Swimming efficiency of spherical squirmers: Beyond the Lighthill theory
Swimming efficiency of spherical squirmers: Beyond the Lighthill theory
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DOI：
10.1103/physreve.90.012704
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发表时间：
2014-07-17
影响因子：
2.4
通讯作者：
Gaffney, Eamonn A.
中科院分区：
文献类型：
--
作者：
Ishimoto, Kenta;Gaffney, Eamonn A.
非可逆的形状变形可以驱动无惯性的细胞游泳，正如泰勒和莱特希尔在20世纪50年代首次探索的那样，分别用于平面和球面的小幅蠕动。特别是莱特希尔的蠕动器，已经在纤毛微生物的背景下广泛研究了大的波数。小振幅平面蠕动运动的最大功率效率的特点和退化，与非唯一的最佳游泳行程。我们明确表明，这种简并保留在高波数的小振幅球形蠕动，如纤毛微生物，但打破低波数。因此，进一步的复杂性出现在参数制度以外的纤毛虫游泳，即使在小幅度。大幅度蠕动也是最近观察到的驱动眼虫、中性粒细胞和盘基网柄藻运动的大幅度/低波数膜变形的特征。因此，边界元数值方法被用来探索游泳的变形幅度增加，特别是在功率效率和游泳性能的背景下。随着径向蠕动振幅的增加，即使名义上的低变形振幅，小振幅线性化理论也可能是不可靠的。此外，即使是一个简单的单模异时波，一个高度能动的和有效的大变形/小波数游泳的方式出现，这可以超越纯粹的切向蠕动给定的约束表面变形速度的理论限制。
Nonreciprocal shape deformations can drive inertialess cellular swimming, as first explored by Taylor and Lighthill in the 1950s, for the small-amplitude squirming of a planar and a spherical surface, respectively. Lighthill's squirmer, in particular, has been extensively studied for large wave numbers in the context of ciliated microbes. The maximal power efficiency for small-amplitude planar squirming motility is well characterized and degenerate, with nonunique optimal swimming strokes. We explicitly show that this degeneracy is retained at high wave numbers for the small-amplitude spherical squirmer such as a ciliated microbe but is broken for low wave numbers. Hence further complexity emerges in parameter regimes outside that of ciliate swimming even at small amplitudes. Large-amplitude squirming also characterizes more recent observations of large-amplitude/low-wave-number membrane deformations driving the motility of Euglena, neutrophils, and Dictyostelium discoideum. Thus boundary element numerical methods are used to explore swimming with increased deformation amplitudes, especially in the context of power efficiency and swimming performance. As radial squirming amplitudes are increased, small-amplitude linearized theories can be unreliable even for nominally low deformation amplitudes. Furthermore, even for a simple single-mode metachronal wave, a highly motile and efficient large-deformation/small-wave-number swimming modality arises, which can surpass theoretical limitations of purely tangential squirming given a constrained surface deformation velocity.