Pedley T J, Brumley D R, Goldstein R E
Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Centre for Mathematical Sciences , Wilberforce Road , Cambridge CB3 0WA , UK.
Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093 Zurich, Switzerland.
J Fluid Mech. 2016 Jul 10;798:165-186. doi: 10.1017/jfm.2016.306. Epub 2016 May 31.
Colonies of the green alga are spheres that swim through the beating of pairs of flagella on their surface somatic cells. The somatic cells themselves are mounted rigidly in a polymeric extracellular matrix, fixing the orientation of the flagella so that they beat approximately in a meridional plane, with axis of symmetry in the swimming direction, but with a roughly [Formula: see text] azimuthal offset which results in the eponymous rotation of the colonies about a body-fixed axis. Experiments on colonies of held stationary on a micropipette show that the beating pattern takes the form of a symplectic metachronal wave (Brumley , vol. 109, 2012, 268102). Here we extend the Lighthill/Blake axisymmetric, Stokes-flow model of a free-swimming spherical squirmer (Lighthill , vol. 5, 1952, pp. 109-118; Blake , vol. 46, 1971, pp. 199-208) to include azimuthal swirl. The measured kinematics of the metachronal wave for 60 different colonies are used to calculate the coefficients in the eigenfunction expansions and hence predict the mean swimming speeds and rotation rates, proportional to the square of the beating amplitude, as functions of colony radius. As a test of the squirmer model, the results are compared with measurements (Drescher , vol. 102, 2009, 168101) of the mean swimming speeds and angular velocities of a different set of 220 colonies, also given as functions of colony radius. The predicted variation with radius is qualitatively correct, but the model underestimates both the mean swimming speed and the mean angular velocity unless the amplitude of the flagellar beat is taken to be larger than previously thought. The reasons for this discrepancy are discussed.
绿藻群体呈球形，通过其表面体细胞上成对鞭毛的摆动在水中游动。体细胞本身牢固地固定在聚合的细胞外基质中，从而固定鞭毛的方向，使它们大致在子午面内摆动，对称轴沿游动方向，但有大约[公式：见原文]的方位角偏移，这导致群体绕身体固定轴进行同名旋转。对固定在微量移液器上的群体进行的实验表明，其摆动模式呈辛异时波形式（布鲁姆利，第109卷，2012年，268102）。在此，我们扩展了自由游动球形蠕动者的莱特希尔/布莱克轴对称斯托克斯流模型（莱特希尔，第5卷，1952年，第109 - 118页；布莱克，第46卷，1971年，第199 - 208页），以纳入方位角涡旋。利用对60个不同群体异时波的测量运动学数据来计算本征函数展开式中的系数，进而预测与摆动幅度平方成正比的平均游动速度和旋转速率，作为群体半径的函数。作为对蠕动者模型的检验，将结果与另一组220个群体的平均游动速度和角速度的测量值（德雷舍尔，第102卷，2009年，168101）进行比较，这些测量值同样表示为群体半径的函数。预测的随半径的变化在定性上是正确的，但该模型低估了平均游动速度和平均角速度，除非将鞭毛摆动的幅度设定得比先前认为的更大。本文讨论了这种差异的原因。
