Dynamic evolution of the particle size distribution in suspension polymerization reactors: A comparative study on Monte Carlo and sectional grid methods

Abstract

In the present study, an efficient Monte Carlo (MC) algorithm and a fixed pivot technique (FPT) are described for the prediction of the dynamic evolution of the droplet/particle size distribution (DSD/PSD) in both non-reactive liquid-liquid dispersions and reactive liquid(solid)-liquid suspension polymerization systems. Semi-empirical and phenomenological expressions are employed to describe the breakage and coalescence rates of dispersed monomer droplets/particles, in terms of the type and concentration of suspending agent, quality of agitation, and evolution of the physical, thermodynamic and transport properties of the polymerization system. Moreover, the validity of the numerical calculations is first examined via a direct comparison of simulation results obtained by both numerical methods with experimental data on average particle diameter and droplet/particle size distributions for both non-reactive liquid-liquid dispersions and the free-radical suspension polymerization of methyl methacrylate (MMA). Additional comparisons between the MC and the FP numerical methods are carried out under different polymerization conditions. The simulation results reveal that both numerical methods are capable of predicting the mean and the distributed particulate properties of both non-reactive and reactive suspension processes.On décrit dans cet article un algorithme de Monte Carlo (MC) efficace et une technique de pivot fixe (FPT) pour prédire l'évolution dynamique de la distribution de taille de gouttelettes/particules (DSP/PSD)à la fois dans des dispersions liquide-liquide non réactives et des systèmes de polymérisation par suspensions liquide (solide)-liquide réactifs. On emploie des expressions semi empiriques et phénoménologiques pour décrire les taux de rupture et de coalescence de gouttelettes/particules de monomères dispersés, en fonction du type et de la concentration d'agent de suspension, de la qualité de l'agitation et de l'évolution des propriétés physiques, thermodynamiques et de transport du système de polymérisation. En outre, la validité des calculs numériques est d'abord examinée par une comparaison directe des résultats de simulation obtenus par les deux méthodes numériques avec les données expérimentales du diamètre de particule et de la distribution de taille de gouttelettes/particules moyensà la fois pour les dispersions liquide-liquide non réactives et la polymérisation par suspensions de radicaux libres du méthacrylate de méthyle (MMA). D'autres comparaisons entre les méthodes numériques MC et FP sont effectuées pour des différentes conditions de polymérisation. Les résultats de simulation révèlent que les deux méthodes numériques sont capables de prédire les propriétés particulaires moyennes et distribuées des deux procédés par suspension non réactif et réactif.

Liquid–liquid two-phase systems for the production of porous hydrogels and hydrogel microspheres for biomedical applications: A tutorial review

“…The size of the monomer droplets is determined by two major factors, the rate at which droplets are broken up by the input of mechanical energy (e.g. stirring rate) and the rate at which monomer droplets grow in size by merging with other droplets (coalescence) [23]. In a suspension polymerization, the large particles that form tend to aggregate and settle out, while a stable latex of particles may result from an emulsion polymerization [20].…”

“…In less viscous solutions, coalescence may dominate due to the ability of the phase separated domains to encounter each other by diffusion [56]. With mechanical stirring, droplets will encounter each other frequently and the kinetics of the phase separation process will be similar to those that govern droplet size in a stirred suspension polymerization [23]. …”

A differentially weighted Monte Carlo method for two-component coagulation

“…Kruis et al [4,18] adopted the stepwise constant volume method to track the time evolution of multivariate systems including particle size, charge and component. Saliakas et al [19] also used the stepwise constant volume method to predict the dynamic evolution of the droplet/particle size distribution in both non-reactive liquid-liquid dispersions and reactive liquid (solid)-liquid suspension polymerization systems. Matsoukas et al [20,21] used the constant number method to investigate the mixing and granulation of components.…”

Stochastic Simulation of Droplet Interactions in Suspension Polymerization of Vinyl Chloride

“…Namely, here time continuous processes and discrete event processes occur in parallel thus solution of the system of equations requires a special technique -combination of a continuous time and discrete event treatment. This phenomenon was studied by Salikas et al [8] but they didn't describe the problem explicitly.…”