Comparing Phenomenological Models of Shear Thinning of Alkanes at Low and High Newtonian Viscosities

Abstract

There is an ongoing debate concerning the best rheological model for fluids sheared in elastohydrodynamic lubrication (EHL) where high pressures lead to a dramatic rise in Newtonian viscosity and high strain rates lead to pronounced shear thinning. Two classes of phenomenological models at the center of this debate are based on the work of Eyring and Carreau. We use intermediate scaling plots and a justification criterion proposed by Gao and Müser in a recent article (Tribol Lett 72(1):16, 2024) to evaluate the fitting of Eyring, Carreau, and Carreau–Yasuda (CY) models to rheological data on the shear thinning of squalane, a model EHL fluid, at 293 K over a wide range of pressures \(P \in (0.1,955)\) MPa that change the Newtonian viscosity \(\eta _0\) of squalane from \(\sim 10\) to \(\sim 10^7\) mPa s. The justification criterion enables a fair comparison of Eyring, Carreau, and CY models that have two, three, and four fitting parameters, respectively. We find that the use of Eyring model to describe shear thinning of squalane is justified over Carreau model and CY model with crossover parameter \(a>1\) for \(\eta _0 > 10^2\) mPa s and \(\eta _0 > 10^3\) mPa s, respectively. The unrestricted CY model produces \(a<1\) in all fits and fares better but is not justified over Eyring for squalane sheared at high Newtonian viscosities \(\eta _0 > 10^4\) mPa s. More importantly, CY models fitted with \(a<1\) fail to produce a physical low-rate asymptotic behavior and an appropriate crossover to Newtonian flow. Our findings show that CY models with \(a > 1\) guarantee a proper description of the crossover from shear thinning to Newtonian zone, and should be the phenomenological model of choice for shear thinning at low pressures. As pressure rises and \(\eta _0\) becomes large (e.g., \(> 10^3\) mPa s for squalane), the use of Eyring model to describe shear thinning is justified.