An official website of the United States government
Abstract 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.
more »
« less
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.
more »
« less
- Award ID(s):
- 1854572
- 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
More Like this
-
-
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
-
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
-
Recent experiments reveal that adhesive interactions can play a key role in causing surface instability in soft lubrication. Instances of instability include fluid entrapment in isolated pockets upon a soft sphere’s normal contact with a hard substrate and surface wrinkling of a soft substrate as a hard sphere slides across it. These phenomena underscore a substantial distinction between hard and soft lubrication. They are of paramount importance from a fundamental standpoint, providing an entirely new explanation for the transition mechanism from elasto-hydrodynamic to the mixed lubrication regimes. Here, we introduce a new theory to elucidate these observations. Our theory modifies the Reynolds elasto-hydrodynamic equation by incorporating adhesive interaction across the fluid layer, investigating the interplay between adhesion, fluid flow and elastic instability. Our analysis proposes the addition of a new dimensionless parameter in lubrication theory, that compares the stiffness of the adhesive interaction to that of the substrate. When this parameter exceeds unity, the soft solid surface exhibits instability to small perturba- tions in its shape. In mathematical terms, the Reynolds equation undergoes a transition from a nonlinear diffusion equation to a nonlinear wave equation at this critical point. Post-transition, the diffusivity of the nonlinear diffusion equation turns negative, rendering the problem ill- posed. We investigate the transition using the method of characteristics and present an exact analytic solution. This solution offers insights into the occurrence of a vanishing liquid film thickness at specific locations, resulting in dry contact—initiating transition to mixed lubrication.more » « less
-
We report on viscous adhesion measurements conducted in sphere-plane geometry between a rigid sphere and soft surfaces submerged in silicone oils. Increasing the surface compliance leads to a decrease in the adhesive strength due to elastohydrodynamic deformation of the soft surface during debonding. The force-displacement and fluid film thickness-time data are compared to an elastohydrodynamic model that incorporates the force measuring spring and finds good agreement between the model and data. We calculate the pressure distribution in the fluid and find that, in contrast to debonding from rigid surfaces, the pressure drop is non-monotonic and includes the presence of stagnation points within the fluid film when a soft surface is present. In addition, viscous adhesion in the presence of a soft surface leads to a debonding process that occurs via a peeling front (located at a stagnation point), even in the absence of solid–solid contact. As a result of mass conservation, the elastohydrodynamic deformation of the soft surface during detachment leads to surfaces that come closer as the surfaces are separated. During detachment, there is a region with fluid drainage between the centerpoint and the stagnation point, while there is fluid infusion further out. Understanding and harnessing the coupling between lubrication pressure, elasticity, and surface interactions provides material design strategies for applications such as adhesives, coatings, microsensors, and biomaterials.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C9SM02447F
