Phenomenological equations for the electrical conductivity of microscopically inhomogeneous materials

Phenomenological equations for the electrical conductivity of microscopically inhomogeneous materials are proposed. These equations combine ideas from the effective-medium theory and from percolation theory and, for some interesting cases, improve on the effective-medium theory in the vicinity of the percolation threshold. The equations are compared, without adjustable parameters, to three different experimental situations and agree with data remarkably well.