Non-Quadratic Mixing and Combining Rules

For multi-component mixtures Mathias et proposed a x) should have the form  

Zabaloy presented a cubic mixing rule for a(x) given by 

Methods were introduced in ref. 77, based initially on the work of Mathias et al. to estimate the interaction parameter ky from existing values of ky. When the approach has been adopted, it apparently satisfies the invariance test of ref. 75 but, because of the cubic dependence on mole fraction, the conditions given by eq 5.17 are not met. Valderrama et al have proposed a general nonquadratic mixing rule that also fails to comply with the requirements of Michelsen and Kisternmacher.  

The relationship between an activity coelScient, /, and the fugacity coelS-cients, (j), obtained from an equation of state is 

Any error in the virial coefficient of the pure component will also introduce an error into the calculated fugacity independent of the choice of mixing and combining rules. 

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