分形结构中介质渗透性对扩散过程的影响

The Influence of Medium Permeability on Diffusion Process in Fractal Structure

土壤孔隙由于其结构的不均匀特征使得溶质的运移规律不符合经典的菲克定律。为了研究溶质在土壤等不均匀结构中的扩散行为,建立了Sierpinski分形地毯模型模拟非均匀性的土壤结构,并通过投放大量粒子进行随机行走模拟,目的是研究土壤中污染物等溶质的扩散规律。选用同一种Sierpinski分形地毯模型,并取相同的起始投放点位置,粒子数量以及运动步数,以不同规则下粒子的随机运动模拟为手段,探索不同介质条件下溶质的运动规律。根据分形结构中溶质位移与时间的二阶矩关系,通过数值模拟、对比两种条件下的Hurst值及其影响因素,从而得到分形结构中粒子的扩散规律。

The structural of soil has been proved to be a heterogeneous one,which causes the solute transport behavior is quite different from the ideal homogeneous medium and violates Fick’s law. To explore the transport behavior in fractured medium,a Sierpinski fractal carpet model was established to represent the heterogeneity of soil structure. Random particle motion simulation under different rules were applied to characterize the random motion of solute particles under different medium conditions based on Sierpinski fractal carpet model with same starting point,particle number and number of moving steps. Finally,the diffusion behavior in the fractal structure is explored according to the second-order moment expression of displacement in the fractal structure. The influencing factor Hurst are obtained by comparison in the two cases.