Abstract Presented in this paper is a theoretical analysis of migration of active particles in a surface flow constructed wetland, in which the longitudinal and vertical swimming behaviors are taken into account besides the hydrodynamic effects in the conventional analysis of passive particle dispersion. Theoretical solutions of mass distribution, moving velocity of the mass center, and the longitudinal dispersion coefficient are rigorously derived for a gyrotactic micro-organisms patch, based on Aris’ moment method and the method of separation of variables for linear partial differential equations. It is found that the mass distribution, motion of the mass center, and longitudinal dispersion of the gyrotactic micro-organisms patch can reach a stable status on the time scale 3 / ( π 2 + Pe V 2 / 4 ) , where Pe V is the Peclet number characterized by the total vertical diffusivity and vertical swimming velocity, and the necessary time corresponding to the dispersion of soluble contaminants can be embodied as a case of Pe V = 0 . The total quantity of gyrotactic micro-organisms in each streamline satisfies exponential distribution for large Pe V , while it approximately satisfies linear distribution for small Pe V . The asymptotic velocity of mass center for gyrotactic micro-organisms in each streamline is, in general, not equal to the depth-averaged flow velocity, due to the longitudinal mean swimming caused by gyrotaxis in the shear flow. The increase of Pe V and U r (dimensionless flow velocity at free water surface relative to swimming speed) can enhance the motion of the mass center and longitudinal dispersion of the gyrotactic micro-organisms patch, while the increase of α (a dimensionless parameter to reflect shape of flow velocity profile) can weaken them.

中文翻译：

---

表流人工湿地中活性粒子的迁移

摘要 本文提出了表面流人工湿地中活性颗粒迁移的理论分析，其中除了传统被动颗粒分散分析中的水动力效应外，还考虑了纵向和垂直游动行为。基于Aris矩方法和线性偏微分方程的变量分离方法，严格推导出回旋微生物贴片的质量分布、质心移动速度和纵向色散系数的理论解。发现回旋微生物斑块的质量分布、质心运动和纵向弥散在时间尺度3 / ( π 2 + Pe V 2 / 4 ) 上可以达到稳定状态，其中Pe V 是Peclet 数，以总垂直扩散率和垂直游动速度为特征，可溶污染物分散所需的时间可体现为Pe V = 0 的情况。每条流线中回旋微生物的总数对于大Pe V 满足指数分布，而对于小Pe V 则近似满足线性分布。由于剪切流中的回旋引起的纵向平均游泳，每个流线中回旋微生物的质心渐近速度通常不等于深度平均流速。