Particle Impact Breakage in Particulate Processing

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-scale particle breakage behaviour. Particulate breakage in f luidised bed granulation, high-shear granulation and pneumatic conveying systems are explored with a focus on presenting techniques and results connected with furthering understanding and modelling.


Introduction
The processing and transport of particulate material, from raw material to final product, is of great importance to a wide range of industries.The role of particle breakage is significant in many cases in terms of yield and quality of product, whether the desire is to cause breakage or avoid it.However, the mechanisms and prediction of particle breakage are only understood to a limited extent.This paper seeks to review and present current research into the area of particulate breakage, from the individual particle scale to the process scale.

Impact Experiments
Single particle breakage has been studied to a limited extent in order to improve the understanding of ensemble breakage in particulate processing applications.Typical research has focussed on the impact or compression of spherical particles made from a range of materials.Single particle impact studies allow the isolation and prediction of breakage in systems where particulate transport leads to impacting conditions, such as pneumatic conveying and high-shear granulation.
Bemrose and Bridgewater 1 state that multipleimpact studies can give empirical data that is useful for the direct application to realistic contexts, but do not generally reveal the basic failure mechanisms.Single-impact studies can be used to develop an understanding of failure processes and mechanisms, as well as providing useful statistical data that can be used for predictive analysis.Single-particle impact is typically achieved by propelling a particle from a pneumatic rif le at a rigid target in an arrangement similar to that depicted in Figure 1.This arrangement allows analysis of particle fracture mechanisms using high-speed imaging, and measurement of fragment size distribution.

