Mullite fibers/whiskers hierarchical porous materials: Experimental characterization and fractal model to predict thermal conductivity

It is an effective method to predict thermal conductivity of porous materials by using fractal models. In this work, mullite fibers/whiskers hierarchical porous materials (MFWs) were prepared via in-situ growth method. The fractal dimension was obtained by calculating the microstructure photo after binarization according to the box-dimension method. Based on fractal theory and fractal dimension, improved Sierpinski carpet models were established. The models were then converted into electrical fractal patterns to solve the iterative formulas of effective thermal conductivity (K_eff) and porosity. The results show that K_eff decreases gradually with the increase of porosity. The thermal conductivity of the solid phase has a significant effect on K_eff at low porosity. Pore size and its spatial distribution, especially the spatial distribution of the larger pore, have a substantial impact on K_eff, and the smaller and uniformly distributed pore can reduce K_eff, effectively. The calculated results are close to the experimental results, suggesting that the fractal model is suitable for predicting the thermal conductivity of MFWs. More crucially, the calculated results have guiding significance for the experimental preparation, and it is possible to reduce the thermal conductivity of MFWs by increasing whiskers length and growing efficiency.