Nonlinear dynamics of a thin liquid film on an axially oscillating cylindrical surface subjected to double-frequency forcing.
Nonlinear dynamics of a thin liquid film on an axially oscillating cylindrical surface subjected to double-frequency forcing.
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DOI：
10.1063/1.3327932
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发表时间：
2010-03
期刊：
影响因子：
--
通讯作者：
Ory Haimovich;A. Oron
中科院分区：
文献类型：
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作者：
Ory Haimovich;A. Oron
本文研究了水平圆柱形衬底上的轴对称薄液膜在不同振幅和频率的两分量的轴向双频强迫和可能的相移作用下的非线性动力学。导出了薄膜界面在长波极限下的时空动力学非线性演化方程。与我们早期工作中考虑的单频强迫的情况类似，存在一个临界强迫振幅，低于该振幅，薄膜经历一个长时间的毛细管破裂，这是静态圆柱体的典型特征，而高于该振幅，薄膜保持连续。我们发现，即使两个分量中的每一个的强迫参数分别对应于发生破裂的区域，也有可能阻止破裂。结果表明，当两个强迫频率相等时，单频情况下的临界强迫幅值很容易确定。在不同强迫幅值和频率的情况下，临界强迫幅值随频率比的变化表现出一种独特的特征，即出现峰值。本文还讨论了调幅单频强迫的一个相关情况。对于足够小的调幅频率，可以观察到图案幅度的显著增加。在强迫频率相等的情况下，发现流动是准周期的。
The nonlinear dynamics of a thin axisymmetric liquid film on a horizontal cylindrical substrate subjected to an axial double-frequency forcing that consists of two components of different amplitudes and frequencies and a possible phase shift is considered in this paper. A nonlinear evolution equation governing the spatiotemporal dynamics of the film interface has been derived in the long-wave limit. Similar to the case of a single-frequency forcing considered in our earlier work, there exists a critical forcing amplitude below which the film undergoes a long-time capillary rupture typical for a static cylinder, whereas above it the film remains continuous. We find that it is possible to arrest the rupture even if the forcing parameters of each of the two components correspond separately to the domain where rupture takes place. It is shown that the critical forcing amplitude is easily determined via a single-frequency case when the two forcing frequencies are equal. In the case of different forcing amplitudes and frequencies, the variation of the critical forcing amplitude as a function of the frequency ratio exhibits a unique behavior displaying the emergence of spikes. A related case of an amplitude-modulated single-frequency forcing is also addressed here. For a sufficiently small frequency of the amplitude modulation, a significant increase of the pattern amplitude is observed. In the case of commensurate forcing frequencies, the flow is found to be quasiperiodic.