-
摘要: 本文综述剪切流中的弥散问题. 经典Taylor–Aris理论源于截面平均浓度的长时间渐近展开, 并不适用于刻画早期阶段所呈现的多尺度动力学结构. 针对剪切弥散全过程, 本文在Lagrange坐标系下揭示其多尺度扩散叠加的物理本质, 构建统一时空尺度的弥散模型. 通过引入兼具空间各向异性和时间非线性特征的等效扩散度张量, 实现层流与湍流弥散全过程的对流与扩散动力学解耦. 在此基础上, 进一步阐述解析模型向主动物质领域的跨尺度拓展, 涵盖浮游微生物和人工粒子的弥散机理与研究进展, 重点考虑旋转动力学和剪切弥散的耦合效应及其引发的反常标度律. 结合复杂系统从个体行为到集体涌现的演化规律, 探讨发展剪切弥散解析理论的基础价值, 展望水体环境中污染物迁移转化、微藻水动力学聚集以及微纳机器人协同调控等应用前景.Abstract: This review revisits Taylor dispersion in shear flows. Since the classical theory relies on long-time asymptotic expansions of mean concentration, it inevitably overlooks the multi-scale dynamics inherent in early regimes. To address the entire evolution of shear dispersion, we unveil its physical nature as a set of superposable diffusive processes from a Lagrangian perspective—An approach naturally yields an analytic streamwise dispersion model. By formulating an equivalent diffusivity tensor characterized by spatial anisotropy and temporal nonlinearity, we successfully decouple the dynamics of advection and diffusion in laminar and turbulent flows across timescales. Further, we examine the dispersion of active-matter systems, including suspensions of motile micro-organisms and synthetic particles. Special emphasis is placed on the interplay between rotational dynamics and shear dispersion, particularly regarding the anomalous scaling. Finally, we discuss the fundamental significance of analytic theory for shear dispersion in complex systems, with applications spanning from pollutant transport and the hydrodynamic focusing of micro-algae, to the coordinated control of micro-robots.
-
Key words:
- diffusion /
- shear dispersion /
- multi-scale modelling /
- analytic theory /
- fluid mechanics
-
图 1 多尺度弥散过程. (a) 剪切弥散初始段、过渡段和渐近段的示意图, 其演化可通过在流动路径的不同位置测量峰值宽度得到 (Moser & Baker 2021); (b) 微通道中纳米粒子的多尺度弥散演化阶段 (Vilquin et al. 2021)
图 2 湍流场中的弥散 (Xia et al. 2013). (a) 弱电磁驱动湍流, (b) 强电磁驱动湍流, (c)法拉第波驱动的二维湍流
图 3 复杂流动中剪切弥散过程的理论与实验对比. (a) 微通道中带电纳米粒子在开放吸附边界下的Taylor 弥散过程, 实验结果(左列)和Taylor–Aris弥散理论(右列)的对比 (Vilquin et al. 2023); (b) 植被水流中弥散系数随均匀植被有效直径的变化 (Tanino & Nepf 2008); (c) 不同横截面管道中溶质弥散的空间分布 (Aminian et al. 2016); (d) 圆管泊肃叶流中点源弥散的全过程演化, Guan和Chen (2024) 的理论预测与Aminian 等(2016) 的实验观测定性一致
图 4 主动物质的水动力学聚集和致旋性捕获及非定常等效捕获机理. (a) 水动力学聚集现象 (Kessler 1985a): 极地雪藻在下沉流(左侧)和上涌流(右侧)中分别呈现中心和壁面聚集. 由于细胞比水沉, 高浓度细胞在上涌流中下沉, 形成致旋型羽流和失稳; (b) 致旋性捕获现象 (Durham et al. 2009): 在水平剪切流中, 致旋型微生物在弱剪切区向上迁移, 而在强剪切区则快速旋转并被捕获, 形成浮游植物薄层, 这可能是赤潮等自然灾害的潜在机理; (c) 在上涌流中, 朝向中轴线内侧的致旋型主动粒子的运动($ -\text{π} \lt \phi \lt 0 $)是不稳定的, 因为重力矩$ {T}_{{\mathrm{G}}} $和黏性力矩$ {T}_{{\text{ν}} } $的共同作用使粒子发生向外、向上的运动. 因此, 主动粒子在管壁和中轴线之间被短暂捕获, 最终随致旋性效应的时间积累而聚集在管壁. 在下沉流中, 致旋型主动粒子稳定地向内侧迁移($ 0 \lt \phi \lt \text{π} $). Guan 等 (2023)揭示了非定常等效捕获与水动力学聚集竞争下的丰富现象
图 5 角度空间中的弥散与基于趋向性的控制策略. (a) 振荡剪切流中的角度分布, 下方是通过保角变换得到的云图, 其第一行和第二行分别为随机游走模拟和实验结果 (Leahy et al. 2013); (b) 基于趋向性控制主动粒子的集体行为: 对称破缺现象的全局机理和局部机理 (Théry et al. 2024)
图 6 浮游微生物的多种游动模式与机理 (Koch & Subramanian 2011). (a) 细菌通过螺旋状鞭毛束的旋转推动前进; (b) 游动细菌产生的偶极子流场; (c) 跑动–翻转(run-and-tumble)运动; (d) 伸展的流体运动会使推动者(pusher, 如细菌)沿特定方向排列, 使其力偶极子(红色箭头)增强流动, 而拉动者(puller, 如微藻)则会阻碍流动
图 7 浮游微生物密度分布的实验与理论对比. (a) 左图为抛物型流动中极地雪藻(C. nivalis)与赤潮异弯藻(H. akashiwo)形成的浮游植物薄层. 中间图片为归一化密度分布的实验数据(实线)与数值模拟(虚线)对比, 在长时间尺度下吻合得较好. 右图中垂向游动速度的实验(实线)与数值(虚线)定量一致, 蓝色条带为观测标准差. 在$ S\approx 0 $处的峰值速度的衰减(灰线)与重力致旋性理论的预测相符, 这表明致旋性可能是导致有害藻类薄层形成的重要机理 (Durham et al. 2009); (b) 二维圆柱点涡流动中重力致旋性微藻密度$ n $随径向位置$ r $的分布(各类符号对应不同时刻)的密度分布实验数据与(实线) Gauss解在长时间后高度吻合. Gauss解中, $ \varOmega $表示圆柱转动的恒定角速度, $ g $是重力加速度常数, $ {v}_{{\mathrm{s}}} $表示游动速度大小, $ B $为重力致旋性对应的特征重定向时间, $ \lambda =1/(2B{D}_{{\mathrm{r}}}) $是重力致旋性参数, $ {D}_{{\mathrm{r}}} $是旋转扩散度, 而$ F(\lambda ) $是关于$ \lambda $的无量纲函数, 具体表达式详见文献 (Cencini et al. 2019). 小图为渐近长时间后微藻群体的平均径向位置随旋转频率$ f $的变化, 红点是实验测量值, 实线为理论预测对应的解析解; (c) 三维球形点涡流动中枯草芽孢杆菌(B. subtilis)的概率密度随游动方向的分布, 左侧为Sokolov和Aranson (2016) 的实验结果, 右侧为Smoluchowski模型的理论预测结果, 实验数据经归一化后落在本文解析理论所预测的统一曲线上 (Guan et al. 2026b)
图 8 微生物群体输运、微流控混合与细菌湍流. (a) 2只草履虫因碰撞导致的角度变化, 红色符号表示实验结果, 蓝色符号为基于squirmer模型的数值模拟 (Ishikawa 2025); (b) 概率密度分布的实验测量与理论模拟结果对比, 包括新月柄杆菌 (▲, Aranson 2022)、大肠杆菌 (▼, Berke et al. 2008) 及公牛精子 (■, Rothschild 1963), 虚线表示均匀分布. 插图则展示了对应于不同鞭毛长度和旋转扩散度的数值模拟分布 (Aranson 2022); (c) 被动微通道混合器, 加粗斜线表示通道底部的交错人字形沟槽, 下方的荧光显微图像展示了等量荧光溶液和非荧光溶液的混合搅拌过程 (Stroock et al. 2002). 随着横截面上溶质的快速混合, 沿主流方向的剪切弥散效应显著减弱; (d) 两图分别为枯草芽孢杆菌Lagrange湍流的可视化实验观测和连续介质模型预测的二维云图 (Dunkel et al. 2013)
表 1 剪切弥散理论发展史
文献 代表性贡献 文献 代表性贡献 Taylor 1953, 1954b 开创剪切弥散理论研究 Yasuda 1984 分析振荡流中的弥散特性 Townsend et al. 1954 揭示湍流剪切流中扩散机理 Chatwin & Allen 1985 建立河流与河口弥散模型 Aris 1956 建立严格的Taylor–Aris理论 Brenner & Edwards 1993 提出广义Taylor弥散理论 Batchelor 1957 奠定湍流弥散的数学基础 Stone & Brenner 1999 发展高维流动的弥散理论 Saffman 1960 给出渐近短时间的近似源解 Mei & Vernescu 2010 引入均质化方法分析弥散 Lighthill 1966 寻找早期弥散阶段的理论解 Lauga 2011a 研究往复运动粒子的弥散 Gill 1967 构建反应–对流–扩散模型 Ishikawa & Pedley 2014 构建微生物群体输运模型 Fischer 1973, 1976 系统综述剪切弥散理论 Jiang & Chen 2019 解析主动粒子弥散理论 Smith 1982 提出弥散过程的Gauss拟合 Guan & Chen 2024 建立沿流线的弥散理论 注: “Taylor obtained his solution by a display of the sort of brilliance we can only admire.” — Fischer (1979) 
下载: 导出CSV
