Drop mixing in suspension polymerisation

In suspension polymerisation, monomer is suspended as liquid droplets in a continuous water phase by means of strong agitation and the presence of a suspending agent. As the suspension polymerisation proceeds, the viscosity of a monomer-polymer droplet increases with conversion. Hence, the physical behaviour of the droplet changes during the process. When new dispersible material is added to the existing suspension drops, the new material and existing drops can remain segregated for significant amounts of time. The aim of this project was to study the behaviour of drop mixing when new material is added to the existing suspension polymerisation. This study concentrated on the effect of the dispersed phase viscosity on drop mixing. The results show that viscosity affects drop size and that may then affect the rate of coalescence between drops. A critical drop size exists which determines the coalescence efficiency effect. Above the critical drop size, mixing rate increases as the drop viscosity decreases. While below the critical drop size, drop size of the dispersion determines the coalescence rate; as the drop size increases, coalescence rate also increases. The investigation of the effect of suspending agent shows that Tween 20 is more efficient in stabilising and protecting the drops, based on a weight basis, than PVA as the coalescence rate is lower with Tween 20.     

Operation of semi-batch emulsion polymerisation reactors: Modelling, validation and effect of operating conditions

A detailed dynamic model was developed for a styrene emulsion polymerisation semi-batch reactor to predict the evolution of the product particle size distribution (PSD) and molecular weight distribution (MWD) over the entire range of monomer conversion. A system exhibiting zero-one kinetics was employed, with the model comprising a set of rigorously developed population balance equations to predict monomer conversion, PSD and MWD. The modelling equations included diffusion-controlled kinetics at high monomer conversion where the transition from the zero-one regime to a pseudo-bulk regime occurs. The model predictions were found to be in good agreement with experimental results. Both particle growth and the PSD were found to be strongly affected by the monomer feedrate. Reactor temperature had a major influence on the MWD which was, however, insensitive to changes in the monomer feedrate. These findings were confirmed experimentally. As a result, it seems reasonable to propose that the use of the monomer feedrate to control the PSD and the reactor temperature to control the MWD are appropriate in practical situations. Consequently, an optimal monomer feed trajectory was developed off-line (using the validated reactor simulation) and verified experimentally by producing a polymer with specific PSD characteristics.     

Population balance model versus lumped model for emulsion polymerisation: Semi-batch and continuous operation

In this article, a systematic comparison is made of a detailed population balance model of the emulsion polymerisation process that accounts for the dynamic evolution of the entire particle size distribution with a simple model of the process that accounts only for the dynamic evolution of the average particle size and the total particles. Both models account for the underlying mechanisms of the process to the level admissible within their respective frameworks. The predictions of the two models are compared under both batch and continuous operation. The aim is to elucidate the degree of disparity of model predictions for batch operation, and to elucidate the ability of the simple lumped models to predict oscillatory dynamics for continuous operation. The focus is on the comparison of the predictions of important control variables such as solids content (conversion), total particles and average particle size, but also those of important particle phenomena of nucleation, growth and coagulation. It is found that with respect to these lumped control variables, the simple model performs well in matching the detailed model, and hence will be a very valuable tool for the purpose of on-line feedback control. However, the detailed models will be important for distributed control variables such as the entire particle size distribution.     

Particulate stabilisers for drops in suspension polymerisation: Use of a wax model

Finely divided inorganic solids can be used for drop stabilisation in suspension polymerisation. In order to clarify the role of these solids, experiments have been carried out using a model system in which wax drops were dispersed in water in the presence of magnesium hydroxide. Drop sizes were reduced if the hydroxide was precipitated in situ before dispersion of the wax. As the loading of this precipitate increased, the average drop size passed through a minimum. The presence of a surfactant modified the effect of the hydroxide. Electrolyte, which is formed in the precipitation reaction, also influences the drop size. The separate effects of solid hydroxide, surfactant and electrolyte are not additive. There is some evidence for a nucleating effect which may not be desirable in suspension polymerisation.     

Energy and population balances in comminution process modelling based on the informational entropy

The results of theoretical and experimental studies of a comminution process are presented. There are two random functions: the selection function and the breakage function in the stochastic model based on a population balance. This model enables prediction of particle size distributions of comminution products after determination of both random functions. Maximum entropy method is used in the entropy model for determining the breakage function. Two cases are analysed, based on continuous and discrete particle size distribution functions of the fed material. Apart from mass balance, the energy balance of comminution process is also used. Searched form of breakage function is determined with the application of methodology of calculus of variations. The results of experimental identification of both models are presented. The parameters that occur in the discrete form of the selection and breakage functions were the identification objects. The results of experimental investigations of quartz sand single comminution in a laboratory jet mill provided an identification base. The experimentally identified results of the entropy model confirmed the adequacy of the theoretical analysis and demonstrated the possibility of adequate prediction of particle size distributions resulting from single comminution.     

