Time scale analysis for fluidized bed melt granulation-II: Binder spreading rate

The spreading time of liquid binder droplet on the surface a primary particle is analyzed for Fluidized Bed Melt Granulation (FBMG). As discussed in the first paper of this series (Chua et al., in press) the droplet spreading rate has been identified as one of the important parameters affecting the probability of particles aggregation in FBMG. In this paper, the binder droplet spreading time has been estimated using Computational Fluid Dynamic modeling (CFD) based on Volume of Fluid approach (VOF). A simplified analytical solution has been developed and tested to explore its validity for predicting the spreading time. For the purpose of models validation, the droplet spreading evolution was recorded using a high speed video camera. Based on the validated model, a generalized correlative equation for binder spreading time is proposed. For the operating conditions considered here, the spreading time for Polyethylene Glycol (PEG1500) binder was found to fall within the range of 10⁻² to 10⁻⁵ s. The study also included a number of other common binders used in FBMG. The results obtained here will be further used in paper III, where the binder solidification rate is discussed.     

Time scale analysis for fluidized bed melt granulation I: Granule–granule and granule–droplet collision rates

Fluidized bed spray granulators (FBMG) are widely used in the process industry for particle size growth; a desirable feature in many products, such as granulated food and medical tablets. In this paper, the first in a series of four discussing the rate of various microscopic events occurring in FBMG, theoretical analysis coupled with CFD simulations have been used to predict granule–granule and droplet–granule collision time scales. The granule–granule collision time scale was derived from principles of kinetic theory of granular flow (KTGF). For the droplet–granule collisions, two limiting models were derived; one is for the case of fast droplet velocity, where the granule velocity is considerable lower than that of the droplet (ballistic model) and another for the case where the droplet is traveling with a velocity similar to the velocity of the granules. The hydrodynamic parameters used in the solution of the above models were obtained from the CFD predictions for a typical spray fluidized bed system. The granule–granule collision rate within an identified spray zone was found to fall approximately within the range of 10⁻²–10⁻³ s, while the droplet–granule collision was found to be much faster, however, slowing rapidly (exponentially) when moving away from the spray nozzle tip. Such information, together with the time scale analysis of droplet solidification and spreading, discussed in part II and III of this study, are useful for probability analysis of the various event occurring during a granulation process, which then lead to be better qualitative and, in part IV, quantitative prediction of the aggregation rate.     

Computer simulation of granule microstructure formation

The diagenesis (porous microstructure evolution) of granules formed by a layering growth mechanism in a wet granulation process has been modelled. The model includes the packing of primary particles with a given size and shape distribution, and the deposition, spreading, and solidification of binder droplets within the growing granule. The dependence of granule porosity on the binder/solids ratio, primary particle size and morphology, and the rates of binder spreading and solidification has been investigated. The results are presented in the form of structure maps relating volume-averaged microstructure parameters with dimensionless groups including the ratio of droplet spreading and solidification times and the mean time between particle collisions. These graphs can guide the selection of process operating conditions or formulation ingredient properties required to obtain a particular granule microstructure.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

Kinetics of fluidized bed melt granulation—II: Modelling the net rate of growth

Previous work [Tan, H.S., Goldschmidt, M.J.V., Boerefijn, R., Hounslow, M.J., Salman, A.D., Kuipers, J.A.M. (2004a). Building population balance for fluidized bed granulation: lessons from kinetic theory of granular flow. Powder Technology, 142, 103-109] shows that we can derive an aggregation kernel (equi-partition of kinetic energy (EKE)) on the basis of the kinetic theory of granular flow and use it effectively to describe the net granule growth in fluidized bed melt granulation (FBMG). In this paper, we incorporate the EKE kernel into a population balance model to extract the effective aggregation rate constant that accounts for the net granule growth for the series of FBMG experiments shown in Tan, et al. [(2004b). Kinetics of fluidized bed melt granulation I: effect of process variables, Chemical Engineering Science, to be submitted]. These extracted rate constants are subsequently expressed as a function of different operating condition. The results consistently show that the aggregation rate constant increases in direct proportion with binder spray rate, from where we conclude that the rate of granule formation is directly dependent on the amount of binder available for aggregation per unit time. The aggregation rate constant was also observed to increase with higher bed temperature when a higher viscosity binder was used, but showed a maximum value for a less viscous binder as a function of temperature. The aggregation rate was also seen to be faster when granulating using a larger droplet size and at a lower fluidizing air velocity. The observations in the rate constant plot can be effectively explained by the physical parameters in the EKE model and the sequence of rate events proposed in Tan, et al. [(2004b). Kinetics of fluidized bed melt granulation I: effect of process variables, Chemical Engineering Science, to be submitted].     

