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.     

Growth and breakup of a wet agglomerate in a dry gas–solid fluidized bed

Using CFD‐DEM simulations, a wet agglomerate of particles was placed in a void region of a dry vigorously fluidized bed to understand how wet agglomerates grow or breakup and how liquid spreads when agglomerates interact with dry fluidized particles. In the CFD‐DEM model, cohesive and viscous forces arising from liquid bridges between particles were modeled, as well as a finite rate of liquid bridge filling. The liquid properties were varied between different simulations to vary Bond number (surface tension forces/gravitational forces) and Capillary number (viscous forces/surface tension forces) in the system. Resulting agglomerate behavior was divided into regimes of (i) the agglomerate breaking up, (ii) the agglomerate retaining its initial form, but not growing, and (iii) the agglomerate retaining its initial form and growing. Regimes were mapped based on Bo and Ca. Implications of agglomerate behavior on spreading of liquid to initially dry particles were investigated. This article identifies a new way to map agglomerate growth and breakup behavior based on Bo and Ca. In modeling both liquid forces and a finite rate of liquid transfer, it identifies the complex influence viscosity has on agglomeration by strengthening liquid bridges while slowing their formation. Viewing Ca as the ratio of bridge formation time to particle collision and separation time capture why agglomerates with high Ca struggle to grow. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2520–2527, 2017     

CFD–DEM modeling of gas fluidization of fine ellipsoidal particles

Particle characteristics are important factors affecting gas fluidization. In this work, the effects of both particle size and shape on fluidization in different flow regimes are studied using the combined computational fluid dynamic–discrete element method approach. The results are first analyzed in terms of flow patterns and fluidization parameters such as pressure drop, minimum fluidization, and bubbling velocities. The results show that with particle size decreasing, agglomerates can be formed for fine ellipsoidal particles. In particular, “chain phenomenon,” a special agglomerate phenomenon exists in expanded and fluidized beds for fine prolate particles, which is caused by the van der Waals force. The minimum fluidization velocity increases exponentially with the increase of particle size, and for a given size, it shows a “W” shape with aspect ratio. A correlation is established to describe the dependence of minimum fluidization velocity on particle size and shape. Ellipsoids have much higher minimum bubbling velocities and fluidization index than spheres. © 2015 American Institute of Chemical Engineers AIChE J, 62: 62–77, 2016     

声场流化床中超细颗粒聚团受力与尺寸

在内径40 mm的流化床中,采用平均粒径为7.4 mm的超细铁矿颗粒进行声场流态化实验. 结果显示,聚团尺寸随声压级增大逐渐减小,在固定声压级的条件下存在最优声波频率,本实验为130 Hz. 由铁矿颗粒声场流态化中聚团受力分析提出聚团受力平衡模型,当促进聚团破碎的力和促进聚团形成的力相等时,计算出一定频率不同声压级下的聚团尺寸,在频率130 Hz、声压120.5 db下,根据模型计算得到的聚团直径为384 mm,而通过最小流化速度计算值为367 mm,二者较接近.     

Application of discrete element method simulation for studying fluidization of nanoparticle agglomerates

The usefulness of discrete element method simulation for studying fluidization of nanoparticle agglomerates is explored. Nanoparticle agglomerates were simulated by using solid particles of equivalent sizes and densities. Validity of the present simulation was assessed through comparisons of simulation results and experimental observations of bed expansion, characteristic fluidization behaviour, and dense‐bed settling. The simulation was then used to investigate initial bed expansion and bed uniformity under particulate fluidization conditions. The role of inter‐agglomerate interparticle force in fluidization of nanoparticle agglomerates was examined. A stability analysis originally developed for addressing the transition from particulate to bubbling fluidization for conventional particles was used for predicting the start of bubbling in fluidized beds of nanoparticle agglomerates.     

Numerical modelling of the breakage of loose agglomerates of fine particles

This paper presents a numerical study of the breakage of loose agglomerates based on the discrete element method. Agglomerates of fine mannitol particles were impacted with a target wall at different velocities and angles. It was observed that the agglomerates on impact experienced large plastic deformation before disintegrating into small fragments. The velocity field of the agglomerates showed a clear shear zone during the impacts. The final breakage pattern was characterised by the damage ratio of agglomerates and the size distribution of fragments. While increasing impact velocity improves agglomerate breakage, a 45-degree impact angle provides the maximum breakage for a given velocity. The analysis of impact energy exerted from the wall indicated that impact energy in both normal and tangential directions should be considered to characterise the effects of impact velocity and angle.     