A generalized population balance model for the prediction of particle size distribution in suspension polymerization reactors

In the present study, a comprehensive population balance model is developed to predict the dynamic evolution of the particle size distribution in high hold-up (e.g., 40%) non-reactive liquid-liquid dispersions and reactive liquid(solid)-liquid suspension polymerization systems. Semiempirical and phenomenological expressions are employed to describe the breakage and coalescence rates of dispersed monomer droplets 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. The fixed pivot (FPT) numerical method is applied for solving the population balance equation. The predictive capabilities of the present model are demonstrated by a direct comparison of model predictions with experimental data on average mean diameter and droplet/particle size distributions for both non-reactive liquid-liquid dispersions and the free-radical suspension polymerization of styrene and VCM monomers.     

Miniemulsion polymerisation in pseudo-bulk regime: Mathematical modelling, prediction and optimal strategy of operation

A dynamic mathematical model based on pseudo-bulk kinetics was developed for styrene miniemulsion polymerisation and validated using experimental data. Key findings are that the developed model match reasonably with experimental data and is able to predict the polymerisation attributes and product properties such as fractional conversion, average molecular weight, molecular weight distribution (MWD), average particle size and particle size distribution (PSD) in miniemulsion polymerisation. Optimal strategy of semibatch operation was developed using reaction temperature and monomer feed rate as process variables with specified initial conditions.     

Population balance modelling of droplet coalescence and break-up in an oscillatory baffled reactor

This paper presents new population balance analysis to describe simultaneous coalescence and break-up in the formation of methylmethacrylate droplets in a batch oscillatory baffled reactor. It is concluded that the droplet data can very well be described by a model in which coalescence is taken to be shear induced, selection for break-up proceeds at a rate proportional to droplet volume and approximately four equally sized break-up fragments are produced per break-up event. It is shown that the experimental droplet size distribution data are self-similar in form and exhibit asymptotic behaviour characteristics also seen in the model. The coalescence rate is found to vary as the square of the oscillation frequency and the selection rate to vary with the oscillation frequency to the power five. As a result the asymptotic mean droplet volume is inversely proportional to the oscillation frequency.     

Coalescence during bubble formation at two neighbouring pores: An experimental study in microscopic scale

This work studies the effect of the liquid properties and the operating conditions on the interactions between under-formation bubbles in a cell equipped with two adjacent micro-tubes (i.d. ) for the gas injection, placed 210, 700 and apart. This set-up simulates, though in a simplified manner, the operation of the porous sparger in a bubble column, and it is used to study the bubble interactions observed on the sparger surface. Various liquids covering a wide range of surface tension and viscosity values are employed, while the gas phase is atmospheric air. A fast video recording technique is used both for the visual observations of the phenomena occurring onto the tubes and for the bubble size measurements. The experiments reveal that the interactions between under-formation bubbles as well as the coalescence time depend strongly on the liquid properties, the distance between the tubes and the gas flow rate. Two correlations, which can be found helpful for the bubble column design, have also been formulated and are in good agreement with the available experimental data.     

Antisolvent crystallization: Model identification, experimental validation and dynamic simulation

This paper is concerned with the development, simulation and experimental validation of a detailed antisolvent crystallization model. A population balance approach is adopted to describe the dynamic change of particle size in crystallization processes under the effect of antisolvent addition. Maximum likelihood method is used to identify the nucleation and growth kinetic models using data derived from controlled experiments. The model is then validated experimentally under a new solvent feedrate profile and showed to be in good agreement. The resulting model is directly exploited to understand antisolvent crystallization behavior under varying antisolvent feeding profiles. More significantly, the model is proposed for the subsequent step of model-based optimization to readily develop optimal antisolvent feeding recipes attractive for pharmaceutical and chemicals crystallization operations.     

