Characterization of agglomerate dispersion by erosion in simple shear flows

The extent of dispersion of solid agglomerates in hydrodynamic flow fields is believed to depend on the material properties as well as flow conditions. The purpose of this study has been to investigate the mechanism of agglomerate breakup in simple shear flows and to correlate the various parameters affecting the dispersion process. Experiments were performed in a transparent cone and plate device. Two distinct breakup mechanisms, denoted as “rupture” and “erosion”, were observed. The rupture process is characterized by an abrupt breakage of the agglomerate into a few large pieces. The erosion process is more gradual and initiates at lower applied shear stresses than rupture. The erosion process is characterized by the detachment of small fragments from the outer surface of the agglomerate. For the erosion of carbon black agglomerates suspended in Newtonian fluids, it was found that the kinetics of the process follows a first order rate equation and the size of the eroded fragments obeys a normal distribution. The strength of the flow field does affect the kinetics of the dispersion process, and a parameter α, scaling the applied shear stress with the cohesive strength of the agglomerate, is characteristic for the erosion process.     

Effect of the impact angle on the breakage of agglomerates: a numerical study using DEM

The study of agglomerate strength is of vital importance in several industrial applications such as pharmaceutical, detergent and food manufacturing. Agglomerates could experience a size reduction during the production and handling processes due to collisions with other agglomerates or with the moving components and walls as well as during bulk flow due to shear deformation. In this analysis, we focus on the agglomerate damage due to oblique impact on walls, as this is a common damage process during, for example, pneumatic conveying and size reduction in pin mills.

Computer simulations have been carried out using Distinct Element Analysis, where the breakage characteristics of oblique impacts and the effect of the interparticle bond strength have been analysed. The procedure adopted here provides an isotropic and spherical agglomerate (uniform mass distribution and coordination number within radial segments of the agglomerate). The results indicate that the damage ratio (i.e. the number fraction of the broken bonds) depends on the normal component of the impact velocity only, i.e. the tangential component has little effect. However, the position of the clusters produced on impact does depend on the impact angle, which influences the pattern of breakage and in turn the size distribution of the large clusters.     

Alumina Agglomerate Effects on Toughness-Curve Behavior of Alumina–Mullite Composites

Toughness-curve ( T -curve) behavior of composites of spherical, polycrystalline, coarse-grained, alumina agglomerates dispersed throughout a constant-toughness, fine-grained, 50–50 vol% alumina–mullite matrix has been evaluated as a function of agglomerate content for the range 15 to 45 vol%. T -curve behavior was evaluated using the indentation-strength method. Increasing alumina agglomerate content resulted in a progressive increase of large indentation load strengths with negligible change of plateau strength levels at small indentation loads. This behavior is consistent with underlying T -curves that rise to greater values and are shifted toward longer crack lengths with increasing agglomerate content, suggesting that both bridge spacing and bridge potency increase with increasing agglomerate content over the range tested. The proposed relationships between bridge spacing and agglomerate content, and bridge potency and agglomerate content, are rationalized in terms of residual stress considerations. The indentation-strength data also demonstrated that the composite containing the greatest alumina agglomerate content, 45 vol%, exhibited the greatest flaw tolerance.     

Agglomeration during the Drying of Fine Silica Powders, Part II: The Role of Particle Solubility

The effect of particle solubility and the dissolution rate on agglomeration was studied by drying silica and titania particles from aqueous slurries with pH values in the range of 2–12. The agglomerate strength and strength distribution were measured by a calibrated ultrasonic force, and the strength increased as the solubility and dissolution rate increased. Two silica powders of different particle size (60 nm and 500 nm) were studied, and smaller-sized particles formed stronger agglomerates. The drying rate of the powders was varied by using spray drying and tray drying, and slower drying was shown to lead to higher agglomerate strength. The agglomerate strength of titania powder (insoluble in water) was independent of pH, whereas the agglomerate strength of silica was dependent on pH. It was concluded that the solubility and dissolution rate are important parameters that govern the strength of agglomerates.     

Effect of Agglomerate Strength on Sintered Density for Yttria Powders Containing Agglomerates of Monosize Spheres

The effect of agglomerate strength on sintered density, was determined for several yttria powders made by intentionally agglomerating 0.1-μm, monodisperse yttrium hydroxycarbonate precursor spheres and calcining separate portions of the precursor at different temperatures to vary the strength of the intraagglomerate bonds. In this way, the effects of differences in particle morphology and other characteristics among the powders were minimized and the effect of agglomerate strength could be seen more clearly. The sintered density of the yttria powders decreased with increasing agglomerate strength, and even a small fraction of unbroken fragments of agglomerates in the pressed powder caused a substantial decrease in the sintered density.     

