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) x
i×Ψi + 0.5 Σ(over
i = 1 to 3) Σ(over
j = 1 to 3) Σ(over
k = 0 to nTerms) a
ijk×x
i×x
j×(x
i - x
j)
k,
where a
ijk are binary parameters. If
i =
j, then a
ijk = 0.
Special Case 1: Viscosity
ln(
h/
ho) = Σ(over
i = 1 to 3) x
i×ln(
hi/
ho) + 0.5 Σ(over
i = 1 to 3) Σ(over
j = 1 to 3) Σ(over
k = 0 to nTerms) a
ijk×x
i×x
j×(x
i - x
j)
k,
where a
ijk are binary parameters. If
i =
j, then a
ijk = 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) a
ijk×x
i×x
j×(x
i - x
j)
k,
where a
ijk are binary parameters, and if
i =
j, then a
ijk = 0.
The Vector ai is temperature dependent with 1 to 5 terms.