An experimental procedure to quantify solid-liquid surface energy in wetting configurations

Wettability is correlated with the affinity between a solid and a liquid. Roughness is a primary factor affecting the wettability of a solid surface. When a droplet sitting on a surface is infused with more liquid (through a syringe or a small hole underneath the droplet), the droplet footprint begins to advance from its equilibrium position. During this motion, the droplet experiences a “pinning” force, analogous to the solid-solid frictional force, which opposes fluid motion; this force has its origins in the roughness of the surface. We perform experiments on different hydrophilic surfaces with varying degrees of topological roughness. We find that the pinning force during contact-line advancement increases linearly with surface roughness, and the slope of the line is equal to the surface energy between the solid and the liquid. This method reveals a new and simple way to predict the value of the solid-liquid surface energy for a wetting configuration.  The experimental findings are elucidated using well-known arguments from wetting theory and contact angle hysteresis.