Two-dimensional pulse dynamics and the formation of bound states on electrified falling films
Two-dimensional pulse dynamics and the formation of bound states on electrified falling films
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DOI：
10.1017/jfm.2018.592
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发表时间：
2017-06
影响因子：
3.7
通讯作者：
M. Blyth;D. Tseluiko;Te-Sheng Lin;S. Kalliadasis
中科院分区：
文献类型：
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作者：
M. Blyth;D. Tseluiko;Te-Sheng Lin;S. Kalliadasis
本文研究了带电液膜沿斜面壁的流动，重点研究了液膜表面以行波形式存在的相干结构，特别是单峰孤立脉冲及其相互作用。本文首先采用长波模型对流场结构进行了分析，该模型在存在弱惯性的情况下是有效的，其次采用斯托克斯方程对流场结构进行了分析。对于钝角，引力是不稳定的，即使在没有电场的情况下也存在孤脉冲。对于锐角，空间非均匀解只存在于电场强度的临界值之外；此外，孤立脉冲解只有在足够高的超临界电场强度下才存在。电场增加了脉冲的振幅，可以在峰中产生再循环区，并改变脉冲尾部的远场衰减从指数衰减到代数衰减，对脉冲相互作用有重要影响。弱相互作用理论预测了非带电流的束缚态解的无限序列和带电流的有限集。通过边界元计算，证实了Stokes方程的单峰脉冲解和双脉冲边界态的存在性。此外，电场显示触发从绝对不稳定到对流不稳定的转换，从而使动力学正则化，这是由长波模型的时间相关模拟证实的。
The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.