Failure pattern description
To demonstrate typical fracture pattern analysis, the failure patterns of spheres made from different materials will be discussed.The impact velocities are divided into three relative regimes at which failure can occur.A low-velocity regime is that at which the first signs of breakage occur with increasing impact velocity.The intermediate-velocity regime is a higher velocity at which a change in failure form occurs compared with the low-velocity regime.The high-velocity regime is again where a change in failure form is observed upon increasing impact velocity.Failure forms from these regimes are shown for a variety of spherical materials in Figures 2, 3 and 4, respectively 19 .
Figure 2 shows low impact velocity regime fractures of several different materials.Typical Hertzian ring and cone cracks, which are usually the first failure patterns with increased normal impact velocity of glass spheres, can be seen in Figure 2(a) 9 .This failure is very similar to well-documented forms of failure under quasi-static indentation of a glass surface by a rigid sphere 15 .The principal Hertzian cone crack is labelled C1.Small, annular fragments of glass are removed when secondary cone cracks travel toward the free surface.It is expected that this section forms during the unloading post-impact phase, by analogy with similar cracks observed during slow indentation tests.Again by analogy with static indentation experiments, it has been proposed that additional cracks which form inside the main Hertzian ring are associated with inelastic deformation processes such as densification 15 .Figure 2(b) illustrates the low impact velocity regime failure of aluminium oxide.Local cracking and the development of a flat region over the contact area can be observed.Similar fracture patterns are also observed in tungsten carbide, solid granules, polystyrene, sapphire, zircon, steel, nylon, and fertiliser.The labelled compression failure is conical in shape.In aluminium oxide, fertiliser and solid granules, this conical region often disintegrates.Fractures can propagate from this region along meridian planes, producing hemispheres or quadrants (less the conical region).The low impact velocity regime failure of PMMA spheres (Figure 2(c)) reveals characteristic 'angel wing' radial cracks, sometimes joined by sections of circumferential crack and always associated with circumferential crazing.No observable deformation of the surface can be found.Wet granule deformation can be observed at very low velocities (Figure 2(d)) with f lattening of the impact region into a relatively large contact area, but with no ob-servable cracking.There is a significant increase in the diameter parallel with the impacting surface and a reduction of diameter perpendicular to the impacting surface.A slight increase in impact velocity above this causes a number of small cracks to propagate from the deformed contact area parallel to the impact axis.The higher end of the low impact velocity regime for wet granules sees an increase in the number of these small cracks, but with the granule still remaining a single entity.In the low impact velocity regime failure of binderless granules, a flattened impact zone is formed with small cracks propagating from this to the upper hemisphere of the granule.A small increase in impact velocity leads to the detachment of a small amount of material around the impact zone, and increased oblique cracks.
Figure 3 shows intermediate impact velocity regime 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 to the low velocity regime pattern (Figure 2(b)), except for the production of more segments from meridian plane cracks.Further failure forms become evident for the normal impact of glass spheres at increasing velocity, as illustrated in Figure 3(a).Oblique cracks are observed to propagate from under the contact area, forming a large fragment and several smaller ones.The Hertzian cone crack (C1) is usually found inside one of the smaller fragments, and does not contribute to the size reduction process.A significant volume of material from under the contact area is pulverised by the impact, and hence is normally missing when the recovered fragments are reconstructed.The intermediate impact velocity failure of PMMA (Figure 3(b)) shows the sphere divided by a meridian plane crack.A roughly conical region below the contact area is defined by varying combinations of sections of surface ring cracks, cracks along the conical surfaces, or cracks across the conical region.However, the surface of the conical region seems to be undamaged.It has suffered no f lattening and still remains transparent.Intermediate impact velocity failure forms of wet granules are shown in Figure 3(c).A distinct cone-shaped fragment is formed at the contact area, with the remaining granules forming a mushroom-cup shape.A further increase in impact velocity leads to the mushroom cup fragmenting into several equal-sized pieces.The intermediate impact velocity failure of binderless granules leads to splitting into several equally-sized segmental fragments, leaving a compacted cone on the impact surface.A further increase in impact velocity leads to an increase in the size of the compacted zone, and an increase in the number of fragments, albeit of smaller size.
Figure 4(a) shows a generic high impact velocity failure pattern for a large number of materials, including glass, aluminium oxide, tungsten carbide, solid granules, polystyrene, sapphire, zircon, steel, nylon, fertiliser, and PMMA.A cone of crushed and compacted material and several oblique cracks can be observed.A large part of the sphere remains as a single characteristically shaped piece (marked F in the figure).Examples of this piece from a number of materials are presented in Figure 4(b).Meridian plane cracks observed at lower velocities do not form part of this high impact velocity form.A further increase in impact velocity reduces most of the fragments to millimetre and submillimetre dimensions.However, the large central fragment (F) remains coherent the longest, gradually becoming narrower and shorter.At exceptionally high impact velocities, specimens can disintegrate into fine powder and leave no recognisable fragments at all, leaving a cone of compacted powder on the impact surface.The high impact velocity regime failure of wet granules shows a significant fragment size reduction.The contact area cone size increases, and can even be larger than the initial diameter of the granule.The presence of wet binder allows significant plastic-like deformation to take place.Binderless granules completely disintegrate into a single compacted zone on the target at high impact velocities.This type of analysis allows impact velocity regimes to be defined for different materials.Changes in failure form are often accompanied by a marked change in fragment size distribution.Coupled with knowledge of typical particle impact velocities in a given system, a certain level of qualitative prediction of particle breakage is possible.This allows more control in the design of comminution processes for the production of specific particle characteristics, or the reduction of particulate breakage in other systems.

