High Pressure Rheology of Lubricants (Part 5): Derivation of van der Waals Type Viscosity Equation

• Published in: Tribology Online 2022/11/15, Vol.17(4), pp.257-275
• Main Author: Kaneko, Masato
• Format: Article
• Language: English
• Subjects: Absolute zero; Convergence; Equations of state; High pressure; Linear equations; lubricant; Lubricants & lubrication; pressure; Rheological properties; Rheology; temperature; van der Waals type viscosity equation; Viscosity; viscosity equation; Walther equation
• ISSN: 1881-2198; 1881-218X; 1881-2198
• DOI: 10.2474/trol.17.257

The Walther equation is often used for the viscosity temperature characteristics of lubricants. However, it was found that it cannot be applied to high pressure viscosity. In this study, the relationship between viscosity, temperature and pressure was analyzed. As a result, viscosity at each pressure was found to be negatively proportional to the square of temperature, and linear equations converges at absolute zero were derived. In parallel, a thought experiment was conducted on the viscosity of ideal liquid. It was found that the absolute zero viscosity (ηt=0) of ideal liquid is constant regardless of the pressure. This is consistent with the convergence point at absolute zero of the linear equation in the above analysis. Furthermore, a high pressure viscosity temperature linear equation incorporating the pressure was derived. This eqaution is a van der Waals type viscosity equation consisting of three intrinsic constants: absolute zero viscosity ηt=0 [mPa·s], viscosity constant 1/B [GPa/K2] and pressure constant C/B [GPa]. It was found that this is liquid viscosity equation. This equation is also ideal liquid viscosity equation. Furthermore, C/B was found to be equivalent to PR [GPa] of liquid state equation. By this, the high pressure viscosity of lubricant can be estimated from the derived van der Waals type viscosity equation.