Numerical Study of the Effect of Particle Size on the Coating Efficiency and Uniformity of an Electrostatic Powder Coating Process

This paper reports on a research project that studies the effect of particle size on the coating efficiency and coating uniformity in a powder coating system using the computational fluid dynamics as a modelling tool. The numerical simulations are conducted for different particle sizes with different distances between the spray gun and the coating part and different positions of the powder spray gun pattern adjuster sleeve (PAS). This study can provide detailed information on air flow pattern and particle trajectories inside the powder coating booth, and the coating film thickness on the coated part as well as the particle transfer efficiency (PTE). In numerical simulations, the air flow field is obtained by solving three‐dimensional Navier‐Stokes equations with standard κ‐ϵ turbulence model and non‐equilibrium wall function. The second phase, the coating powder, consists of spherical particles that are dispersed in the continuous phase, the air. In addition to solving transport equations for the air, the trajectories of the particles are calculated by solving the particle motion equations using the Lagrangian method. It is assumed that particle‐particle interaction can be neglected. The electrostatic field is modelled by solving the Laplace equation.     

Monte Carlo modeling of fluidized bed coating and layering processes

A stochastic modeling approach based on a Monte Carlo method for fluidized bed layering and coating is presented. In this method, the process is described by droplet deposition on the particle surface, droplet drying and the formation of a solid layer due to drying. The model is able to provide information about the coating coverage (fraction of the particle surface covered with coating), the particle‐size distribution, and the layer thickness distribution of single particles. Analytical solutions for simplified test cases are used to validate the model theoretically. The simulation results are compared with experimental data on particle‐size distributions and layer thickness distributions of single particles coated in a lab‐scale fluidized bed. Good agreement between the simulation results and the measured data is observed. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2670–2680, 2016     

Multiscale modeling of interface debonding effect on mechanical properties of nanocomposites

Mechanical behavior of SiO₂ nanoparticle‐epoxy matrix composites was investigated via finite element analysis with an emphasis on the nanofiller‐interphase debonding effect using a three‐dimensional nanoscale representative volume element (RVE). The new model, in which a cohesive zone material (CZM) layer is considered as an inclusion‐interphase bonding, can be applied to polymer nanocomposites reinforced by inclusions of different forms, including spherical, cylindrical, and platelet shapes. Upon validation by experimental data, the model was used to study the effects of interphase properties, nanoparticle size, and inclusion volume fraction on the mechanical properties of nanocomposites. According to the results, taking into account the inclusion‐interphase debonding provides more precise results compared with perfect bonding, especially in nanocomposites with nanoparticles of smaller size. Moreover, the outcomes disclosed that the amount of changes in the elastic modulus by particle size variation is higher when the relative thickness (the interphase thickness to the particle diameter ratio) increases. For relative thicknesses lower than a critical value, the particle size and the interphase properties have negligible effect on the elastic modulus of the nanocomposite, and the elastic modulus of nanocomposite mostly depends on nanofiller content. POLYM. COMPOS., 38:789–796, 2017. © 2015 Society of Plastics Engineers     

Yodel: A Yield Stress Model for Suspensions

A model for the yield stress of particulate suspensions is presented that incorporates microstructural parameters taking into account volume fraction of solids, particle size, particle size distribution, maximum packing, percolation threshold, and interparticle forces. The model relates the interparticle forces between particles of dissimilar size and the statistical distribution of particle pairs expected for measured or log-normal size distributions. The model is tested on published data of sub-micron ceramic suspensions and represents the measured data very well, over a wide range of volume fractions of solids. The model shows the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter. Not all the parameters in the model could be directly evaluated; thus, two were used as adjustable variables: the maximum packing fraction and the minimum interparticle separation distance. The values for these two adjustable variables provided by the model are in good agreement with separate determinations of these parameters. This indicates that the model and the approximations used in its derivation capture the main parameters that influence the yield stress of particulate suspensions and should help us to better predict changes in the rheological properties of complex suspensions. The model predicts the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter, but the experimental results do not show a clear dependence on diameter. This result is consistent with previous evaluations, which have shown significant variations in this dependence, and the reasons behind the yield stress dependence on particle size are discussed in the context of the radius of curvature of particles at contact.     

