
Homogenization of boundary conditions for surfaces with regular arrays of traps.具有规则陷阱阵列的表面边界条件的均匀化
J Chem Phys. 2006 Jan 21;124(3):036103. doi: 10.1063/1.2161196.
9
Homogenization of boundary conditions on surfaces randomly covered by patches of different sizes and shapes.在随机覆盖着不同大小和形状斑块的表面上对边界条件进行均匀化处理。
J Chem Phys. 2005 Jun 15;122(23):236102. doi: 10.1063/1.1930827.
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布朗粒子在周期性扩张锥形管中的有效扩散系数。

Effective diffusion coefficient of a Brownian particle in a periodically expanded conical tube.

作者信息

Antipov Anatoly E, Barzykin Alexander V, Berezhkovskii Alexander M, Makhnovskii Yurii A, Zitserman Vladimir Yu, Aldoshin Sergei M

机构信息

Moscow State University, Faculty of Fundamental Physical and Chemical Engineering, GSP-1, 1-51 Leninskie Gory, Moscow 119991, Russia.

The Royal Bank of Scotland, 250 Bishopsgate, London EC2M 4AA, United Kingdom.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):054101. doi: 10.1103/PhysRevE.88.054101. Epub 2013 Nov 7.

DOI:10.1103/PhysRevE.88.054101
PMID:24329385
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4959108/
Abstract

Diffusion in a tube of periodically varying diameter occurs slower than that in a cylindrical tube because diffusing particles get trapped in wells of the periodic entropy potential which is due to variation of the tube cross-section area. To quantify the slowdown one has to establish a relation between the effective diffusion coefficient of the particle and the tube geometry, which is a very complicated problem. Here we show how to overcome the difficulties in the case of a periodically expanded conical tube, where we find an approximate solution for the effective diffusion coefficient as a function of the parameters determining the tube geometry.

摘要

在直径周期性变化的管道中，扩散比在圆柱形管道中发生得慢，这是因为扩散粒子被困在由管道横截面积变化所导致的周期性熵势阱中。为了量化这种减速，必须建立粒子的有效扩散系数与管道几何形状之间的关系，这是一个非常复杂的问题。在这里，我们展示了如何在周期性扩张的锥形管道的情况下克服这些困难，在这种情况下，我们找到了有效扩散系数作为确定管道几何形状的参数的函数的近似解。