-
[1] 程洋, 尹海龙. 2025. 基于特征提取优化的CNN-LSTM市政泵站水质预测模型研究. 环境科学学报, 45: 120-128 (Cheng Y, Yin H L. 2025. Research on water quality prediction model for municipal pumping station based on CNN-LSTM with enhanced feature extraction. Acta Scientiae Circumstantiae, 45: 120-128). doi: 10.13671/j.hjkxxb.2025.0240Cheng Y, Yin H L. 2025. Research on water quality prediction model for municipal pumping station based on CNN-LSTM with enhanced feature extraction. Acta Scientiae Circumstantiae, 45: 120-128 doi: 10.13671/j.hjkxxb.2025.0240 [2] 崔智文, 赵立豪. 2021. 近壁湍流中微小非球形颗粒取向行为研究综述. 空气动力学学报, 39: 99-108 (Cui Z W, Zhao L H. 2021. Reviews on alignment of non-spherical particles in wall-bounded turbulence. Acta Aerodynamica Sinica, 39: 99-108). doi: 10.7638/kqdlxxb-2021.0045Cui Z W, Zhao L H. 2021. Reviews on alignment of non-spherical particles in wall-bounded turbulence. Acta Aerodynamica Sinica, 39: 99-108 doi: 10.7638/kqdlxxb-2021.0045 [3] 管明阳. 2025. 多尺度弥散: 从溶质到主动粒子. 北京: 北京大学 (Guan M Y. 2025. Multi-scale dispersion: From solutes to active particles. Beijing: Peking University).Guan M Y. 2025. Multi-scale dispersion: From solutes to active particles. Beijing: Peking University [4] 槐文信, 梁雪融. 2019. 基于随机位移方法的植被水流纵向离散研究. 工程科学与技术, 51: 138-143 (Huai W X, Liang X R. 2019. Simulation of longitudinal dispersion in vegetated flows based on random displacement model. Advanced Engineering Sciences, 51: 138-143). doi: 10.15961/j.jsuese.201800633Huai W X, Liang X R. 2019. Simulation of longitudinal dispersion in vegetated flows based on random displacement model. Advanced Engineering Sciences, 51: 138-143 doi: 10.15961/j.jsuese.201800633 [5] 槐文信, 杨柳, 张皎. 2021. 植被化河道中细颗粒泥沙沉积分布特征的实验及数值研究//第三十二届全国水动力学研讨会论文集 (上册)(Huai W X, Yang L, Zhang J. 2021. Experimental and numerical investigation on fine sediment deposition in the open channel flows with aquatic vegetation//Proceedings of the 32nd National Conference on Hydrodynamics [6] 刘雅钰, 林颖典, 袁野平, 等. 2021. 线性层结环境和浸没式植被对斜坡异重流运动的影响. 上海交通大学学报, 55: 412-420 (Liu Y Y, Lin Y D, Yuan Y P, et al. 2021. Effect of linearly stratified environment and submerged vegetation on hydrodynamic characteristics of downslope gravity currents. Journal of Shanghai Jiao Tong University, 55: 412-420). doi: 10.16183/j.cnki.jsjtu.2019.228Liu Y Y, Lin Y D, Yuan Y P, et al. 2021. Effect of linearly stratified environment and submerged vegetation on hydrodynamic characteristics of downslope gravity currents. Journal of Shanghai Jiao Tong University, 55: 412-420 doi: 10.16183/j.cnki.jsjtu.2019.228 [7] 陆夕云, 林建忠. 2017. 能否发展关于湍流动力学和颗粒材料运动学的综合理论?. 科学通报, 62: 1115-1118 (Lu X Y, Lin J Z. 2017. Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials?. Chinese Science Bulletin, 62: 1115-1118).Lu X Y, Lin J Z. 2017. Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials?. Chinese Science Bulletin, 62: 1115-1118 [8] 孙壮, 陈高峰, de Pablo J J, 等. 2024. 球腔内低雷诺数流体中颗粒输运研究进展. 力学学报, 56: 1284-1296 (Sun Z, Chen G F, de Pablo J J, et al. 2024. Particulate transport in the low-Reynolds-number fluid confined in a spherical cavity. Chinese Journal of Theoretical and Applied Mechanics, 56: 1284-1296). doi: 10.6052/0459-1879-23-627Sun Z, Chen G F, de Pablo J J, et al. 2024. Particulate transport in the low-Reynolds-number fluid confined in a spherical cavity. Chinese Journal of Theoretical and Applied Mechanics, 56: 1284-1296 doi: 10.6052/0459-1879-23-627 [9] 陶建军. 2020. 槽流的亚临界转捩与局地湍流. 空气动力学学报, 38: 128-136 (Tao J J. 2020. Subcritical transition in channel flow and localized turbulence. Acta Aerodynamica Sinica, 38: 128-136). doi: 10.7638/kqdlxxb-2019.0159Tao J J. 2020. Subcritical transition in channel flow and localized turbulence. Acta Aerodynamica Sinica, 38: 128-136 doi: 10.7638/kqdlxxb-2019.0159 [10] 王平. 2016. 带有界面吸收的典型弥散过程的浓度矩分析. 北京: 北京大学 (Wang P. 2016. Taylor dispersion in typical flows with wall absorption: Spatial concentration moments analysis. Beijing: Peking University).Wang P. 2016. Taylor dispersion in typical flows with wall absorption: Spatial concentration moments analysis. Beijing: Peking University [11] 伍梓. 2014. 典型泰勒弥散过程的两尺度摄动分析. 北京: 北京大学 (Wu Z. 2014. Two-scale perturbation analysis for typical Taylor dispersion process. Beijing: Peking University).Wu Z. 2014. Two-scale perturbation analysis for typical Taylor dispersion process. Beijing: Peking University [12] 徐兴亚, 赖瑞勋, 黄磊, 等. 2025. 基于粒子滤波的河道含沙量数据同化及参数校正研究. 泥沙研究, 50: 1-8 (Xu X Y, Lai R X, Huang L, et al. 2025. Data assimilation of suspended sediment concentration in open channels and model parameters updating based on particle filter. Journal of Sediment Research, 50: 1-8). doi: 10.16239/j.cnki.0468-155x.2025.06.001Xu X Y, Lai R X, Huang L, et al. 2025. Data assimilation of suspended sediment concentration in open channels and model parameters updating based on particle filter. Journal of Sediment Research, 50: 1-8 doi: 10.16239/j.cnki.0468-155x.2025.06.001 [13] 杨延涛, 朱金阳, 吴介之. 2024. 边界层控制: 从微扰到改造. 