Influence of Surface Roughness on Lubricated Contact of Soft Surfaces

The Stribeck curve, which measures the coefficient of friction against the dimensionless sliding speed, is notably different for patterned surfaces compared with smooth surfaces (Peng et.al, 2021, Nat. Mater.). The elastohydrodynamic flow behind this observation is not entirely understood. Here, we introduce a model for the lubricated contact of soft surfaces that are locally patterned but globally cylindrical. We solve the resulting system of equations numerically for various geometrical parameters that characterize the surface patterns. Additionally, we examine how the properties of the fluid layer and the soft solid affect the Stribeck curve. At low sliding speeds, where the fluid film is thin, the lubricated flow treats each asperity as a distinct degenerate contact. Conversely, at high sliding speeds, where the fluid film is thicker than the typical depth of the asperity, the entire patterned surface can be approximated as a smooth parabola. Using the method of multiple scales and perturbation analysis, we obtain an analytical solution for the coefficient of friction at high sliding speeds and demonstrate its consistency with our numerical results. This study offers a quantitative understanding of friction in the contact of soft wet objects and lays the groundwork for incorporating the friction coefficient into haptic signals in robotics and haptic engineering.