I has Bruggeman’s symmetric mixture formula, when I use it for prediction of conductivity of composite it has noisy data near percolation, but it should be monotonic.
It is monotonic when conductivity of filler near conductivity of matrix.
Hei,
The Bruggerman formula is, in fact, unstable at the point you have found.
The up-and-downs from your plot are numerical instabilities from the computer, coming from the 10^-18 conductivity.
If you invert it analitically, it is monotonic (altough singular in one point in the middle)
This formula holds only for small concentration of filler, or if conductivity is of the same orders of magnitude for both components.
In the middle, specially at 33% concentration, it gives pretty bad predictions if you have very large difference in conductivity.
Since the conductivity of your filler is so much higher than that of the medium, you can drastically simplify the formula
\sigma_c= \sigma_m *( 1 + 3 * \phi_f)
here, conductivity of the filler is basically infinity. Check the 3 factor, I'm unsure.
If you have high concentration of filler(when percolation occurs) forget this formula, all conductivity will go through percolation, and this formula is all wrong.
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