Stability of Self-similar Solutions for Van der Waals Driven Thin Film Rupture
Stability of Self-similar Solutions for Van der Waals Driven Thin Film Rupture
复制标题
范德华驱动薄膜破裂自相似解的稳定性
DOI：
10.1063/1.870138
复制
发表时间：
1999
影响因子：
4.6
通讯作者：
A. Bernoff
中科院分区：
文献类型：
--
作者：
Thomas P. Witelski;A. Bernoff
最近对薄膜中丝的夹断和断裂的研究已经发现了无限组的第一类相似解。其中，动态稳定的相似解在流动模型中产生了作为局部有限时间奇点的可观测的破裂行为。在这封信中，我们描述了一种计算此类解并确定其线性稳定性的系统技术。对于最近由Zhang和Lister研究的轴对称van der Waals驱动破裂问题，我们证明了薄膜点破裂的唯一稳定相似解和对应于环形“环破裂”的另一种奇点形成模式。
Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”