Dynamics of a treadmilling microswimmer near a no-slip wall in sample shear
Dynamics of a treadmilling microswimmer near a no-slip wall in sample shear
复制标题
DOI：
10.1017/jfm.2017.220
复制
发表时间：
2017-06-25
影响因子：
3.7
通讯作者：
Crowdy, Darren G.
中科院分区：
文献类型：
--
作者：
Ishimoto, Kenta;Crowdy, Darren G.
流动的诱导通常用于控制微游泳者在诸如微通道的受限系统中的迁移。游泳者的运动，一般来说，是由非线性方程，由于非平凡的流体动力学之间的相互作用的流动和游泳者附近的墙壁。本文将Stokes流的功的互等定理与圆柱体近壁拖曳问题的精确解相结合，导出了无滑移壁面附近受简单剪切作用的圆形铣削游动体运动方程的解析表达式。我们证明了约化动力系统具有一个Hamilton结构，我们用它来表明，游泳者不能在一个恒定的距离从一个墙壁，但只能表现出周期性的振荡运动沿着壁，或从它逃脱。一个最低的两个cummilling模式的cummilling游泳者通过约化动力系统的分支分析进行了详细的研究。有人发现，振荡运动的游泳方向澄清的符号的哈密顿量在没有流动，和诱导的流动抑制上游迁移，但在下游迁移对齐游泳者的取向。这些结果可以为微生物和微型机器的运输和控制策略提供信息。
Induction of flow is commonly used to control the migration of a microswimmer in a confined system such as a microchannel. The motion of a swimmer, in general, is governed by nonlinear equations due to non-trivial hydrodynamic interactions between the flow and the swimmer near a wall. This paper derives analytical expressions for the equations of motion governing a circular treadmilling swimmer in simple shear near a no-slip wall by combining the reciprocal theorem for Stokes flow with an exact solution for the dragging problem of a cylinder near a wall. We demonstrate that the reduced dynamical system possesses a Hamiltonian structure, which we use to show that the swimmer cannot migrate stably at a constant distance from a wall but only exhibit periodic oscillatory motion along the wall, or to escape from it. A treadmilling swimmer with the lowest two treadmilling modes is investigated in detail by means of a bifurcation analysis of the reduced dynamical system. It is found that the swimming direction of oscillatory motion is clarified by the sign of the Hamiltonian in the absence of flow, and that the induction of the flow suppresses upstream migration but aligns swimmer orientations in downstream migration. These results could inform strategies for the transport and control of micro-organisms and micromachines.