Mixture rule (thermodynamics)

A mixture rule is used to calculate the properties of mixtures from the properties of the pure substances .

calculation

General form

${\displaystyle E_{m}=\sum _{i}\sum _{j}y_{i}\cdot x_{i}\cdot E_{ij}}$

With

E _m : property of the mixture

x _i : mole fraction in the liquid phase

y _i : mole fraction in steam

E _ii and E _jj : basic substance properties

E _ij and E _ji : interaction terms

Interaction terms

The interaction terms E _ij and E _ji must be determined using so-called combination rules. The arithmetic and geometric mean values ​​are common.

Arithmetic mean

${\displaystyle E_{ij}={\frac {E_{ii}+E_{jj}}{2}}}$

This gives for E _m :

${\displaystyle E_{m}=\sum _{i}y_{i}E_{i}}$

Geometric mean

${\displaystyle E_{ij}={\sqrt {E_{ii}E_{jj}}}}$

This gives for E _m :

${\displaystyle E_{m}=\left(\sum _{i}y_{i}{\sqrt {E}}_{i}\right)^{2}}$

with E _i = E _ii

Binary interaction parameters

Binary interaction parameters k _ij are used to improve the quality of a combination rule. An example of inserting such a parameter is

${\displaystyle E_{ij}={\frac {k_{ij}(E_{ii}+E_{jj})}{2}}}$

k _ij are generally determined by regression of experimental material data of binary mixtures.

See also

Dortmund database : database of experimental material properties

literature

1. ^ Robert C. Reid, John M. Prausnitz, Bruce E. Poling: The Properties of Gases and Liquids . 4th ed. McGraw-Hill, New York 1988, ISBN 0-07-051799-1 .