Reciprocal locomotion of dense swimmers in Stokes flow
Reciprocal locomotion of dense swimmers in Stokes flow
复制标题
斯托克斯流中密集游泳者的往复运动
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
E. Lauga
中科院分区：
文献类型：
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作者：
David Gonzalez;E. Lauga
由于斯托克斯流的运动学可逆性，执行往复运动的物体（在时间反演下物体构型序列保持相同的运动）不能在可忽略惯性的极限下在粘性流体中推进自身;这个结果被称为珀塞尔的扇形定理。在此极限下，基于流体惯性和物体惯性的雷诺数均为零。以前的研究特征的扇贝定理的故障与流体惯性。在本文中，我们表明，即使在没有流体惯性，某些密集的机构进行往复运动能够游泳。利用洛仑兹的互等定理，我们首先推导出一般的微分方程，支配密集游泳运动学。我们证明，没有往复游泳是可能的，如果身体运动只包括切向表面变形（蠕动）。然后，我们应用我们的一般公式来计算运动的四个简单的游泳者，每个具有不同的空间不对称性，执行正常的表面变形。我们表明，由此产生的游泳速度（或旋转速率）的规模作为一个正确定义的“游泳者雷诺数”的第一个权力，从而展示了连续故障的扇贝定理与身体惯性。
Due to the kinematic reversibility of Stokes flow, a body executing a reciprocal motion (a motion in which the sequence of body configurations remains identical under time reversal) cannot propel itself in a viscous fluid in the limit of negligible inertia; this result is known as Purcell’s scallop theorem. In this limit, the Reynolds numbers based on the fluid inertia and on the body inertia are all zero. Previous studies characterized the breakdown of the scallop theorem with fluid inertia. In this paper we show that, even in the absence of fluid inertia, certain dense bodies undergoing reciprocal motion are able to swim. Using Lorentz’s reciprocal theorem, we first derive the general differential equations that govern the locomotion kinematics of a dense swimmer. We demonstrate that no reciprocal swimming is possible if the body motion consists only of tangential surface deformation (squirming). We then apply our general formulation to compute the locomotion of four simple swimmers, each with a different spatial asymmetry, that perform normal surface deformations. We show that the resulting swimming speeds (or rotation rates) scale as the first power of a properly defined ‘swimmer Reynolds number’, demonstrating thereby a continuous breakdown of the scallop theorem with body inertia.