Kinetics of fluidised bed melt granulation V: Simultaneous modelling of aggregation and breakage

The main purpose of this paper is to quantify the aggregation and breakage rates in fluidised bed melt granulation (FBMG) and to subsequently relate them to various experimental conditions. The earlier paper of this series (2004d, Powder Technology 143-144, 65-83) illustrated a sequence of development and verification work on a breakage model for FBMG, based on the population balance modelling work on tracer experimental studies. A new error-weighted integral technique was also developed, which allows simultaneous extraction of the aggregation and breakage selection rate constant, as well as the attrition constant that reveals the relative amount of attrition during FBMG. Further research is conducted here, as the similar modelling strategy is employed to extract the aggregation and breakage kinetics at different operating conditions. A series of plots revealing the influence of operating conditions (binder spray rates, bed temperature, droplet size and fluidising air flow rate) on these extracted constants are therefore established. The aggregation rate constant plots reveal that the particle aggregation rate is dependent on the amount of binder available per unit time, and hence scales directly with the binder spray rate. The aggregation rate is also observed to increase with increased bed temperature when a higher viscosity binder is used, but reveals a maximum aggregation rate for a less viscous binder. The aggregation rate also increases with larger droplet size and lower fluidising air velocity. The breakage selection rate and attrition constant plot both reveal no direct dependence on binder spray rate, due to the separation in time scale over which the granule breakage occurs. The breakage rate and the extent of granule attrition is also found to decrease with increased bed temperature and increased fluidising air velocity. Due to scatter in the data, it is not possible to deduce any sensible trend on the influence of droplet size on its relative breakage rate and attrition.     

Dynamics of bubble breakup in a microfluidic T-junction divergence

The aim of this work is to investigate experimentally the bubble breakup in a microfluidic T-junction divergence using a high-speed digital camera and a micro-Particle Image Velocimetry (micro-PIV) system. The breakup and non-breakup of N₂ bubbles in glycerol–water mixtures with several concentrations of sodium dodecyl sulphate (SDS) as surfactant were studied with capillary number ranging from 0.001 to 0.1. The cross section of PMMA square microchannel is 400 μm wide and 400 μm deep. Four various flow patterns were observed at the T-junction by changing gas and liquid flow rates. The dynamics of three various types of symmetric breakup of bubbles were investigated. The symmetric breakup of bubbles type I is mainly controlled by the augmented pressure in liquid phase. The symmetric breakup of bubbles type II is controlled by both the increased pressure and viscous forces. In the symmetric breakup of bubbles type III, a scaling law for the minimum bubble neck and the remaining time during bubble breaking process were found. The transitions between breakup and non-breakup of bubbles were investigated, and a power–law relationship between bubble extension and capillary number was proposed to predict the transitions between adjacent regimes. Our experimental results reveal that the bubble breakup in a microfluidic T-junction divergence is similar to the droplet behaviours in such a device ( [Jullien et al., 2009] , [Leshansky and Pismen, 2009] and [Link et al., 2004] ).     

Experimental investigation on two-phase air/high-viscosity-oil flow in a horizontal pipe

The flow of very-viscous-oil and air through a horizontal pipe (inner diameter 22 mm) is experimentally studied. We first build and analyze the flow pattern map; a comparison between the air–water and the air–oil flow pattern maps shows a strong influence of the fluid properties. The experimental flow maps are compared with empirical and theoretical ones – Baker (1954), Mandhane et al. (1974), and Petalas and Aziz (1998) – showing a poor agreement. Experimental pressure gradients are also reported and compared with theoretical model, but also in this case the agreement is not very satisfactory. Finally, the elongated bubble velocity and length are measured and compared to model present in the literature. We conclude that the high viscosity of the liquid phase has a strong influence on the results and that the current models are not able to predict the flow features satisfactorily.     

