Wetting at Curved Substrates: Non-Analytic Behavior of Interfacial Properties

TL;DR

This paper demonstrates that the interfacial properties during complete wetting on curved substrates exhibit non-analytic behavior in the inverse of the curvature, with implications for solvation of solvophobic particles.

Contribution

It reveals the non-analytic dependence of wall-fluid surface tension and density profiles on substrate curvature during complete wetting, supported by density functional calculations.

Findings

Wall-fluid surface tension is non-analytic in curvature inverse.

Density profile includes a term proportional to surface tension times curvature inverse.

Results confirmed by density functional calculations for model liquids.

Abstract

We argue that for complete wetting at a curved substrate (wall) the wall-fluid surface tension is non-analytic in $R_i^{-1}$, the curvature of the wall and that the density profile of the fluid near the wall acquires a contribution proportional to the gas-liquid surface tension $\times R_i^{-1}$ plus higher-order contributions which are non-analytic in $R_i^{-1}$. These predictions are confirmed by results of density functional calculations for the square-well model of a liquid adsorbed on a hard sphere and on a hard cylinder where complete wetting by gas (drying) occurs. The implications of our results for the solvation of big solvophobic particles are discussed.