Research On Two-component Particle’s Size And Component Distribution On Coagulation Process

In recent years, frequently hazy weathers do serious harm to the environment and human health. Pathological study shows that the degree of harm one hand depends on particle size, on the other hand, depends on the particle component and morphology. Therefore, the one-component particle model can not fully illustrate the complexity of haze particles. Under such background, this paper uses the theoretical analysis and numerical simulation to study the particle size and component distribution.Firstly, the analytical solutions of the two-component particle balance equation with component-dependent kernel are analyzed in this paper. The paper focuses on the component effects on coagulation, especially for the component dependent kernel(,; ’, ’)(, ’ ’)a b a b a b a bK v v v v(28)k av(10)v av(10)v. By using the Laplace transform and the Charpit-Lagrange method, we obtain the analytic solutions of the component-dependent additive kernel and the product kernel. Based on the analysis of the solution of the additive kernel, we find that for larger particles the component mixed better, and for lager particles a-component tend to be the normal function which is independent with the parameter a after large time. For the product kernel, we find the parameters a have different influence on the component distribution before and after the gelation.Secondly, the paper mainly focuses on the particles size and component distribution after long time evolution. For the classical component-independent and component-dependent kernel, we analyze the two parameter scaling function with the scaling limit, when the time tends to infinity and the average size tends to infinity such that the scaling variable is constant. We find for the component-dependent additive kernel the scaling function also fit the Vigil-Ziff conjecture. And the result extend the Vigil-Ziff conjecture to the component dependent kernel.Thirdly, the paper pays attention to the simulation method for two-component coagulation. Based on Simmel’s one-component Linear Discrete Method(LDM), we develop two-component linear discrete method. The method is used to simulate two classical cases, and the simulation results fit the theoretical analysis well. This method makes up Bott’s two-dimensional linear flow method(TFM) that can only handle the case one component is dominant on the coagulation process.Finally, the paper simulates the component distribution of submicron haze particles. And we focus on the trace heavy metal’s distribution in the submicron particles which are controlled by Brown coagulation in the continuation regime. It is found that heavy metals gradually increases and tend to the normal distribution in large particles, and heavy metals mass fraction fits power law in small particles.These results of theoretical analysis and numerical simulation on classical kernels can provide reference to the research on the size and component distributions in haze particles under realistic conditions.