Experimental study and modeling of fluidized bed coating and agglomeration

This work deals with the fluidized bed coating and agglomeration of solid particles. The effect of particle size on coating criteria was investigated using sand particles as the coating support and aqueous solutions containing NaCl as coating liquid. The results showed that both growth rate and efficiency increase with decreasing the particle size. The growth was mainly governed by layering for particles larger than 200 μm, whereas for finer particles it occurred by agglomeration. As the particle size became less than 90 μm, the coating operation led to uncontrolled growth and bed quenching. However, the coating of the same particles was successfully achieved by adding some coarser particles. In addition, a mathematical model based on the population balance concept, taking into account the simultaneous growth by layering and agglomeration, was established to predict the time evolution of the particle size distribution. The comparison between experimental and calculated data permitted the establishment of a law for the size dependency of the agglomeration kernel.     

Size control of polystyrene beads by multistage seeded emulsion polymerization

Micron‐sized monodisperse crosslinked polystyrene (PS) beads have been prepared by a multistage emulsion polymerization using styrene monomer, divinylbenzene crosslinking agent, and potassium persulfate initiator in the absence of emulsifier. In the first stage of the reaction, the lower the reaction temperature, the larger the bead size obtained. In the later stages of the reaction, the particle size is increased with the initiator concentration and monomer content. Particle nucleation of the preexisting polymer seed of 0.7–0.8 μm in diameter is prepared at 60°C, then the monodisperse crosslinked PS beads > 2 μm are synthesized up to the third stage of the reaction. As the particle size grows, the number of free radicals in the growing particles increases, and the conversion of the next stage is continuously increased. The reaction mechanism is suggested that the continuous polymerization be conducted due to the diffusion of monomer into the preexisting particles to induce spherical beads in the later stages of the reaction. Otherwise, phase separation or the formation of protrusion by the capture of free radicals will be taking place. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2259–2269, 1999     

旋转床填料中的传质及其模型化

用氮气解吸水中溶解氧,发现了三个在前人研究中未曾提及的重要现象：（１）保持填料外径而扩大内径,平均体积传质系数增大;（２）比表面积大小并不是传质好坏的决定因素;（３）转子填料与旋转床机壳间空腔中液滴表面的传质量,对整个装置中的传质总量,有不可忽略的贡献。据此,建立了基于液体在填料内微粒化,传质同时在填料和液滴表面进行的传质模型。模型计算结果较好地与实验结果吻合,并对上述三个现象作出了合理的解释。     

Mass Transfer Modeling of SO2 into Large Water Drops

This article concerns the modeling of the SO₂ absorption and desorption by falling drops through air with low to high concentration of sulfur dioxide. In the liquid phase, a model based on local scales, interfacial liquid friction velocity and drop size diameter is used. In the continuous gas phase a more classical model is applied. Data obtained by the modeling of the SO₂ absorption and desorption by a single water drop are compared to published experimental results and a fairly good correspondence was found. On the other hand, the model shows that at high gas concentration (> 1 %) the internal resistance to diffusion dominates, while at low gas concentration (< 1000 ppb) the external resistance to diffusion dominates.     

Modeling the Heat and Mass Transfer in Microwave Drying of White Oak

A 2D comprehensive heat and mass transfer model was developed to simulate the free liquid, vapor, and bound water movement in microwave drying of white oak specimens. The experimental and model results showed that, for white oak, moisture movement was easily impeded and high gradient of internal vapor pressure occurred. The internal vapor pressure was affected by sample dimension (length and thickness). At the same input power density, the internal pressure generated in the core increased with the sample length and thickness. However, as compared with sample length, sample thickness has less effect on the pressure gradient because of the high ratio of permeability between longitudinal and transverse directions.     