A Die Pressing Test for the Estimation of Agglomerate Strength

A die pressing test was developed for quick and inexpensive estimation of the agglomerate strength of ceramic powders. The critical nominal pressure ( p _c) at which contact areas between agglomerates start to increase rapidly was found from the relationship between change in sample height and applied pressure in uniaxial single-ended die pressing. A quantitative microscopic method was used for measuring the area fraction (Ψ) of agglomerates which transmits the force through the assembly. A die pressing agglomerate strength, σ_d, is defined as σ_d= 0.7 p _c/Ψ. This strength was compared with the agglomerate tensile strength obtained from single agglomerate diametral compression tests and found to be 50% higher than the latter because of multipoint loading. A suggested guideline is that the mean agglomerate tensile strength is approximately 52% of p _c determined in a die pressing test for spherical agglomerates. In addition to agglomerate tensile strength, the mean agglomerate size, the interior macropore structure of agglomerates, as well as the packing efficiencies between and inside agglomerates can be estimated by the procedure.     

A regime map for the normal surface impact of wet and dry agglomerates

The normal surface impacts of wet and dry agglomerates are simulated in a discrete element modeling framework. While the impact behavior of dry agglomerates has been addressed previously, similar studies on wet agglomerate impact are missing. By adding a small amount of liquid to a dry agglomerate, the impact behavior changes significantly. The impact behavior of the agglomerates at different moisture contents and impact energies are analyzed through postimpact parameters and coupled to their microscopic and macroscopic properties. While increasing the impact energy breaks more interparticle bonds and intensifies damage and fragmentation, increasing the moisture content is found to provide the agglomerates with higher deformability and resistance against breakage. It is shown that the interplay of the two latter parameters together with the agglomerate structural strength creates various impact scenarios, which are classified into different regimes and addressed with a regime map. © 2018 American Institute of Chemical Engineers AIChE J, 64: 1975–1985, 2018     

聚合物熔体中团聚体分散问题的研究进展

从团聚体结构和外界流场对团聚体的应力作用两个方面综述了各因素时团聚体分散过程的影响。讨论了不同的团聚体强度模型、“腐蚀”和“破碎”分散方式厦其影响因素，并对团聚体分散效果进行了理论分析。评价了相关模型的特点和局限性，所提出的理论模型厦模拟研究对混合设备中实际分散过程的深入研究具有指导意义。     

Effect of morphology and extent of infiltration on the cohesivity and dispersion mechanisms of particle agglomerates

A unified approach to predict the tendency for dispersion of particle agglomerates, inclusive of a wide range of particle and agglomerate properties, is presented. This framework is applied to analyze the behavior of three prototypical materials (fumed silica, calcium carbonate and titanium dioxide) across a range of agglomerate packing densities. Simulations of dispersion phenomena, which employ our previously developed solution for liquid-bridge interactions for wet interparticle contacts and the Rumpf model for the tensile strength of the dry and wet portions of the agglomerate, have been performed. Various mechanisms of dispersion are predicted for various conditions of agglomerate density and extent of fluid infiltration. These range from an adhesive mechanism at the wet-dry interface for sparse materials to a cohesive mechanism by erosion as agglomerate density increases. The results correspond well with the results of earlier experimental studies involving the same materials.     

Effect of granulation scale-up on the strength of granules

Granulation is commonly used to enlarge particle size to impart desirable characteristics and functionality to the granules. In this work, the effect of operating scale of the granulator on the physical properties of granules is analysed. Three scaling up rules of constant tip speed, constant shear stress and constant Froude number have been evaluated using 1, 5 and 50 l Cyclomix high shear mixer granulators, calcium carbonate powder and Polyethylene glycol (PEG) as binder. The strength of granules produced in different granulator scales is analysed by side crushing test. The results indicate that the condition of constant tip speed for scale-up produces granules with relatively similar strength. When the condition of constant shear stress is used to scale-up the granulator, the granules produced in 5 and 50 l have relatively similar strength, but 1 l produces much weaker granules than those of 5 and 50 l. Work has also been carried out to analyse the flow field of granules in the granulator to provide a better insight into the velocity and stress profiles as a function of equipment scale. Positron Emission Particle Tracking (PEPT) analysis shows that under constant shear stress condition macroscopic flow field of 1 l and 5 l granulators are different, a feature which could affect the final structure of the agglomerates. The PEPT results are used to describe the velocity gradient in the Distinct Element Method (DEM) simulation of the agglomerate deformation under bulk shearing. DEM modelling of microscopic interactions in agglomerate behaviour within a shearing bed shows that flow conditions of 1 l granulator make the agglomerate with a higher elongation factor and lower packing fraction, indicating that the agglomerate would be weaker. This feature has also been observed experimentally.     

