A new methodology for measuring solid/liquid interfacial energy

Abstract

Hypothesis

The interfacial energy ${\gamma }_{\mathrm{sl}}$ between a solid and a liquid designates the affinity between these two phases, and in turn, the macroscopic wettability of the surface by the fluid. This property is needed for precise control of fluid-transport phenomena that affect the operation/quality of commercial devices/products. Although several indirect or theoretical approaches can quantify the solid/liquid interfacial energy, no direct experimental procedure exists to measure this property for realistic (i.e. rough) surfaces. Makkonen hypothesized that the frictional resistance force per unit contact-line length is equal to the interfacial energy on smooth surfaces, which, however, are rarely found in practice. Consequently, the hypothesis that Makkonen’s assumption may also hold for rough surfaces (which are far more common in practice) arises naturally. If so, a reliable and simple experimental methodology of obtaining ${\gamma }_{\mathrm{sl}}$ for rough surfaces can be put forth. This is accomplished by performing dynamic contact-angle experiments on rough surfaces that quantify the relationship between the frictional resistance force per unit contact-line length acting on an advancing liquid ($F_{p,a}$) and the surface roughness in wetting configurations.

Experiment

We perform static and advancing contact-line experiments with aqueous and organic liquids on different hydrophilic surfaces (Al, Cu, Si) with varying Wenzel roughnesses in the range 1-2. These parameters are combined with the liquid’s known surface tension to determine $F_{p,a}$.

Findings

$F_{p,a}$ rises linearly with the surface roughness. Analysis based on existing theories of wetting and contact-angle hysteresis reveals that the slope of $F_{p,a}$ vs. Wenzel roughness is equal to the solid/liquid interfacial energy, which is thus determined experimentally with the present measurements. Interfacial energies obtained with this experimental approach are within 12% of theoretically predicted values for several solid/liquid pairs, thereby validating this methodology.