Quantitative Modelling
Modelling the fragment size distribution mathematically allows the extent of fracture to be assessed quantitatively.Typical models have been reviewed as follows 20 .In comminution, the Rosin-Rammler model has been widely used to describe skewed particle size distributions 21 .This model is characterised by two parameters, namely the mean size and the width of the distribution.An alternative two-parameter equation used in describing fragment size distribution was the Schuhmann equation 22 , which was defined by distribution and size parameters.According to Ryu and Saito 23 , no physical significance of the size parameter was given by Schuhmann.Gilvarry and Bergstrom 24 proposed a three-parameter distribution function to describe the fragment size distribution of brittle solids.This function was in good agreement with experimental results in the fine size region between 1 µm and 1000 mm.However, this idealised function was not satisfied outside the size interval specified due to the fact that the size of a real specimen was finite.Similarly, Arbiter et al. 2 found only reasonable agreement in the fine sizes when the Gaudin-Schuhmann double logarithmic plot was used to describe the overall size distribution of glass fragments produced in double-impact and slow compression tests.Ryu and Saito 23 found only a relatively good fit to both the coarse and fine fragments when reviewing the Gaudin-Meloy-Harris equation.This equation states that the volume (or weight) fraction, y′, passing fragment size of x takes the following form, where α, β and x 0 are the empirical parameters.However, this equation was not favourable due to the large number of parameters required.
The impact of large numbers of single particles has also been modelled quantitatively by Salman et al. 25 .In a typical experiment, 100 particles are individually impacted at a constant velocity and the number of particles exhibiting failure is counted.A relationship between the number of unbroken particles (N 0 ) and the impact velocity (v p ) can be derived by a two-parameter cumulative Weibull distribution: In equation ( 2), c is the scale parameter and m is the Weibull modulus.The scale parameter c has no direct physical definition, but its value is equal to the impact velocity at which the number of unbroken particles is 36.8%.The Weibull modulus, m, corresponds to the standard deviation of the distribution.Figure 5 illustrates a typical relationship between normal impact velocity and number of unbroken particles for fertilizer 25 .This analysis can also be used for particle impact under oblique angles.It allows particle breakage under impact conditions to be quantified through the use of two parameters, c and m. Figure 6 shows these parameters for 7-mm spheres made from a range of materials.This data can be used to predict the extent of breakage at a range of impact velocities.The short duration of particle impact breakage has meant that the physical experimental investigation has been replaced by the post-mortem examination of the fragments generated.However, advances in numerical simulations of single-particle and in particular single-agglomerate impact have allowed more detailed study of particle breakage during impact [26][27][28][29] .
Typical numerical simulations use the discrete element method (DEM) incorporated with autoadhesive interparticle interaction laws.The motion of each primary particle constituting the agglomerate is traced throughout the impact event using Newton's law of motion.A slightly different two-dimensional DEM approach was adopted by Potapov and Campbell 26 to simulate the breakage behaviour of homogeneous elastic solids impacting against a rigid wall.Instead of discrete particles, the elastic solid was divided into polygonal elements contacting with each other.The contacts were considered to be broken once the tensile force experienced was found to exceed a certain limit.Their simulation results indicated that a fan-like fracture pattern, with elongated fragments, existed over the range of solid material properties and impact velocities used.The formation of fan-like crack systems was accelerated when there was an increase in impact velocity.Potapov and Campbell also concluded that the impact kinetic energy was dissipated by elastic wave propagation through the elastic body under consideration.
The primary disadvantage with single-particle impact studies is that in a typical particulate system, particles do not exist as isolated entities, but rather discrete parts of an ensemble population.Interparticle interaction is likely to have a large effect on particle breakage forms and rates.However, it is only through study on the single particle, and even the intra-particle level that a mechanistic understanding of particulate breakage can be achieved.

Particulate Processing
Two specific areas of particulate processing are now discussed in order to present a range of research concerning particulate breakage on a process scale.In granulation, an understanding of particle breakage rates is fundamental to control of the final granular product.In pneumatic conveying, an understanding of particulate breakage is important to permit a design that minimises product loss.

