Current reversal and particle separation in Brownian transport

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.