Upstream swimming and Taylor dispersion of active Brownian particles
Upstream swimming and Taylor dispersion of active Brownian particles
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DOI：
10.1103/physrevfluids.5.073102
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发表时间：
2020-07
影响因子：
2.7
通讯作者：
Zhiwei Peng;J. Brady
中科院分区：
文献类型：
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作者：
Zhiwei Peng;J. Brady
自行式颗粒的运动，如可移动的细菌或磷酸盐游泳者，通常在外加流动和限制边界的情况下发生。这些活跃的游泳者与流动环境的相互作用对于理解许多生物过程是重要的，包括移动细菌的感染和生物膜的形成。最近的实验和理论工作表明，Poiseuille流中的活性粒子表现出有趣的动力学行为，包括壁面堆积和上游游动。与已被广泛研究的被动布朗粒子的Taylor弥散相比，对于压力驱动流中主动布朗粒子(ABPs)输运的理论研究相对较少。本文利用描述粒子分布的Smoluchowski方程的小波数展开，显式地导出了傅里叶空间中粒子数密度的横截面平均值的有效平流扩散方程。我们表征了活性粒子的平均漂移(特别是上游游动)和有效纵向弥散系数与流动速度、活性粒子的本征游动速度、活性粒子的布朗扩散和受限程度的关系。与被动布朗粒子不同，ABPs的平均漂移和纵向弥散度均随流速呈现非单调变化。特别是，ABPs的色散包括经典的剪切增强(Taylor)色散和一个称为游泳扩散率的主动贡献。在没有平移扩散的情况下，经典的泰勒色散是不存在的，在强流动极限下，我们观察到了巨大的纵向弥散。我们的连续统理论被控制每个ABP运动的朗之万方程的直接布朗动力学模拟所证实。
Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical works have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation at the wall and upstream swimming. Compared to the well-studied Taylor dispersion of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is relatively less developed. In this paper, employing a small wave-number expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density in Fourier space. We characterize the average drift (specifically upstream swimming) and effective longitudinal dispersion coefficient of active particles in relation to the flow speed, the intrinsic swimming speed of the active particles, their Brownian diffusion, and the degree of confinement. In contrast to passive Brownian particles, both the average drift and the longitudinal dispersivity of ABPs exhibit a nonmonotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. In the absence of translational diffusion, the classical Taylor dispersion is absent and we observe a giant longitudinal dispersion in the strong flow limit. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each ABP.