Effective sliding friction of lubricated soft patterned surfaces

Recent work on the wet sliding contact of soft robotic fingers showed that the Stribeck curve (coefficient of friction versus dimensionless sliding speed) for patterned surfaces is non-monotonic (Peng et.al, 2021, Nat. Mater.). The elastohydrodynamic flows underlying this non-trivial behavior are only partly understood. In this work, we develop a modeling framework for the lubricated contact of locally patterned but globally flat surfaces. We solve the resulting system of integrodifferential equations numerically for a wide range of geometrical parameters characterizing the surface patterns. Additionally, we investigate the effects of properties of the entrained fluid layer and soft solid on the Stribeck curve. In the limit of small sliding speeds, when the fluid film is thin, the lubrication flow observes each asperity as a separate degenerate contact. At the other extreme, where the fluid film is thicker than the typical depth of the asperity, the entire patterned surface can be approximated by a nearly flat surface with a small roughness. We find analytic results for the coefficient of friction in both limits using the method of multiple scales, and show them to be in agreement with our numerical predictions. By explaining the quantitative behavior of friction in the contact of soft wet objects, this work can pave the way for encoding friction coefficient into haptic signals in robotic and haptic engineering.