分形结构及尺度对粒子扩散行为的影响

土壤污染对人体健康和生态环境会产生极大危害.探明污染物扩散机理,准确预测污染物在土壤中的输运过程是高效控制和修复的前提.已有研究表明,土壤结构及尺度差异对污染物输运行为具有明显影响.为定量分析上述差异对预测结果的影响,在建立单块Sierpinski分形地毯模型的基础上,构建了四块拼接Sierpinski分形地毯模型模拟土壤结构,分别探究了分形结构和空间尺度对粒子扩散行为的影响,重点讨论了分形结构的边界效应问题.通过粒子在两种分形结构中的随机行走过程分析,得到了不同分形结构中粒子的空间位移、密度分布及粒子运动的统计均方位移与时间的关系.数值模拟结果表明,在尺度较小的单块分形结构中,当粒子的扩散过程未受到边界效应影响时,其扩散行为呈现次扩散现象;当粒子的扩散过程受到边界效应影响时,粒子的扩散行为在短时间内发生明显变化,由次扩散过渡为正常扩散.而在尺度较大的拼接分形结构中,边界效应对粒子的扩散过程没有明显影响,扩散行为在相当长的时间内保持稳定,呈次扩散现象.

The influence of fractal structure and scale on particle diffusion behavior

Soil pollution may cause great harm to human health and ecological environment. Improvement of simulation accuracy for contaminant transport in soil, is an important precondition of pollution control and remediation. Previous studies have shown that soil structure and scale difference have significant influences on contaminant transport. In order to quantitatively analyze the influence of the above differences on the prediction results, four spliced Sierpinski fractal carpet model was constructed to simulate the soil structure based on the establishment of a single Sierpinski fractal carpet model, to investigate the influences of fractal structure and spatial scale on the diffusion behavior, and the boundary effect of fractal structure was discussed emphatically. By analyzing the particle random walk in two kinds of fractal structures, the spatial displacement, density distribution and mean square displacement in different fractal structures are obtained. The results of numerical simulation show that the diffusion behavior is sub-diffusion in the single fractal structure with small scale when the diffusion process is not affected by boundary restrictions. When the diffusion process of particles is affected by the boundary effect, the diffusion behavior changes from sub-diffusion to normal diffusion in a short time period. However, the boundary has little influence on the diffusion process in the spliced fractal structure with large scale. In addition, the diffusion behavior is sub-diffusion and keeps stable for a long time period.