Effective thermal conductivity of composite materials made of a randomly packed densified spherical phase

The prediction of the effective thermal conductivity of composite materials is of paramount importance for many applications. While there exist correlations for bi-phase materials made of rigid spherical inclusions in a continuum matrix, there is lack of correlations for composites whose spherical phase is densely packed, as in densified granular materials or in foams with overlapping bubbles. In this study we combine a packing algorithm with a finite difference solver to determine the effective thermal conductivity when the spherical phase is highly overlapping, with volume fraction larger than 55%, for all the conductivity ratios of the two phases. Three fit relations are proposed to encompass the whole range of conductivities, showing good accuracy for both simulated and experimental data and outperforming existing relations commonly used for the estimation of the effective thermal conductivity. Our relations can also be used for estimating the effective electric conductivity, magnetic permeability and mass diffusivity in continuum regime.