气动研究与试验, 2: 1-35 (Yang Y T, Zhu J Y, Wu J Z. 2024. Boundary layer control: From perturbation to transformation. Aerodynamic Research & Experiment, 2: 1-35). doi: 10.20118/j.issn2097-258X.2024.02.001Yang Y T, Zhu J Y, Wu J Z. 2024. Boundary layer control: From perturbation to transformation. Aerodynamic Research & Experiment, 2: 1-35 doi: 10.20118/j.issn2097-258X.2024.02.001 [14] 郑晓静, 王国华. 2020. 高雷诺数壁湍流的研究进展及挑战. 力学进展, 50: 202001 (Zheng X J, Wang G H. 2020. Progresses and challenges of high Reynolds number wall-bounded turbulence. Advances in Mechanics, 50: 202001). doi: 10.6052/1000-0992-19-009Zheng X J, Wang G H. 2020. Progresses and challenges of high Reynolds number wall-bounded turbulence. Advances in Mechanics, 50: 202001 doi: 10.6052/1000-0992-19-009 [15] Alert R, Casademunt J, Joanny J F. 2022. Active turbulence. Annual Review of Condensed Matter Physics, 13: 143-170. doi: 10.1146/annurev-conmatphys-082321-035957 [16] Aminian M, Bernardi F, Camassa R, et al. 2016. How boundaries shape chemical delivery in microfluidics. Science, 354: 1252-1256. doi: 10.1126/science.aag0532 [17] Aranson I S. 2022. Bacterial active matter. Reports on Progress in Physics, 85: 076601. doi: 10.1088/1361-6633/ac723d [18] Aris R. 1956. On the dispersion of a solute in a fluid flowing through a tube. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 235: 67-77. doi: 10.1098/rspa.1956.0065 [19] Ashrafizadeh S N, Khatibi M, Aslani I. 2026. A deep dive into hydrodynamic dispersion in microfluidic systems. Lab on a Chip, 26: 1610-1657. doi: 10.1039/D5LC00869G [20] Balwada D, Xie J H, Marino R, et al. 2022. Direct observational evidence of an oceanic dual kinetic energy cascade and its seasonality. Science Advances, 8: 41: eabq2566. [21] Barry M T, Rusconi R, Guasto J S, et al. 2015. Shear-induced orientational dynamics and spatial heterogeneity in suspensions of motile phytoplankton. Journal of the Royal Society Interface, 12: 20150791. doi: 10.1098/rsif.2015.0791 [22] Batchelor G K. 1957. Diffusion in free turbulent shear flows. Journal of Fluid Mechanics, 3: 67-80. [23] Bearon R N, Hazel A L. 2015. The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel. Journal of Fluid Mechanics, 771: R3. doi: 10.1017/jfm.2015.198 [24] Bearon R N, Hazel A L, Thorn G J. 2011. The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields. Journal of Fluid Mechanics, 680: 602-635. doi: 10.1017/jfm.2011.198 [25] Bechinger C, Di Leonardo R, Löwen H, et al. 2016. Active particles in complex and crowded environments. Reviews of Modern Physics, 88: 045006. doi: 10.1103/RevModPhys.88.045006 [26] Be’er A, Ariel G. 2019. A statistical physics view of swarming bacteria. Movement Ecology, 7: 9. doi: 10.1186/s40462-019-0153-9 [27] Bees M A. 2020. Advances in bioconvection. Annual Review of Fluid Mechanics, 52: 449-476. doi: 10.1146/annurev-fluid-010518-040558 [28] Bees M A, Croze O A. 2010. Dispersion of biased swimming micro-organisms in a fluid flowing through a tube. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466: 2057-2077. doi: 10.1098/rspa.2009.0606 [29] Bello M S, Rezzonico R, Righetti P G. 1994. Use of Taylor-Aris dispersion for measurement of a solute diffusion coefficient in thin capillaries. Science, 266: 773-776. doi: 10.1126/science.266.5186.773 [30] Berg H C, Turner L. 1990. Chemotaxis of bacteria in glass capillary arrays: Escherichia coli, motility, microchannel plate, and light scattering. Biophysical Journal, 58: 919-930. doi: 10.1016/s0006-3495(90)82436-x [31] Berke A P, Turner L, Berg H C, et al. 2008. Hydrodynamic attraction of swimming microorganisms by surfaces. Physical Review Letters, 101: 038102. doi: 10.1103/PhysRevLett.101.038102 [32] Biswas R R, Sen P N. 2007. Taylor dispersion with absorbing boundaries: A stochastic approach. Physical Review Letters, 98: 164501. doi: 10.1103/PhysRevLett.98.164501 [33] Brenner H. 1991. Macrotransport processes: Brownian tracers as stochastic averagers in effective-medium theories of heterogeneous media. Journal of Statistical Physics, 62: 1095-1119. doi: 10.1007/BF01128179 [34] Brenner H, Edwards D. 1993. Macrotransport processes. Stoneham, MA: Butterworth-Heinemann. [35] Brenner M P, Stone H A. 2000. Modern classical physics through the work of G I Taylor. Physics Today, 53: 30-35. doi: 10.1063/1.883100 [36] Cates M E, Tjhung E. 2018. Theories of binary fluid mixtures: From phase-separation kinetics to active emulsions. Journal of Fluid Mechanics, 836: P1. doi: 10.1017/jfm.2017.832 [37] Cencini M, Guido B, Matteo B, et al. 2019. Gyrotactic phytoplankton in laminar and turbulent flows: A dynamical systems approach. The European Physical Journal E, 42: 31. doi: 10.1017/jfm.2017.832 [38] Chatwin P C. 1970. The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe. Journal of Fluid Mechanics, 43: 321-352. doi: 10.1017/S0022112070002409 [39] Chatwin P C. 1971. On the interpretation of some longitudinal dispersion experiments. Journal of Fluid Mechanics, 48: 689-702. doi: 10.1017/S0022112071001800 [40] Chatwin P C. 1972. The cumulants of the