Analytical and numerical identification of the skeleton thermal conductivity of a geopolymer foam using a multi-scale analysis

A quantitative characterization of the pore volume fractions has been made by image analysis, taking into account the multi-scale aspect of these foams. Motivated by the character of the microstructure, an inverse multi-scale analytical method was applied to find the value of the thermal conductivity of the skeleton λs. In fact, due to the range of pore volume fractions, standard analytical relations describing thermal conductivity were found to be of limited use. In order to take into account the local aspects of the microstructure and to treat the actual pore volume fractions, an inverse numerical approach, based on a finite element calculation coupled with a homogenization method, was used. As a result, the multi-scale analytical approach evaluates the value of λs between 0.95 and 1.19 W m−1 K−1. Numerical results, taking faithfully into account local parameters of the pore network, give λs values within the range 1.09-1.12 W m−1 K−1. The numerical values of λs are in agreement with values obtained in the literature.