Modeling of the Spray Zone for Particle Wetting in a Fluidized Bed

In a spray agglomeration process the particle wetting influences the agglomerate growth and particle dynamics in the granulator. The mass of binder liquid that is deposited on single particles affects the amount of energy dissipation during particle contacts. For the agglomeration of colliding particles the whole impact energy has to be dissipated due to viscous and capillary adhesion forces in the liquid film and plastic deformation of the material. Therefore, a detailed knowledge of the particle wetting is necessary to model the agglomeration process. This contribution uses a coupled DEM‐CFD approach to describe the spray zone of a two‐fluid nozzle in a fluidized bed agglomerator. Droplets modeled as discrete elements showed the formation of a spray zone with a conical shape. Simulations of the spray zone and the wetting of single particles are in good agreement with experimental results.     

Structural Property Effect of Nanoparticle Agglomerates on Particle Penetration through Fibrous Filter

Most filtration studies have been conducted with spherical particles; however, many aerosol particles are agglomerates of small primary spheres. Filtration efficiency tests were conducted with silver NP agglomerates, with the agglomerate structure controlled by altering the temperature of a sintering furnace. The mobility diameter and mass of the silver NP agglomerates were measured using a differential mobility analyzer together with an aerosol particle mass analyzer. From these measurements, it was found that the fractal-like dimension, D _fm, varied from 2.07 to 2.95 as the sintering temperatures was increased from ambient to 600°C. The agglomerates were essentially fully coalesced at 600°C allowing direct comparison of the filtration behavior of the agglomerate to that of a sphere with the same mobility diameter. Other agglomerate properties measured include the primary diameter, the agglomerate length and aspect ratio, and the dynamic shape factor.

Agglomerate filtration modeling with no adjustable parameters has been investigated in terms of diffusion, impaction, and interception. The model results agree qualitatively with the experimental results in the particle size range of 50 to 300 nm. The results indicated that the larger interception length of agglomerates is responsible for the smaller penetration through a fibrous filter in comparison to spherical particles with the same mobility diameters.     

A mechanistic study of agglomeration in fluidised beds at elevated pressures

Effect of operating pressure on the hydrodynamics of agglomerating gas–solid fluidised bed was investigated using a combination of discrete element method (DEM) for describing the movement of particles and computational fluid dynamic (CFD) for describing the flow of the gas phase. The inter‐particle cohesive force was calculated based on a time dependent model developed for solid bridging by the viscous flow. Motion of agglomerates was described by the multi‐sphere method. Fluidisation behaviour of an agglomerating bed was successfully simulated in terms of increasing the size of agglomerates. The results showed that increasing the operating pressure postpones de‐fluidisation of the bed. Since the DEM approach is a particle level simulation and study about particle–particle interactions is possible, a micro‐scale investigation in terms of cohesive force and repulsive force during agglomeration at elevated pressures was done. The micro‐scale results showed that although the number of contacts between particles was decreased by increasing operating pressure, stronger solid bridge formed between colliding particles at higher pressures. © 2012 Canadian Society for Chemical Engineering     

Effect of agglomerate properties on agglomerate stability in fluidized beds

Fluidized bed agglomeration is used to stabilize particulate mixtures and reduce dust emissions. This technology is applied to a variety of production processes for the pharmaceutical, chemical, fertilizer and food industries. In most of these applications, agglomerate stability is an essential criterion. Agglomerates and granules that do not conform to size and shape specifications may create problems in downstream processes, such as tableting, thus compromising process efficiency and product quality. When an agglomerate is formed in a fluidized bed, it can grow by incorporating other bed particles, split into smaller fragments, or be eroded by fluidized bed solids. The objective of the present study is to determine the critical agglomerate liquid content at which the rates of agglomerate growth and shrinkage are balanced when artificial agglomerates made from glass beads and water are introduced into a fluidized bed. This study examined the effects of agglomerate size, agglomerate density, liquid viscosity, binder concentration, and fluidizing gas velocity on the critical initial liquid content. This study found that small agglomerates and low density agglomerates displayed higher critical initial moisture contents. When the viscosity was increased by using sugar solutions, agglomerates were very stable and had very low critical initial moisture contents. The study also found that as the superficial gas velocity increased, the agglomerates started to fragment, rather than erode.     

