The Solution Of Kinetic Equation And The Analysis Of Self-preserving Of Coagulation

The kinetic equation (i.e. the Smoluchowski equation) has described the process of particles' collision and coagulation. Mastering the law of particle size distribution (PSD) has great importance on improving coagulation efficiency and controlling the coagulation process. Because of the non-linear characteristic of the Smoluchowski equation, analytical solutions have been obtained only in certain special cases, corresponding to simplified forms of the collision frequency function and/or the initial particle size distribution. Based on the questions above, Monte-Carlo method was used to gain the numerical solutions. Two collision mechanisms: Brownian motion and fluid shear were taken into account and the effect of particles' configuration was considered too.This article has built the main idea about the Monte-Carlo method for finding the Smoluchowski equation's solutions: though many random samplings, which were carried out based on probability density function and random number arrays, many characteristic parameters were recorded, coagulation process were simulated, and the numerical solutions were gained at last. Compared with computing method, it is needn't to solve a large amount of integro-differential equation directly by Monte-Carlo method.From the solutions obtained, it is shown that the particle size distribution is self-preserving, that is, when the dimensionless particle size exceeds some values, the PSD maybe in the approximately analytical form Cη^αe^-bη. We find that during coagulation, the particle's configuration has great effect on its size distribution; the PSD broadens with decreasing fractal dimension, which is more distinct for the collision mechanisms of fluid shear. The difference about the PSD for Brownian motion and fluid shear may lie in: the form of the PSD is connected with the collision frequency functions. Brownian motion is temperature dependent and allows for collisions based on molecular movement while shear driven collision is related to the hydraulic environment about the system. Different collision mechanism causes different floc configuration. The flocs formed by shearing have more compacted structure (higher fractal dimension) than those from Brownian motion.