Optimizing the balance between viscosity/modulus and impact in particulate composites

The objective of this study was to develop some new concepts of importance when trying to optimize the viscosity/modulus and impact relative to the particle‐size distribution in suspensions and particulate composites. The results of this study appear to indicate that, conceptually, it is possible to significantly improve the viscosity versus the impact balance for material formulations by optimizing the particle‐size distribution. For binary particle‐size distributions, the influence of the preferred particle‐size distribution, as determined using a square‐root distribution, did not yield the most desirable particle‐size distribution if the particle‐to‐particle component of the interaction coefficient was high. However, if three or more particles were utilized in the distribution, then the optimum particle‐size distribution utilized can apparently be characterized using the square‐root distribution even when the particle–particle component, σ_pc, of the interaction coefficient, σ, was found to be quite high. In addition, this same square‐root particle‐size distribution can also satisfactorily predict a probability of impact that can remain consistently high as long as the particles utilized are well chosen and not too close in size. Thus, this preferred particle‐size distribution can be utilized to predict at least one of the preferred distributions to optimize the balance of properties between impact and the viscosity/modulus. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 291–304, 2002     

Pseudo two‐dimensional modeling of sediment build‐up in centrifuges: A compartment approach using compressional rheology

Both a new modeling approach and new experimental data for the sediment build‐up in centrifuges are presented. In semibatch apparatus, the suspension is continuously fed to the centrifuge, separating the particles inside the rotor and discharging the clarified liquid. The solid phase is removed once the capacity of the centrifuge is reached. The solids fraction of the sediment depends on the rheological properties of the cake. The sediment growth and consolidation throughout the process can be calculated using a pseudo two‐dimensional approach that takes into account particle‐size dependent settling, sediment compressibility, the centrifugal force field, and the geometry of the bowl. The predictions of the separation behavior and the particle‐size distributions of the sediment and overflow are compared with experimentally obtained results, showing improved accuracy when compared to simpler models. The model presented is applicable to all solid‐bowl centrifuges without conveying systems. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3843–3855, 2013     

Numerical Simulation for Particle Penetration Depth Distribution in Deep Bed Filtration

A two‐dimensional model has been developed to simulate particle penetration through porous media. The particle penetration depends on many parameters including the Reynolds number, particle drag coefficient, the ratio of the diameter of injected to filtered particles, fluid velocity, and pore size, etc. The numerical model for separation efficiency in periodic porous media was studied. Previous work has described the effects of injected particle size, Reynolds number and particle drag coefficient. In this study, the porous media flow is modeled (solution of the Navier‐Stokes equations) by using the finite element method, and the analysis is restricted to the case of two‐dimensional periodic porous media. The effects of these factors and particle depth distribution in porous media are investigated. It is noted that the results for the three Reynolds numbers 1, 16.56, and 100, are qualitatively similar, and about 40 % of particles are trapped in the top part of the filter.     

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.     

Stress development in drying fibers and spheres

Stress development during drying is a critical factor that affects the final structure and properties of a coated fiber or spherical product. Stress development during drying of the coating is due to nonuniform shrinkage and physical constraints. In this study, a large deformation elasto‐viscoplastic model is developed to predict stress development in drying fibers and spheres after the coatings solidify. From the model, stress evolution in the drying fibers/spheres can be predicted by a partial differential equation of diffusion in one dimension, a first‐order partial differential equation of pressure distribution, and two ordinary differential equations on local evolution of the stress‐free state. The system of equations is solved by the Galerkin/finite element method in the one dimensional axial/spherical symmetric coatings. Solutions show changes in solvent concentration and viscous stress as the coating dries. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 3934–3944, 2003     

Dynamic Compartmental Models of Uniformly‐Mixed and Inhomogeneously‐Mixed Gibbsite Crystallizers

The use of simple compartmentalized population balance (PB) models was investigated for describing the crystal size distributions (CSD) of two different laboratory batch gibbsite crystallizers, one uniformly‐mixed and the other inhomogeneously‐mixed with respect to particulate phase. The compartments were selected on the basis of the shear rate and solids concentration distribution maps generated by the computational fluid dynamics (CFD). In the inhomogeneously‐mixed case, the CSD predicted by the compartmental model was highly sensitive to the relationship between the agglomeration kernel and shear rate used to describe the local agglomeration rate. This observation is consistent with recent findings reported in the literature that to correctly account for the agglomeration process in crystallizers its kinetic formulation should be based on the local rather than the volume‐averaged properties.     

