Cross-property connections between overall electric conductivity and fluid permeability of a random porous media with conducting sceleton

The paper addresses the problem of cross-property connection between electrical conductivity and fluid permeability of a porous material with conducting solid phase. Variational inequality connecting the said two properties is obtained. Development of explicit closed-form connection is complicated by the fact that the two properties are governed by different microstructural parameters. This complication can be overcome if certain rather rough information about the spatial distribution of phases is available. As an illustration, material with randomly distributed interconnected phases is discussed in details. The cross-property connection for this case is obtained in closed explicit form.