Hydrodynamic analysis of the mechanisms of agglomerate dispersion

Hydrodynamic dispersion of particle agglomerates occurs whenever the applied shear stresses can break the interparticle bonds responsible for the cohesivity of the agglomerate. Various mechanisms of hydrodynamic dispersion have been demonstrated for silica agglomerates infiltrated to different extents by the suspending fluid. In some cases, hydrodynamic forces are sufficient to induce the removal of incompletely infiltrated fragments from the parent agglomerate (dry cohesive failure) or the breakage of wetted fragments from the infiltrated portion of the parent agglomerate (wet cohesive failure). Dispersion can also occur such that a portion of the fracture surface originates at the interface between the infiltrated periphery of the agglomerate and its dry core (adhesive failure). To elucidate the tendencies for dispersion via various modes, a hydrodynamic analysis of the forces acting on and within the agglomerate has been performed for both uninfiltrated and partially infiltrated structures. This analysis reveals that the size of the region on which the hydrodynamic stress bears is sensitive to the degree of infiltration, which is consistent with the observed shifts in dispersion mechanism.     

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.     

Quantifying growth and breakage of agglomerates in fluid-particle flow using discrete particle method

The cohesive solids in liquid flows are featured by the dynamic growth and breakage of agglomerates, and the difficulties in the development, design and optimization of these systems are related to this significant feature.In this paper, discrete particle method is used to simulate a solid–liquid flow system including millions of cohesive particles, the growth rate and breakage rate of agglomerates are then systematically investigated. It was found that the most probable size of the agglomerates is determined by the balance of growth and breakage of the agglomerates the cross point of the lines of growth rate and breakage rate as a function of the particle numbers in an agglomerate, marks the most stable agglomerate size. The finding here provides a feasible way to quantify the dynamic behaviors of growth and breakage of agglomerates, and therefore offers the possibility of quantifying the effects of agglomerates on the hydrodynamics of fluid flows with cohesive particles.     

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     

Hydrodynamics of inhomogeneous agglomerates for a fractal dimension of 2.5 at intermediate Reynolds numbers: Effect of agglomerate sizes and Reynolds numbers

In this study, the effect of agglomerate sizes for a fractal dimension (D_f) of 2.5 on the hydrodynamics at intermediate Reynolds numbers (Re) of 1–120 was assessed. The results show that a core behaves like a solid sphere that exists in the central region inside the agglomerate. In addition, increasing the agglomerate diameter represents adding an extra permeable layer outside the agglomerate. For a larger Re or a smaller agglomerate diameter, the fluid can enter and penetrate through the agglomerate more easily, and the hydrodynamic characteristics of agglomerates deviate more from those of solid spheres. The effect of diameters on the velocity and pressure profiles becomes less significant with the increase in the diameter. Based on the simulated results, the drag ratio has an approximately linear relationship with Re, and its intercept has an exponential relationship with the dimensionless agglomerate diameter. Compared with homogeneous porous spheres, the drag ratio of the agglomerate is different. The effect of diameters on the drag ratio decreases as the diameter increases. It should be noted that the effect of radially varying permeability on inhomogeneous agglomerates should not be ignored and that the effect weakens as Re increases.     

Effect of interparticle forces on the conical spouted bed behavior of wet particles with size distribution

This paper aims to analyze air-solid flow behavior in conical spouted beds composed of glass bead mixtures coated by glycerol. Four mixtures of glass beads are used as the solid phase. Although these mixtures have the same mean Sauter diameter, each one is characterized by a different size distribution function (mono-sized; flat, Gaussian or binary size distribution). When glycerol is added to the bed of these particles, which are spouted by air, the gas-solid flow characteristics are changed due to the growth of interparticle forces; however, the trends of these changes are affected by the glass bead mixture type as well as by the concentration of glycerol. For beds of mono-sized particles, the minimum spouting velocity is maintained almost unchanged as the glycerol concentration rises; while, for beds of inert particle mixtures, this velocity increases, becoming greater for flat and binary size distribution particles. Conversely, the minimum spouting pressure drop decreases as the glycerol concentration rises for all beds of particles used. Based on theoretical prediction of interparticle forces, it is shown that these changes in the minimum spouting conditions can be explained by the magnitude of these forces.     

