Similarity solutions for van der Waals rupture of a thin film on a solid substrate
Similarity solutions for van der Waals rupture of a thin film on a solid substrate
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固体基底上薄膜范德华破裂的相似解
DOI：
10.1063/1.870110
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发表时间：
1999
影响因子：
4.6
通讯作者：
J. Lister
中科院分区：
文献类型：
--
作者：
Wendy W. Zhang;J. Lister
在不稳定的货车德瓦尔斯压力和稳定的毛细管压力的平衡下，固体基底上的薄粘性膜的破裂被证明具有可数无穷多个相似解，其中每个解的水平长度尺度减小如（tR−t）2/5，膜厚度减小如（tR−t）1/5，其中tR−t是破裂前剩余的时间。在控制偏微分方程的时间相关数值模拟中，只观察到对应于最小振荡曲率轮廓的自相似解。从相似方程的远场渐近分析出发，提出了求解自相似解的数值方法。
Rupture of a thin viscous film on a solid substrate under a balance of destabilizing van der Waals pressure and stabilizing capillary pressure is shown to possess a countably infinite number of similarity solutions in each of which the horizontal lengthscale decreases like (tR−t)2/5 and the film thickness decreases like (tR−t)1/5, where tR−t is the time remaining before rupture. Only the self-similar solution corresponding to the least oscillatory curvature profile is observed in time-dependent numerical simulations of the governing partial differential equation. The numerical strategy employed to obtain the self-similar solutions is developed from far-field asymptotic analysis of the similarity equations.