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/ β that can be interpreted as a normalized sliding velocity. Solving this fundamental soft-lubrication problem poses significant computational difficulty for large β , 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 β . Scaling laws for these relationships are given in closed form for a range of β not previously accessible theoretically but that is typical in applications. The computational method presented here can be used to study other soft lubrication problems.
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- Award ID(s):
- 1854572
- NSF-PAR ID:
- 10181558
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 16
- Issue:
- 11
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 2760 to 2773
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
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.more » « less
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Zinc dialkyldithiophosphate (ZDDP), the most widely used antiwear additive in engine oils, has been extensively studied over the last few decades to help understand the origin of its effectiveness. Glassy phosphate-based tribofilms, approximately 100 nm thick, are often formed on surfaces sliding in ZDDP-containing oils, which help to prevent or reduce wear. Recent studies reveal that a combination of applied shear and compressive stresses drive mechanochemical reactions that promote tribofilm growth, and that growth is further accelerated by increased temperature. While recent work has shown that compressive stress alone is insufficient to form tribofilms, the individual effects of the shear stress and compressive stress are not fully understood. Here, shear and compressive stresses are studied separately by using different ratios of high-viscosity, high-traction fluids for testing. This allows the areal mean compressive and shear stresses in the fluid when confined at a loaded sliding interface, to be independently controlled while driving tribofilm growth, which is a system we refer to as a stress-controlled mechanochemical reactor. Tribofilms derived from a secondary ZDDP were generated using a tungsten carbide/tungsten carbide ball-on-disk contact in the full elastohydrodynamic lubrication (EHL) regime using a mini-traction machine (MTM), meaning that solid–solid contact is avoided. The MTM was equipped with a spacer layer imaging (SLIM) capability, permitting in situ measurement of the tribofilm thickness during its growth. The well-separated sliding surfaces generated by the high-viscosity fluids confirm that solid–solid contact is not required for tribofilm formation. Under these full fluid film EHL conditions, shear stress and temperature promote tribofilm growth in accordance with stress-augmented thermal activation. In contrast, under constant shear stress and temperature, compressive stress has the opposite effect, inhibiting tribofilm growth. Using the extended Eyring model for shear- and hydrostatic pressure-affected reaction kinetics, an activation energy of 0.54 ± 0.04 eV is found, consistent with prior studies of ZDDPs. The activation volume for shear stress is found to be 0.18 ± 0.06 nm 3 , while that for the compressive stress component is much smaller, at 0.010 ± 0.004 nm 3 . This not only confirms prior work supporting that shear stress drives tribofilm growth, but demonstrates and quantifies how compressive stress inhibits growth, consistent with the rate-limiting step in tribofilm growth involving a bond-breaking reaction. Implications of these findings are discussed.more » « less
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An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically uses iteration techniques. A difficulty with iteration schemes is that convergence becomes increasingly difficult under increasingly heavy loads. Here we devise a numerical scheme that does not involve iteration. Instead, a linear problem is solved at every time step. The scheme is fully automatic, stable and efficient. We illustrate this technique by solving a relaxation test in which a rigid spherical indenter is brought rapidly into normal contact with a thick elastic substrate lubricated by a liquid film. The sphere is then fixed in position as the pressure relaxes. We also carried out relaxation experiments on a lubricated soft PDMS (polydimethysiloxane) substrate under different conditions. These experiments are in excellent agreement with the numerical solution.more » « less
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Abstract While many mechanistic studies have focused on the lubricious properties of ionic liquids (ILs) on ideally smooth surfaces, little is known about the mechanisms by which ILs lubricate contacts with nanoscale roughness. Here, substrates with controlled density of nanoparticles are prepared to examine the influence of nanoscale roughness on the lubrication by 1‐hexyl‐3‐methyl imidazolium bis(trifluoromethylsulfonyl)imide. Atomic force microscopy is employed to investigate adhesion, hydrodynamic slip, and friction at the lubricated contact as a function of surface topography for the first time. This study reveals that nanoscale roughness has a significant influence on the slip along the surface and leads to a maximum slip length on the substrates with intermediate nanoparticle density. This coincides with the minimum friction coefficient at sufficiently small contact stresses, likely due to the lower resistance of the IL film to shear. However, at the higher pressures applied with a sharp tip, friction increases with nanoparticle density, indicating that the IL is not able to alleviate the increased dissipation due to roughness. The results of this work point toward a complex influence of the surface topology on friction. This study can help design ILs and nanopatterned substrates for tribological applications and nano‐ and microfluidics.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C9SM02447F
