Micromechanics-based model for the effective thermal conductivity of three-phase composites with bimodal particle size distribution

Particles with high thermal conductivity exhibiting a bimodal size distribution can significantly improve the effective thermal conductivity (ETC) of particulate reinforced three-phase composites (TPCs). Traditionally, the primary mechanisms governing ETC have been elucidated through the concept of packing density, as established in granular powder mechanics for hybrid particle mixtures with bimodal size distributions. However, this conventional packing density is inapplicable to TPCs prepared by mechanical mixing and mold casting, where porosity reduction is absent. To date, a micromechanics-based model specifically addressing this phenomenon remains undeveloped. Given that the matrix phase possesses low thermal conductivity, the matrix regions distant from high TC fillers are analogous to air voids in granular materials, and are thus termed ineffective matrix. According to packing theory, the utilization of a binary size distribution effectively reduces the volume fraction of the ineffective matrix. Based on this concept, the interpolated double inclusion method was employed to construct a fictitious inclusion comprising the particle and its surrounding matrix. The Chang-Deng model was applied to quantify the concentration of the ineffective matrix, and the Zehner, Bauer and Schlunder model was used to predict the ETC of TPCs. The predictions were validated against relevant experiments to assess the validity of the developed model. Additionally, parametric analyses were performed to elucidate the effect of various factors on model performance. The proposed micromechanics model demonstrates potential as an effective tool for the design and optimization of multiphase composites with enhanced ETCs.