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.
Highlights
In transport of micro- or nanosized particles through a confined space, e.g., a restricted channel, the influence of thermal fluctuations is predominant
Current reversal and particle separation cases explicitly demonstrating the separation phenomenon for f0 = 5.0, f0 = 8.0, and f0 = 11.0, where the direction of v depends on the particle radius and particles of different sizes move in different directions on average
For particles with rp = 0.5a, 0.7a, and 0.9a, the critical values are εc ≈ 0.90, εc ≈ 0.75, and εc ≈ 0.62, respectively. This indicates that the larger the particle size, the smaller the threshold parameter ε is required for current reversal
Summary
In transport of micro- or nanosized particles through a confined space, e.g., a restricted channel, the influence of thermal fluctuations is predominant. Assuming that particle diffusion in the transverse cross section can reach an equilibrium rapidly, we invoke the concept of entropy barrier to treat the influence of the boundary constraint of the channel. This physical approach enables us to obtain analytic expressions for the key quantities underlying the diffusion dynamics such as the mean particle velocity and the effective diffusion coefficient, and their dependence on the particle size. This should be distinguished from the previous studies [35,36] in which the particles were driven by a sinusoidal periodic force and an increase in the phase shift of the oscillating density at high frequencies can led to a current reversal
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