A new type of instability: explosive disturbances in a liquid film inside a rotating horizontal cylinder
A new type of instability: explosive disturbances in a liquid film inside a rotating horizontal cylinder
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一种新型的不稳定性：旋转水平圆柱体内液膜中的爆炸性扰动
DOI：
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发表时间：
2003
影响因子：
3.7
通讯作者：
I. Sazonov
中科院分区：
文献类型：
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作者：
E. Benilov;S. O'Brien;I. Sazonov
我们研究了在有水平轴的圆柱体的内表面上的粘性流体薄膜的动力学，绕着这个轴旋转。导出了一个渐近方程，该方程考虑了所谓的两阶润滑近似。该方程有一个解，描述了膜在圆柱体周围的稳态分布，并检验了该解的稳定性。证明了线性化问题允许无穷多个谐波解，它们都具有实频率（中性稳定）。另一方面，也有在有限时间内“爆炸”（发展出奇点）的非调和解。在文献中从未描述过同时具有两种类型解的系统。这一现象的一个例子是本文的主要结论。
We examine the dynamics of a thin film of viscous fluid on the inside surface of a cylinder with horizontal axis, rotating around this axis. An asymptotic equation is derived, which takes into account two orders of the so-called lubrication approximation. The equation admits a solution describing a steady-state distribution of film around the cylinder, and we examine the stability of this solution. It is demonstrated that the linearized problem admits infinitely many harmonic solutions, all of which have real frequencies (are neutrally stable). On the other hand, there are non-harmonic solutions that ‘explode’ (develop singularities) in a finite time. Systems having solutions of both types simultaneously have never been described in the literature. An example of this phenomenon is the main result of this paper.