Research On Brownian Coagulation Of Aerosols Via The Method Of Moments

As is known to us, the Earth is covered with a thick atmosphere and the atmosphere, which provides the oxygen we live by, is necessary to humans as water is to fish. With the rapid economic development, a large number of industrial emissions and automobile exhausts rich in tiny particulate matter are released into the atmosphere, which results in the increase of the number of particles in the atmosphere. Once the number of particles is beyond the self-purification capacity of the environment, the environmental problems such as haze will appear.The atmosphere together with the tiny particles in it makes up what we call the aerosol system. Understanding the dynamic behavior of aerosol particles will help us to better understand the generation, dissemination and evolution of atmospheric pollutants and to better solve the air pollution problem. Brownian coagulation, which is one of the most important dynamics for aerosol particles, is a process whereby particles collide with one another and stick together to form larger particles due to their relative Brownian motion. All contents of this article center on the Brownian coagulation of aerosols and can be divided into two parts:one is about the theory of efficiency of aerosol Brownian coagulation in different regimes; the other is about the numerical methods for Brownian coagulation kinetics.Firstly, we studied the coagulation efficiency in the near continuum regime taking account of the influence of the change in resistance coefficient as well as the appearance of the van der Waals interaction when two particles get close to each other. When calculating the resistance coefficient, we assumed all the particles move as if the surrounding particles are at rest. When two particles were close enough, the slip effect of gas molecules on the surfaces and the van der Waals interaction between particles were considered. Using the classical model for calculating Brownian coagulation efficiency, we finally obtained the coagulation efficiency by numerical integration method for various particle radii. For aerosols in the continuum and free molecule regimes, i.e., when the size of particles is much larger than the mean free path of gas molecules and far less than the mean free path, the Brownian coagulation efficiency can be predicted by the diffusion theory and the kinetic theory of free molecules, respectively. When the particle size and the mean free path of gas molecule have the same order of magnitudes, or with regard to the aerosols in the transition regime, both theories fail to predict the accurate coagulation efficiency. In order to derive a formula of Brownian coagulation efficiency in the transition regime, researchers divided the transport process of aerosol particles into two stages, one is described by the classical diffusion theory, the other by the kinetic theory of free molecules. In this thesis, we replaced the free molecule kinetic process with a process that was described by a modified diffusion theory taking into account the influence of the tangential relative motion of two particles. The basic idea of this model is that the tangential relative motion causes two particles to move away from each other, which thereby reduces the probability of collisions. Solving the equations of two different processes under given boundary conditions and matching the coagulation efficiency in the free molecule regime, we finally derived an expression for calculating the coagulation efficiency in the transition regime. Using this expression, we can easily determine the critical particle size when the theory of near continuum regime begins to fail.As to the numerical solution of aerosol Brownian coagulation process, this thesis mainly involves two commonly used methods, namely the sectional method and the method of moments. In the framework of the sectional method, we derived different sectional models by introducing an approximation factor into the conventional sectional method and compared the accuracy of these approximate models. As to the method of moments, we analytically derived the asymptotic behavior of self-preserved aerosols as well as the coagulation time required for an aerosol to achieve the self-preserving distribution based on the theory of Taylor expansion method of moments. Taking advantage of the results provided by the high-precision sectional method, we derived a new set of moment evolution equations that is able to predict the asymptotic behavior of a ’real’ aerosol on the base of Taylor expansion method of moments. By dimensional analysis, we also derived a general expression for different methods of moments that only involved the first three moments. There is a variable coefficient that depends on a dimensionless parameter in the general expression and the relation between this coefficient and the dimensionless parameter differs between different methods of moments. Using the basic idea of the Taylor expansion method of moments, we proposed a new approach named the direct expansion method of moments to close the moment evolution equations. In order to improve the accuracy of the new method, we introduced two fractional order moments into the moment evolution equations by variable substitution. Using numerical differential method, we extended the direct method of moments to the Brownian coagulation in the transition and entire size regimes.