Mixing rules

Mixing rules (see also Combining rules).

van der Waals mixing rules

The van der Waals equation of state can be written as

$\left(p+{\frac {an^{2}}{V^{2}}}\right)\left(V-nb\right)=nRT$

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

$a\rightarrow \sum _{i}^{n}\sum _{j}^{n}x_{i}x_{j}a_{ij}$

and

$b\rightarrow \sum _{i}^{n}\sum _{j}^{n}x_{i}x_{j}b_{ij}$

where

$a_{ij}=(1-k_{ij}){\sqrt {(a_{ii}a_{jj})}}~~~~~~~~i\neq j$

and

$b_{ij}={\frac {(b_{ii}b_{jj})}{2}}~~~~~~~~i\neq j$

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)