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

A liquid film of thickness h<100 nmh<100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Π. Since Π   dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives Π=Π(h)Π=Π(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h→0h→0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of Π   that depends on the slope hxhx as well as the height h   of the film. When this theory is implemented for Lennard–Jones liquid films, the new Π=Π(h,hx)Π=Π(h,hx) is bounded near a contact line as h→0h→0. Thus, the singularity in Π(h)Π(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new Π 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 a precursor film is linearly stable.

Graphical abstractComputed drop profiles for different pressure difference C  . The critical value C1C1 gives a uniform film, whereas C2C2 yields a drop with an unbounded precursor film.Figure optionsDownload full-size imageDownload as PowerPoint slide