Hydrodynamic synchronization between objects with cyclic rigid trajectories
Hydrodynamic synchronization between objects with cyclic rigid trajectories
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DOI：
10.1140/epje/i2012-12135-5
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发表时间：
2012-12-01
影响因子：
1.8
通讯作者：
Golestanian, Ramin
中科院分区：
文献类型：
--
作者：
Uchida, Nariya;Golestanian, Ramin
由长程流体动力学相互作用引起的同步作为纤毛和鞭毛协调跳动背后的候选机制引起了人们的注意。在这里，我们考虑一个最小模型的流体动力学同步在低雷诺数限制。该模型由转子组成，每个转子被假定为在周期性变化的驱动力下形成固定轨迹的刚性珠。本文通过线性分析，导出了双转子同步的充要条件。我们还推导出一个非线性演化方程的相位差，这是减少到最小化的一个有效的潜力。计算了各种轨迹形状和几何形状（无论是散装或substrated）的有效电位，确定系统的稳定和亚稳态。有限大小的轨迹诱导的电位的不对称性，这也依赖于敏感的轨迹的倾斜。我们的研究结果表明，纤毛或鞭毛的灵活性是不是一个必要的同步运动，在以前的预期相反。我们讨论了直接实现该模型的可能性，并通过光驱动胶体验证了我们的结果。
Synchronization induced by long-range hydrodynamic interactions is attracting attention as a candidate mechanism behind coordinated beating of cilia and flagella. Here we consider a minimal model of hydrodynamic synchronization in the low Reynolds number limit. The model consists of rotors, each of which assumed to be a rigid bead making a fixed trajectory under periodically varying driving force. By a linear analysis, we derive the necessary and sufficient conditions for a pair of rotors to synchronize in phase. We also derive a non-linear evolution equation for their phase difference, which is reduced to minimization of an effective potential. The effective potential is calculated for a variety of trajectory shapes and geometries (either bulk or substrated), for which the stable and metastable states of the system are identified. Finite size of the trajectory induces asymmetry of the potential, which also depends sensitively on the tilt of the trajectory. Our results show that flexibility of cilia or flagella is not a requisite for their synchronized motion, in contrast to previous expectations. We discuss the possibility to directly implement the model and verify our results by optically driven colloids.