A model for contact angle hysteresis

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.