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 the 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; vol. 899, 2020, A18), this work makes a semi-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, initial condition, wall accumulation and particle shape on the transient dispersion process. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Although 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 impacts slightly on the drift and the skewness.

中文翻译：

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活性粒子的瞬态分散过程

活性粒子经常在密闭环境中游动。传输机制，尤其是泰勒色散模型所反映的全局机制，对各种应用具有重要的实际意义。对于受限流中的主动色散过程，以往的分析研究主要集中在色散特征的长期渐近值上。只有几项数值研究初步研究了时间演变。扩展江和陈最近的研究（J.流体机械。, 卷。877，2019，第 1-34 页；卷。899, 2020, A18），这项工作对研究瞬态过程进行了半分析性的尝试。基于分布矩探讨了受限截面定向空间中局部分布的时间演变、漂移、分散性和偏度。我们引入了双正交展开法来求解，因为被动运输问题的经典积分变换方法由于自推进效应不适用。分别施加了两种边界条件，反射条件和壁面堆积的 Robin 条件。对分散在平面泊肃叶流中的球形和椭圆形游泳者的详细研究证明了游泳、剪切流、初始条件、壁面堆积和颗粒形状对瞬态分散过程的影响。游动引起的扩散使局部分布比被动粒子更快地达到平衡状态。虽然壁面堆积显着影响了局部分布和漂移的演变，但达到泰勒状态的时间尺度没有明显改变。椭圆体颗粒的剪切诱导排列可以扩大分散性，但对漂移和偏斜有轻微影响。