活性粒子的瞬态扩散过程
Transient dispersion process of active particles
AI总结：
本文首次解析研究活性粒子在受限流中的瞬态扩散过程，采用双正交展开法求解，揭示游动、剪切流、壁面累积及粒子形状对扩散演化的影响。
摘要：
活性粒子常在受限环境中游动。其输运机制，尤其是泰勒扩散模型所反映的全局输运机制，对各种应用具有重要的实际意义。对于受限流中的活性扩散过程，以往的分析研究集中于扩散特性的长时间渐近值，仅有少数数值研究初步探讨了其时间演化。本文在江与陈（Jiang & Chen, J. Fluid Mech., vol. 877, 2019, pp. 1–34; J. Fluid Mech., vol. 899, 2020, A18）近期研究的基础上，首次尝试对瞬态过程进行解析研究。基于分布的矩，探讨了受限截面-取向空间中的局部分布、漂移、扩散率和偏度的时间演化。由于自推进效应使得经典的被动输运问题的积分变换方法不再适用，我们引入了双正交展开法来求解。分别施加了两种边界条件：反射条件和用于壁面累积的Robin条件。对在平面泊肃叶流中扩散的球形和椭球形游动体的详细研究，展示了游动、剪切流、壁面累积和粒子形状对点源释放后瞬态扩散过程的影响。游动诱导的扩散使局部分布比被动粒子更快地达到平衡状态。尽管壁面累积显著影响局部分布和漂移的演化，但达到泰勒 regime 的时间尺度并未明显改变。椭球形粒子的剪切诱导取向可以增大扩散率，但对漂移和偏度的影响较小。
英文摘要：
Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For active dispersion process in confined flows, previous analytical studies focused on the long-time asymptotic values of dispersion characteristics. Only several numerical studies preliminarily investigated the temporal evolution. Extending recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1--34; J. Fluid Mech., vol. 899, 2020, A18), this work makes the first analytical attempt to investigate the transient process. The temporal evolution of the local distribution in the confined-section--orientation space, drift, dispersivity and skewness, is explored based on moments of distributions. We introduce the biorthogonal expansion method for solutions because the classic integral transform method for passive transport problems is not applicable due to the self-propulsion effect. Two types of boundary condition, the reflective condition and the Robin condition for wall accumulation, are imposed respectively. A detailed study on spherical and ellipsoidal swimmers dispersing in a plane Poiseuille flow demonstrates the influences of the swimming, shear flow, wall accumulation and particle shape on the transient dispersion process after a point-source release. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Though the wall accumulation significantly affects the evolution of the local distribution and the drift, the time scale to reach the Taylor regime is not obviously changed. The shear-induced alignment of ellipsoidal particles can enlarge the dispersivity but has less influence on the drift and the skewness.
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