Granulation
Granulation has been widely used in the chemical, agricultural, pharmaceutical, foodstuff and mineral industries to consolidate fine powder into larger entities known as granules.Granules are formed by typically agitating fine powder together with a liquid binder, typically termed wet granulation.Agitation is achieved, for example, using unit operations such as a f luidised bed, high-shear mixer, rotating drum, or Traditionally, granulation behaviour has been described in terms of a number of different mechanisms such as nucleation or wetting, abrasion transfer, crushing and layering 30 .Recently, it was proposed that granulation could be considered as a combination of three sets of rate processes [31][32][33] .They are (1) wetting and nucleation, (2) consolidation and growth, and (3) attrition and breakage.However, there is still little understanding as to the sequence and importance of each mechanism 34 .During granulation, granules can interact with each other, and with solid walls, which can lead to deformation, attrition/breakage, rebounding, or sticking.The behaviour of the granules under impact loading is often very important.Granule breakage may also affect transportation processes by causing undesirable changes in the size, shape or appearance of the granular product.
On a process level, the modelling of breakage in granulation can be incorporated into a population balance model which allows prediction of the size distribution.For batch, well-mixed systems, with size being the only internal coordinate, a population balance equation can be expressed as [35][36][37][38] : ҃BҀD with B and D representing sources of creation and destruction of granules of size v. Mechanisms that are often included in batch granulation population balance modelling for these terms are that of aggregation and breakage.Both aggregation and breakage mechanisms have associated birth (B) and death (D) functions.The aggregation of two granules of size u and v will lead to a loss of one granule each of size u and v and the creation of another granule of size uѿv.
Likewise, breakage of a granule of size v will lead to a loss of one granule of size v but the creation of a number of smaller granules dictated by the fragment size distribution.Source terms for breakage can be expressed as: Here, S, the selection rate constant, describes the rate of breakage of particles of a given size, and can also be considered time-dependent.This time dependence is related to the expected densification of granules during the granulation process, leading to stronger granules and hence a changing breakage ∂n(v,t) ∂t rate.In fact, the breakage rate should be a function of a number of granule properties, but as these are not taken into account in the single-dimensional population model, the term often becomes time-dependent.The breakage function, b, describes the sizes of the fragments from the breaking particle.It was not until fairly recently that breakage was incorporated into the modelling of granulating processes.It is noted qualitatively by 39 that the modelling of aggregation terms only in batch granulation processes is not sufficient to describe the system.

Fluidised Bed Granulation
In f luidised bed granulation, a bed of primary particles are typically agitated by an air flow.Liquid binder is sprayed over the agitated bed, causing agglomeration between primary particles and leading to granule formation and growth.An understanding of the rates of agglomeration and breakage process within the system are fundamental to the successful control and prediction of the final granular product.
Only a limited amount of work has been conducted into the breakage of granules within fluidised beds.Pitchumani and Meesters 40 describe the breakage behaviour of different enzyme granules, manufactured using a f luidised bed, subjected to repeated impacts using a new instrument.The two types of granules used for the impact testing are produced from spray drying and f luidised bed granulation.The impact test involves bombarding the particles repeatedly against a f lat target.The main feature of this new test is its ability to repeatedly impact a large number of particles against a f lat target, and to generate extremely reproducible results.They have tested a large number of particles, yielding a statistically satisfactory result.The repeated impacts also provide information on the breakage behaviour of the particles based on their history.Their impact test allows the enzyme granules to undergo very low impact velocities of the order of 5m/s.These low impact velocities lead to attrition and chipping of the granules.However, although this test allows attrition and fragmentation to be quantified, it is also noted that it is still not possible to explain the concept of particle breakage for use in theoretical development, such as in a population balance model.
The inclusion of breakage in a population balance model of f luidised bed granulation has been presented by Biggs et al. 41 .They hypothesised that the breakage process was due to a reversal of the growth process, and hence able to be modelled using a negative aggregation rate.Breakage was observed experi-mentally by stopping the binder spray, and hence effectively terminating agglomeration in a system where the binder solidified once it had cooled to the f luidised bed temperature.Figure 7 shows a comparison between their experimental and simulation work.A mean diameter, represented as the ratio of the fourth moment to the third moment of the granule size distribution, is plotted against operating time.The triangular points on the graph indicate experimental results, with the filled-in triangles representing data gathered after the spray of binder had been stopped.This shows that breakage becomes a dominant mechanism in this system when no further wet binder is introduced, due to solidification of the binder in the f luidised bed.The population balance model results are represented in Figure 7 as the dashed line.It can be seen that during the spray-and agglomeration-dominant period, there is very good agreement.However, after spraying, during the breakage-dominant period, the model is observed to underpredict the rate of decrease in mean size.These results are a promising step towards including breakage kinetics in the population balance modelling of f luidised bed granulation, but some discrepancies between the experimental and modelling results indicate that further work is needed to include the description of faster breakage kinetics in their current model.

