A new percolation-threshold relation for the porosity dependence of thermal conductivity

A simple second-order relation for the porosity dependence of thermal conductivity is proposed which allows for the occurrence of a critical porosity (percolation threshold). This new relation is simpler than McLachlanʹs power-law relation and thus more advantageous for fitting purposes. It is based on a Coble–Kingery-type relation for the effective thermal conductivity and formally analogous to a relation for the effective tensile modulus recently proposed by the authors. In the case of model systems where the percolation threshold is known a priori it can provide a prediction of the porosity dependence of thermal conductivity.