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

The Reynolds Lubrication Equation (RLE) is widely employed to design sliding contacts in mechanical machinery. While providing an excellent description of the hydrodynamic lubrication regime, friction in boundary lubrication regions is usually considered by empirical laws, since continuum theories are expected to fail for lubricant film heights ℎ0 ≪ 10 nm, especially in highly loaded tribosystems with normal pressures 𝑝𝑛 ≫ 0.1 GPa. Here, the performance of RLEs is validated by molecular dynamics sliding simulations of pressurized (with 𝑝𝑛 = 0.2 - 1 GPa) hexadecane in a gold converging-diverging channel with minimum gap heights ℎ0 = 1.4 - 9.7 nm. For 𝑝𝑛 ≤ 0.4 GPa and ℎ0 ≥ 5 nm, agreement with the RLE only requires accurate constitutive laws for pressure-dependent density and viscosity. An additional non-linear wall slip law relating wall slip velocities to local shear stresses extends the RLE’s validity range to even the most severe loading condition 𝑝𝑛 = 1 GPa and ℎ0 = 1.4 nm. Our results demonstrate an innovative route for non-empirical predictive continuum modeling of highly loaded tribological contacts under boundary lubrication conditions.