Hierarchical field compositions for simulations of near-percolation thermal transport in particulate materials

In this paper, we simulate heat transport in complex three-dimensional particulate microstructures using a computational procedure based on the formalism of hierarchical partition of unity field compositions (HPFC) recently developed by the authors. The computational procedure is based on constructing complex behavioral fields through Boolean compositions of primitive fields. It is demonstrated that the Boolean compositions efficiently model topological changes caused by the modification/rearrangement of the second phases in the heterogeneous material microstructure. The developed method is applied to evaluate the effective thermal conductivity of two particulate systems, namely, alumina particles in silicone oil and aluminum particles in silicone oil. Three-dimensional simulations of thirty random arrangements of the heterogeneous microstructure at a fixed 58% volume fraction were carried out so as to enable comparisons with experiments (15 measurements of each particle–matrix combination) conducted at an identical volume loading. The microstructures are systematically (and statistically) characterized using matrix-nearest surface exclusion probability functions. The agreement between the experiments and the simulations (mean values were within 10% of each other) validated the near-percolation transport mechanism in these practical material systems. The simulations also underscore the importance of capturing complex three-dimensional (random) particle arrangements and inter-particle interactions. It is demonstrated that these complex three-dimensional microstructural effects may explain experimental results that are sometimes ascribed to an imperfect interface and a non-verifiable interfacial resistance.