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Keller and Mendelsen 2-D result for conductivity

 

Another general conductivity result, due to Keller and Mendelson [18,19], for a general 2-D isotropic two phase microstructure, is that

σ(σ1, σ2) σ(σ2,σ1) = σ1σ2(57)

where σ(σ1, σ2) means the effective conductivity obtained when phase 1 has conductivity σ1 and phase 2 has conductivity σ2, and σ(σ2, σ1) means the phase conductivities have been interchanged before determining the effective conductivity.