多孔介质中溶质有效扩散系数预测的分形模型

Fractal model for predicting effective diffusion coefficient of solute in porous media

依据分形理论和方法,探索溶质在多孔介质中的有效扩散系数的替代预测方法。在多孔介质溶质扩散的弯曲毛细管束模型的基础上,以分形维数作为介质的基本几何特性参数,建立了多孔介质中溶质扩散的分形毛细管束模型,推导出了溶质有效扩散系数与介质孔隙度之间的幂定律关系式,幂指数是介质孔隙分维和表面分维的函数,反映了介质孔隙体积的层次分布与孔隙通道曲折程度对扩散的影响。对粘性土的分形维数测定数据和有效扩散系数试验测定数据的分析表明,利用该关系式预测多孔介质中溶质的有效扩散系数是较为准确可靠的。

An alternative method is explored to predict effective diffusion coefficient of solute in porous media by using the fractal approach. A fractal capillary tube model is established to be an improvement of the classical sinuous capillary tube model and a power law equation is derived. The power exponent is a function of pore volume fractal dimension and surface fractal dimension, which respectively characterize the hierarchical structure and the tortuosity of pores. Analytical comparison of the reported experimental data of fractal dimension of clayey soils with the corresponding effective diffusion coefficients indicates that the derived power law equation is valid to predict the effective diffusion coefficient of solute in porous media.