Temperature-dependent wall slip of Newtonian lubricants

Abstract

We discuss (i) the measurement, (ii) interpretation and (iii) technical impact of temperature-dependent wall slip and its activation energy for polar and non-polar hydrocarbon Newtonian fluids moving relative to machined metal surfaces. A newly developed apparatus, the slip length tribometer (SLT), overcomes the drawbacks of existing measurement devices in terms of characterising relevant rough surfaces by measuring the slip length at different temperatures over a sufficiently large wetted area. The experimental data show that the bulk viscosity and slip length at the fluid–metal interface is independent of the shear rate up to $10^5\,\mathrm {s}^{-1}$ , being consistent with recent results from molecular dynamics simulations by Mehrnia & Pelz (J. Mol. Liq., vol. 336, 2021, 116589). Furthermore, the activation energies for wall slip and bulk shear determined by means of the SLT differ by a factor of two, i.e. $E_{\lambda }\approx 0.5 E_\mu$ for non-polar hydrocarbon molecules sliding relative to metal walls. This difference is explained by a generalised Eyring model applied to wall slip. The paper closes with the impact of wall slip on Sommerfeld's similarity theory of tribology and the resulting Stribeck curve (Sommerfeld, Z. Math. Phys., vol. 50, 1904, pp. 97–155; Z. Tech. Phys., vol. 2. Jahrg., 1921; Mechanik der deformierbaren Medien, 1944, Akademische Verlagsgesellschaft Becker & Erler). For this purpose, Reynolds’ equation generalised for wall slip is solved in combination with the experimentally determined constitutive relations for bulk shear and wall slip to predict typical characteristics of journal bearings. The results show that, for a typical journal bearing, where the ratio of slip length to average bearing clearance is of the order of $10^{-2}$ , the influence of wall slip on both load-carrying capacity and dissipation is not negligible. This work combines nanofluidics and tribology in order to provide methods and knowledge for e.g. tailor-made fluids and interfaces.

Tribological Design by Molecular Dynamics Simulation: Influence of the Molecular Structure on Wall Slip and Bulk Shear

“…According to the MD results, the slip length increases when the temperature decreases, indicating an Arrhenius process. This finding was also confirmed in an empirical investigation by Pelz et al [17]. However, it should be noticed that this is not a general conclusion for any tribology system.…”

“…According to our results, the slip length for the PAO‐iron system yielded a maximum value of 40 nm. However, the MD results were ten times smaller than the estimated value by the experimental research of a PAO 6‐steel system 17. That experimental study applied an indirect integral technique by measuring the torque to determine the slip length of PAO 6 confined between nitrided stainless‐steel surfaces with a roughness of 10 nm, whereas the calculation of the slip length in the current paper was by the Couette velocity profile.…”

Tribological Design by Molecular Dynamics Simulation - The Influence of Polar Additives on Wall Slip and Bulk Shear

“…The relationship between the slip length and the effective molecular length 𝑎 is evident, as discussed by Pelz et al [1] through the developed generalized Eyring model for wall slip and Bocquet [12]. This means the slip length scales with the effective molecular length 𝑎.…”

“…Notably, the constancy of the real shear stress across the channel height and its equivalence to the wall shear stress (𝜏(𝑧) = 𝜏 𝑤 ) in stationary Couette flow illuminate the prevalence of molecular (viscous) forces in the overall flow field, particularly under conditions of a small Reynolds number. This fundamental understanding underscores the significance of viscous forces in dictating the shear stress distribution, a critical aspect in the study and analysis of tribological phenomena within confined spaces [1,2]. The relationship between bulk shear and wall slip can be expressed through Navier's slip 𝜏 = 𝑘 𝑢 𝑠 , and Newton's shear 𝜏 = 𝜇 𝛾̇ equations.…”

“…Through MD simulations, it investigated the structural and dynamic properties of the lubricant film in the presence of the polar additives, aiming to comprehend their influence on bulk shear and develop insights into optimizing lubricant formulations. In the investigation of non-polar molecules in lubrication, several studies have explored the phenomenon of wall slip and bulk shear with hydrocarbon oils interacting with metal surfaces [1][2][3][4][5]. For instance, a slip model was proposed for linear hydrocarbon lubricants confined between metal atom surfaces, considering specific surface parameters and shear viscosity [4].…”