A Study of Lennard–Jones Equivalent Analytical Relationships for Modeling Viscosities

An analytical representation of the viscosity density temperature relationship of the Lennard Jones (LJ) fluid, over wide ranges of temperature and density, is critically assessed and combined with an LJ pressure density temperature equation of state to allow LJ viscosity calculations at a given temperature and pressure. Both LJ equivalent analytical relationships (EARs) are accurate. The potential of using an LJ-based model to represent the viscosities of real fluids is evaluated in two steps. First, the qualitative trends generated by the two combined LJ EARs are studied. Second, viscosity predictions for real, relatively simple, fluids are performed. For these, it is assumed that a real fluid behaves as an LJ fluid having a critical temperature Tc and a critical pressure Pc exactly matching the real-fluid experimental values of Tc and Pc . Such an assumption is equivalent to supposing that real fluids behave as LJ fluids with effective iIntermolecular potential parameters consistent with the experimental critical coordinates. The viscosity predictions are based only on molecular weight, Tc , and Pc . The quantitative evaluation is relative to a database of 30 relatively simple compounds including 4 noble gases and the olefinic and aliphatic straight-chain hydrocarbons through 8 carbon atoms. Conditions for the evaluation ranged from 0.6 to 3 for reduced temperatures and from 0 to 3 for LJ reduced densities. The average error is usually less than 100 for vapor and supercritical viscosity and usually less than 250 for liquid viscosity. In its present form, the methodology is actually a corresponding-states model where the reference fluid is an LJ fluid.