先驱膜的连续流体动力学模型

CONTINUUM HYDRODYNAMIC MODEL OF A PRECURSOR FILM

研究具有先驱膜的流体团扩散的模型．流体团和先驱膜作为一个整体用与组分序参数耦合的Navier- Stokes方程,CHW(Cahn,Hilliard,van der Waales)方程和GNBC(广义Navier边界条件)进行数值模拟和分析．流体团在VW(van der Waals)分子长程力和表面张力以及黏性力的共同作用下开始扩散,纳米尺度厚的先驱膜在VW力达到一定值时缓慢生成,它的长时间演变的剖面形状表现为与理论结果一致的1/x次律．膜的前沿——接触线随时间演变具有幂次律,这种对时间的依赖关系也在实验结果(Leger,1984)中得出．分界面的相对拉伸对时间也具有幂次相似律,但幂次指数比前者要稍微大一点．

This paper studies a model for a fluid lump spreading with a precursor film. In the description, the fluid lump and the precursor film are calculated as a whole using order parameter coupled Navier-Stokes equations, CHW （Cahn, Hilliard and van der Waales） equation and GNBC （Generalized Navier boundary condi- tion）. The fluid lump spreads under the actions of certain long-range force -VW （van der Waals） intermolecular long-range force, surface tension and viscous force. A film of nanoscopic thickness emerges as VW force reaches a certain wlue. The profile of the film after spreading a long time approaches to 1/x power law, which agrees well with the theoretical results of Ref.[1]. The frontal position of the film is found to has a power-law dependence on time, which is also shown in the results of some experiments[6]. The interfacial stretching has a power-law dependence on time as well. The exponent of the later is a little bigger than that of the former.