Complete Wetting of Pits and Grooves

TL;DR

This paper investigates the complete wetting behavior of volatile fluids on structured substrates with various geometries using a density functional theory approach, revealing covariance relations and scaling laws near phase coexistence.

Contribution

It introduces a microscopic density functional theory-based analysis of wetting on patterned surfaces, highlighting covariance relations and effective scaling regimes for different geometries.

Findings

Center cavity film thicknesses follow a covariance relation.

Lateral average film thicknesses do not obey covariance.

Deep cavities exhibit a power-law scaling with exponent -1/3.

Abstract

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: (i) one-dimensional periodic arrays of rectangular or parabolic grooves and (ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.