Oxygen diffusion in porous media (ODPM) with rough surfaces (RS) under dry and wet conditions is of great interest. In this work, a novel fractal model for the oxygen effective diffusivity of porous media with RS under dry and wet conditions is proposed. The proposed fractal model is expressed in terms of relative roughness, the water saturation, fractal dimension for tortuosity of tortuous capillaries, fractal dimension for pores, and porosity. It is observed that the normalized oxygen diffusivity decreases with increasing relative roughness and fractal dimension for capillary tortuosity. It is found that the normalized oxygen diffusivity increases with porosity and fractal dimension for pore area. Besides, it is seen that that the normalized oxygen diffusivity under wet condition decreases with increasing water saturation. The determined normalized oxygen diffusivity is in good agreement with experimental data and existing models reported in the literature. With the proposed analytical fractal model, the physical mechanisms of oxygen diffusion through porous media with RS under dry and wet conditions are better elucidated. Every parameter in the proposed fractal model has clear physical meaning, with no empirical constant.
Stickiness of randomly rough surfaces with high fractal dimension: is there a fractal limit?
