Peng Zhiwei
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada.
J Chem Phys. 2024 Oct 21;161(15). doi: 10.1063/5.0232614.
Transport and dispersion of active particles in structured environments, such as corrugated channels and porous media, are important for the understanding of both natural and engineered active systems. Owing to their continuous self-propulsion, active particles exhibit rectified transport under spatially asymmetric confinement. While progress has been made in experiments and particle-based simulations, a theoretical understanding of the effective long-time transport dynamics in spatially periodic geometries remains less developed. In this paper, we apply generalized Taylor dispersion theory to analyze the long-time effective transport dynamics of active Brownian particles (ABPs) in periodic channels and fields. We show that the long-time transport behavior is governed by an effective advection-diffusion equation. The derived macrotransport equations allow us to characterize the average drift and effective dispersion coefficient. For the case of ABPs subject to a no-flux boundary condition at the channel wall, we show that regardless of activity, the average drift is given by the net diffusive flux along the channel. For ABPs, their activity is the driving mechanism that sustains a density gradient, which ultimately leads to rectified motion along the channel. Our continuum theory is validated against direct Brownian dynamics simulations of the Langevin equations governing the motion of each ABP.
活性粒子在结构化环境（如波纹通道和多孔介质）中的输运和扩散，对于理解自然和工程活性系统都很重要。由于其持续的自推进，活性粒子在空间不对称限制下表现出整流输运。虽然在实验和基于粒子的模拟方面已经取得了进展，但对空间周期性几何结构中有效的长时间输运动力学的理论理解仍不够完善。在本文中，我们应用广义泰勒弥散理论来分析活性布朗粒子（ABP）在周期性通道和场中的长时间有效输运动力学。我们表明，长时间输运行为由一个有效的平流 - 扩散方程控制。导出的宏观输运方程使我们能够表征平均漂移和有效弥散系数。对于在通道壁处受无通量边界条件约束的ABP情况，我们表明，无论活性如何，平均漂移由沿通道的净扩散通量给出。对于ABP，其活性是维持密度梯度的驱动机制，这最终导致沿通道的整流运动。我们的连续介质理论通过对控制每个ABP运动的朗之万方程的直接布朗动力学模拟进行了验证。
