Scaling of conductivity and Young’s modulus in replicated microcellular materials

Scaling exponents for the conductivity and stiffness of replicated microcellular materials exceed commonly predicted values of 1 and 2. We show here that this is caused by the fact that, in replicated microcellular materials, the solid architecture varies with the relative density: a simple derivation based on the physics of powder consolidation returns and explains the observed scaling behaviour. The same derivation also gives an explanation for Archie's law, known to describe the conductivity of wet soils.