Makhnovskii Yurii A, Berezhkovskii Alexander M, Antipov Anatoly E, Zitserman Vladimir Yu
Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, Moscow 119991, Russia.
Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20819, USA.
J Chem Phys. 2015 Nov 7;143(17):174102. doi: 10.1063/1.4934728.
This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients--mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small.
本文致力于研究在存在外部偏置力的情况下，由宽窄交替的部分构成的管道中的粒子输运。重点在于有效输运系数——迁移率和扩散率，它们是偏置力和管道几何参数的函数。在无偏置和强偏置的极限情况下，有效迁移率和扩散率对管道几何参数的依赖关系是已知的。用于获得这些结果的近似方法在偏置力的中间值时不适用。为了弥合这两个极限，进行了布朗动力学模拟，以确定力的中间值时的输运系数。针对一系列具有代表性的管道几何形状，在很宽的偏置力范围内进行了模拟。结果表明，存在一个窄段长度范围，在该范围内迁移率对力的依赖关系存在最大值。相比之下，扩散率是力的单调递增函数。提出了一个简单公式，该公式在零偏置和强偏置这两个极限情况下都简化为扩散率对管道几何参数的已知依赖关系。在偏置力的中间值时，如果这些窄段的半径不太小，该公式能够捕捉到扩散率对窄段长度的依赖关系。
