Study On Method Of Moments Model For Coagulation Problem In Aerosol Dynamic Control Process

The Brownian coagulation process of aerosol particles is a spontaneous and thermal driven dynamic phenomenon of micro nano particle two-phase system.This process determines the evolution of particle scale spectrum and the state of system on time scale.This process is inevitable in the industrial process involving the micro nano particle systems such as control and removal of atmospheric particles,atmospheric environment monitoring and development of instruments for preparation of micro nano particles.Therefore,according to the specific purpose,it is particularly important to realize the control and human intervention of this process.In terms of mathematical description,this process can be described by Smouchowski Coagulation Equations(SCE),also known as Population Balance Equation(PBE),but it is difficult to solve directly due to the strong nonlinearity of the equation.The method of moments can convert the population balance equation into the moment equations,and has good calculation efficiency and accuracy.The inverse Gaussian distribution method of moments is a new preset distribution method of moments proposed by the author’s research group.It has been applied to the solution of Brownian coagulation related problems and achieved good results.The work of this paper is based on the inverse Gaussian distribution method of moment proposed by us,which mainly includes the following aspects:(1)Combined with the inverse Gaussian distribution method of moments and Taylor expansion method of moments,the inverse Gaussian distribution model of free molecular regime is reconstructed.Through the comparison with other methods,it is verified that the new model has higher calculation accuracy than the lognormal distribution method of moments,which shows that the new method can be applied to the solution of Brownian coagulation population balance equation in free molecular regime.According to the Dahneke’s solution and harmonic mean solution,combined with the reconstructed new model,the inverse Gaussian distribution method of moments is extended to the solution of the particle coagulation problem in the entire size regime.It is verified that in the whole evolution process,even if the fractal dimension is different,the geometric standard deviation and shape factor have no asymptotic value,and the aerosol particles cannot reach the self-preserving state.(2)Combined with the theory of self-preserving size distribution,the analytical solution of the inverse Gaussian distribution method of moments in continuum regime and free molecular regime,the expressions of self-preserving time and self-preserving size distribution are analyzed and deduced.It is found that the analytical solution of the inverse Gaussian distribution method of moments has the same or even higher accuracy than the lognormal distribution method of moments.At the same time,the selfpreserving theory is verified and realized,which provides additional evidence for the self-preserving distribution theory.(3)We propose a bimodal distribution model based on the inverse Gaussian distribution,and give the derivation process of bimodal inverse Gaussian distribution method of moments and the moment closure equations of continuum regime and free molecular regime.It is verified that the bimodal inverse Gaussian distribution method of moments has higher accuracy than the unimodal model in the calculation of several key moments and shape factors,and can better predict the evolution of particle size distribution of engineered nanoparticles with time.