An Application of a Free Volume Model to Lubricant Rheology I—Dependence of Viscosity on Temperature and Pressure

Analyses of the dependence of lubricant viscosity on temperature and pressure, μ(T,P), have been carried out by using a modified WLF equation in which pressure effects on viscosity are given in terms of the pressure dependence of the glass transition temperature, T_g, and of thermal expansivity of free volume, α_f. where C₁ and C₂ are well known WLF constants, and μ_g is a viscosity at T_g. T_g(P) and F(P) are functions for describing the pressure dependence of T_g and α_f, respectively. On the basis of the iso-viscous concept for T_g(P), μ_g has been assumed to have a constant value, 1 TPa•s, at any pressure (SCHEME I). SCHEME I yields a reasonable variation in T_g and α_f with pressure for synthetic lubricants, while this analysis suggests a lower μ_g for mineral oils. In order to improve the applicability of the free volume model, a reference temperature T_s(P), at which the viscosity is 10 MPa•s, has been introduced instead of T_g(P) (SCHEME II). Analyses of dielectric transition for some lubricants and of μ(T,P) in the ASME Pressure-Viscosity Report have confirmed the excellent applicability of the present free volume model over wide ranges of temperature and pressure.