Particle Impact Breakage in Particulate Processing

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<ul><li><p>88 KONA No.21 (2003)</p><p>1. Introduction</p><p>The processing and transport of particulate mate-rial, from raw material to final product, is of greatimportance to a wide range of industries. The role ofparticle breakage is significant in many cases interms of yield and quality of product, whether thedesire is to cause breakage or avoid it. However, themechanisms and prediction of particle breakage areonly understood to a limited extent. This paper seeksto review and present current research into the areaof particulate breakage, from the individual particlescale to the process scale.</p><p>2. Single Particle Breakage</p><p>2.1 Impact ExperimentsSingle particle breakage has been studied to a lim-</p><p>ited extent in order to improve the understanding ofensemble breakage in particulate processing applica-tions. Typical research has focussed on the impact orcompression of spherical particles made from a rangeof materials. Single particle impact studies allow theisolation and prediction of breakage in systems whereparticulate transport leads to impacting conditions,</p><p>such as pneumatic conveying and high-shear granula-tion. </p><p>Bemrose and Bridgewater1 state that multiple-impact studies can give empirical data that is usefulfor the direct application to realistic contexts, but donot generally reveal the basic failure mechanisms.Single-impact studies can be used to develop an un-derstanding of failure processes and mechanisms, aswell as providing useful statistical data that can beused for predictive analysis. Single-particle impact istypically achieved by propelling a particle from apneumatic rif le at a rigid target in an arrangementsimilar to that depicted in Figure 1. This arrange-ment allows analysis of particle fracture mechanismsusing high-speed imaging, and measurement of frag-ment size distribution.</p><p>The single particle impact of a large number ofmaterials has been studied in the literature, in par-ticular glass2-9, polymers10-13, ionic crystals14, sand-cement 2, aluminium oxide7, 15, and agglomerates16-18.</p><p>A.D. Salman, G.K. Reynolds and M.J. HounslowDepartment of Chemical and Process Engineering,University of Sheffield*</p><p>Particle Impact Breakage in Particulate Processing</p><p>Abstract</p><p>The study of particle breakage in particulate processing is presented at two principal scales.Single-particle impact results are shown to be useful in deducing and understanding process-scaleparticle breakage behaviour. Particulate breakage in f luidised bed granulation, high-shear granula-tion and pneumatic conveying systems are explored with a focus on presenting techniques and resultsconnected with furthering understanding and modelling.</p><p>* Mappin Street Sheffield SI 3JD United KingdomEmail: a.d.salman@shef.ac.uk</p><p> Accepted: July, 2003</p><p>Gas cylinder(Pressurised gas) </p><p>Pressuregauge </p><p>Electromagneticvalve </p><p>Openbreech Acceleration</p><p>tube </p><p>Axis of gun </p><p>Cage</p><p>Target</p><p>Velocitysensors</p><p>Fig. 1 Typical arrangement for single-particle impact</p></li><li><p>2.2 Failure pattern descriptionTo demonstrate typical fracture pattern analysis,</p><p>the failure patterns of spheres made from differentmaterials will be discussed. The impact velocities aredivided into three relative regimes at which failurecan occur. A low-velocity regime is that at which thefirst signs of breakage occur with increasing impactvelocity. The intermediate-velocity regime is a highervelocity at which a change in failure form occurs com-pared with the low-velocity regime. The high-velocityregime is again where a change in failure form isobserved upon increasing impact velocity. Failureforms from these regimes are shown for a variety ofspherical materials in Figures 2, 3 and 4, respec-tively19.</p><p>Figure 2 shows low impact velocity regime frac-tures of several different materials. Typical Hertzianring and cone cracks, which are usually the first fail-ure patterns with increased normal impact velocity ofglass spheres, can be seen in Figure 2(a)9. This fail-ure is very similar to well-documented forms of fail-ure under quasi-static indentation of a glass surfaceby a rigid sphere15. The principal Hertzian cone crackis labelled C1. Small, annular fragments of glass areremoved when secondary cone cracks travel towardthe free surface. It is expected that this section formsduring the unloading post-impact phase, by analogywith similar cracks observed during slow indentationtests. Again by analogy with static indentation experi-ments, it has been proposed that additional crackswhich form inside the main Hertzian ring are associ-ated with inelastic deformation processes such asdensification15. Figure 2(b) illustrates the low impactvelocity regime failure of aluminium oxide. Localcracking and the development of a f lat region overthe contact area can be observed. Similar fracture pat-terns are also observed in tungsten carbide, solidgranules, polystyrene, sapphire, zircon, steel, nylon,and fertiliser. The labelled compression failure is con-ical in shape. In aluminium