Instabilities and bifurcations of liquid films flowing down a rotating fibre
Instabilities and bifurcations of liquid films flowing down a rotating fibre
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沿着旋转纤维流动的液膜的不稳定性和分叉
DOI：
10.1017/jfm.2020.441
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发表时间：
2020-07
影响因子：
3.7
通讯作者：
Ding Zijing
中科院分区：
文献类型：
--
作者：
Liu Rong;Ding Zijing
本文研究了绕其轴旋转的垂直纤维涂层的重力驱动流动力学。这种流动表现出丰富的动力学，包括珠状结构的形成和由重力和旋转作用下的瑞利高原机制驱动的不同类型的稳定或振荡行波。线性稳定性表明，当旋转较慢时，轴对称模态占主导地位，这使得我们可以推导出长波假设下的二维模型方程。然后利用模型方程研究了时空动力学和非线性波动解。时空稳定性分析表明，旋转增强了绝对不稳定性。在模型方程的数值模拟中观察到稳态行波态和相对周期态，表明旋转倾向于抑制相对周期态的形成。为了验证这一点，对稳定行波进行了线性稳定性分析，表明旋转对稳定行波有稳定作用。这一结果不利于旋转对初始均匀薄膜线性稳定性的破坏作用。分岔分析表明，相对周期态是由定常行波的不稳定性产生的，它代表了一个大液滴和一系列小得多的液滴之间的聚并和破裂过程。
Abstract We consider the dynamics of a gravity-driven flow coating a vertical fibre rotating about its axis. This flow exhibits rich dynamics including the formation of bead-like structures and different types of steady or oscillatory travelling waves driven by a Rayleigh–Plateau mechanism modified by the presence of gravity and rotation. Linear stability shows that the axisymmetric mode dominates the instability when the rotation is slow, which allows us to derive a two-dimensional model equation under the long-wave assumption. The spatio-temporal dynamics and nonlinear wave solutions are then investigated by the model equation. The spatio-temporal stability analysis showed that the absolute instability is enhanced by the rotation. Steady travelling-wave states and relative periodic states are observed in the numerical simulations of the model equation, which show that the rotation tends to suppress the formation of relative periodic states. To examine this, a linear stability analysis of steady travelling waves is performed, indicating that the rotation has a stabilizing effect on the steady travelling waves. This result is adverse to the destabilizing effect of rotation on the linear stability of initially uniform films. A bifurcation analysis shows that the relative periodic state is born from the instability of steady travelling wave, which represents the coalescence and breakup process between a large droplet and a serial of much smaller droplets.
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