甘露醇喷雾干燥过程中液滴粒度分布变化的群体粒数衡算模拟和实验研究

利用群体粒数衡算（population balance，PB）计算机模拟和实验研究了甘露醇水溶液的喷雾干燥过程中液滴的粒度分布的变化规律。液滴干燥过程中的颗粒粒度的萎缩速率，在群体粒数衡算模型中描述为液滴的逆（或负）生长项，通过单个液滴反应动力学方法（reaction engineering approach，REA）获得。基于单个液滴干燥的反应工程方法模型REA和群体粒数衡算模型PB集成建立了PBREA模型。PBREA 模型的求解是通过高分辨率数值方法。本文模拟研究了不同工况下，不同粒径液滴的干燥时间、液滴平均含湿量以及液滴粒度分布随时间的变化。结果显示，液滴粒径越大，干燥时间越长，模型预测的颗粒平均粒径为实验值的1.0~1.5倍，粒度分布跨度是实验值的0.61~0.89倍。模拟误差主要来源于液滴及颗粒粒径分布统计精度、单个静止液滴与群体运动液滴干燥的差异、热导率及扩散系数是经验值3个方面。在使用Buchi 290 小型喷雾干燥仪进行的实验中，使用了图像采集和分析方法得到了液滴及颗粒的数密度分布，并和模拟结果做了对比。结果表明该模型可以有效地预测喷雾干燥过程中干燥颗粒的平均粒度及分布跨度。     

Modeling of aggregation kernel using Monte Carlo simulations of spray fluidized bed agglomeration

The present work attempts to consider the microscopic mechanisms of spray fluidized bed agglomeration while modeling the macroscopic kinetics of the process. A microscale approach, constant volume Monte‐Carlo simulation, is used to analyze the effects of micro‐processes on the aggregation behavior and identify the influencing parameters. The identified variables, namely the number of wet particles, the total number of particles, and the number of droplets are modeled and combined in the form of an aggregation kernel. The proposed kernel is then used in a one‐dimensional population balance equation for predicting the particle number density distribution. The only fitting parameters remaining in the population balance system are the collision frequency per particle and a success fraction accounting for the dissipation of kinetic energy. Predictions of the population balance model are compared with the results of Monte‐Carlo simulations for a variation of significant operating parameters and found to be in good agreement. © 2014 American Institute of Chemical Engineers AIChE J, 60: 855–868, 2014     

Oil‐absorption function of physical crosslinking in the high‐oil‐absorption resins

The concept of physical crosslinking was introduced into the research field of oil‐absorption resins, which were traditionally synthesized only by chemical crosslinking. Specifically, the partially physical crosslinking acrylic series for high‐oil‐absorption resins were prepared in the suspension process, and the swelling behavior of the samples was observed and recorded online. This demonstrated that a kind of relaxing three‐dimensional network was indeed formed by the introduction of polybutadiene (PB). The effects of monomer feed ratios, crosslinking agent concentration and type, particle size, and temperature on the oil absorbency and oil‐absorption speed were investigated. The results indicated that there were an optimum monomer feed ratio and an optimum amount of ethylene glycol dimethacrylate or PB. In addition, the particle size and temperature had a serious influence on the oil‐absorption speed in comparison with the monomer feed ratio and the crosslinking agent concentration and type. The results also showed that particle size affected oil absorbency to a great degree and that the effect of temperature on oil absorbency was complex. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 3945–3950, 2003     

Combined numerical/experimental investigation of particle diameter and interphase effects on coefficient of thermal expansion and young's modulus of SiO2/epoxy nanocomposites

A combined numerical/experimental approach is used to study the effects of the particle/matrix interphase on the coefficient of thermal expansion (CTE) and Young's modulus of SiO₂/epoxy nanocomposites having nanoparticle reinforcements of different sizes. Our experiments showed that the composite CTE decreases and composite Young's modulus increases with decreasing nanoparticle diameter at the same volume fraction, but our finite element (FE) model predictions did not match the expected trends when the interphase was not accounted for. The new models include an interphase region around the nanoparticle which results in an “effective particle volume fraction” that is larger than the actual particle volume fraction. The results from the models are compared with the experimental results and the new models are accurately fitted to the experimental results using the interphase thickness as a curve‐fitting parameter. We believe that this is the first published report on the use of combined numerical/experimental investigations of both elastic stiffness and thermal expansion characteristics to demonstrate the existence of a particle size‐dependent “effective particle volume fraction” due to the particle/matrix interphase region in a nanoparticle‐reinforced composite. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Statistical modelling of the spouted bed coating process using positron emission particle tracking (PEPT) data

