Empirical Analysis of Frictional Forces in Advancing and Receding Triple-Phase Contact Lines: Effect of Surface Roughness

Predicting the open-surface movement of liquids on solids requires a fundamental understanding of adhesion and the interplay of frictional forces at the moving contact line. Frictional forces are commonly studied in two main contexts: (1) static and kinetic friction acting on droplets subjected to lateral forces, and (2) resisting (frictional) forces opposing the motion of advancing or receding liquid contact lines on solid surfaces. While conventional studies assume identical advancing and receding frictional forces for any liquid–solid pair, recent studies have challenged this notion, emphasizing the need for deeper insight into these forces, especially when the solid is rough. This study employs sessile-droplet experiments for unpinned Wenzel (penetrating) states to quantify frictional forces at the triple-phase contact line, revealing an empirical relationship between frictional force ratio and surface roughness. Contact angle (CA) measurements at constant contact-line speeds under negligible viscous effects (Capillary number, Cα < <1) demonstrate that the advancing-to-receding friction force ratio scales solely with Wenzel roughness, being independent of liquid surface tension, viscosity, or chemical composition. This relationship enables accurate predictions of intrinsic CAs (<2% error) for wetting scenarios where experimental determination is challenging. The findings provide a predictive framework for characterizing new materials and their surface energies, while promoting the understanding and application of wetting dynamics on realistic (rough) surfaces.