oxide, fertiliser and solidgranules, this conical region often disintegrates. Frac-tures can propagate from this region along meridianplanes, producing hemispheres or quadrants (less theconical region). The low impact velocity regime fail-ure of PMMA spheres (Figure 2(c)) reveals charac-teristic angel wing radial cracks, sometimes joinedby sections of circumferential crack and always asso-ciated with circumferential crazing. No observabledeformation of the surface can be found. Wet granuledeformation can be observed at very low velocities(Figure 2(d)) with f lattening of the impact regioninto a relatively large contact area, but with no ob-</p><p>servable cracking. There is a significant increase inthe diameter parallel with the impacting surface and areduction of diameter perpendicular to the impactingsurface. A slight increase in impact velocity abovethis causes a number of small cracks to propagatefrom the deformed contact area parallel to the impactaxis. The higher end of the low impact velocityregime for wet granules sees an increase in the num-ber of these small cracks, but with the granule still</p><p>KONA No.21 (2003) 89</p><p>C1</p><p>(a) soda lime glass</p><p>compression failure</p><p>meridian plane fracture</p><p>(b) aluminium oxide</p><p>(c) PMMA</p><p>(d) Wet granule</p><p>Fig. 2 Normal low impact velocity regime failure patterns of sev-eral materials</p></li><li><p>remaining a single entity. In the low impact velocityregime failure of binderless granules, a f lattenedimpact zone is formed with small cracks propagatingfrom this to the upper hemisphere of the granule. Asmall increase in impact velocity leads to the detach-ment of a small amount of material around the impactzone, and increased oblique cracks.</p><p>Figure 3 shows intermediate impact velocity re-gime breakage patterns for (a) glass, (b) PMMA, (c)wet granules. The failure form of aluminium oxide,and the other materials similar to it, is very similar tothe low velocity regime pattern (Figure 2(b)), exceptfor the production of more segments from meridianplane cracks. Further failure forms become evidentfor the normal impact of glass spheres at increasingvelocity, as illustrated in Figure 3(a). Oblique cracks</p><p>are observed to propagate from under the contactarea, forming a large fragment and several smallerones. The Hertzian cone crack (C1) is usually foundinside one of the smaller fragments, and does not con-tribute to the size reduction process. A significant vol-ume of material from under the contact area ispulverised by the impact, and hence is normally miss-ing when the recovered fragments are reconstructed.The intermediate impact velocity failure of PMMA(Figure 3(b)) shows the sphere divided by a merid-ian plane crack. A roughly conical region below thecontact area is defined by varying combinations ofsections of surface ring cracks, cracks along the con-ical surfaces, or cracks across the conical region.However, the surface of the conical region seems tobe undamaged. It has suffered no f lattening and stillremains transparent. Intermediate impact velocity fail-ure forms of wet granules are shown in Figure 3(c).A distinct cone-shaped fragment is formed at the con-tact area, with the remaining granules forming amushroom-cup shape. A further increase in impactvelocity leads to the mushroom cup fragmenting intoseveral equal-sized pieces. The intermediate impactvelocity failure of binderless granules leads to split-ting into several equally-sized segmental fragments,leaving a compacted cone on the impact surface. Afurther increase in impact velocity leads to an in-crease in the size of the compacted zone, and an in-crease in the number of fragments, albeit of smallersize.</p><p>Figure 4(a) shows a generic high impact velocityfailure pattern for a large number of materials, includ-ing glass, aluminium oxide, tungsten carbide, solidgranules, polystyrene, sapphire, zircon, steel, nylon,fertiliser, and PMMA. A cone of crushed and com-pacted material and several oblique cracks can beobserved. A large part of the sphere remains as a sin-gle characteristically shaped piece (marked F in thefigure). Examples of this piece from a number ofmaterials are presented in Figure 4(b). Meridianplane cracks observed at lower velocities do not formpart of this high impact velocity form. A furtherincrease in impact velocity reduces most of the frag-ments to millimetre and submillimetre dimensions.However, the large central fragment (F) remainscoherent the longest, gradually becoming narrowerand shorter. At exceptionally high impact velocities,specimens can disintegrate into fine powder and leaveno recognisable fragments at all, leaving a cone ofcompacted powder on the impact surface. The highimpact velocity regime failure of wet granules showsa significant fragment size reduction. The contact</p><p>90 KONA No.21 (2003)</p><p>(b) PMMA</p><p>(c) Wet granule</p><p>Fig. 3 Intermediate impact velocity regime failure patterns of sev-eral materials</p><p>C1</p><p>M1</p><p>(a) soda lime glass</p></li><li><p>area cone size increases, and can even be larger thanthe initial diameter of the granule. The presence ofwet binder allows significant plastic-like deformationto take place. Binderless granules completely disinte-grate into a single compacted zone on the target athigh impact velocities.