Coating of particles larger than about 1 mm can be achieved in a spouted bed, a particle mobilization device in which a strong particle circulation occurs, rapidly upwards in a lean central “spout” region and downwards in a slowly moving annular settled bed. In a spouted bed coater, a spray nozzle is placed at the base of the spout, spraying upwards into a distinct coating zone. The coating formation in a spouted bed is inter alia a function of (i) the particle motion, that is, how often and where particles enter and traverse the coating zone and (ii) the extent of droplet collection by individual particles passing through the coating zone. The coating model proposed here is based on the statistical history of individual particles, whose projected area governs the collection of spray droplets in the coating zone. Positron emission particle tracking (PEPT) has been used to determine the particle trajectories, the distribution of cycle times and the size and voidage of the spout. Whilst the model is not capable of delivering absolute values of coating mass a priori, it can predict deviations from a mean, which can itself be determined from an overall mass balance. To validate the model, a spouted bed coating process was studied in which coarse PVC spheres were coated with the hot‐melt coating material polyethylene glycol (PEG) 1500. Coating mass distributions, derived from the weight data of individual particles before and after manual coating removal, compared (for the studied conditions) very well with the predictions of the model.     

The structure of model coatings: latex-bound plastic pigment coatings

The immobilization and consolidation of model coatings based on monodisperse polystyrene (plastic pigment) and S/B latexes of known particle sizes were studied in terms of their packing volumes and the extent of latex shrinkage, which was found to increase with increasing pigment volume up to the critical pigment volume concentration (CPVC). The maximum latex shrinkage was estimated from the CPVC. Then, the porosity of model coatings was calculated based on three proposed latex shrinkage models: maximum, minimum, and linearly decreasing latex shrinkage. The number of pores and the average equivalent spherical pore diameters were subsequently calculated. The opacity and gloss of model coatings on polyester films were measured and their porosity was also determined by a simple coat weight-thickness method. The CPVC values determined by the opacity, gloss, and porosity versus PVC relationships, respectively, agreed very well with each other. The CPVCs determined by the opacity and porosity versus PVC curves were identical. The comparison between the theoretically calculated and experimental porosity values showed that the linearly decreasing value between the maximum and minimum latex shrinkage would best fit the experimental porosity data. The effect of plastic pigment particle size on the optical properties and porosity of model coatings was also studied and it was observed that the coating opacity and porosity increased with increasing plastic pigment particle size, but the gloss decreased. Additionally, a minimum crack-free temperature (MCFT) of latex-bound coatings was proposed to better predict the behaviors of latexes as pigment binders. The wet state of model coating dispersions, the surfaces of consolidated model coatings, and their internal structure were examined by both electron and atomic force microscopy, and their micrographs were found to be consistent with our immobilization and consolidation models.     

Two‐dimensional model of methane thermal decomposition reactors with radiative heat transfer and carbon particle growth

A two‐dimensional model of methane thermal decomposition reactors is developed which accounts for coupled radiative heat and polydisperse carbon particle nucleation, growth, and transport. The model uses the Navier–Stokes equations for the fluid dynamics, the radiative transfer equation for methane and particle species radiation absorption, the advection–diffusion equation for gas and particle species transport, and a sectional method for particle species nucleation, heterogenous growth, and coagulation. The model is applied to a tubular laminar flow reactor. The simulation results indicate the development of a reaction boundary layer inside the reactor, which results in significant variation of the local particle size distribution across the reactor. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2545–2556, 2012     

65 t/h高低差速循环流化床流动特性模拟

对一台65 t/h高低差速循环流化床炉内流动特性进行二维数值模拟。采用基于颗粒动力学理论的欧拉双流体模型来描述气固流动,湍流模型、气固曳力模型和不同粒径颗粒间曳力模型分别采用RNG k-ε per phase模型、Gidaspow模型和Schiller-naumann模型,并应用商业计算流体力学软件Fluent进行数值计算,得到炉内颗粒速度分布、压力分布和颗粒浓度分布,并将压力分布与实测值进行对比。在欧拉双流体模型中分别采用单粒径固相模型和多粒径固相模型,并对模拟结果进行对比分析。结果表明,单粒径固相模型能够较好预测高低差速循环流化床炉内流动特性,为其优化设计、运行及大型化提供了理论依据。