Mixture rule (mineralogy)

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In mineralogy, the mixture rule is used to calculate the matrix density of a mineral mixture .

If the percentages by weight are given, the following applies: ${\displaystyle m_{i}\ }$

${\displaystyle \rho _{m}={\frac {100}{m_{1}/\rho _{1}+m_{2}/\rho _{2}+...+m_{i}/\rho _{i}}}}$

If the volume percentages are given, the following applies: ${\displaystyle v_{i}\ }$

${\displaystyle \rho _{m}=v_{1}\,\rho _{1}+v_{2}\,\rho _{2}+...+v_{i}\,\rho _{i}}$ or ${\displaystyle \rho _{m}=\sum _{i=1}^{n}v_{i}\cdot \rho _{i}}$

Here mean:

${\displaystyle \rho _{m}\ }$

Matrix density of the mineral mixture in kg / m³,

${\displaystyle \rho _{i}\ }$

Matrix density of the mixture component i in kg / m³,

${\displaystyle m_{i}\ }$

Mass fraction of the mixture component i in% by weight

${\displaystyle v_{i}\ }$

Volume fraction of the mixture component i in% by volume

Calculation of the bulk density of a porous body from the matrix density and the porosity:

${\displaystyle \rho _{r}={\frac {\rho _{m}(100-\Phi )}{100}}}$

With the formula letters:

${\displaystyle \rho _{r}\ }$

Gross density in kg / m³,

${\displaystyle \rho _{m}\ }$

Matrix density of the porous body in kg / m³,

${\displaystyle \Phi \ }$

Porosity of the body in vol .-%