distribution of concentration of a solute dispersing in solvent flowing through a tube. Journal of Fluid Mechanics, 51: 63-67. doi: 10.1017/S0022112072001077 [41] Chatwin P C. 1976. The initial dispersion of contaminant in Poiseuille flow and the smoothing of the snout. Journal of Fluid Mechanics, 77: 593-602. doi: 10.1017/S0022112076002279 [42] Chatwin P C. 1977. The initial development of longitudinal dispersion in straight tubes. Journal of Fluid Mechanics, 80: 33-48. doi: 10.1017/S0022112077001529 [43] Chatwin P C, Allen C M. 1985. Mathematical models of dispersion in rivers and estuaries. Annual Review of Fluid Mechanics, 17: 119-149. doi: 10.1146/annurev.fl.17.010185.001003 [44] Chen K, Jiang W, Guo J, et al. 2025. Manipulating alignment and dispersion of confined micro-swimmers through gradient-induced orienting fields. Physics of Fluids, 37: 021926. doi: 10.1063/5.0258072 [45] Chikwendu S C. 1986. Calculation of longitudinal shear dispersivity using an N-zone model as N → ∞. Journal of Fluid Mechanics, 167: 19-30. doi: 10.1017/S0022112086002707 [46] Chikwendu S C, Ojiakor G U. 1985. Slow-zone model for longitudinal dispersion in two-dimensional shear flows. Journal of Fluid Mechanics, 152: 15-38. doi: 10.1017/S0022112085000544 [47] Collings P J, Goodby J W. 2020. Introduction to liquid crystals: Chemistry and physics. Second edition. Boca Raton: CRC Press. [48] Craske J, Debugne A L R, van Reeuwijk M. 2015. Shear-flow dispersion in turbulent jets. Journal of Fluid Mechanics, 781: 28-51. doi: 10.1017/jfm.2015.417 [49] Craske J, van Reeuwijk M. 2016. Generalised unsteady plume theory. Journal of Fluid Mechanics, 792: 1013-1052. doi: 10.1017/jfm.2016.72 [50] Croze O A, Sardina G, Ahmed M, et al. 2013. Dispersion of swimming algae in laminar and turbulent channel flows: Consequences for photobioreactors. Journal of the Royal Society Interface, 10: 20121041. doi: 10.1098/rsif.2012.1041 [51] del Refugio Cabañas-Mendoza M, Olguín E J, Sánchez-Galván G, et al. 2024. Contribution of the root system of Cyperus papyrus and Pontederia sagittata to microplastic removal in floating treatment Wetlands in two urban ponds. Ecological Engineering, 206: 107334. doi: 10.1016/j.ecoleng.2024.107334 [52] Dai S, Tang D, Younis B A, et al. 2026. Large-eddy simulations of oscillatory flow around a cylinder at high Keulegan-Carpenter and Reynolds numbers. Acta Mechanica Sinica, 42: 325204. doi: 10.1007/s10409-025-25204-x [53] Deleanu M, Hernandez J F, Cipelletti L, et al. 2021. Unraveling the speciation of β-amyloid peptides during the aggregation process by Taylor dispersion analysis. Analytical Chemistry, 93: 6523-6533. doi: 10.1021/acs.analchem.1c00527 [54] Dewey R J, Sullivan P J. 1982. Longitudinal-dispersion calculations in laminar flows by statistical analysis of molecular motions. Journal of Fluid Mechanics, 125: 203-217. doi: 10.1017/S0022112082003310 [55] Du Y, Wang F, Calzavarini E, et al. 2025. Sea ice aging by diffusion-driven desalination. Physical Review Letters, 135: 104201. doi: 10.1103/mct1-6hbw [56] Dunkel J, Heidenreich S, Drescher K, et al. 2013. Fluid dynamics of bacterial turbulence. Physical Review Letters, 110: 228102. doi: 10.1103/PhysRevLett.110.228102 [57] Durham W M, Climent E, Barry M, et al. 2013. Turbulence drives microscale patches of motile phytoplankton. Nature Communications, 4: 2148. doi: 10.1038/ncomms3148 [58] Durham W M, Kessler J O, Stocker R. 2009. Disruption of vertical motility by shear triggers formation of thin phytoplankton layers. Science, 323: 1067-1070. doi: 10.1126/science.1167334 [59] Einstein A. 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik, 322: 549-560. doi: 10.1002/andp.19053220806 [60] Ezhilan B, Saintillan D. 2015. Transport of a dilute active suspension in pressure-driven channel flow. Journal of Fluid Mechanics, 777: 482-522. doi: 10.1017/jfm.2015.372 [61] Fischer H B. 1973. Longitudinal dispersion and turbulent mixing in open-channel flow. Annual Review of Fluid Mechanics, 5: 59-78. doi: 10.1146/annurev.fl.05.010173.000423 [62] Fischer H B. 1976. Mixing and dispersion in estuaries. Annual Review of Fluid Mechanics, 8: 107-133. doi: 10.1146/annurev.fl.08.010176.000543 [63] Fischer H B. 1979. Mixing in inland and coastal waters. London: Academic Press. [64] Foister R T, Van De Ven T G M. 1980. Diffusion of Brownian particles in shear flows. Journal of Fluid Mechanics, 96: 105-132. doi: 10.1017/S0022112080002042 [65] Frankel I, Brenner H. 1989. On the foundations of generalized Taylor dispersion theory. Journal of Fluid Mechanics, 204: 97-119. doi: 10.1017/S0022112089001679 [66] Gill W N. 1967. A note on the solution of transient dispersion problems. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 298: 335-339. doi: 10.1098/rspa.1967.0107 [67] Gill W N. 1972. Dispersion of non-uniformly distributed time-variable continuous sources in time-dependent flow. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 327: 191-208. doi: 10.1098/rspa.1972.0040 [68] Gill W N, Sankarasubramanian R. 1970. Exact analysis of unsteady convective diffusion. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 316: 341-350. doi: 10.1098/rspa.1970.0083 [69] Gouiller C, Raynal F, Maquet L, et al. 2021. Mixing and unmixing induced by active camphor particles. Physical Review Fluids, 6: 014501. doi: 10.1103/PhysRevFluids.6.014501 [70] Guan M Y, Li Z, Chen G, et al. 2026a. Streamwise dispersion in a turbulent open channel flow across all time regimes. Journal of Fluid Mechanics, 1033: A8. doi: 10.1017/jfm.2026.11422 [71] Guan M Y, Ling B, Liu E, et al. 2026b. Active phase-space topology unifies depletion and alignment in bacterial flows. arXiv: 2605.29333. [72] Guan M Y, Chen G Q. 2024. Streamwise dispersion of soluble matter in solvent flowing through a tube. Journal of Fluid Mechanics, 980: A33. doi: 10.1017/jfm.2024.34 [73] Guan M Y, Jiang W Q, Tao L, et al. 2024. Migration of confined micro-swimmers subject to anisotropic diffusion. Journal of Fluid Mechanics, 985: A44. doi: 10.1017/jfm.2024.349 [74] Guan M Y, Jiang W, Wang B, et al. 2023. Pre-asymptotic dispersion of active particles through a vertical pipe: The origin of hydrodynamic focusing. Journal of Fluid Mechanics, 962: A14. doi: 10.1017/jfm.2023.273 [75] Guan M Y, Zeng L, Jiang W, et al. 2022. Effects of wind on transient dispersion of active particles in a free-surface wetland flow. Communications in Nonlinear Science and Numerical Simulation, 115: 106766. doi: 10.1016/j.cnsns.2022.106766 [76] Guan M Y, Zeng L, Li C, et al. 2021. Transport model of active particles in a tidal wetland flow. Journal of Hydrology, 593: 125812. doi: 10.1016/j.jhydrol.2020.125812 [77] Guo R, Yang Y. 2026. Enhancing the heat-transfer rate by inhomogeneous porous boundary in turbulent convection. Journal of Fluid Mechanics, 1028: R1. doi: 10.1017/jfm.2026.11127 [78] Haber S, Mauri R. 1988. Lagrangian approach to time-dependent laminar dispersion in rectangular conduits. Part 1. Two-dimensional flows. Journal of Fluid Mechanics, 190: 201-215. doi: 10.1017/s0022112088001284 [79] Hamed A M, Sadowski M J, Nepf H M, et al. 2017. Impact of height heterogeneity on canopy turbulence. Journal of Fluid Mechanics, 813: 1176-1196. doi: 10.1017/jfm.2017.22 [80] Hill J, Kalkanci O, McMurry J L, et al. 2007. Hydrodynamic surface interactions enable Escherichia coli to seek efficient routes to swim upstream. Physical Review Letters, 98: 068101. doi: 10.1103/PhysRevLett.98.068101 [81] Hill N A, Bees M A. 2002. Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow. Physics of Fluids, 14: 2598-2605. doi: 10.1063/1.1458003 [82] Hill N A, Pedley T J. 2005. Bioconvection. Fluid Dynamics Research, 37: 1-20. doi: 10.1127/algol_stud/77/1995/67 [83] Hong J, Wu H, Zhang R, et al. 2020. The coupling of Taylor dispersion analysis and mass spectrometry to differentiate protein conformations. Analytical Chemistry, 92: 5200-5206. doi: 10.1021/acs.analchem.9b05745 [84] Houseworth J E. 1984. Shear dispersion and residence time for laminar flow in capillary tubes. Journal of Fluid Mechanics, 142: 289-308. doi: 10.1017/S0022112084001117 [85] Howse J R, Jones R A L, Ryan A J, et al. 2007. Self-motile colloidal particles: From directed propulsion to random walk. Physical Review Letters, 99: 048102. doi: 10.1103/PhysRevLett.99.048102 [86] Ishikawa T. 2025. Transport phenomena in microswimmer suspensions: Migration, collective motion, diffusion and rheology. Journal of Fluid Mechanics, 1016: P1. doi: 10.1017/jfm.2025.10388 [87] Ishikawa T, Hota M. 2006. Interaction of two swimming Paramecia. Journal of Experimental Biology, 209: 4452-4463. doi: 10.1242/jeb.02537 [88] Ishikawa T, Pedley T J. 2014. Dispersion of model microorganisms swimming in a nonuniform suspension. Physical Review E, 90: 033008. doi: 10.1103/PhysRevE.90.033008 [89] Jiang W, Chen G. 2018. Solution of Gill’s generalized dispersion model: Solute transport in Poiseuille flow with wall absorption. International Journal of Heat and Mass Transfer, 127: 34-43. doi: 10.1016/j.ijheatmasstransfer.2018.07.003 [90] Jiang W, Chen G. 2019. Dispersion of active particles in confined unidirectional flows. Journal of Fluid Mechanics, 877: 1-34. doi: 10.1017/jfm.2019.562 [91] Jiang W, Chen G. 2021. Transient dispersion process of active particles. Journal of Fluid Mechanics, 927: A11. doi: 10.1017/jfm.2021.747 [92] Jiang W, Zeng L, Fu X, et al. 2022. Analytical solutions for reactive shear dispersion with boundary adsorption and desorption. Journal of Fluid Mechanics, 947: A37. doi: 10.1017/jfm.2022.656 [93] Kessler J O. 1984. Gyrotactic buoyant convection and spontaneous pattern formation in algal cell cultures. Nonequilibrium Cooperative Phenomena in Physics and Related Fields, 116. Boston, MA: Springer US: 241-248 [94] Kessler J O. 1985a. Hydrodynamic focusing of motile algal cells. Nature, 313: 218-220. doi: 10.1038/313218a0 [95] Kessler J O. 1985b. Co-operative and concentrative phenomena of