Theoretical modelling of the effect of surface active species on the mass transfer rates in bubble column reactors

The complex composition of the liquid media in bubble column reactors makes their understanding and theoretical modelling challenging. In this work we have studied the effect of surface tension and contaminants, salts, on the mass transfer rates from a theoretical point of view, looking for a deeper understanding on the effect of surface active species which usually reduce surface tension and modify bubble surface behaviour. The specific contact area is obtained using a population balance where the effect of the presence of contaminants is addressed by the proper theoretical closures for bubble coalescence efficiency, for partially and fully immobile surfaces, and bubble break-up. Meanwhile, the contribution of contaminants to the liquid-film resistance is implemented as function of the coverage of the surface of the bubbles. It was found that the degree of bubble surface coverage not only affects bubble coalescence but also their break-up. The ion strength defines bubbles stability and the critical Weber number can be predicted as function of ion strength. Furthermore, the mass transfer rates are function of the surface coverage by the electrolytes. The model was able to predict k_La taking into account the fact that the concentration profiles surrounding individual bubbles are not completely developed due to the presence of other bubbles, in agreement with previous results from the literature.     

Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling. Part 2: Kinetic modelling and identification

The batch seeded cooling solution crystallization of a fine organic material, exhibiting a platelet-like habit, was investigated and a model of the time variations of the crystal size distribution (CSD) was designed using two-dimensional population balance equations. Activated surface secondary nucleation and attrition secondary nucleation mechanisms were considered, coupled with growth mechanisms of two main dimensions of the crystal, resulting in a set of eight kinetic parameters. The model relates the effects of the main batch operating conditions: seeding temperature, cooling rate and total area of the seed particles, on both the supersaturation profile and bi-dimensional CSD. Surface secondary nucleation occurs first since it is promoted by the introduction of seeds and remains active as long as the relative supersaturation exceeds a threshold value of about 16%. It vanishes below which could be expected as we deal with an activated mechanism. Contact secondary nucleation occurs later when the concentration of solid is sufficient. It is spread over time until supersaturation disappears at the end of the batch process. This contact secondary mechanism is assumed to be the dominant nucleation mechanism as it generates about two-thirds of the final crystal number. Sharp desupersaturation profile following the introduction of seeds, which was observed experimentally, is shown to be quantitatively described through the growth of seed particles. The termination of the batch process is more difficult to represent. Due to crystal attrition, distinct growth rates between initial and secondary crystals or growth rate dispersion might explain such difficulty.     

Semi-batch emulsion copolymerization of styrene and butyl acrylate for production of high solids content latexes: Experiments and mathematical model

Polymer latexes with high solids content exhibit several advantages such as lower costs of transport and storage and shorter drying and film formation times. To keep the apparent viscosity at satisfactory levels, the particle size distributions should be either broad or multimodal. In the present work, the production of high solid content latexes by emulsion copolymerization of styrene and butyl acrylate was studied in a semi-batch process in which the nucleation of a second population of particles is promoted by the instantaneous (shot) feeding of an additional charge of emulsifiers. Latexes of about 64 wt% of solids with bimodal particle size distributions and reasonably low apparent viscosity were produced. A representative mathematical model for the copolymerization processes that accounts for the changes in the particle size distribution that occurred in the process is presented, tested and validated with the experimental data measured during the experiments.     

On the prediction of internal particle morphology in suspension polymerization of vinyl chloride. Part I:: The effect of primary particle size distribution

The present study provides a comprehensive investigation on the determination of the primary particle size distribution in the suspension “powder” polymerization of vinyl chloride. The primary particle size distribution inside the polymerizing monomer droplets is determined by the solution of a population balance equation governing the nucleation, growth, and aggregation of the primary particles. The stability of the colloidal primary particles is expressed in terms of the electrostatic and steric stabilization forces. The primary particle stability model includes the effects of agitation, temperature, electrolyte as well as primary and secondary stabilizer concentrations. It also includes both diffusive and shear-induced particle destabilization mechanisms. The proposed stability model is shown to accurately describe existing experimental data on particle number, mean particle size and particle size distribution for both bulk and suspension vinyl chloride polymerizations. The primary particle population balance model can predict the critical monomer conversion at which massive particle aggregation occurs leading to the formation of a continuous network of primary polymer particles inside the polymerizing monomer droplets. A detailed investigation on the predicted critical monomer conversion is carried out including its dependence on the rate of agitation, temperature, electrolyte concentration, as well as the concentrations of the primary and secondary stabilizers.     

