Numerical Simulation Of Dynamic Coagulation Equation

Coagulation kinetic equation mainly describes motion, collision and coagulation processes of particles. DU GON LEE has studied the traditional coagu-flocculaion power with CFS (Fractal Model) using fractal theory in 2000, and three-dimensional model of a specific coagulation dynamic equation was established. In the coagulation processes of water treatment, small particles in water collide, aggregate, fragment and re-aggregate, which is a stochastic coagulation process. The flocs formatted randomly has the characteristics of fractal structure, so the fractal theory can be applied in coagulation process reasonably.In this paper, the coagu-flocculaion dynamic equation obtained with fractal theory is numerically solved. It is more practical to choose the initial particles as the same diameter particles in the Brownian motion and select the particles with diameters in a normal distribution in the shear force field. The coagu-flocculaion dynamic equations are transformed into algebraic equations using forward difference scheme of finite difference method, the practical coagulation processes are simulated using mathematical software Matlab. The characteristics of floc size distribution under different mechanisms and the influence of fractal dimension on the floc are obtained, which is of important significance to control the coagulation process.The results show that the influence of fractal dimension to the coagulation processes under shear force field is significantly greater than that under the Brownian motion, which is because the particles are relatively smaller, more symmetric and denser under the Brownian motion, meanwhile, the scope of fractal dimension is relatively smaller. There is little difference of particle size distributions under different fractal dimensions in the coagulation processes of the Brownian motion. In the coagulation processes of the shear force field mechanism, the fractal dimension is smaller and the particle size range is larger with the increase of the coagulation speed. Collision efficiency can be increased to improve coagulation, increasing the proportion of particles.The particle size distribution is fitted, and the graph is close to the CRae-bR function under the shear mechanism while it is more close to the Ce-ad function under Brownian motion. In the coagulation process, the fractal dimension is decreasing and the values of C, a, b are also gradually decreasing and tend to stable. It can be seen from the perspective of graphics that the graphs change gradually from the exponential distribution to the normal distribution, which indicates that it is transited from the Brownian motion to the shear force field at the time t.