Computational modeling of inhibitor release and transport from multifunctional organic coatings

A computational code that was originally designed to model crevice corrosion was extended to multifunctional coatings on Al alloys exposed to thin layers of electrolytes. The model is able to calculate the transient distributions of potential, current density, and all chemical species concentration, enabling the dynamic simulation of inhibitor release, inhibitor transport, and sacrificial cathodic protection. The model has been applied to both inhibitor release from and aggressive anion capture by hydrotalcites (HTs) pigments in epoxy primer coatings applied to AA2024-T3. Computational studies were carried out to investigate the effects of HT/vanadate (HT/V) epoxy coating system parameters including scratch size, inhibitor release rate, Cl⁻ gettering rate (GR), cathodic kinetics on the bare AA2024-T3, and solution layer thickness on system performance. The analyses of the computational results have quantified the important factors controlling successful corrosion inhibition by inhibitor release from coatings. The pH-dependence of the steady state inhibitor release rate was found to be the most important parameter controlling system performance. Cl⁻ gettering can also reduce the aggressiveness of solution at long times, especially when considered in conjunction with inhibitor release. However, the ion exchange capacity required poses stiff design challenges involving the loading of the ion exchanger into the resin and the service conditions. The effectiveness of inhibition decreased significantly for the larger scratch sizes. The cathodic kinetics within the scratch play an important role in determining the ability of a given inhibitor to function effectively. When the scratch is the cathode in the galvanic couple with the substrate under the coating, inhibition was more effective. For the conditions simulated here, the net effect of a decreased solution layer thickness is to increase the protection ability of the system. The increase in the inhibitor concentration overcomes the decrease in the pH at the anode.     

Immobilization of polyphenol oxidase on carboxymethylcellulose hydrogel beads: preparation and characterization

Carboxymethylcellulose (CMC) beads were prepared by a liquid curing method in the presence of trivalent ferric ions, and epicholorohydrin was covalently attached to the CMC beads. Polyphenol oxidase (PPO) was then covalently immobilized onto CMC beads. The enzyme loading was 603 µg g⁻¹ bead and the retained activity of the immobilized enzyme was found to be 44%. The K_m values were 0.65 and 0.87 mM for the free and the immobilized enzyme, and the V_max values were found to be 1890 and 760 U mg⁻¹ for the free and the immobilized enzyme, respectively. The optimum pH was 6.5 for the free and 7.0 for the immobilized enzyme. The optimum reaction temperature for the free enzyme was 40 °C and for the immobilized enzyme was 45 °C. Immobilization onto CMC hydrogel beads made PPO more stable to heat and storage, implying that the covalent immobilization imparted higher conformational stability to the enzyme. © 2000 Society of Chemical Industry     

Mass transfer coefficient prediction method for CFD modeling of riser reactors

In gas-solid reactors, particularly circulating fluidized beds (CFB) and riser it is becoming increasingly more important to be able to predict the conversion and yield of reactant species given the ever rising cost of the reactants and the ever decreasing acceptable level of effluent contaminants. As such, the development and use of predictive models for the reactors are necessary for most processes today. These models need to take into account the interphase mass transfer. Unless equipped with specific experimentally based empirical correlations for the reactor system under consideration, the modeler is required to go to the open literature to obtain correlations for the mass transfer coefficient between the solid and gas phases. This is a difficult task at present since these literature values differ by up to 7 orders of magnitude as found in the literature dating back to 1949. The wide variation in the prediction of mass transfer coefficients in the existing literature is credited to flow regime differences that can be identified in the cited literature upon careful inspection.Applying a new theory developed by Breault and Guenther [1] that takes into account the local hydrodynamics, a predictive methodology is presented that allows the local mass transfer coefficient to be calculated based upon local properties in a CFD simulation. A sample calculation is presented and compared with the data used in developing the theory as well as correlation for the literature.     

Mass transport and surface reactions in microfluidic systems

We provide analysis of different regimes of diffusion and laminar flow convection combined with bimolecular surface reactions relevant to biochemical assays performed in microfluidic devices. Analytic solutions for concentration fields are compared to predictions from two-dimensional finite element simulations for the various operation regimes. The analytic and numerical results extend the transport models beyond the models commonly used to interpret results from surface plasmon resonance (SPR) experiments. Particular emphasis is placed on the characterization of transport in shallow microfluidic channels in which the fully developed transport regime dominates rather than the mass transfer boundary layer transport typically encountered in SPR. Under fast reaction and diffusion conditions, the surfaces saturate following moving front kinetics similar to that observed in chromatographic columns. Two key parameters relevant to on-chip biochemical assays and microfluidic sensors are studied and compiled: the capture fraction of the bulk analyte at the surface and the saturation time scale of the reactive surfaces. The physical processes in the different regimes are illustrated with data from the relevant microfluidics literature.     

