分形扩散的渗滤模型

多孔介质系统在多个尺度上具有复杂的非均质结构 ,多孔介质中的扩散过程要比体相中的扩散过程复杂得多 ,且表现出许多奇异的特点。以渗滤网络作为多孔介质的理论模型 ,建立了分形多孔介质中扩散和弥散过程的离散模型。分析了奇异扩散的机理 ,在此基础上建立了奇异扩散和弥散的幂律关系。应用扩散的离散网络 ,建立了广义扩散方程 ,推导了多孔介质的等效介质理论 ,得到了扩散系数的微观解释 ,为扩散过程的模拟提供了理论依据。

Percolation Model for Fractal Diffusion

Porous medium system has the complicated heterogeneous structures, in which the diffusion process is much more complicate than that of ordinary diffusion of tank liquid and shows many anomalous properties. This paper presents the percolation models for the diffusion process of porous medium in the fractal porous medium. The basic mechanism of anomalous diffusion is analyzed. The percolation network model and power law for anomalous diffusion and dispersion are obtained. By using discrete network simulation, a generalized diffusion equation and effective medium approximation formulas of porous medium are proposed. The microscale implication of diffusivity and theoretical basis for diffusion simulation are given.