A study on gas diffusion through unsaturated fibrous porous materials based on fractal multi-scale model

The drying process of fibrous porous materials, such as wood and paper, is fundamentally governed by the dynamics of gas transport within their multi-scale pore networks under unsaturated conditions. Accurately modeling gas diffusion behavior is critical for improving the drying performance of fibrous porous materials. To address this, fractal dimensions are introduced to quantitatively characterize multi-scale pore structures, and a gas diffusion model integrating molecular diffusion and Knudsen diffusion mechanisms is developed based on capillary bundle framework. The explicit relationship between gas diffusivity and microstructural parameters, including porosity, pore and tortuosity fractal dimensions, liquid saturation, and Knudsen number, is proposed. And finite element method is also performed on gas–liquid two-phase flow in anisotropic fibrous material to reveal the sensitivity of relative diffusivity to these structural parameters. The present fractal model is validated by comparing with available experiment data for gas diffusivity. It has been shown that porosity and liquid saturation serve to promote and inhibit gas diffusion, respectively. Furthermore, effective diffusivity exhibits positive and negative correlations with the pore and tortuosity fractal dimensions, respectively. The proposed model provides a robust theoretical framework to predict the gas diffusion properties of unsaturated fibrous porous materials, offering a foundation for refining mathematical models of drying process and optimizing drying techniques.