Breakage patterns of agglomerates

The experimental information available in the literature regarding the patterns of breakage of agglomerate materials is scarce, particularly in dynamic loading. The primary objective of this paper is to present our findings on the breakage patterns of the agglomerates and the interparticle bond. A high-speed digital video imaging technique is used here to gain an insight into the impact behaviour of individual agglomerates against a target plate. Several breakage patterns are observed. Agglomerates may suffer localised damage only, with the disintegration of the damaged zone into very fine debris, or localised damage combined with fracture. The frequency of occurrence of these patterns depends on the impact velocity and agglomerate structure. The pattern of breakage affects significantly the size distribution of the impact product. An investigation of the breakage of individual interparticle bonds is also presented. Two forms of failure are observed, internal (cohesive) and interfacial (adhesive) failure. The morphology of the fractured surface depends greatly on the type of breakage. Internal breakage shows irregular surfaces due to crack jumping, whereas interfacial failure produces clean, smooth fracture surfaces. These observations should provide the necessary foundation for the development of a fundamental model of agglomerate breakage.     

Fluidization of nanoparticles: A simple equation for estimating the size of agglomerates

In this work, we revise data published in the last decade on the size of agglomerates in gas-fluidized beds of nanoparticles. Experimental measurements reviewed are based on non-invasive techniques, mainly consisting of laser-based planar visualization of agglomerates in the splash zone and indirect derivation from the fit of bed expansion, settling, and/or minimum fluidization velocity data to empirical correlations. Special attention is focused on the effect of fluidization aids such as vibration, magnetic assistance, sound excitation or centrifugation. Independent measurements performed by diverse authors or by the same authors using different techniques are confronted. Empirical models proposed to predict agglomerate size are also reviewed. Most of these models are difficult to apply in practice because they rely on parameters that need to be measured in the fluidization experiment or assumed. We propose a simple equation to estimate agglomerate size derived from the balance between the local shear force on the particle attached at the outer layer of the agglomerate and the interparticle adhesion force. In general, the results predicted by this equation are in satisfactory agreement with the reviewed experimental data.     

粘性SiC颗粒聚团流态化特性

对不同粒径的°SiC粘性颗粒的流态化实验表明,颗粒粒径对流化性能有较大影响,颗粒粒径越小,颗粒间粘附力越大,其流化性能越差;提出了粘性颗粒自然聚团数Ae_n和流态化聚团数Ae_f,用来表征颗粒的流化性能;指出了应开展粘性颗粒聚团流态化的研究。     

Effect of particle characteristics on particle pickup velocity

Particle entrainment is investigated by measuring the velocity required to pick up particles from rest, also known as pickup velocity. Pickup velocity is a function of individual particle characteristics and interparticle forces. Although 5-200 μm particles are investigated, the work presented here focuses on the pickup of particles in a pile in the size range of 5-35 μm. These smaller particle sizes are more typical for pharmaceutical and biomedical applications, such as dry powder inhalers (DPIs). Pickup velocities varied from 3.9 to 16.9 m/s for the range of particle sizes investigated.There is a strong correlation between particle size and the dominating forces that determine the magnitude of the pickup velocity. Preliminary data investigating pickup velocity as a function of particle size indicate the existence of a minimum pickup velocity. For larger particle sizes, the mass of the particle demands a greater fluid velocity for entrainment, and for smaller particle sizes, greater fluid velocities are required to overcome particle-particle interactions. Pickup velocity remains relatively constant at very small particle diameters, specifically, less than 10 μm for glass spheres and 20 μm for nonspherical alumina powder. This can be attributed to the negligible changes in London-van der Waals forces due to a hypothesized decrease in interparticle spacing. At intermediate particle diameters, electrostatic forces are dominant.