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     

Impact breakage of spherical, cuboidal and cylindrical agglomerates

A numerical study of the micro-mechanics of breakage of agglomerates impacting with a target wall has been carried out using discrete element simulations. Three agglomerates of different shapes are examined, namely spherical, cuboidal and cylindrical. Each agglomerate consists of 10,000 polydisperse auto-adhesive elastic spheres with a normal size distribution. The effect of agglomerate shape and impact site on the damage of the agglomerates under an impact velocity of 1.0 m/s for an interface energy of 1.0 J/m² is reported. It is found from the simulations that cuboidal edge, cylindrical rim and cuboidal corner impacts generate less damage than spherical agglomerate impacts. The cuboidal face, cylindrical side and cylindrical end impacts fracture the agglomerates into several fragments. Detailed examinations of the evolutions of damage ratio, number of wall contacts and total wall force indicate that the size of the contact area and the rate of change of the contact area play important roles in agglomerate breakage behaviour. Internal damage to the agglomerate is closely related to the particle deceleration adjacent to the impact site. However, the local microstructure may not be a decisive factor in terms of the breakage mode for non-spherical agglomerates.     

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.     

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.     

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.     

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.     

Discrete particle simulation of agglomerate impact coalescence

This paper describes computer simulations of pendular state wet agglomerates undergoing pair-wise collisions. The simulation method is based upon a ‘soft’ discrete particle formulation. Each agglomerate comprised 1000 primary particles with the interparticle interactions modelled as the combination of the solid–solid contact forces and also the forces developed at discrete liquid bridges between neighbouring particles. For the range of collisional velocities implemented, the agglomerates invariably coalesced. The energy dissipated was associated primarily with the viscous resistance of the fluid and the interparticle friction rather than by liquid bridge bond rupture. The structure of the resultant coalesced agglomerate was highly disordered and depended on the impact velocity. As the impact velocity approached zero, the agglomerates behaved like two rigid bodies bonded together. When the impact velocity was increased, the size of the circumscribing sphere of the coalesced agglomerate decreased and reached a minimum value at a critical velocity above which an increase in the circumscribing sphere size occurred due to extensive flattening. An increase in the viscosity of the interstitial fluid resulted in an increase in the proportion of energy dissipated by viscous resistance and a decrease in the proportion dissipated due to interparticle friction. An increase in the fluid viscosity also resulted in an increase in the critical impact velocity at which the size of the circumscribing sphere of the coalesced agglomerate was a minimum.     

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.     

Mechanistic analysis and computer simulation of impact breakage of agglomerates: Effect of surface energy

Agglomerates are ubiquitous as intermediate or manufactured products in chemical, pharmaceutical and food industries. During handling and processing they may suffer breakage if they are weak. On the other hand, if they are too strong, their dispersion and disintegration could be difficult. The control of their mechanical strength is therefore highly desirable. However, the analysis of agglomerate strength is complex due to the large number of parameters that influence agglomerate behaviour, such as the primary particle size, density and elastic modulus, and the interparticle bond strength.A simple mechanistic model is presented here which relates the number of broken contacts in agglomerate due to impact velocity, interparticle adhesion energy and the particle properties of the particles forming the agglomerate. The model is based on the hypothesis that the energy used to break contacts during impact is proportional to the incident kinetic energy of the agglomerate. The damage ratio defined as the ratio of broken contacts to the initial number of bonds is shown to depend on the dimensionless group, Δ, in the form (ρV²D^5/3E^2/3)/Γ^5/3, where V is the impact velocity, E the elastic modulus, D the particle diameter, ρ the particle density and Γ the interface energy. This dimensionless group, Δ, incorporates the Weber number, (ρDV²/Γ), which was previously shown to be influential in agglomerate breakage, and may be presented in the form, , where I_e=ED/Γ.The predicted dependency of the damage ratio on the surface energy has been tested using distinct element method (DEM). Four different agglomerates have been formed and impacted against a target for three different values of the surface energy of the primary particles. The simulation results show that the effect of surface energy is better described by the above mechanistic model than by the Weber number alone, as previously used to characterise the impact strength of agglomerates.     

