A model for contact angle hysteresis

TLDR

The study examines liquid wetting on solid surfaces with small but finite equilibrium contact angles, considering flat chemically heterogeneous or rough substrates. The authors propose testing the derived contact angle formulas through controlled surface contamination. They analyze a single localized defect to show two stable contact line positions via a simple graphic construction, then extend the analysis to a dilute defect system to derive formulas for advancing and receding contact angles based on defect strength and sharpness. They find that weak heterogeneities produce no hysteresis but a wiggly contact line, whereas stronger heterogeneities generate hysteresis once defect strength exceeds a threshold.

Abstract

We discuss the behavior of a liquid partially wetting a solid surface, when the contact angle at equilibrium θ0 is small, but finite. The solid is assumed to be either flat, but chemically heterogeneous (this in turn modulating the interfacial tensions), or rough. For weak heterogeneities, we expect no hysteresis, but the contact line becomes wiggly. For stronger heterogeneities, we first discuss the behavior of the contact line in the presence of a single, localized defect, and show that there may exist two stable positions for the line, obtained by a simple graphic construction. Hysteresis shows up when the strength of the defect is above a certain threshold. Extending this to a dilute system of defects, we obtain formulas for the ‘‘advancing’’ and ‘‘receding’’ contact angles θa, θr, in terms of the distribution of defect strength and defect sharpness. These formulas might be tested by controlled contamination of a solid surface.