Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK.
J R Soc Interface. 2013 Feb 13;10(81):20121041. doi: 10.1098/rsif.2012.1041. Print 2013 Apr 6.
Shear flow significantly affects the transport of swimming algae in suspension. For example, viscous and gravitational torques bias bottom-heavy cells to swim towards regions of downwelling fluid (gyrotaxis). It is necessary to understand how such biases affect algal dispersion in natural and industrial flows, especially in view of growing interest in algal photobioreactors. Motivated by this, we here study the dispersion of gyrotactic algae in laminar and turbulent channel flows using direct numerical simulation (DNS) and a previously published analytical swimming dispersion theory. Time-resolved dispersion measures are evaluated as functions of the Péclet and Reynolds numbers in upwelling and downwelling flows. For laminar flows, DNS results are compared with theory using competing descriptions of biased swimming cells in shear flow. Excellent agreement is found for predictions that employ generalized Taylor dispersion. The results highlight peculiarities of gyrotactic swimmer dispersion relative to passive tracers. In laminar downwelling flow the cell distribution drifts in excess of the mean flow, increasing in magnitude with Péclet number. The cell effective axial diffusivity increases and decreases with Péclet number (for tracers it merely increases). In turbulent flows, gyrotactic effects are weaker, but discernable and manifested as non-zero drift. These results should have a significant impact on photobioreactor design.
剪切流对悬浮游动藻类的输运有显著影响。例如，粘性和重力扭矩使底部较重的细胞偏向于向下流动的区域（旋泳）。有必要了解这种偏差如何影响自然和工业流动中的藻类分散，特别是考虑到人们对藻类光生物反应器的兴趣日益增加。受此启发，我们使用直接数值模拟 (DNS) 和先前发表的分析游动分散理论，研究了旋泳藻类在层流和湍流通道流中的分散情况。将时变分散测量值作为上涌和下涌流动中的佩克莱特数和雷诺数的函数进行评估。对于层流，将 DNS 结果与使用剪切流中偏向游动细胞的竞争描述的理论进行比较。使用广义泰勒分散的预测结果非常吻合。结果突出了旋泳游动者相对于被动示踪剂的分散特殊性。在层流下降流中，细胞分布漂移超过平均流，随着佩克莱特数的增加而增加。细胞有效轴向扩散系数随佩克莱特数增加而增加，随佩克莱特数减少而减少（对于示踪剂，它仅随佩克莱特数增加而增加）。在湍流中，旋泳效应较弱，但可察觉，并表现为非零漂移。这些结果应该对光生物反应器的设计有重大影响。
