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We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force. We consider gently engineered sinusoidal patterns with small slopes. Three dimensionless parameters govern the system: a speed, and the amplitude and wavelength of the pattern. Using numerical solutions of the Reynolds lubrication equation, we investigate the effects of these dimensionless parameters on key variables such as contact pressure and the coefficient of friction of the lubricated system. For small pattern amplitudes, the coefficient of friction increases with the amplitude. However, our findings reveal that increasing pattern amplitude beyond a critical value can decrease the friction coefficient, a result that contradicts conventional intuition and classical studies on the lubrication of rigid surfaces. For very large amplitudes, we show that the coefficient of friction drops even below the corresponding smooth case. We support these observations with a combination of perturbation theory and physical arguments, identifying scaling laws for large and small speeds, and for large and small pattern amplitudes. This study provides a quantitative understanding of friction in the contact of soft, wet objects and lays theoretical foundations for incorporating the friction coefficient into haptic feedback systems in soft robotics and haptic engineering. 

We study the coupling between rotation and translation of a submerged cylinder in lubricated contact with a soft elastic substrate. Using numerical solutions and asymptotic theory, we analyze the elastohydrodynamic problem over the entire range of substrate deformations relative to the thickness of the intervening fluid film. We find a strong coupling between the rotation and translation of the cylinder when the surface deformation of the substrate is comparable to the thickness of the lubricating fluid layer. In the limit of large deformations, we show that the bodies are in near-Hertzian contact and cylinder rolls without slip, reminiscent of dry frictional contact. When the surface deformation is small relative to the separation between the surfaces, the coupling persists but is weaker, and the rotation rate scales with the translation speed to the one-third power. We then show how the external application of a torque modifies these behaviors by generating different combinations of rotational and translational motions, including back-spinning and top-spinning states. We demonstrate that these behaviors are robust regardless of whether the elastic substrate is thick or thin relative to the length scales of the flow.