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先驱膜的连续流体动力学模型

The characteristic of precursor film in Navier-Stokes equations frame

  • 摘要: 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, vander 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 derWaals)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.

     

    Abstract: This paper studies a model for a fluid lumpspreading with a precursor film. In the description, the fluid lump and theprecursor film are calculated as a whole using order parameter coupledNavier-Stokes equations, CHW (Cahn, Hilliard and van der Waales) equationand GNBC (Generalized Navier boundary condition). The fluid lump spreads underthe actions of certain long-range force -VW (van der Waals) intermolecularlong-range force, surface tension and viscous force. A film of nanoscopicthickness emerges as VW force reaches a certain value. The profile of thefilm after spreading a long time approaches to 1/x power law, which agreeswell with the theoretical results of Ref.1. The frontal position of thefilm is found to has a power-law dependence on time, which is also shown inthe results of some experiments6. The interfacial stretching has apower-law dependence on time as well. The exponent of the later is a littlebigger than that of the former.

     

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