絮凝体的三维DLA模型分形模拟

以MATLAB为平台,编写三维扩散限制凝聚(DLA)模型程序,模拟絮体的生成,计算分形维数、空隙率等参数。用回旋半径法计算絮体分形维数,为了更好地计算分形维数,采用分段线性拟合。模拟结果表明:随着凝聚粒子数目从200增加到12000,分形维数随着粒子数增大而增大,最终趋于某一定值,空隙率则随着粒子数增大而减小。即随着凝聚体中粒子数的增加,凝聚体的扩张度逐渐加大,对于以DLA模式生长的凝聚体,随机运动的粒子较易进入凝聚体内部,从而引起分形维数增加,生成的絮体结构越来越紧密。空隙率的减小是分形维数增加的首要因素。

Simulation on Flocs Using Three-dimensional DLA Model

At the base of MATLAB,the flocs growth was simulated with three-dimensional diffusion-limited aggregation（DLA） model.Parameters such as fractal dimensions and porosity were calculated with cyclotron radius method.To calculate the fractal dimensions preferably,the data was fitted with piecewise linear method.The simulation results showed that with the amount of agglomerating particles rising from 200 to 12 000,the fractal dimensions increased and reached a certain value at last,while the porosity decreased.That is,the more agglomerating particles were,the more hard-packed the flocs were.Because with the rising amount of agglomerating particles rising,the divergence rate of flocs will increase.For the flocs growing in DLA model,the particles in random movement can easily enter its interior,so as to increase the fractal dimensions.The decrease of porosity was the most important factor in fractal dimensions rising.