Hardness of moist agglomerates in relation to interparticle friction, capillary and viscous forces

Wet agglomerates deform plastically until they break through crack propagation. On the particulate level, liquid bridges are responsible for the strength of the wet agglomerate as they hold the particles together. Recent micro-scale studies have identified the role of liquid surface tension, bridge Laplace pressure and liquid viscosity, which, in combination, explain the axial strength of pendular liquid bridges. Different situations exist depending on the degree the liquid wets the particles and on the saturation of the agglomerate mass.On the wet agglomerate level, the hardness is related to three factors: the liquid binder surface tension and viscosity and the interparticle friction. A simple model is developed in this paper, based on the powder and liquid binder properties, which shows that the forces due to interparticle friction are generally predominant in wet agglomerates made from non-spherical particles. Although mechanical interlocking is not accounted for, the model yields accurate prediction of wet agglomerate hardness independently measured on wet masses of varying composition. This theoretical hardness could prove an interesting tool for wet granulation research and technology.     

Mathematical modelling of the MCFC cathode

Different models for the NiO cathode have been compared with respect to their abilities to predict polarization curves and the influence of the amount of electrolyte on the electrode performance. It has been shown that the agglomerate model for the MCFC cathode gives more reasonable results when the exterior agglomerate surface area is specifically taken into account. In the cathode only the outermost layer of nickel oxide particles in the agglomerate is utilized for the electrochemical reaction. The pseudohomogeneous approach is questionable for these agglomerates since the individual particles constituting the agglomerate are of the same size as the reaction zone thickness. A thin-film model with a roughness factor for the electrode surface appears to be as good a model as the agglomerate model. A model based on a chain of spherical agglomerates and the partially drowned agglomerate model are physically more realistic models than the homogeneous agglomerate model for the prediction of the influence of electrolyte fill on the electrochemical performance.     

A theoretical model of the effect of distributed loading on the tensile strength of agglomerates as measured in the diametral compression test

The tensile strength of particle agglomerates is analyzed to indicate the effect of distributed loading through contact flattening during the diametral compression test. It is assumed that only the contact regions of the agglomerate are flattened and that the free boundary maintains its original position during loading. The increased packing density so produced is related to the total loading as a reaction force through an empirical relationship used to describe die compaction of powders. Agglomerate failure occurs when the maximum tensile stress caused by the platen loading exceeds the cohesive strength of the particle assemblage. Theoretical predictions of the effects of parameters such as bulk powder properties and the extent of load distribution on agglomerate strength are presented from the analysis.     

Agglomeration Characteristics of Aluminum Particles in AP/AN Composite Propellants

Most solid rockets are powered by ammonium perchlorate (AP) composite propellant including aluminum particles. As aluminized composite propellant burns, aluminum particles agglomerate as large as above 100 μm diameter on the burning surface, which in turn affects propellant combustion characteristics. The development of composite propellants has a long history. Many studies of aluminum particle combustion have been conducted. Optical observations indicate that aluminum particles form agglomerates on the burning surface of aluminized composite propellant. They ignite on leaving the burning surface. Because the temperature gradient in the reaction zone near a burning surface influences the burning rate of a composite propellant, details of aluminum particle agglomeration, agglomerate ignition, and their effects on the temperature gradient must be investigated. In our previous studies, we measured the aluminum particle agglomerate diameter by optical observation and collecting particles. We observed particles on the burning surface, the reaction zone, and the luminous flame zone of an ammonium perchlorate (AP)/ammonium nitrate (AN) composite propellant. We confirmed that agglomeration occurred in the reaction zone and that the agglomerate diameter decreased with increasing the burning rate. In this study, observing aluminum particles in the reaction zone near the burning surface, we investigated the relation between the agglomerates and the burning rate. A decreased burning rate and increased added amount of aluminum particles caused a larger agglomerate diameter. Defining the extent of the distributed aluminum particles before they agglomerate as an agglomerate range, we found that the agglomerate range was constant irrespective of the added amount of aluminum particles. Furthermore, the agglomerate diameter was ascertained from the density of the added amount of aluminum particles in the agglomerate range. We concluded from the heat balance around the burning surface that the product of the agglomerate range and the burning rate was nearly constant irrespective of the added amount of aluminum particles. Moreover, the reduced burning rate increased the agglomerate range.     

