Third-order model of thermal conductivity for random polydisperse particulate materials using well-resolved statistical descriptions from tomography

For heterogeneous materials, obtaining an accurate statistical description has remained an outstanding problem. We accurately evaluate the three-point microstructural parameter that arises in third-order bounds and approximations of effective material properties. We propose new adaptive methods for computing n-point probability functions obtained from three-dimensional microstructures. We show that for highly packed systems our methods result in a 45% accuracy improvement compared to the latest techniques, and third-order approximations agree well with simulation data. Furthermore, third-order estimates of the effective behavior are computed for tomographically characterized systems of highly filled polydisperse ellipsoids and cuboids for the first time.