Model of a liquid nanofilm on a solid substrate based on the van der Waals concept of capillarity.
Van der Waals attractive forces drastically change the material properties of thin liquid layers several nanometers when in contact with a solid. At this scale, the fluid is no longer homogeneous. Moreover, it has properties which are analogous to those of solids. In particular, in equilibrium the stress tensor is no longer spherical. For such fluids, we use a long-wave approximation to derive the evolution of a liquid nanofilm on a substrate. We establish that the driving pressure in the nanofilm should be associated with the mean value of the component of the pressure tensor tangential to the liquid interface (along the substrate). Finally, we derive the equation for nanofilm dynamics by using a mass conservation formulation. This is not a conventional, conservative equation for the position of the free surface normally used in the theory of thick films where the density is homogeneous, but rather a conservative equation for the liquid mass. The equation turns out to be a nonlinear parabolic equation with a diffusion coefficient of a "good" sign.
Gavrilyuk
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CNRS UMR 6595, IUSTI, Project SMASH, 5 rue E. Fermi, 13453 Marseille Cedex 13, France. sergey.gavrilyuk@polytech.univ-mrs.fr
Akhatov
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