Computational fluid dynamic simulations of chemical looping fuel reactors utilizing gaseous fuels

A computational fluid dynamic (CFD) model for the fuel reactor of chemical looping combustion technology has been developed, with special focus on accurately representing the heterogeneous chemical reactions. A continuum two-fluid model was used to describe both the gas and solid phases. Detailed sub-models to account for fluid–particle and particle–particle interaction forces were also incorporated. Two experimental cases were analyzed in this study (Son and Kim, 2006; Mattison et al., 2001). Simulations were carried out to test the capability of the CFD model to capture changes in outlet gas concentrations with changes in number of parameters such as superficial velocity, metal oxide concentration, reactor temperature, etc. For the experiments of Mattisson et al. (2001), detailed time varying outlet concentration values were compared, and it was found that CFD simulations provided a reasonable match with this data.     

Gas–liquid flows in medium and large vertical pipes

Gas–liquid bubbly flows with wide range of bubble sizes are commonly encountered in many industrial gas–liquid flow systems. To assess the performances of two population balance approaches – Average Bubble Number Density (ABND) and Inhomogeneous MUlti-SIze-Group (MUSIG) models – in tracking the changes of gas volume fraction and bubble size distribution under complex flow conditions, numerical studies have been performed to validate predictions from both models against experimental data of Lucas et al. (2005) and Prasser et al. (2007) measured in the Forschungszentrum Dresden-Rossendorf FZD facility. These experiments have been strategically chosen because of flow conditions yielding opposite trend of bubble size evolution, which provided the means of carrying out a thorough examination of existing bubble coalescence and break-up kernels. In general, predictions of both models were in good agreement with experimental data. The encouraging results demonstrated the capability of both models in capturing the dynamical changes of bubbles size due to bubble interactions and the transition from “wall peak” to “core peak” gas volume fraction profiles caused by the presence of small and large bubbles. Predictions of the inhomogeneous MUSIG model appeared marginally superior to those of ABND model. Nevertheless, through the comparison of axial gas volume fraction and Sauter mean bubble diameter profiles, ABND model may be considered an alternative approach for industrial applications of gas–liquid flow systems.     

Controlled peroxide-induced degradation of polypropylene in a twin-screw extruder: Change of molecular weight distribution under conditions controlled by micromixing

Controlled degradation of polypropylene (PP) by peroxide was carried out in a laboratory twin-screw extruder ZSK 18 and the change in Molecular Weight Distribution (MWD) was measured using Size Exclusion Chromatography–Differential Viscosimetry (SEC–DV). The MWD results were compared to MWD predictions from a kinetic model developed and validated in earlier work (Iedema et al., 2001) assuming ideal mixing. Clear deviations were observed – the measured MWD was broader – that could only be explained by unaccounted heterogeneity in the extruder. Incorporating the relatively narrow Residence Time Distribution (RTD) in the twin-screw extruder did not lead to MWD broadening. In contrast, the exponential RTD of a Continuously Stirred Tank Reactor (CSTR) yielded a MWD widening that was too extreme. A new micromixing model, based on the striation thinning model by Ottino (1980), was constructed partly based on Monte Carlo sampling using a monomer scission probability (Tobita, 1996). This model was adapted to the geometry of the extruder entrance and the peroxide feed practice consisting of introducing a few per thousand peroxide-rich PP particles among pure PP particles. This micromixing model indeed allowed obtaining very good matches between measured and modeled MWD. Under different experimental conditions with respect to initial PP quality and amount of peroxide added, with a constant value for the striation thinning parameter the errors between measured and predicted MWD were around 5%.     

A new experimental method for determining particle capture efficiency in flotation

A single bubble experiment has been developed for the determination of the capture efficiency of particles by bubbles in flotation under well-controlled hydrodynamics and physico-chemical conditions. In a glass column, small single bubbles (d_b=0.22−1.16 mm) are produced in pure water and then rise at their terminal velocity through a suspension consisting of spherical glass particles where bubble–particle capture takes place. The capture efficiency E_capt is calculated as the ratio of the number of particles captured by one bubble to the number of particles present in the volume swept out by this bubble. Images recorded at high optical magnification show that particles slip on the interface, then adhere to air bubbles individually or as aggregates and cover the rear part of bubble surface. The bubble's effective density and interface contamination level are increased by captured particles. As a result, bubble's rising velocity U_b is reduced along the experimental device. By establishing the relationship between capture efficiency E_capt, bubble rise velocity U_b and bubble clean angle θ_clean, a new approach to measure particle–bubble capture efficiency is proposed. This new experimental technique is applied to provide a new set of data for capture efficiency in the case of bubbles with a clean interface. E_capt is found to grow as d_b decreases and d_p increases, within the range between 0.02 and 0.20, which is in the order of magnitude of experimental results of Ralston and Dukhin (1999) as well as of numerical results of Sarrot et al. (2005). These data are favorably compared to numerical modeling of collision efficiency.     

Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of [Alves et al., 2002a] and [Alves et al., 2002b] . The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.     

Water network design with stochastic optimization approach

Water network (called also water allocation) problem has been addressed in more than 200 papers to date – see recent reviews by Je?owski (2010) and Foo (2009). Though various solution methods have been developed they all have some limitations. This paper addresses water usage network with regeneration processes. Multiple contaminants and two types of water using processes are taken into regard. Simultaneous one stage optimization method was developed to synthesize the network. In order to solve complex MINLP formulation we propose to apply meta-heuristic optimization – adaptive random search method.The paper contains detailed solution algorithm. Several examples with specific features are solved to show efficiency and flexibility of the approach.     

Meso-scale structures of bidisperse mixtures of particles fluidized by a gas

Flow characteristics of bidisperse mixtures of particles fluidized by a gas predicted by the mixture based kinetic theory of [Garzó et al., 2007a] and [Garzó et al., 2007b] and the species based kinetic theory model of Iddir and Arastoopour (2005) are compared. Simulations were carried out in two- and three-dimensional periodic domains. Direct comparison of the meso-scale gas-particle flow structures, and the domain-averaged slip velocities and meso-scale stresses reveals that both mixture and species based kinetic theory models manifest similar predictions for all the size ratios examined in this study. A detailed analysis is presented in which we demonstrate when the species based theory of Iddir and Arastoopour (2005) will reduce to a mathematical form similar to the mixture framework of [Garzó et al., 2007a] and [Garzó et al., 2007b] . We also find that the flow characteristics obtained for bidisperse mixtures are very similar to those obtained for monodisperse systems having the same Sauter mean diameter for the cases examined; however, the domain-averaged properties of monodisperse and bidisperse gas-particle flows do demonstrate quantitative differences. The use of filtered two-fluid models that average over meso-scale flow structures has already been described in the literature; it is clear from the present study that such filtered models are needed for coarse-grid simulations of polydisperse systems as well.     

Heterogeneously doped polyethylene glycol as nano-composite soft matter electrolyte

We have applied the concept of heterogeneous doping [1] to prepare and examine composite electrolytes, consisting of silica particles, low molecular weight polyethylene glycol solvents and lithium perchlorate salt. These “soggy sand” electrolytes combine high ionic conductivities (on the order of mS cm⁻¹) and high Li transference numbers (typically 60–80%) with improved mechanical properties. They were characterized using differential scanning calorimetry, dc-polarization and ac-impedance spectroscopy, zeta potential measurements and viscosimetry. Oxide, size and concentration as well as solvent molecular weight were varied to better understand the influence of ceramic oxide fillers on the ion conduction in these systems. As regarding the filler content, we observe that both conductivity and transference number of Li⁺ start increasing already at low volume fractions of oxide particles, reach a maximum and subsequently decrease to low values. The percolating network is – after initial partial coarsening – found to be stable within the time periods of the measurements.     

Quantitative proof of liquid penetration-involved granule formation in a high shear mixer

Previous work of the authors [K. van den Dries, H. Vromans, Qualitative proof of liquid penetration-involved nucleation in a high shear mixer, Eur. J. Pharm. Sci. 58 (2004), 551–559.] revealed that the granule formation in a high shear mixer depends on a balance between the rate of liquid penetration and binder dispersion. Three distinct nucleation mechanisms could be qualified; (I) granule formation by liquid penetration followed by granule breakage or (II) absence of granule breakage and (III) complete dispersion of the binder liquid. The aim of this study was to quantify the mechanisms of granule formation. A substandard amount (1.5% w/w) of binder liquid was added to a lactose mixture, while the mixer was operating. The powder mixture was frozen with liquid nitrogen after 15 s and analysed by sieving. The results show that, despite the minimal liquid amount, granules are formed under most conditions. It is argued granules are being formed by a liquid penetration process. These freshly formed granules are broken down at low viscosity (< 1 Pa s) and remain intact at higher viscosity (> 1 Pa s). Only at extreme conditions (viscosity > 30 Pa s) hardly any granules are formed. In this case penetration of the liquid becomes practically impossible and the binder is completely dispersed. A model based on the processes of liquid penetration, binder dispersion and granule breakage, confirms the observed nucleation behaviour. It is conclusively shown that an increase in viscosity results in a transition from nucleation mechanism I→II→III.     

