Unsteady spreading of thin liquid films with small surface tension
Unsteady spreading of thin liquid films with small surface tension
复制标题
DOI：
10.1063/1.858006
复制
发表时间：
1991-05
影响因子：
4.6
通讯作者：
J. Moriarty;L. Schwartz;E. Tuck
中科院分区：
文献类型：
--
作者：
J. Moriarty;L. Schwartz;E. Tuck
本文用匹配渐近展开法求解了重力作用下沿垂直壁面流下的薄液滴的自由液面。分析是基于润滑方程中的表面张力项很小。在液滴前部的局部区域中，其中表面曲率大，表面张力显著。在其他地方，表面曲率很小，表面张力的作用可以忽略不计。一个数值时间推进方案，它没有小的表面张力假设，提供了一个基准，从它来衡量小表面张力理论的准确性。对于较小的表面张力值，数值方案与小表面张力理论之间的一致性良好。此外，还讨论了通过旋转和用空气射流吹来扩展液滴的传播。结果表明，所有三种传播机制之间有内在的相似之处。
The method of matched asymptotic expansions is used to solve for the free surface of a thin liquid drop draining down a vertical wall under gravity. The analysis is based on the smallness of the surface tension term in the lubrication equation. In a region local to the front of the drop, where the surface curvature is large, surface tension forces are significant. Everywhere else, the surface curvature is small, and surface tension plays a negligible role. A numerical time‐marching scheme, which makes no small surface tension assumptions, is developed to provide a datum from which to gauge the accuracy of the small surface tension theory. Agreement between the numerical scheme and the small surface tension theory is good for small values of surface tension. Extension to the propagation of drops by spinning and by blowing with a jet of air is also discussed. It is shown that there are inherent similarities between all three spreading mechanisms.