Modeling particle size distribution in emulsion polymerization reactors

Abstract

A review of the use and limitations of Population Balance Equations (PBE) in the modeling of emulsion polymerisation (EP), and in particular of the particle size distribution of the dispersed system is presented. After looking at the construction of the general form of PBEs for EP, a discussion of the different approaches used to model polymerization kinetics is presented. Following this, specific applications are presented in terms of developing a two-dimensional PBE for the modeling of more complex situations (for example the particle size distribution, PSD, and the composition of polymerizing particles). This review demonstrates that while the PBE approach to modeling EP is potentially very useful, certain problems remain to be solved, notably: the need to make simplifying assumptions about the distribution of free radicals in the particles in order to limit the computation complexity of the models; and the reliance of full models on approximate coagulation models. The review finishes by considering the different numerical techniques used to solve PBEs.

Development of a Computational Framework to Model the Scale‐up of High‐Solid‐Content Polymer Latex Reactors

“…The coagulation kernel employed in this work is based on the DLVO approach; an overview of the kernel is provided in Appendix A. It has been shown in previous studies [12,24,25] that this coagulation kernel can predict the rate of particle coagulation in relatively dilute latexes (around 30 vol.-% solids content). In more concentrated systems, the expression used to calculate the inverse Debye length must be modified to account for concentration effects [26] (see Eq.…”

“…Kemmere et al [38] studied the influence of process conditions on the coagulation behavior of polystyrene and polyvinyl acetate latexes in mixing vessels ranging in size from 0.9 L to 7.5 L. They concluded that even at higher solid contents (∼50 vol.-%), perikinetic coagulation was the dominant mechanism. Orthokinetic aggregation is thought to be prevalent in mixing systems where particles are constantly subjected to high rates of shear (c > 100 s -1 ) and the particles are of relatively large size (d p > 1 lm) [12]. In this work, perikinetic aggregation is assumed to be the dominant mechanism of coagulation, a reasonable assumption given that the maximum particle diameter allowed for in the simulations is 700 nm and operating predominantly within the laminar regime (c max < 100 s -1 ).…”

“…Over the past decade, significant progress has been made in the development of mathematical models for predicting the evolution of PSD under different operating conditions. The complex PSDs required to HSC latexes necessitate the use of population balances for PSD prediction [12].…”

Modeling Particle Size Distribution in Heterogeneous Polymerization Systems Using Multimodal Lognormal Function

“…The particle size distribution (PSD) is one of the most important characteristics of polymer latexes/resins, since properties such as viscosity, maximum solids content, adhesion and drying time depend on the profile of this distribution (Vale and McKenna, 2005). Furthermore, the understanding of the dynamics of PSD is very important for process monitoring and final quality control of heterogeneous polymerization processes (Hosseini et al, 2013).…”

“…Therefore, PSD modeling has received great attention with the proposal of models such as Population Balance Equations (PBE) (Machado et al, 2000;Araújo et al, 2001;Kiparissides et al, 2002;Immanuel et al, 2002;Coen et al, 2004). However, according to Vale and McKenna (2005), even when these difficulties in coagulation modeling are overcome, the PBEs are difficult to solve if they include kinetic and/or hydrodynamic complete models. Despite recent advances in techniques for experimental determination, difficulties in determining important variables related to the quality and productivity of polymers still remain (Machado et al, 2007).…”