液体纳米膜动力学
Dynamics of liquid nanofilms
摘要：
范德华力穿过与平面固体壁接触的非常薄的液体层（纳米膜）使液体不均匀。在等温条件下，研究了这种扁平液体纳米膜的动力学行为。纳维-斯托克斯方程不能描述非常薄的薄膜中的流体运动。分离气体和液体层的尖锐界面的表面自由能的概念是不合格的。分离压力的概念取代了表面能模型。在纳米膜中，补充自由能必须被认为是密度的函数。流体沿纳米膜的运动方程是通过Hamilton变分原理通过在润滑近似中向保守力添加粘性力而获得的。推导了考虑分离压力沿膜层变化的膜厚演化方程。
英文摘要：
The van der Waals forces across a very thin liquid layer (nanofilm) in contact with a plane solid wall make the liquid nonhomogeneous. The dynamics of such flat liquid nanofilms is studied in isothermal case. The Navier-Stokes equations are unable to describe fluid motions in very thin films. The notion of surface free energy of a sharp interface separating gas and liquid layer is disqualified. The concept of disjoining pressure replaces the model of surface energy. In the nanofilm a supplementary free energy must be considered as a functional of the density. The equation of fluid motions along the nanofilm is obtained through the Hamilton variational principle by adding, to the conservative forces, the forces of viscosity in lubrication approximation. The evolution equation of the film thickness is deduced and takes into account the variation of the disjoining pressure along the layer.
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