The transition from Elasto-Hydrodynamic to Mixed Regimes in Lubricated Friction of Soft Solid Surfaces.

Lubricated contacts in soft materials are common in various engineering and natural settings, such as tires, haptic applications, contact lenses, and the fabrication of soft electronic devices. Two major regimes are elasto-hydrodynamic lubrication (EHL), in which solid surfaces are fully separated by a fluid film, and mixed lubrication (ML), in which there is partial solid-to-solid contact. The transition between these regimes governs the minimum sliding friction achievable and is thus very important. Generally, the transition from EHL to ML regimes is believed to occur when the thickness of the lubricant layer is comparable with the amplitude of surface roughness. Here, it is reported that in lubricated sliding experiments on smooth, soft, poly(dimethylsiloxane) substrates, the transition can occur when the thickness of the liquid layer is much larger than the height of the asperities. Direct visualization of the "contact" region shows that the transition corresponds to the formation of wave-like surface wrinkles at the leading contact edge and associated instabilities at the trailing contact edge, which are believed to trigger the transition to the mixed regime. These results change the understanding of what governs the important EHL-ML transition in the lubricated sliding of soft solids.

Lubricated steady sliding of a rigid sphere on a soft elastic substrate: hydrodynamic friction in the Hertz limit.

Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings. It very often occurs in the iso-viscous elasto-hydrodynamic lubrication (EHL) regime (e.g., soft solid, low pressure). In this regime, for sliding of a smooth sphere on a soft solid, a "Hertz-like" effective contact region forms. Much of the fluid is squeezed out of the contact region although enough is retained to keep the solid surfaces fully separated. This is accompanied by complex deformation of the soft solid. The behavior of such soft lubricated contacts is controlled by a single dimensionless parameter 1/ß that can be interpreted as a normalized sliding velocity. Solving this fundamental soft-lubrication problem poses significant computational difficulty for large ß, which is the limit relevant for soft solids. As a consequence, little is known about the structure of the flow field under soft lubrication in the intake and outlet regions. Here we present a new solution of this soft lubrication problem focusing on the "Hertz" limit. We develop a formulation in polar coordinates that handles difficult computational issues much better than previous methods. We study how hydrodynamic pressure, film thickness and hydrodynamic friction vary with ß. Scaling laws for these relationships are given in closed form for a range of ß not previously accessible theoretically but that is typical in applications. The computational method presented here can be used to study other soft lubrication problems.

Enhancement of elastohydrodynamic friction by elastic hysteresis in a periodic structure.

Lubricated contacts are present in many engineering and biological systems involving soft solids. Typical mechanisms considered for controlling the sliding friction in such lubricated conditions involve bulk material compliance, fluid viscosity, viscoelastic response of the material (hysteretic friction), and breaking of the fluid film where dry contact occurs (adhesive friction). In this work we show that a two-phase periodic structure (TPPS), with a varying modulus across the sliding surface, provides significant enhancement of lubricated sliding friction when the system is in the elastohydrodynamic lubrication (EHL) regime. We propose that the enhanced friction is due to extra energy loss during periodic transitions of the sliding indenter between the compliant and stiff regions during which excess energy is dissipated through the fluid layer. This is a form of elastic hysteresis that provides a novel mechanism for friction enhancement in soft solids under lubricated conditions.

Indentation versus Rolling: Dependence of Adhesion on Contact Geometry for Biomimetic Structures.

Numerous biomimetic structures made from elastomeric materials have been developed to produce enhancement in properties such as adhesion, static friction, and sliding friction. As a property, one expects adhesion to be represented by an energy per unit area that is usually sensitive to the combination of shear and normal stresses at the crack front but is otherwise dependent only on the two elastic materials that meet at the interface. More specifically, one would expect that adhesion measured by indentation (a popular and convenient technique) could be used to predict adhesion hysteresis in the more practically important rolling geometry. Previously, a structure with a film-terminated fibrillar geometry exhibited dramatic enhancement of adhesion by a crack-trapping mechanism during indentation with a rigid sphere. Roughly isotropic structures such as the fibrillar geometry show a strong correlation between adhesion enhancement in indentation versus adhesion hysteresis in rolling. However, anisotropic structures, such as a film-terminated ridge-channel geometry, surprisingly show a dramatic divergence between adhesion measured by indentation versus rolling. We study this experimentally and theoretically, first comparing the adhesion of the anisotropic ridge-channel structure to the roughly isotropic fibrillar structure during indentation with a rigid sphere, where only the isotropic structure shows adhesion enhancement. Second, we examine in more detail the anomalous anisotropic film-terminated ridge-channel structure during indentation with a rigid sphere versus rolling to show why these structures show a dramatic adhesion enhancement for the rolling case and no adhesion enhancement for indentation.