Most organic fluids, including lubricant base oils, exhibit a reversible viscosity increase with the application of high pressure, due to molecular mobility restrictions imposed by the forces being exerted. This phenomenon is especially important for lubricants because, in most mechanical applications, films of fluid are compressed between sliding or rolling surfaces under very high loads. The pressure-viscosity coefficient, α, is an important parameter for the selection of gear and bearing lubricants. Nevertheless, there are several methods for determining the pressure-viscosity coefficients of lubricants, being the values obtained from these different methods not coherent in most of the cases.

Recently, Roland et al. [1] have shown for several glass-forming materials that viscosity is a unique function of TV, where the exponent  is related to the steepness of the intermolecular repulsive potential, determining this exponent for several compounds, among them squalane. Subsequently, we have determined the exponent  [2] for several pure and mixed pentaerythritol esters. In the present work we have combined the thermodynamic scaling of the viscosity proposed by Roland et al. with the relation of Pensado et al. [3], to derive an expression for α/, the ratio of the viscosity-pressure derivative (/p)T and viscosity-temperature derivative (/T)p, which includes the scaling exponent , and the internal pressure. We have verified this equation for several lubricants, among them pentaerythritol esters and squalane. For this task, previous experimental viscosity measurements performed from 303.15 K to 353.15 K and up to 60 MPa for pure pentaerythritol esters and squalane [3,4] have been used. The pressure-viscosity derivative obtained from the new relation and from experimental data on the isothermal compressibility, on the isobaric thermal expansion coefficient and the temperature-viscosity derivative, agrees well with the experimental (/p)T values, for several lubricants. The proposed equation is useful to estimate the molecular structure of suitable lubricants for each mechanical application.

In addition, in this work, a revision of the different definitions of the viscosity-pressure coefficient has been presented. Experimental viscosity data previously measured in our laboratory [3,4] and from the literature have been used to test the results obtained with the different definitions of this coefficient. The values of the pressure-viscosity coefficient obtained using the definition proposed by Dowson and Higginson [5] are lower to those obtained with secant pressure-viscosity coefficient definition. The general film-forming pressure-viscosity coefficient, αfilm, proposed by Bair et al. [6] permits to obtain accurate values of the pressure-viscosity coefficient, even if the experimental viscosity measurements were performed at moderate pressures. Both, the film thickness determined from αfilm values and the α/β ratio are useful tools to determine the most appropriate oil for the different lubricated applications.

References [1] Roland, C.M., Bair, S., Casalini, R. “Thermodynamic Scaling of the Viscosity of Van der Waals, H-bonded and Ionic Liquids”, J. Chem. Phys., 125, 124508/1-124508/11, 2006. [2] Fandiño, O., Comuñas, M.J.P., Lugo, L., López, E.R., Fernández, J., “Density Measurements under Pressure for Mixtures of Pentaerythritol Ester Lubricants. Analysis of a Density-Viscosity Relationship”, J. Chem. Eng. Data, in press, 2007. [3] Pensado, A.S., Comuñas, M.J.P., Fernández, J., “Relationships between Viscosity Coefficients and Volumetric Properties: Measurements and Modeling for Pentaerythritol Esters”, Ind. Eng. Chem. Res., 45, 9171-9183, 2006. [4] Pensado, A.S., Comuñas, M.J.P., Lugo, L., Fernández, J., “High-pressure characterization of Dynamic Viscosity and Derived Properties for Squalane and two Pentaerythritol Ester Lubricants: Pentaerythritol Tetra-2-ethylhexanoate and Pentaerythritol Tetranonanoate”, Ind. Eng. Chem. Res., 45, 2394-2404, 2006. [5] Dowson, D., Higginson, G.R., “Elastohydrodynamic Lubrication”, Pergamon Press, ed. Oxford, 1966. [6] Bair, S., Liu, Y., Wang, Q.J., “The Pressure-Viscosity Coefficient for Newtonian EHL Film Thickness with General Piezoviscous Response”, J. Tribol. 128, 624-631, 2006.