Effect of size ratio on the behaviour of agglomerates embedded in a bed of particles subjected to shearing: DEM analysis

This paper presents the results of analysis of the deformation and breakage of spherical agglomerates embedded in a bed of particles and subjected to shearing, a situation commonly encountered in powder granulation. The study is based on three dimensional distinct element method (DEM), in which the inter-particle interactions are governed by theories of contact mechanics. An agglomerate was first generated in a bed of particles having the same size as the primary particles forming the agglomerate. Different size ratios (i.e., the ratio of the diameter of agglomerate to the diameter of surrounding particles) in the range 3-10 were then simulated by varying the size and number of surrounding particles. The agglomerates were subjected to shearing (shear rate and strain of about and 0.3, respectively) and their breakage characteristics were analysed. The agglomerate with the size ratio 10 does not break but undergoes some structural deformation by re-arrangements of contacts. However, the agglomerates with ratio about 7 or smaller suffer breakage. For the size ratio equal or smaller than 5, the agglomerate breaks significantly leading to full disintegration. The results of stress analysis of the agglomerates suggest that the resistance to breakage for the agglomerate with size ratio of 10 is due to the nature of stresses exerted on the agglomerate. For large size ratios the stress on the agglomerate is predominantly hydrostatic. The ratio of deviatoric stress over hydrostatic pressure increases as the size ratio of the agglomerate is reduced. The nature of stresses experienced by agglomerates with smaller size ratios is predominantly deviatoric, thus causing shear deformation and breakage. The results are compared with physical experiments and a satisfactory agreement is obtained.     

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.     

Influence of interface energy of primary particles on the deformation and breakage behaviour of agglomerates sheared in a powder bed

In this paper, the parameters that affect the deformation and breakage of agglomerates embedded in a bed of particles subjected to rapid shearing are identified and analysed. The influences of interface energy between the primary particles and the size ratio (between agglomerates and particles of the bed) on the deformation characteristics of the agglomerate are addressed. The study is based on computer simulations using the distinct element method (DEM). It has recently been shown that for agglomerates having a size ratio greater than about 7, the nature of stresses experienced by the agglomerates when sheared inside a particulate bed is predominantly hydrostatic, hence it is difficult to break them (Hassanpour et al., 2007). However, the role of the interface energy between primary particles coupled with the effect of size ratio on the breakage and deformation characteristics of agglomerates during shearing has not been analysed. This feature is of great interest in the agglomeration process and is hence addressed in the present study. It is found that despite the predominantly hydrostatic nature of stresses responsible for retarding the breakage, agglomerates with size ratio greater than about 7 could undergo macroscopic deformation when the surface energy between the primary particles is decreased below a critical value. Furthermore, a failure map of agglomerates is presented in terms of their size ratio and the value of interface energy of the primary particles.     

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.     

Investigation of the dispersion of carbon black agglomerates of various sizes in simple-shear flows

The dispersion of spherical carbon black agglomerates suspended in polydimethyl siloxane liquid and subjected to simple shear flows has been studied in a cone-and-plate shearing device. Sets of dispersion experiments were carried out for agglomerates of various size and packing density. For agglomerates of equal density and under conditions of equivalent cone rotation rates, the dispersion rates of small agglomerates were smaller than those observed for larger agglomerates. Since the agglomerates occupy a significant fraction of the flow domain, the magnitude and distribution of shear stress acting on the agglomerate at a fixed cone rotation rate depends on the ratio of agglomerate size relative to the size of the gap between the cone and plate. To investigate whether this effect could cause the observed variation in dispersion behavior, we performed three-dimensional simulations of the flow fields within the cone-and-plate device and calculated the resulting stress fields acting on spherical agglomerates. These results helped guide additional experiments in which the peak stress acting on agglomerates of various sizes was matched. However, even under matched stress conditions, the dispersion kinetics was found to vary according to the agglomerate size. In addition, the dispersion kinetics for identical sized agglomerates was found to depend on their processing history. Both of these results lead to the conclusion that some other effect, likely the infiltration of the processing fluid within the agglomerate structure, also influences the dispersion behavior.     

