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I have been reading a few papers regarding the estimation of the permittivity $\epsilon_{mix}$ of a mixture of materials of permittivities $\epsilon_1$ and $\epsilon_2$ (I am not a phisicist or a physics student either, btw). I have found that there are many models for estimating it.

Two of those models are:

  1. $\epsilon_{mix} = V_1 \epsilon_1 + V_2 \epsilon_2$ where $V_1$ and $V_2$ are the fractions of the total volume occupied by the original materials, being $V_1 + V_2 = 1$
  2. $\epsilon_{mix}^{0.5} = V_1 \epsilon_1^{0.5} + V_2 \epsilon_2^{0.5}$

My question is, should I use this formulae on the real and imaginary parts of the permittivities separately, or use them on the whole complex permittivites? Obviously, there is no difference in the first model because $\epsilon_{mix}$ is linear with respect to $\epsilon_1$ and $\epsilon_2$, but this is not the case with the second model.

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It would really depend on the model that was used to derive the second equation. Based off experience, my guess is that it'll work out to where you'll use the whole complex permittivites, but I'm not familiar with the model used to derive 2 so I can't be sure. Do you have a reference?

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    $\begingroup$ I've seen it in some papers and also, for example, in the book "Electromagnetic mixing formulas and applications" by Ari Sihvola, published by the IEEE. You may find it there as a special case of the "power-law" models (eq. 9.11 in the book). These models include also as a special case the famous mixing formula of Lichteneker. $\endgroup$
    – Javi
    Nov 11, 2018 at 2:22

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