Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films.

A liquid film of thickness h $<$ 100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure $\Pi $. Since $\Pi $ dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives $\Pi =\Pi $(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h $\to $ 0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of $\Pi $ that depends on the slope $h_x $ as well as the height h of the film.[1] When this theory is implemented for Lennard-Jones liquid films, the new $\Pi $ = $\Pi $(h, $h_x )$ is bounded near a contact line as h $\to $ 0. Thus, the singularity in $\Pi $(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new $\Pi $ can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with an unbounded precursor film is linearly stable. \newline [1] Wu {\&} Wong, J. Fluid Mech. \underline {506}, 157 (2004)