swimming micro-organisms. Contemporary Physics, 26: 147-166. doi: 10.1080/00107518508210745 [96] Kheifets S, Simha A, Melin K, et al. 2014. Observation of Brownian motion in liquids at short times: Instantaneous velocity and memory loss. Science, 343: 1493-1496. doi: 10.1126/science.1248091 [97] Kim S, Karrila S J. 2005. Microhydrodynamics: Principles and selected applications. Boston: Courier Corporation [98] Koch D L, Subramanian G. 2011. Collective hydrodynamics of swimming microorganisms: Living fluids. Annual Review of Fluid Mechanics, 43: 637-659. doi: 10.1146/annurev-fluid-121108-145434 [99] Landers F C, Hertle L, Pustovalov V, et al. 2025. Clinically ready magnetic microrobots for targeted therapies. Science, 390: 710-715. doi: 10.1126/science.adx1708 [100] Lauga E. 2011a. Enhanced diffusion by reciprocal swimming. Physical Review Letters, 106: 178101. doi: 10.1103/PhysRevLett.106.178101 [101] Lauga E. 2011b. Life around the scallop theorem. Soft Matter, 7: 3060-3065. doi: 10.1039/C0SM00953A [102] Lauga E. 2016. Bacterial hydrodynamics. Annual Review of Fluid Mechanics, 48: 105-130. doi: 10.1146/annurev-fluid-122414-034606 [103] Lauga E. 2020. The fluid dynamics of cell motility. Cambridge: Cambridge University Press. [104] Leahy B D, Cheng X, Ong D C, et al. 2013. Enhancing rotational diffusion using oscillatory shear. Physical Review Letters, 110: 228301. doi: 10.1103/PhysRevLett.110.228301 [105] Leahy B D, Koch D L, Cohen I. 2015. The effect of shear flow on the rotational diffusion of a single axisymmetric particle. Journal of Fluid Mechanics, 772: 42-79. doi: 10.1017/jfm.2015.186 [106] Li G, Tang J X. 2009. Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion. Physical Review Letters, 103: 078101. doi: 10.1103/PhysRevLett.103.078101 [107] Lighthill M J. 1966. Initial development of diffusion in poiseuille flow. Journal of the Institute of Mathematics and its Applications, 2: 97-108. doi: 10.1093/imamat/2.1.97 [108] Liu Y, Wang P. 2024. Drag in vegetation canopy: Considering sheltering and blockage effects. Water Resources Research, 60: e2023WR036521. doi: 10.1029/2023WR036521 [109] Ma L, Wang F, Yu Y, et al. 2018. Cu removal and response mechanisms of periphytic biofilms in a tubular bioreactor. Bioresource Technology, 248: 61-67. doi: 10.1016/j.biortech.2017.07.014 [110] Manela A, Frankel I. 2003. Generalized Taylor dispersion in suspensions of gyrotactic swimming micro-organisms. Journal of Fluid Mechanics, 490: 99-127. doi: 10.1017/s0022112003005147 [111] Marchetti M C, Joanny J F, Ramaswamy S, et al. 2013. Hydrodynamics of soft active matter. Reviews of Modern Physics, 85: 1143-1189. doi: 10.1103/RevModPhys.85.1143 [112] Mei C C, Auriault J L, Ng C O. 1996. Some applications of the homogenization theory. Advances in Applied Mechanic, 32: 277-348. [113] Mei C C, Vernescu B. 2010. Homogenization methods for multiscale mechanics. Hackensack, NJ, USA: World Scientific. [114] Mercer G N, Roberts A J. 1990. A centre manifold description of contaminant dispersion in channels with varying flow properties. SIAM Journal on Applied Mathematics, 50: 1547-1565. doi: 10.1137/0150091 [115] Michelin S. 2023. Self-propulsion of chemically active droplets. Annual Review of Fluid Mechanics, 55: 77-101. doi: 10.1146/annurev-fluid-120720-012204 [116] Moser M R, Baker C A. 2021. Taylor dispersion analysis in fused silica capillaries: A tutorial review. Analytical Methods, 13: 2357-2373. doi: 10.1039/D1AY00588J [117] Nagata M. 2025. Spiral vortex flows of the counter-rotating Taylor–Couette system in the narrow-gap limit. Journal of Fluid Mechanics, 1020: A53. doi: 10.1017/jfm.2025.10676 [118] Nakad M, Witelski T, Domec J C, et al. 2021. Taylor dispersion in osmotically driven laminar flows in phloem. Journal of Fluid Mechanics, 913: A44. doi: 10.1017/jfm.2021.56 [119] Nepf H M. 2012. Flow and transport in regions with aquatic vegetation. Annual Review of Fluid Mechanics, 44: 123-142. doi: 10.1146/annurev-fluid-120710-101048 [120] Ng C O. 2006a. Dispersion in open-channel flow subject to the processes of sorptive exchange on the bottom and air–water exchange on the free surface. Fluid Dynamics Research, 38: 359-385. doi: 10.1016/j.fluiddyn.2006.02.002 [121] Ng C O. 2006b. Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462: 481-515. doi: 10.1098/rspa.2005.1582 [122] Pasmanter R A. 1985. Exact and approximate solutions of the convection-diffusion equation. The Quarterly Journal of Mechanics and Applied Mathematics, 38: 1-26. [123] Pavliotis G A, Stuart A M. 2008. Multiscale methods: Averaging and homogenization. New York: Springer. [124] Pedley T J, Kessler J O. 1987. The orientation of spheroidal microorganisms swimming in a flow field. Proceedings of the Royal Society of London B: Biological Sciences, 231: 47-70. doi: 10.1098/rspb.1987.0035 [125] Pedley T J, Kessler J O. 1990. A new continuum model for suspensions of gyrotactic micro-organisms. Journal of Fluid Mechanics, 212: 155. doi: 10.1017/S0022112090001914 [126] Pedley T J, Kessler J O. 1992. Hydrodynamic phenomena in suspensions of swimming microorganisms. Annual Review of Fluid Mechanics, 24: 313-358. doi: 10.1146/annurev.fl.24.010192.001525 [127] Peng Z. 2024. Rotational Taylor dispersion in linear flows. Journal of Fluid Mechanics, 997: A10. doi: 10.1017/jfm.2024.856 [128] Peng Z, Brady J F. 2020. Upstream swimming and Taylor dispersion of active Brownian particles. Physical Review Fluids, 5: 073102. doi: 10.1103/PhysRevFluids.5.073102 [129] Phillips C G, Kaye S R. 1997. The initial transient of concentration during the development of Taylor dispersion. