The Modeling of Thin Liquid Films Along Inclined Surfaces

Abstract

This paper is concerned with the analysis of thin and ultra-thin liquid films. The results are applicable to various geometrical and kinematic conditions, including both stationary and moving surfaces. The new results obtained in this work include: • the derivation of an analytical solution for the evolution of film thickness over the entire multiscale range, from the liquid free surface to the asymptotic (disjoining-pressure controlled) region, and for any surface inclination angle between 0 deg and 90 deg, • the formulation of a method to deduce the Hamaker constant based on a single measured value of film thickness at the beginning of the disjoining-pressure-controlled region, applicable to any inclination angle, • the explanation of the reasons why the thickness of liquid films on moving surfaces is normally beyond the range of Van der Waals forces, • the formulation of an expression for the nondimensional asymptotic film thickness as a function of the capillary number; this new result explicitly accounts for the effect of gravity on the average film velocity.