Mesoscale modeling and semi-analytical approach for the microstructure-aware effective thermal conductivity of porous polygranular materials

We established a comprehensive modeling approach for investigating the microstructure-aware effective thermal conductivity (kappa(eff)) for porous microstructures containing solid particles and gaseous pores. Our approach combines the mesoscale computational modeling framework and the semi-analytical method, allowing for efficient prediction of kappa(eff) for realistic porous microstructures, while considering complicated microstructural thermal conduction pathways effectively in the prediction. We used the diffuse-interface mesoscale computational model to generate extensive simulated kappa(eff) data for realistic digital representations of microstructures with wide ranges of porosity (f(p)), thermal conductivity of the gas phase (kappa(g)), and thermal conductivity of the solid phase (kappa(s)). From the simulated data, we identified two property variation regimes for kappa(eff): (1) a slow kappa(eff) increase for kappa(s) similar to kappa(g); and (2) a faster kappa(eff) increase for kappa(s) >> kappa(g). To capture the key features of the relationship between the microstructure and kappa(eff), we derived a semi-analytical model by introducing structure and intensification factors. The two new factors incorporate the calibrated effective contribution of the solid volume with kappa(s) and additional interfacial effects into the prediction of kappa(eff), respectively, allowing for consideration of parallel, serial, and interfacial conduction mechanisms effectively. Using the selected simulation data, we quantified key model parameters within the semi-analytical model and verified that the parameterized model exhibits excellent agreement with simulated kappa(eff) for the entire range of the parameter space.