Revisiting the supplementary relationship of dynamic contact angles measured by sessile-droplet and captive-bubble methods: Role of surface roughness

Abstract

Hypothesis: Quantitative characterization of surface wettability through contact angle (CA) measurement using the sessile droplet (SD) or captive bubble (CB) methods is often limited by the intrinsic wetting properties of the substrate. Situations may arise when an extreme surface wettability may preclude using one of the two methods for predicting the behaviors of droplets or bubbles on the surface. This warrants a relationship between the dynamic CAs measured via the SD and CB methods. While the two dynamic CAs (e.g., the advancing CA of SD and receding CA of CB) add up to 180° on a smooth surface, the simple geometric supplementary principle may not apply for rough surfaces.Experiments: We perform a systematic wettability characterization of solid substrates with varying degrees of roughness using the sessile-droplet and captive-bubble methods, and interpret the experimental observations using a theoretical model.Findings: The dynamic contact angles measured by the sessile-droplet and captive-bubble methods deviate from the supplementary principle as the surface roughness is increased. We present a theoretical explanation for this disparity and predict the values of the contact angles using prevalent thermodynamic models of wetting and contact-angle hysteresis on rough substrates. The theoretical prediction is in good agreement with the experimental observations.