Agglomeration in suspension of salicylic acid fine particles: influence of some process parameters on kinetics and agglomerate final size

Agglomeration in suspension is a size-enlargement method that facilitates operations of solid processing (filtration, transport, galenic) and preserves the solubilization properties of fine particles. It consists in adding to a suspension of microparticles a small quantity of a second liquid acting as an interparticle binder; in a suitably agitated equipment with a critical quantity of binder, spherical and dense agglomerates of a few millimeters in diameter may be formed. This paper presents a new methodology to study the agglomeration process. The system [salicylic acid/aqueous solution/chloroform] is chosen as a model system. To follow in situ the agglomerate formation and growth, an original device based on image acquisition and analysis is developed; agglomerate porosity and compressive strength are also measured. These measurements allow us to identify the influence of the process parameters on the agglomeration kinetics, the size and the compressive strength of the final agglomerates. They also give interesting insights into the mechanisms.     

Fracture behavior of vinylester resin matrix composites reinforced with alkali‐treated jute fibers

Jute fibers were treated with 5% NaOH solution for 4 and 8 h, respectively, to study the mechanical and impact fatigue properties of jute‐reinforced vinylester resin matrix composites. Mechanical properties were enhanced in case of fiber composites treated for 4 h, where improved interfacial bonding (as evident from scanning electron microscopy [SEM]) and increased fiber strength properties contributed effectively in load transfer from the matrix to the fiber; but their superior mechanical property was not retained with fatigue, as they showed poor impact fatigue behavior. The fracture surfaces produced under a three‐point bend test and repeated impact loading were examined under SEM to study the nature of failure in the composites. In case of untreated fiber composites, interfacial debonding and extensive fiber pullout were observed, which lowered the mechanical property of the composites but improved their impact fatigue behavior. In composites treated for 4 h under repeated impact loading, interfacial debonding occurred, followed by fiber breakage, producing a sawlike structure at the fracture surface, which lowered the fatigue resistance property of the composites. The composites with fibers treated with alkali for 8 h showed maximum impact fatigue resistance. Here, interfacial debonding was at a minimum, and the fibers, being much stronger and stiffer owing to their increased crystallinity, suffered catastrophic fracture along with some microfibrillar pullout (as evident from the SEM micrographs), absorbing a lot of energy in the process, which increased the fatigue resistance property of the composites. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2588–2593, 2002     

Compression of polymer bound alumina agglomerates at the micro deformation scale

In this paper, the mechanical properties of alumina particle based agglomerates, prepared in a tumble mixer by using a poly (vinyl alcohol) (PVA) binder (ca. 5% by volume) in conjunction with water solvent, are described at a micro deformation level. Uniaxial compressive deformation profiles of these alumina agglomerates, typically 180–200 μm in diameter, are reported and their diverse behaviour during compression have been observed, which vary from a clear brittle rupture to progressive ductile deformation. However, certain common patterns of the agglomerate reaction force response, as a function of the compressive displacement, are identified, such as the similarities in the reloading response after each discrete fracture event. The Hertz Theory and a slope and peak force analysis are applied to establish the common patterns and trends, and generalize the intrinsic deformation characteristics of these agglomerates.     

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.     

Breakage of carbon nanotube agglomerates within polypropylene matrix by solid phase die drawing

Melt blending of polyolefin/carbon nanotube (CNT) composites always leads to serious agglomeration of CNTs and hence inferior properties. Thus, well-dispersed CNTs within matrix are urgently required during processing. In this work, effective breakage of CNT agglomerates was achieved by solid-phase die drawing at a temperature below but near to the melting temperature of the matrix. Experimental results indicate that the incurred extensional stress provides a high orientation degree on the polypropylene (PP) matrix and consequently helps rupture CNT agglomerates, leading to improved alternating current（AC） conductivity by ~5–6 orders in magnitude. The reduced agglomerate ratio, the altered CNT networks (3D→2D), and the improved interfacial morphology between CNT and matrix are suggested to be responsible for the viscoelasticity variation of the composite melt and the improved property of PP/multiwalled CNTs (MWCNTs) composite. The initial loss of tensile ductility by the incorporation of MWCNTs is recovered by nearly 100%, which was attributed to the low agglomeration rate and improved interfacial morphology. This article provided the potential inspiration for the melt blending of polymer melt and CNTs.