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23.5.6 Maximum Packing Limit in Binary Mixtures

The packing limit is not a fixed quantity and may change according to the number of particles present within a given volume and the diameter of the particles. Small particles accumulate in between larger particles increasing the packing limit. For a binary mixture FLUENT uses the correlations proposed by [ 101].

For a binary mixture with diameters $d_{1}>d_{2}$, the mixture composition is defined as $X_{1} = \frac{\alpha_1}{\alpha_1 + \alpha_2}$

where


 X_{1} <= \frac{\alpha_{1,max}}{(\alpha_{1,max}+(1-\alpha_{1,max})\alpha_{2,max})} (23.5-58)

The maximum packing limit for the mixture is given by


$\displaystyle \alpha_{s,max}$ $\textstyle =$ $\displaystyle (\alpha_{1,max} - \alpha_{2,max} + [1 - \sqrt{\frac{d2}{d1}}](1-\alpha_{1,max})\alpha_{2,max} )$ (23.5-59)
    $\displaystyle * (\alpha_{1,max}+(1-\alpha_{1,max})\alpha_{2,max}) \frac{X_{1}}{\alpha_{1,max}}$  
    $\displaystyle + \alpha_{2,max}$ (23.5-60)

otherwise, the maximum packing limit for the binary mixture is


[1 - \sqrt{\frac{d2}{d1}}] (\alpha_{1,max}+(1-\alpha_{1,max})\alpha_{2,max}) (1-X_{1}) + \alpha_{1,max} (23.5-61)

The packing limit is used for the calculation of the radial distribution function.


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