引入分形维数的混凝动力学方程数值求解

Numerical Calculation of Coagulation Kinetics Incorporating Fractal Theory

运用Smoluchowski基本原理,建立了引入絮凝体分形维数的混凝动力学模型.该模型在絮凝过程中考虑了不同时刻形成的絮凝体中引入的初始颗粒数目和空隙率,并以此来推求不同时刻形成的絮凝体所对应的分形维数.采用有限差分法对建立的混凝动力学模型进行了数值计算.结果表明,初始颗粒的结构特征和碰撞效率是影响絮凝体粒径分布的主要因素.初始颗粒的分形维数和碰撞效率越大,絮凝体粒径分布越宽泛,大尺寸的颗粒所占的份额越多.同时计算结果表明,絮凝体的分形维数有随其粒径增大而逐渐降低的趋势,其原因是絮凝体的成长粒径与絮凝体中所包含的初始颗粒增长速度不成比例.以腐殖酸为混凝对象,采用硫酸铝作为混凝剂进行混凝实验,并以其初始絮凝条件作为数值计算初始条件,研究表明数值计算分析结果和模拟结果吻合较好.

Based on the Smoluchowski equation,a kinetic model was formulated by introducing the fractal dimension.In the kinetic model,fractal dimension at different time is calculated by considering of the void and primary particles contained in the flocs.Using the kinetic model,the coagulation kinetics was calculated by the method of finite difference.The calculation results showed that the characteristics of the structure and collision efficiency play an important role in particle size distribution.The higher of the fractal dimension and the collision efficiency,the broader of the particle size distribution will be obtained,which indicated the flocs with large size were formed.The results also revealed a tendency of decrease in the fractal dimension with the increase of floc size, which is resulted from the unproportionate growth between the floc size and the number of the primary particles contained in the flocs.The validity of the calculation was proved by a series of experiments using aluminum sulfate as coagulant for the flocculation of humic substances.