We investigate the relationship between the metachronal wavelength of an array of beating cilia and the resulting fluid flow rate through numerical simulations. Our model is based on a hybrid immersed boundary lattice Boltzmann algorithm. Our results suggest that varying the metachronal wavelength of the cilium array affects the fluid flow rate by increasing or decreasing the spread of cilia during their active strokes. We quantify this behaviour by constructing an analytical model of the system and deriving an equation for free area within the cilium array that depends on the metachronal wavelength. We show that there is a strong correlation between free area and fluid flow rate that holds for different values of cilium spacing.

中文翻译：

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纤毛跳动的机制：量化异时波长与流体流速之间的关系

我们通过数值模拟研究了跳动纤毛阵列的异时波长与由此产生的流体流速之间的关系。我们的模型基于混合浸入式边界晶格 Boltzmann 算法。我们的结果表明，改变纤毛阵列的异时波长会通过增加或减少纤毛在主动中风期间的扩散来影响流体流速。我们通过构建系统的分析模型并推导出纤毛阵列内取决于异时波长的自由区域的方程来量化这种行为。我们表明自由面积和流体流速之间存在很强的相关性，适用于不同的纤毛间距值。