Mixing rules

Mixing rules (see also Combining rules).

van der Waals mixing rules

The van der Waals equation of state can be written as

$(p+\frac{a{n}^2}{V^2})(V-nb)=nRT$

For mixtures one replaces $a$ and $b$ with expressions that depend on the composition:

$a\to \sum _i^n\sum _j^n{x}_i{x}_j{a}_{ij}$

and

$b\to \sum _i^n\sum _j^n{x}_i{x}_j{b}_{ij}$

where

$a_{ij}=(1-k_{ij})\sqrt{(a_{ii}{a}_{jj})}i\ne j$

and

$b_{ij}=\frac{(b_{ii}{b}_{jj})}{2}i\ne j$

where $k_{ij}$ is obtained from a fit.

See also

References

Related reading

• T. Y. Kwak and G. A. Mansoori "Van der waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling", Chemical Engineering Science 41 pp. 1303-1309 (1986)
• Kenneth R. Hall, Gustavo A. Iglesias-Silva, and G. Ali Mansoori "Quadratic mixing rules for equations of state: Origins and relationships to the virial expansion", Fluid Phase Equilibria 91 pp. 67-76 (1993)