Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall
Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall
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DOI：
10.1137/100808745
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发表时间：
2011-01-01
影响因子：
2.1
通讯作者：
Murray, Richard M.
中科院分区：
文献类型：
--
作者：
Or, Yizhar;Zhang, Sebastian;Murray, Richard M.
微生物和微小人工游泳者的运动受低雷诺数流体动力学控制，其中粘性效应占主导地位，惯性效应可以忽略不计。虽然低雷诺数运动理论在无界流体域中已经得到了很好的研究，但边界的存在对游泳者的运动轨迹有重大影响，并对其运动的动态稳定性提出了问题。本文考虑了一个简单的壁上微游泳者的理论模型，研究了其动力学，并分析了其运动的稳定性。我们强调了动力学的基本几何结构，并建立了系统的反转对称性与近壁运动周期解和稳态解的存在性和稳定性之间的关系。数值模拟和大尺度游泳机器人原型的运动实验验证了上述结果。
The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer's trajectories and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with macroscale robotic swimmer prototypes.