Coagulative nucleation model

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

Nomura and Fujita (12), Dougherty (13-14), and Storti et al. (12). Space does not permit a review of each of these papers. This paper presents the development of a more extensive model in terms of particle formation mechanism, copolymer kinetic mechanism, applicability to intervals I, II and III, and the capability to simulate batch, semibatch, or continuous stirred tank reactors (CSTR). Our aim has been to combine into a single coherent model the best aspects of previous models together with the coagulative nucleation theory of Feeney et al. (8-9) in order to enhance our understanding of... 

Aerosol Dynamics. Inclusion of a description of aerosol dynamics within air quaUty models is of primary importance because of the health effects associated with fine particles in the atmosphere, visibiUty deterioration, and the acid deposition problem. Aerosol dynamics differ markedly from gaseous pollutant dynamics in that particles come in a continuous distribution of sizes and can coagulate, evaporate, grow in size by condensation, be formed by nucleation, or be deposited by sedimentation. Furthermore, the species mass concentration alone does not fliUy characterize the aerosol. The particle size distribution, which changes as a function of time, and size-dependent composition determine the fate of particulate air pollutants and their... 

Prindle and Ray (ZB.) have recently analyzed the same styrene data using a hybrid model consisting of the micellar nucleation mechanism above the CMC and of the homogeneous nucleation and coagulation mechanism below the CMC. Their simulations show a much steeper rise in the particle number concentration precisely at the CMC than predicted by EPM. Their hybrid model does not appear to predict that the particle concentration levels off at high surfactant concentrations. 

The aerosol module treats condensation, evaporation, nucleation, deposition and coagulation of aerosols (Baklanov 2002) as shown in Fig. 16.3a. The numerical evolution of aerosols is solved by treating the aerosol size distributions as normal distributions. However, the aerosol module as a part of the modelling system has not been routinely tested yet in the 3D version, i.e. only in OD (see Gross and Baklanov 2004) and although it was evaluated in the 3D Enviro-HILAM research version of the model (see Korsholm et al. 2008a, b). 

Perhaps the first studies to employ agglomeration were those related to the formation of the solar system. The use of the coagulation equation, essentially a macroscopic version of the master equation for systems which can be treated as being controlled by one independent variable and time, has been of some importance in recent simulations of the process of star formation. Employed for some time in the study of nucleation, " the results were first used extensively by Safronov and his collaborators in the modeling of planetary formation in the solar nebula. 

At the beginning of the chapter it is shown that the usual models for coagulation and nucleation presented in Chapters 7 and 10 arc special cases of a more general theory for very small particles. An approximate criterion is given for determining whether nucleation or coagulation is rate controlling at the molecular level. The continuous form of the GDE is then used to derive balance equations for several moments of the size distribution function. 

Suppose the aerosol contained in a large chamber is composed of particles larger than the mean free path of the gas. The surface-to-volume ratio of the chamber is sufficiently small to neglect deposition on the walls, and the composition of the system is uniform. Coagulation takes place, and at the same time the particles grow as a result of diffusion-controlled condensation but sedimentation can be neglected. Homogeneous nucleation does not occur and the system is isothermal. A system of this type has been used to model aerosol formation in photochemical air pollution. 

Immanuel, C. D. Doyle, F. J. 2003 Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation application to emulsion... 

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