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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.
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The role of adhesion on soft lubrication: A new theory
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.
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- Award ID(s):
- 1854572
- PAR ID:
- 10525245
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of the Mechanics and Physics of Solids
- Volume:
- 190
- Issue:
- C
- ISSN:
- 0022-5096
- Page Range / eLocation ID:
- 105720
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jmps.2024.105720