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 453: 2669-2688. doi: 10.1098/rspa.1997.0142 [130] Polin M, Tuval I, Drescher K, et al. 2009. Chlamydomonas swims with two “gears” in a eukaryotic version of run-and-tumble locomotion. Science, 325: 487-490. doi: 10.1126/science.1172667 [131] Pope S. 2001. Turbulent flows. Cambridge: Cambridge University Press. [132] Purcell E M. 1997. The efficiency of propulsion by a rotating flagellum. Proceedings of the National Academy of Sciences, 94: 11307-11311. [133] Rai P K, Lee J, Brown R J C, et al. 2021. Micro- and nano-plastic pollution: Behavior, microbial ecology, and remediation technologies. Journal of Cleaner Production, 291: 125240. doi: 10.1016/j.jclepro.2020.125240 [134] Rothschild L. 1963. Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature, 198: 1221-1222. doi: 10.1038/1981221a0 [135] Rusconi R, Guasto J S, Stocker R. 2014. Bacterial transport suppressed by fluid shear. Nature Physics, 10: 212-217. doi: 10.1038/nphys2883 [136] Saffman P G. 1960. On the effect of the molecular diffusivity in turbulent diffusion. Journal of Fluid Mechanics, 8: 273-283. doi: 10.1017/S0022112060000591 [137] Saintillan D, Shelley M J. 2008. Instabilities and pattern formation in active particle suspensions: Kinetic theory and continuum simulations. Physical Review Letters, 100: 178103. doi: 10.1103/PhysRevLett.100.178103 [138] Shaik V A, Peng Z, Brady J F, et al. 2023. Confined active matter in external fields. Soft Matter, 19: 1384-1392. doi: 10.1039/D2SM01135B [139] Smith R. 1981. A delay-diffusion description for contaminant dispersion. Journal of Fluid Mechanics, 105: 469-486. doi: 10.1017/S0022112081003297 [140] Smith R. 1982. Gaussian approximation for contaminant dispersion. The Quarterly Journal of Mechanics and Applied Mathematics, 35: 345-366. doi: 10.1093/qjmam/35.3.345 [141] Sokolov A, Aranson I S. 2016. Rapid expulsion of microswimmers by a vortical flow. Nature Communications, 7: 11114. doi: 10.1038/ncomms11114 [142] Squires T M, Quake S R. 2005. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 77: 977-1026. [143] Stokes A N, Barton N G. 1990. The concentration distribution produced by shear dispersion of solute in Poiseuille flow. Journal of Fluid Mechanics, 210: 201-221. doi: 10.1017/s0022112090001264 [144] Squires T M, Quake S R. 2005. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 77: 977-1026. [145] Stone H A, Brenner H. 1999. Dispersion in flows with streamwise variations of mean velocity: Radial flow. Industrial & Engineering Chemistry Research, 38: 851-854. doi: 10.1021/ie980355f [146] Stone H A, Stroock A D, Ajdari A. 2004. Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annual Review of Fluid Mechanics, 36: 381-411. doi: 10.1146/annurev.fluid.36.050802.122124 [147] Stroock A D, Dertinger S K W, Ajdari A, et al. 2002. Chaotic mixer for microchannels. Science, 295: 647-651. doi: 10.1126/science.1066238 [148] Taghizadeh E, Valdés-Parada F J, Wood B D. 2020. Preasymptotic Taylor dispersion: Evolution from the initial condition. Journal of Fluid Mechanics, 889: A5. doi: 10.1017/jfm.2020.56 [149] Takatori S C, Yan W, Brady J F. 2014. Swim pressure: Stress generation in active matter. Physical Review Letters, 113: 028103. doi: 10.1103/PhysRevLett.113.028103 [150] Tanasijević I, Lauga E. 2022. Microswimmers in vortices: Dynamics and trapping. Soft Matter, 18: 8931-8944. doi: 10.1039/D2SM00907B [151] Tanino Y, Nepf H M. 2008. Lateral dispersion in random cylinder arrays at high Reynolds number. Journal of Fluid Mechanics, 600: 339-371. doi: 10.1017/S0022112008000505 [152] Taylor G I. 1953. Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 219: 186-203. doi: 10.1098/rspa.1953.0139 [153] Taylor G I. 1954a. Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 225: 473-477. doi: 10.1098/rspa.1954.0216 [154] Taylor G I. 1954b. The dispersion of matter in turbulent flow through a pipe. