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Current reversal and particle separation in Brownian transport

Hai-Wei Hu1,2, Lin Du1,2,*, Liang-Hui Qu1,2, Zi-Lu Cao1,2, Zi-Chen Deng1,2,3, and Ying-Cheng Lai4,5

  • 1School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
  • 2MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China
  • 3School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
  • 4School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
  • 5Department of Physics, Arizona State University, Tempe, Arizona 85287, USA

  • *lindu@nwpu.edu.cn
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Phys. Rev. Research 3, 033162 – Published 18 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.033162

Abstract

In transport of micro- or nanosized particles through a confined structure driven by thermal fluctuations and external forcing—a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile, such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerical results is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.

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Phys. Rev. Research 3, 033162– Published 18 August, 2021
  • Received 24 February 2021
  • Accepted 19 July 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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