Elastic contact between rough surfaces: Bridging the gap between theory and experiment

Friction is generated where solids touch, thus quantitative understanding of the microscopic contact area is crucial to predict macroscopic friction. All surfaces are rough, and typically small-scale roughness rather than macroscopic geometry sets the contact area. Rough contact theories have been developed that predict the contact area, using the surface topography and the mechanical properties of the solids as input. However, the validity of these theories remains under debate. Systematic comparison between theory and experiment has been lacking, due to the experimental difficulty to access the contact area, especially at small length scales where idealised assumptions of contact models may not hold. Here, we use a state-of-the-art fluorescence microscopy technique to directly access the contact area of a glass-glass contact with nanometric out-of-plane resolution. We systematically vary the roughness of the contact and carefully measure the surface topography across length scales. Comparison of high-resolution contact experiments to different contact theories enables us to unambigously conclude that only elastic Persson theory quantitatively describes experimental observations.