Power-law scaling of thermal conductivity of highly porous ceramics

In this paper (i) literature data on the thermal conductivity of (highly) porous ceramics and (ii) related analytical modelling schemes based on the effective media theory are reviewed. The latter do not seem to satisfactorily represent the experimentally observed quadratic power-law scaling of effective thermal conductivity with respect to the volume fraction of the solid material phase (or relative density). In the analytical/modelling part, two microstructural configurations of the conducting and the non-conducting material phase, respectively, are investigated: (i) thin, interconnected spherical shells of the conducting material in a simple cubic arrangement and (ii) regular and statistically random packing of solid, conducting spheres. These microstructural configurations differ from the arrangement used for derivation of classical homogenization schemes based on the effective media theory, i.e. non-conducting pores in a conducting solid matrix.