Single Property Equations (Ternary)

Single properties are represented either Directly (e.g., heat capacity, viscosity, etc.) or as Excess properties (e.g., excess volume, excess enthalpy, etc.)

Note: All calculated properties for ternary systems are derived from fitted equations for the 3 binary sub-systems. Experimental data for the ternary systems are used for comparisons only.

General Property Ψ Representation

General Case: Thermal conductivity, Surface tension, and Index of refraction

Ψ = Σ(over i = 1 to 3) xi×Ψi + 0.5 Σ(over i = 1 to 3) Σ(over j = 1 to 3) Σ(over k = 0 to nTerms) aijk×xi×xj×(xi - xj)k,
where aijk are binary parameters. If i = j, then aijk = 0.

Special Case 1: Viscosity

ln(h/ho) = Σ(over i = 1 to 3) xi×ln(hi/ho) + 0.5 Σ(over i = 1 to 3) Σ(over j = 1 to 3) Σ(over k = 0 to nTerms) aijk×xi×xj×(xi - xj)k,
where aijk are binary parameters. If i = j, then aijk = 0.

Special Case 2: Density

r = (x1×M1 + x2×M2 + x3×M3)/Vm, where

Vm = x1×M1/r1 + x2×M2/r2 + x3×M3/r3 + 0.5 Σ(over i = 1 to 3) Σ(over j = 1 to 3) Σ(over k = 0 to nTerms) aijk×xi×xj×(xi - xj)k,
where aijk are binary parameters, and if i = j, then aijk = 0. r is density (kg×m-3), Vm is molar volume (mol×m-3), and M is the molar mass (kg×mol-1).

General Excess Property ΨEX Representation

General Case: Excess Volume and Excess Enthalpy

ΨEX = 0.5 Σ(over i = 1 to 3) Σ(over j = 1 to 3) Σ(over k = 0 to nTerms) aijk×xi×xj×(xi - xj)k,
where aijk are binary parameters, and if i = j, then aijk = 0.

The Vector ai is temperature dependent with 1 to 5 terms.