A model of the coagulation process with solid particles and flocs in a turbulent flow

A mathematical model was developed on the basis of population balances to predict the floc size distribution in a coagulating suspension. The coagulation process is performed in a stirred tank reactor with a turbulent flow field. In the population model the influence of the different local energy charges inside the reactor is taken into account. Moreover two sorts of particles are distinguished, i.e. the originally present and completely dispersed primary particles and the flocs. Contrary to the primary particles the flocs can be disrupted due to pressure and shear forces as they are mechanically not very stable. This different behaviour requires separate population balances for the two sorts of particles. The model parameters that are necessary are adapted to one single experiment.For the steady state the results represent different floc size distributions dependent on the solid concentration and the energy charge. Moreover it is shown that the assumption of an ideally mixed reactor that is often used cannot be maintained to be always true for the prediction of the resulting floc size distribution. The calculation results achieved are validated by image processing measurements of coagulating quartz particles in an aqueous suspension.     

Self-Compacting Concrete: Theoretical and experimental study

This paper addresses experiments and theories on Self-Compacting Concrete. First, the features of “Japanese and Chinese Methods” are discussed, in which the packing of sand and gravel plays a major role. Here, the grading and packing of all solids in the concrete mix serves as a basis for the development of new concrete mixes. Mixes, consisting of slag blended cement, gravel (4-16 mm), three types of sand (0-1, 0-2 and 0-4 mm) and a polycarboxylic ether type superplasticizer, were developed. These mixes are extensively tested, both in fresh and hardened states, and meet all practical and technical requirements such as medium strength and low cost. It follows that the particle size distribution of all solids in the mix should follow the grading line as presented by Andreasen and Andersen. Furthermore, the packing behaviour of the powders (cement, fly ash, stone powder) and aggregates (three sands and gravel) used are analysed in detail. It follows that their loosely piled void fraction are reduced to the same extent (23%) upon vibration (aggregates) or mixing with water (powders). Finally, the paste lines of the powders are used to derive a linear relation between the deformation coefficient and the product of Blaine value and particle density.     

Part IV: Dynamic evolution of the particle size distribution in particulate processes. A comparative study between Monte Carlo and the generalized method of moments

The present work provides a comparative study on the numerical solution of the dynamic population balance equation (PBE) for batch particulate processes undergoing simultaneous particle aggregation, growth and nucleation. The general PBE was numerically solved using three different techniques namely, the Galerkin on finite elements method (GFEM), the generalized method of moments (GMOM) and the stochastic Monte Carlo (MC) method. Numerical simulations were carried out over a wide range of variation of particle aggregation and growth rate models. The performance of the selected techniques was assessed in terms of their numerical accuracy and computational requirements. The numerical results revealed that, in general, the GFEM provides more accurate predictions of the particle size distribution (PSD) than the other two methods, however, at the expense of more computational effort and time. On the other hand, the GMOM yields very accurate predictions of selected moments of the distribution and has minimal computational requirements. However, its main disadvantage is related to its inherent difficulty in reconstructing the original distribution using a finite set of calculated moments. Finally, stochastic MC simulations can provide very accurate predictions of both PSD and its corresponding moments while the MC computational requirements are, in general, lower than those required for the GFEM.     

Characterization of pneumatic transportation of pulverised coal in a horizontal pipeline through measurement and computational modelling

Pneumatic conveyors which feed the burners at coal fired power plants are not designed for the injection of an increasingly wide variety of modern fuels. The objective of this study is to understand and predict the stable delivery of fuel to the burners. The pneumatic transportation of pulverised coal in a horizontal pipeline has been investigated using a classic dual approach: measuring a set of characteristic parameters of the dispersed flow as well as its computational modelling. The Large Eddy Simulation approach is used for the modelling of the air/fuel two-phase flow. A particular treatment for the solid phase has been designed in order to cope with gravity effects. A good qualitative agreement between the modelling results and the experimental data has been found. The importance of gravity effects compared to inter-particle collisions is addressed.     

Drop breakage and coalescence in the toluene/water dispersions with dissolved surface active polymers PVA 88% and 98%

The influence of two PVAs of the same molecular weight (13,000–23,000) and different degree of hydrolysis equal to 88% and 98% on breakage and coalescence of toluene droplets in the liquid/liquid dispersion were considered for PVA concentration range 0.001–0.01%. Analysis of experimental results shows that drop coalescence is significant only in the system containing 0.001% PVA. Drop coalescence for polymer concentration range 0.002–0.01% is strongly limited. Therefore, population balance was solved using breakage and coalescence expressions with assumed partially mobile drop interfaces for the lowest PVA concentration. For c ≥ 0.002% drop size distributions were properly predicted using only breakage model. Multifractal formalism was used to take into account intermittent character of turbulence and explain drop behavior. Larger drop size reduction by PVA of lower degree of hydrolysis observed experimentally was confirmed by the model.