Effect of structural characteristics on impact breakage of agglomerates

The mechanical properties and evolved structure of agglomerates depend strongly on the manufacturing method. There is a great interest in finding a simple way of establishing a rank order in their processing behaviour, e.g., the ease with which they could be dispersed in fluids. For this reason, the breakage propensity of two types of detergent agglomerates produced by different processes but with the same formulation has been evaluated under different conditions by impact testing with a view to diagnose differences in mechanical properties and structure arising from their manufacturing method. The effects of impact velocity, agglomerate size, impact angle, fatigue, humidity, and temperature have been analysed. Both samples show extensive plastic deformation due to the elongation and eventual rupture of the interparticle bridges, especially for the humidified samples. Reducing the temperature increases the extent of breakage substantially. The impact test results of samples kept at −20 °C show brittle failure mode, whilst those of oblique impacts at 45° and ambient conditions show a semi-brittle failure mode by shear deformation. Drying strengthens the agglomerates presumably due to the solidification of bridges. In contrast, humidifying the granules decreases their strength. A general comparison of the impact test results of both samples for different feed sizes shows that, due to the structural differences, the breakage trend of these two types of agglomerate varies with increasing agglomerate size.     

New perspectives on capturing particle agglomerates in CFD modeling of spray dryers

Abstract

Current computational fluid dynamic (CFD) models of spray dryers lack the capability to predict the structure of the agglomerates formed; loose or compact agglomerates. This is mainly due to the conventional simplistic approach in numerically “fusing” of the colliding particles forming the agglomerate. A new theoretical treatment is introduced in this work, suitable for implementation in CFD simulations, which numerically fuses the particles and yet retain information on the structure of the agglomerate. This new theoretical treatment is based on tracking the reduction of the agglomerate surface area as the agglomerate is progressively formed. Analysis revealed that the reduction in the agglomerate surface area exhibits a unified correlation with the degree of compactness of the agglomerate. Further analysis comparing this new approach to the conventional numerical fusing of the particles revealed inherent numerical discrepancies, which has not been noted in the literature before. Understanding these discrepancies will provide clarity to the interpretation of the modelling and simulation of spray drying particle agglomeration in CFD. Moreover, this work lays the groundwork for a more comprehensive CFD model for agglomeration which can be potentially utilized to predict final powder properties.     

Drying-Induced Cracking of Abrasive Rings:Risk Prediction and Process Optimisation by Numerical Simulation

The dependence of the mechanical stresses distribution on the water content and temperature profiles has been numerically investigated in a porous unsaturated hygroscopic abrasive agglomerate of annular shape. The thermophysical, kinetic and mechanical properties of the abrasive agglomerate were determined experimentally. The simulations have been applied to unfired abrasive rings convective drying optimisation by fitting operating conditions in order to avoid cracks formation.     

Experimental and theoretical study on the agglomeration arising from fluidization of cohesive particles—effects of mechanical vibration

A novel technique that can prevent the disruption of agglomerates when sampling the agglomerates from a fluidized bed has been developed and has been applied to the investigation of the agglomeration behaviour of cohesive particles during fluidization with and without mechanical vibration. A new model for the prediction of agglomerate size has also been established on the basis of the energy balance between the agglomerate collision energy, the energy due to cohesive forces and the energy generated by vibration. The accuracy of the model is tested by comparing the theoretical results with the experimental data obtained both in the present work and in the literature. Effects of gas velocity and mechanical vibration on agglomeration for two cohesive (Geldart group C) powders in fluidization are examined experimentally and theoretically. The experimental results prove that mechanical vibration can significantly reduce both the average size and the degree of the size-segregation of the agglomerates throughout the whole bed. However, the experiments also reveal that the mean agglomerate size decreases initially with the vibration intensity, but increases gradually as the vibration intensity exceeds a critical value. This suggests that the vibration cannot only facilitate breaking the agglomerates due to the increased agglomerate collision energy but can also favour the growth of the agglomerates due to the enhanced contacting probability between particles and/or agglomerates. Both the experimental and theoretical results show that a higher gas velocity leads to a smaller agglomerate size.     

Agglomeration of magnesium particles in magnesium-sodium nitrate combustion

Agglomeration phenomenon of magnesium particles during combustion of Mg NaNO₃ propellant has been studied. High speed photographs of combustion zones and the burning surface temperature data indicate that the metal particles form agglomerates on the burning surface in varying degree depending on the mass fraction of NaNO₃. It is found that the increase of oxidizer content increases the metal agglomeration and the agglomerate size depends on the initial particle size of the ingredients. An attempt has been made to predict the size of the agglomerates based on the consideration that the agglomerate size depends on the thickness of the molten oxidizer layer enveloping the metal particles in the condensed phase and surface heat flux providing local temperature environment to agglomerate the metal particles and to eject from the burning surface for the vapour phase combustion. The results were compared with the experimental data. The prediction describes fairly well the observed effects of the concentration and particle size.