Toward a continuum description of lubrication in highly pressurized nanometer-wide constrictions: The importance of accurate slip laws

Abstract

The Reynolds lubrication equation (RLE) is widely used to design sliding contacts in mechanical machinery. While providing an excellent description of hydrodynamic lubrication, friction in boundary lubrication regions is usually considered by empirical laws, because continuum theories are expected to fail for lubricant film heights h 0 ≪ 10 nm, especially in highly loaded tribosystems with normal pressures p n ≫ 0.1 GPa. Here, the performance of RLEs is validated by molecular dynamics simulations of pressurized (with p n = 0.2 to 1 GPa) hexadecane in a gold converging-diverging channel with minimum gap heights h 0 = 1.4 to 9.7 nm. For p n ≤ 0.4 GPa and h 0 ≥ 5 nm, agreement with the RLE requires accurate constitutive laws for pressure-dependent density and viscosity. An additional nonlinear wall slip law relating wall slip velocities to local shear stresses extends the RLE’s validity to even the most severe loading condition p n = 1 GPa and h 0 = 1.4 nm. Our results demonstrate an innovative route for continuum modeling of highly loaded tribological contacts under boundary lubrication.

An All-Atom Force Field for Dry and Water-Lubricated Carbon Tribological Interfaces

“…The water film thickness is measured as the average difference between the maximum and the minimum z -coordinate of O atoms in H 2 O during the time interval from 0.5 to 2 ns. We note that the root-mean-square roughness values of the contacting surfaces (calculated as in ref using square bins with an edge length of 2 Å) are slightly smaller than the thickness values of the thinnest water films. The root-mean-square roughness values are 1.6 and 1.8 Å, 1.5 and 1.6 Å, and 1.4 and 1.6 Å for the 100% H-terminated case, the 75% H-terminated case, and the 50% H-terminated case, respectively.…”

“…This scenario illustrates how in BL, the atomic-scale structure of the a-C interfaces has a decisive effect on friction. Besides governing the interaction between surfaces under dry conditions, the surface structure can also strongly influence the slip length , and the structure of lubricating films for distances up to several nanometers from the surface. This is not only relevant if the total film thickness falls in this order of magnitude – but also for thicker lubricant films under severe pressure conditions as in elastohydrodynamic lubrication conditions .…”

O-glycans Expand Lubricin and Attenuate Its Viscosity and Shear Thinning

“…Recent macroscopic simulations of synovial joint lubrication, such as those considering pressure-induced rehydration by cartilage surfaces, might benefit from MD-informed constitutive relations. Similarly, other effects such as pressure-dependent viscosity, compressibility, or localized shear might be subsequently introduced into hydrodynamic descriptions …”

“…Similarly, other effects such as pressure-dependent viscosity, compressibility, or localized shear might be subsequently introduced into hydrodynamic descriptions. 89 Lubricin acts as a lubricant in the synovial fluid. 2−6 Ludwig et al reported viscosities in the range of a few mPa s for fulllength recombinant lubricin.…”

“…Similarly, other effects such as pressure-dependent viscosity, compressibility, or localized shear might be subsequently introduced into hydrodynamic descriptions. 89 …”