Solid–liquid mass transfers in an Airlift Reactor incorporating alginate beads for the application as a bioartificial liver

Airlift Reactors may present an alternative to fluidized bed bioreactors with integrated alginate beads in order to immobilize hepatocytes for bioartificial liver use. The present study was aimed to examine the bi-directional mass transfers of the marker Vitamin B₁₂ between the surrounding fluid and the empty alginate beads. A simplified mathematical model based on Fick's first law was applied to describe diffusive mass transfer at the interface between the fluid and the beads calculating the overall mass transfer coefficients for both static and dynamic experimental conditions.Comparing with the Fluidized Bed Reactor, the more shear enhanced diffusion coefficient for Vitamin B₁₂ was 1.5 times higher verifying the efficiency of such a device. Increased shear rates in Airlift Reactors are provoked by additional turbulences due to the rising bubbles. Furthermore, it could be proven that the overall mass transfer mainly depends on the relative velocity between the external fluid and the alginate beads.     

Batch top-spray fluid bed coating: Scale-up insight using dynamic heat- and mass-transfer modelling

A mathematical model was developed for batch top-spray fluid bed coating processes based on Ronsse et al. [2007a, b. Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part I—model development and validation. Journal of Food Engineering 78, 296-307; Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part II—model and process analysis. Journal of Food Engineering 78, 308-322]. The model is based on one-dimensional discretisation of the fluid bed into a number of well-mixed control volumes. In each control volume, dynamic heat and mass balances were set up allowing the simulation of the contents of water vapour, water on core particles and deposited coating mass as well as fluidisation gas, particle and chamber wall temperature. The model was used to test different scale-up principles by comparing simulation results with experimental temperature and humidity data obtained from inorganic salt coating of placebo cores in three pilot fluid bed scales being a 0.5 kg small-scale (GEA Aeromatic-Fielder Strea-1), 4 kg medium-scale (GEA Niro MP-1) and 24 kg large-scale (GEA MP-2/3). Results show good agreement between simulated and experimental outlet fluidisation air temperature and humidity as well as bed temperature. Simulations reveal that vertical temperature and humidity gradients increase significantly with increasing scale and that in fluid beds as the simulated 900 kg (RICA-TEC Anhydro) production-scale, the gradients become too large to use the simple combined drying force/relative droplet size scale-up approach without also increasing the inlet fluidisation air temperature significantly. Instead, scale-up in terms of combinations of the viscous Stokes theory with simulated particle liquid layer profiles (obtained with the model) is suggested. In this way, the given fluid bed scale may be optimised in terms of low agglomeration tendency for a given process intensity across scale.     

Mass transfer measurements and modeling in a microchannel photocatalytic reactor

The main objective of this paper was to evaluate the influence of mass transfer on the photocatalytic efficiency at a low flow rate in the order of several mL per hour. Several continuous flow microchannel reactors have been used to study the degradation of salicylic acid (SA) taken as a model pollutant. The photocatalytic degradation of salicylic acid, under UV illumination of 1.5 mW cm⁻², was assessed from the outlet concentration measured by liquid chromatography HPLC. It was shown that the degradation of SA by UV was limited by mass transfer. Numerical simulations have allowed establishing a relationship of the Sherwood number valuable for all the microchannel geometries. Computational fluid dynamics with Comsol Multiphysics is useful for predicting the degradation yield for a given geometry of the microreactor. The best representation of the experimental data is obtained by introducing a kinetic law taking into account mass transfer limitation.     

Modeling of Gas‐Solid Reactions: Kinetics,Mass and Heat Transfer,and Evolution of the Pore Structure

Mathematical models for simulating heterogeneous gas‐solid reactions must describe a complex set of physicochemical and thermal phenomena. These include the chemical reaction itself, at an interface whose area varies during the conversion, the transport of gaseous species by diffusion in the pores of the solid, whose size and number generally change in the course of reaction, diffusional transport in the layer of solid product, the evolution or consumption of heat by the reaction and its transport in the porous solid, etc. The present paper gives details of the equations employed to model each of these processes. Some computed results illustrate how increasingly sophisticated recent models describe the gradual obstruction of pores during reactions, such as the sulfation of lime, or the thermal effects related to the exothermic nature of the oxidation of zinc sulfide.     