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 223: 446-468. doi: 10.1098/rspa.1954.0130 [155] Teague J M, Ding L, Bernardi F. 2025. Adapting Taylor dispersion to measure the dispersion coefficient of electrolyte solutions via an accessible microfluidic setup. Journal of Visualized Experiments, 224: e69040. doi: 10.3791/69040 [156] Théry A, Chamolly A, Lauga E. 2024. Controlling confined collective organization with taxis. Physical Review Letters, 132: 108301. doi: 10.1103/PhysRevLett.132.108301 [157] Toschi F, Bodenschatz E. 2009. Lagrangian properties of particles in turbulence. Annual Review of Fluid Mechanics, 41: 375-404. doi: 10.1146/annurev.fluid.010908.165210 [158] Townsend C T, Yee L, Mercer W A. 1954. Inhibition of the growth of Clostridium botulinum by acidification. Journal of Food Science, 19: 536-542. doi: 10.1111/j.1365-2621.1954.tb17486.x [159] Vilquin A, Bertin V, Raphaël E, et al. 2023. Nanoparticle Taylor dispersion near charged surfaces with an open boundary. Physical Review Letters, 130: 038201. doi: 10.1103/PhysRevLett.130.038201 [160] Vilquin A, Bertin V, Soulard P, et al. 2021. Time dependence of advection-diffusion coupling for nanoparticle ensembles. Physical Review Fluids, 6: 064201. doi: 10.1103/PhysRevFluids.6.064201 [161] Voth G A, Soldati A. 2017. Anisotropic particles in turbulence. Annual Review of Fluid Mechanics, 49: 249-276. doi: 10.1146/annurev-fluid-010816-060135 [162] Wang B, Jiang W, Chen G. 2022. Gyrotactic trapping of micro-swimmers in simple shear flows: A study directly from the fundamental Smoluchowski equation. Journal of Fluid Mechanics, 939: A37. doi: 10.1017/jfm.2022.231 [163] Wang B, Jiang W, Zeng L, et al. 2025a. Buoyancy–flow coupled dispersion of active spheroids in a vertical pipe: Effects of elongation and settling. Journal of Fluid Mechanics, 1007: A67. doi: 10.1017/jfm.2025.181 [164] Wang B, Jiang W, Zeng L, et al. 2025b. Taylor–Aris dispersion of active particles in oscillatory channel flows. Journal of Fluid Mechanics, 1021: A3. doi: 10.1017/jfm.2025.10700 [165] Wang P, Chen G. 2017. Basic characteristics of Taylor dispersion in a laminar tube flow with wall absorption: Exchange rate, advection velocity, dispersivity, skewness and kurtosis in their full time dependence. International Journal of Heat and Mass Transfer, 109: 844-852. doi: 10.1016/j.ijheatmasstransfer.2017.02.051 [166] Wang P, Cirpka O A. 2021. Surface transient storage under low-flow conditions in streams with rough bathymetry. Water Resources Research, 57: e2021WR029899. doi: 10.1029/2021WR029899 [167] Williams C R, Bees M A. 2011. Photo-gyrotactic bioconvection. Journal of Fluid Mechanics, 678: 41-86. doi: 10.1017/jfm.2011.100 [168] Woodhouse F G, Dunkel J. 2017. Active matter logic for autonomous microfluidics. Nature Communications, 8: 15169. doi: 10.1038/ncomms15169 [169] Wu Z, Chen G. 2014. Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe. Journal of Fluid Mechanics, 740: 196-213. doi: 10.1017/jfm.2013.648 [170] Wu Z, Furbish D, Foufoula-Georgiou E. 2020. Generalization of hop distance-time scaling and particle velocity distributions via a two-regime formalism of bedload particle motions. Water Resources Research, 56: e2019WR025116. doi: 10.1029/2019WR025116 [171] Xia H, Francois N, Punzmann H, et al. 2013. Lagrangian scale of particle dispersion in turbulence. Nature Communications, 4: 2013. doi: 10.1038/ncomms3013 [172] Yan W, Brady J F. 2015. The force on a boundary in active matter. Journal of Fluid Mechanics, 785: R1. doi: 10.1017/jfm.2015.621 [173] Yang Q, Jiang M, Picano F, et al. 2024. Shaping active matter from crystalline solids to active turbulence. Nature Communications, 15: 2874. doi: 10.1038/s41467-024-46520-4 [174] Yasuda H. 1984. Longitudinal dispersion of matter due to the shear effect of steady and oscillatory currents. Journal of Fluid Mechanics, 148: 383-403. doi: 10.1017/S0022112084002391 [175] Young W R, Jones S. 1991. Shear dispersion. Physics of Fluids A: Fluid Dynamics, 3: 1087-1101. doi: 10.1063/1.858090 [176] Zeng H, Jiang W, Guan M, et al. 2025. Dispersion of confined microswimmers with diffuse reflection boundary condition: Asymptotic and transient solutions. Journal of Fluid Mechanics, 1018: A27. doi: 10.1017/jfm.2025.10521 [177] Zeng L, Pedley T J. 2018. Distribution of gyrotactic micro-organisms in complex three-dimensional flows. Part 1. Horizontal shear flow past a vertical circular cylinder. Journal of Fluid Mechanics, 852: 358-397. doi: 10.1017/jfm.2018.494 [178] Zeng L, Jiang W, Pedley T J. 2022. Sharp turns and gyrotaxis modulate surface accumulation of microorganisms. Proceedings of the National Academy of Sciences, 119: e2206738119. doi: 10.1073/pnas.2206738119 [179] Zhang L, Hesse M A, Wang M. 2017. Transient solute transport with sorption in Poiseuille flow. Journal of Fluid Mechanics, 828: 733-752. doi: 10.1017/jfm.2017.546 [180] Zhang Y, Cheng J, Hassan M A, et al. 2024. Drag coefficient of emergent vegetation in a shallow nonuniform flow over a mobile sand bed. Water Resources Research, 60: e2023WR036535. doi: 10.1029/2023WR036535 [181] Zöttl A, Stark H. 2023. Modeling active colloids: From active brownian particles to hydrodynamic and chemical fields. Annual Review of Condensed Matter Physics, 14: 109-127. doi: 10.1146/annurev-conmatphys-040821-115500 -
下载:
图(8) / 表(1)
计量
- 文章访问数: 164
- HTML全文浏览量: 43
- PDF下载量: 32
- 被引次数: 0