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.