A general rate model approach for the optimization of the core radius fraction for multicomponent isocratic elution in preparative nonlinear liquid chromatography using cored beads

Cored beads (also known as pellicular, superficially porous, and fused-cored beads or particles) offer advantages over fully porous beads in reduced diffusional mass transfer resistances in particle macropores and separation times in liquid chromatography (LC). They are also used to regulate bead densities. The core of a bead has a relatively small volume and yet presents a large linear distance for diffusional mass transfer inside particle macropores. Using a non-porous inert core, intraparticle diffusional mass transfer resistance can be reduced with a relatively small loss in binding capacities. In multicompnent isocratic elution chromatography, cored beads are a compromise between fully porous beads and non-porous beads. Non-porous beads completely eliminate intraparticle diffusion, providing sharp elution peaks with the shortest retention times. However, they do not provide a sufficient retention time range for peaks to separate in preparative LC because of their limited binding capacities. At the other end, fully porous beads offer the largest retention time differences, but suffering from excessive band broadening. For a particular multicomponent elution system, core radius fraction can be optimized to take the advantages of both fully porous beads and non-porous beads. This work presented a general rate model for cored beads and its numerical solution strategy. The model considered axial dispersion, interfacial mass transfer, intraparticle diffusion, and multicomponent Langmuir isotherm. Computer simulation was used to study the effects of core radius fraction on breakthrough curves and elution peaks. The model was used to optimize the core radius fraction for a preparative ternary elution system as an example case.     

A double linear driving force approximation for non-isothermal mass transfer modeling through bi-disperse adsorbents

The aim of this paper is to derive a double LDF non-isothermal model to describe mass transfer through a fixed bed of bi-disperse adsorbent pellets. Firstly, we perform an analysis concerning the different way the composition within the pellets can be described and the consequence on the model structure and compactness. Secondly, we present a bed model including a simplified intra-particle model that is based on a double LDF approximation. This bi-disperse pellet model reduces the number of variables and parameters that are needed. This simplified model is used to simulate breakthroughs of a methane/carbon dioxide mixture over a 5 A zeolite and of a 2,2-dimethylbutane/2-methylpentane mixture over a silicalite molecular sieve. It is also compared with a more detailed model based on Stefan-Maxwell theory that we have previously developed.     

Effect of surfactants on liquid-side mass transfer coefficients in gas-liquid systems: A first step to modeling

This paper focuses on the effect of surfactants on the mass transfer parameters (volumetric mass transfer coefficient k_La and liquid-side mass transfer coefficient k_L). Tap water and aqueous solutions with surfactants (anionic, cationic and non-ionic at concentrations up to are used as liquid phases. The bubbles are generated into a small-scale bubble column having an elastic membrane with a single orifice as gas sparger. To understand the effects of the surfactants on the mass transfer, not only the static surface tension is used, but also the characteristic adsorption parameters like the surface coverage ratio at equilibrium Se. The liquid-side mass transfer coefficient is obtained from the ratio of the volumetric mass transfer coefficient (measured by a chemical method) and the specific interfacial area. These two parameters are obtained simultaneously. The methods used to obtain these parameters are described in Painmanakul et al. [2005. Effects of surfactants on liquid-side mass transfer coefficients. Chemical Engineering Science 60, 6480-6491].Whatever the liquid phase, three zones are found on the liquid-side mass transfer coefficient variation with the bubble diameter. For bubble diameters less than 1.5 mm, whatever the liquid phases, the k_L values are roughly constant at . For bubble diameters greater than 3.5 mm, the k_L values do not vary much with the bubble diameter, but depend on the surfactant concentration. For bubble diameters between 1.5 and 3.5 mm, the k_L values increase from to the value reached at 3.5 mm. This increase depends on the surfactants. Higbie's model does not represent the k_L values for bubble diameters greater than 3.5 mm, even though there is a small amount of surfactant in the liquid phase. Thus, a model is proposed for each zone described above. Explanations are also proposed for the effect of the surfactant on the k_L values for each of the above zones.     

Inverse modeling applications in emulsion polymerization of vinyl acetate

The optimization of emulsion polymerization processes can benefit from the application of neural networks (NNs). The aim of this paper is to present yet another important example of how NNs can help with the optimization of emulsion polymerization reactors, and more specifically, with the “inverse” problem, i.e., starting from the polymer's properties and productivity to determine the reactor's operating conditions. The procedure presented in this paper combines a mathematical model with a NN that predicts appropriate operating conditions for the reactor with a maximum error of 5%. The specific example is with the emulsion polymerization of vinyl acetate.