Dynamics of liquid nanofilms

TL;DR

This paper investigates the dynamics of liquid nanofilms considering van der Waals forces and disjoining pressure, deriving evolution equations for film thickness beyond traditional Navier-Stokes models.

Contribution

It introduces a new framework using disjoining pressure and a density-dependent free energy functional to model nanofilm dynamics, extending beyond classical fluid mechanics.

Findings

Derived an evolution equation for nanofilm thickness considering disjoining pressure.

Showed the limitations of Navier-Stokes equations for nanofilm flows.

Established a variational principle-based approach for nanofilm dynamics.

Abstract

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.