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titleDerivation


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The total multiphase volume:

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V_f = \sum V_\alpha


where

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bodyV_\alpha
are volumes, occupied by individual phases.


The volume fraction of individual phase is defined as:

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s_\alpha = \frac{V_\alpha}{V_f}


This leads to:

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c_f = \frac{1}{V_f} \, \frac{\partial V_f}{\partial p} = 
\frac{1}{V_f} \sum_\alpha \frac{\partial V_\alpha}{\partial p} = 
 \sum_\alpha \frac{V_\alpha}{V_f} \, \frac{1}{V_\alpha} \frac{\partial V_\alpha}{\partial p} =
 \sum_\alpha s_\alpha \, c_\alpha



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