A pair of adjacent beating flagella can be synchronized via hydrodynamic interactions at low Reynolds numbers. Here, we investigate the factors that determine the relaxation time for elastohydrodynamic synchronization by using the phase reduction theory. The results show that the relaxation time is determined primarily by the natural frequency of a flagellum as well as the coupling intensity between the two flagella. After rescaling with both the natural frequency and the coupling intensity, the relaxation curves are found to be close to each other. This indicates that the number of beatings required for elastohydrodynamic synchronization remains almost unchanged regardless of the waveforms under a common coupling intensity.

一对相邻的跳动鞭毛可以在低雷诺数下通过流体动力相互作用而同步。在这里，我们使用相减理论研究确定弹性流体动力同步弛豫时间的因素。结果表明，松弛时间主要由鞭毛的固有频率以及两个鞭毛之间的耦合强度决定。在用自然频率和耦合强度重新缩放后，发现松弛曲线彼此接近。这表明弹性流体动力同步所需的跳动次数几乎保持不变，而不管在共同耦合强度下的波形如何。