The friction theory ( f-theory) for viscosity modeling

Abstract

In this work, a new theory for viscosity modeling based on friction concepts of classical mechanics and the Van der Waals theory of fluids is presented. The fundamental difference between this theory and other available theories is the fact that the viscosity of dense fluids, which characterizes pure shear flow, is approached as a mechanical, rather than as a transport, property. Thus, separating the total viscosity into a dilute gas term and a friction term, a connection between the Van der Waals repulsive and attractive pressure terms and the Amontons–Coulomb friction law can be established. Then, using only two or three temperature-dependent friction coefficients, this theory links the residual friction term to the Van der Waals repulsive and attractive pressure terms. As a result, a rather simple cubic equation of state (EOS) can be used as a basis for obtaining highly accurate modeling of the viscosity of fluids from low to extreme high pressures. Since the cubic equations of state are well tuned for accurate pressure–temperature performance, and pressure is the main mechanical property linked to friction, the obtained accuracy does not depend on the density performance of the equation. To illustrate the capabilities of the theory, two well-known cubic equations of state are used to model the viscosity of n-alkanes from methane to n-decane, as well as some of their binary mixtures and, in most cases, absolute average deviations within experimental uncertainty are obtained.