A Knudsen diffusion model for predicting VOC emissions from porous wood-based panels based on porosimetry tests

Volatile organic compounds (VOCs) emitted from porous wood-based panels with fractal structure severely pollute indoor environment. Different from previous studies which the diffusion type of VOC in building materials is attributed to Fick diffusion, VOC emission from porous wood-based panels belongs to Knudsen diffusion is firstly determined by comparing the pore diameter of internal channel with VOC molecular free path in this paper. Therefore, a time fractional mass transfer model related to the fractal dimension has been proposed to analyze Knudsen diffusion characteristics firstly. This model considers areal porosity has an impact on surface emission. Analytical solution of the present model is obtained for the first time. Furthermore, it is proved that the finite difference scheme is solvable, unconditionally stable, and convergent, and numerical simulation result and experimental data match well. Moreover, the influences of the fractal dimension d_f, areal porosity ε, and delay time parameter λ on VOC emission are demonstrated and analyzed; results suggest that the higher ε and d_f, and lower λ promote VOC emission, which can provide guidance for improving indoor air quality.