</p><p>This type of analysis allows impact velocity regimesto be defined for different materials. Changes in fail-ure form are often accompanied by a marked changein fragment size distribution. Coupled with knowl-edge of typical particle impact velocities in a givensystem, a certain level of qualitative prediction of par-ticle breakage is possible. This allows more control inthe design of comminution processes for the produc-tion of specific particle characteristics, or the reduc-tion of particulate breakage in other systems.</p><p>2.3 Quantitative ModellingModelling the fragment size distribution mathemat-</p><p>ically allows the extent of fracture to be assessedquantitatively. Typical models have been reviewed asfollows20. In comminution, the Rosin-Rammler modelhas been widely used to describe skewed particle sizedistributions21. This model is characterised by two</p><p>parameters, namely the mean size and the width ofthe distribution. An alternative two-parameter equa-tion used in describing fragment size distribution wasthe Schuhmann equation22, which was defined by dis-tribution and size parameters. According to Ryu andSaito23, no physical significance of the size parameterwas given by Schuhmann. Gilvarry and Bergstrom24</p><p>proposed a three-parameter distribution function todescribe the fragment size distribution of brittle sol-ids. This function was in good agreement with experi-mental results in the fine size region between 1 mand 1000 mm. However, this idealised function wasnot satisfied outside the size interval specified due tothe fact that the size of a real specimen was finite.Similarly, Arbiter et al.2 found only reasonable agree-ment in the fine sizes when the Gaudin-Schuhmanndouble logarithmic plot was used to describe the over-all size distribution of glass fragments produced indouble-impact and slow compression tests. Ryu andSaito23 found only a relatively good fit to both thecoarse and fine fragments when reviewing theGaudin-Meloy-Harris equation. This equation statesthat the volume (or weight) fraction, y, passing frag-ment size of x takes the following form,</p><p>y11 </p><p>(1)</p><p>where , and x0 are the empirical parameters. How-ever, this equation was not favourable due to the largenumber of parameters required. </p><p>The impact of large numbers of single particles hasalso been modelled quantitatively by Salman et al.25.In a typical experiment, 100 particles are individuallyimpacted at a constant velocity and the number of par-ticles exhibiting failure is counted. A relationshipbetween the number of unbroken particles (N0) andthe impact velocity (vp) can be derived by a two-para-meter cumulative Weibull distribution:</p><p>N0100exp m (2)In equation (2), c is the scale parameter and m is theWeibull modulus. The scale parameter c has no directphysical definition, but its value is equal to the impactvelocity at which the number of unbroken particles is36.8%. The Weibull modulus, m, corresponds to thestandard deviation of the distribution. Figure 5 illus-trates a typical relationship between normal impactvelocity and number of unbroken particles for fertil-izer 25. This analysis can also be used for particleimpact under oblique angles. It allows particle break-age under impact conditions to be quantified through</p><p>vpc</p><p>xx0</p><p>KONA No.21 (2003) 91</p><p>Crushed cone</p><p>F</p><p>(a) generic high-velocity form</p><p>(b) segment F for soda lime glass and aluminium oxide, respectively</p><p>Fig. 4 High impact velocity regime failure patterns of severalmaterials</p></li><li><p>the use of two parameters, c and m. Figure 6 showsthese parameters for 7-mm spheres made from arange of materials. This data can be used to predictthe extent of breakage at a range of impact velocities.</p><p>The short duration of particle impact breakage hasmeant that the physical experimental investigationhas been replaced by the post-mortem examination ofthe fragments generated. However, advances in nu-merical simulations of single-particle and in partic-ular single-agglomerate impact have allowed moredetailed study of particle breakage during impact26-29.</p><p>Typical numerical simulations use the discrete ele-ment method (DEM) incorporated with autoadhesiveinterparticle interaction laws. The motion of each pri-mary particle constituting the agglomerate is tracedthroughout the impact event using Newtons law ofmotion. A slightly different two-dimensional DEMapproach was adopted by Potapov and Campbell26 tosimulate the breakage behaviour of homogeneouselastic solids impacting against a rigid wall. Instead ofdiscrete particles, the elastic solid was divided intopolygonal elements contacting with each other. Thecontacts were considered to be broken once the ten-sile force experienced was found to exceed a certainlimit. Their simulation results indicated that a fan-likefracture pattern, with elongated fragments, existedover the range of solid material properties and impactvelocities used. The formatio...</p></li></ul>

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