分形多孔介质中气体稳态扩散

Steady-state gas diffusion in fractal porous media

传统的Fick和Knudsen扩散定律不适用于分形孔中的气体扩散,因此有必要对分形多孔介质中气体扩散规律展开研究。采用随机漫步法生成了分形孔模型,根据分子运动论建立了能应用于分形孔中的气体扩散控制方程,在所建立的扩散模型基础上,研究了分形多孔介质中气体稳态扩散规律并得到了稳态扩散系数表达式。结果表明:扩散系数正比于气体分子平均速度;在Knudsen扩散区,扩散系数正比于平均孔径和孔隙率且与分形维数成指数关系;在过渡扩散区,扩散系数不仅与3个孔结构参数有关还与扩散气体分子的平均自由程有关。

Gas diffusion in fractal pores does not follow the classic Fick＇s and Knudsen＇s laws, so more research on gas diffusion in fractal porous media is needed. Fractal pore models are generated using the random walk method. The gas diffusion governing equations for the fractal pores are derived from the classic kinetic theory of gases. The gas diffusion model is used to study the gas diffusion in fractal porous media and to determine steady-state diffusion coefficient formulas. The results show that the diffusion coefficient is proportional to the mean molecular velocity. The diffusion coefficient is also proportional to the mean pore diameter, porosity, and the exponential function of the fractal dimension in the Knudsen diffusion regime. The diffusion coefficient is not only related to the three pore parameters but is also related to the molecular mean free path in the configurational diffusion regime.