Kinetic model of NOx ozonation and its experimental verification

The most of new technologies of reduction of NO_x emission, as literature survey (Skalska et al., 2010b) suggests is focused on NO_x emission control from power plants and mobile vehicles. Fewer investigations are conducted on the NO_x emission abatement from chemical industry. Recently, Chacuk et al. (2007) proposed the model for the nitrous acid oxidation with the use of ozone in gas–liquid contactor. It is well known that not all of NO_x can be totally absorbed in water or nitrous/nitric acid solution, as well as ozone is not totally consumed in the acidic liquid. The reaction between ozone and NO_x can take place also in the gas phase. The ozone injection into exhaust gas stream followed by absorption was proposed as the NO_x emission abatement. The objective of these studies was to propose kinetic model of the process and to determine the rate constants of NO_x ozonation in the laboratory scale batch reactor. The process was carried out in the 0.5 dm³ volume batch reactor for different concentrations of NO, and NO₂ and varying molar ratios of O₃/NO at temperature 25 °C. Gaseous reagents were analyzed using a Fourier Transform Infrared Spectrometer Jasco FTIR-4200. The kinetic model of NO_x ozonation process was proposed and rate constants were estimated based on experimental data.     

Mass transfer and shear in an airlift bioreactor: Using a mathematical model to improve reactor design and performance

Several studies have shown a strong relationship between morphology and agitation ( [Cui et al., 1997] and [Berzins et al., 2001] ). The shear stress distribution and mass transfer are the important parameters which can improve the performance of bioreactor. In this work, a mathematical model using computational fluid dynamics (CFD) techniques is used to study the gas–liquid dispersion in an airlift reactor. Multiple rotating frame (MRF) technique is used to approximate the movement of the impeller in the stationary reactor. Population balance modeling (PBM) is used to describe the dynamics of the time and space variation of bubble sizes in the reactor. The PBM equation is solved using an approximate method known as the class method (CM) and the bubble sizes are approximated through a discrete number of size ‘bins’, including transport, and different bubble phenomena. These equations of the CM are then written as scalar transport equations and added to the multiphase fluid mechanical equations describing the dynamics of the flow. All these equations are solved using control volume formulation through the use of an open-source CFD package OpenFOAM. The model is used to analyze an existing geometry of an airlift bioreactor and validate the modification on the initial design. The new design of airlift gives a clear performance by the increase of the global and local mass transfer and the decrease of the shear stress.     

Kinetics of fluidised bed melt granulation I: The effect of process variables

This paper is the first of a series to study the influence of operating conditions on the kinetics of fluidised bed melt granulation. First, we identify the rate processes responsible for the net growth in granule size in a top-sprayed fluidised bed granulator and propose a sequence of events based on these rate processes. The overall kinetics during the process is identified to be a combination of particle aggregation, binder solidification and granule breakage. By conducting experiments in a small-scale modified commercial fluidised bed granulator, the influence of various operating conditions (binder spray rate, bed temperature, atomising pressure, fluidising air velocity) on the granule growth behaviour was examined. The results indicate the granule growth rate to be directly dependent on the relative amount of binder sprayed into the bed, which essentially determines the speed of the aggregation process. The overall granule growth rate is observed to increase relatively with increased bed temperature for a more viscous PEG4000, while a maximum growth is seen for a lower viscosity PEG1500. A larger droplet size was also seen to have increased the overall growth rate, even though a smaller droplet seems to be able to induce a faster initial growth. The results also reveal the increase in fluidising air velocity to reduce the overall granule growth rate. The final granule size distribution was also observed to become narrower with increased bed temperature and fluidising air velocity. These observations are effectively explained using the proposed sequence of rate events.