High-Shear Granulation
In high-shear granulation, a powder is typically agitated in a cylindrical bowl by a large impeller.Often an additional smaller impeller, termed a 'chopper', is used.Binder can be added by pouring or spraying onto the powder.
Sources of breakage exist within a high-shear granulator from particle-particle interaction, particle-wall collision, impeller, and the chopper where this is used.Knight et al. 42 observed a lower extent of size enlargement relative to power input at high impeller speeds compared with lower ones.They concluded that the increased impeller speed contributed significantly to breakage that limited growth.
Tracer experiments on high-shear granulation have been conducted by Ramaker et al. 43 .They observed that the growth and destruction of granules from different sieve fractions could be measured with tracers.They derived conversion rate constants from the exponential decay of the colour concentration at different processing times for each sieve fraction.Compared to a dimensionless diameter, similar conversion rate constants were found between two high-shear processes (a coffee grinder and a Gral 10).The conversion rate constants of the smallest granules were higher (compared to the larger ones), which indicated faster growth of the smaller granules due to the destruction of the large pellets.
Clear evidence of breakage in wet high-shear granulation has also been shown by Pearson et al. 44 , through the use of coloured tracer granules.The system used calcium carbonate and polyethylene glycol (1500) as a binder.In the case of polyethylene glycol (1500) as a binder, the binder was added using a 'melt in' technique.The binder is solid at room temperature, and therefore the high-shear granulator is heated above the melting point (60°C).The binder is added as a solid at the start of the process, and melts as it reaches the operating temperature.Granules collected from this process are solid at room temperature, allowing easier handling for analysis.Granules were manufactured in a Fukae FS30, a 30-litre pilotscale mixer, with a base-mounted impeller and a sidemounted chopper.The impeller and chopper had maximum speeds of 300 rpm and 3,000 rpm, respectively.A narrow sieve cut of coloured tracer granules was placed into placebo granulation batches in order Comparison between model and experimental results for the change in mean size for liquid-to-solid ratios of (a) 0.05 (b), 0.1, and (c) 0.2 in f luidised bed granulation [35]     to observe the subsequent redistribution of coloured tracer.A multiple-phase discretised population balance model was constructed in order to extract breakage rates from the experimental data 45 .A bimodal breakage function was proposed.Figure 8 shows a tracer distribution presented in the paper.Based on this, they proposed breakage to proceed as follows.
When a granule breaks, it produces two kinds of fragments: many fine ones of mass-mean size near 150 µm, and a few large pieces of mass-mean size somewhat less than that of the initial granule.In this way, on a mass basis, the breakage function is bimodal.
This breakage function can then be incorporated into a population balance model (see equations 3a and 3b).It was shown by 44 that the selection rate constant was size-independent.They found that plots of the tracerweighted mean-size suggested that the initial breakage rate was considerably greater immediately after the addition of tracer granules, rather than later.Figure 9 was also found to support this hypothesis, as the rate of relegation of the tracer was considerably greater for the younger granules than it was for the older granules.Relegated tracer, χ, is defined as the amount of dye over all sizes smaller than the initial tracer size.It was proposed that the breakage effectively ceased after the first minute or so subsequent to the addition of the tracer (which was introduced after 8 minutes of granulation), i.e. at t҃10min.An exponential decay was then chosen to represent the selection rate constant:  9 Fraction of tracer relegated for tracers of four different ages, but a constant size of 1.09 mm.All tracers were added after 8 minutes of granulation [38]     tion for the heterogeneous granule strength within any single size class is due to heterogeneity in liquid distribution.Good agreement was found between their modelled results and experimental findings, illustrating that breakage can be successfully incorporated into the population balance modelling of granulation processes.

Pneumatic Conveying
Pneumatic conveying systems are a key unit operation in the transport of particulate material.Typically, particles are transported along pipes using highspeed air f low.The breakage of particles in these systems, causing in some cases a change of size distribution and appearance, can lead to particulate products that no longer meet their required and designed specification.Fragmentation can lead to dust generation, handling and storage problems, in particular where breakage is so severe that aeration and flow characteristics are drastically changed 46 .
Extensive studies into the breakage of particles in dilute conveying systems have been presented by a number of authors [47][48][49][50][51][52][53] .Typical measurements are based on circulating the particles on a specific pneumatic conveying system.The change in particle size before and after circulation is observed and related to the air velocity and/or the number of circulations conducted.These studies have provided valuable general information concerning the minimisation of particle breakage during conveying.However, as there are so many variables involved in predicting the mechanisms of particle breakage, and it is difficult to isolate these variables, these studies are typically unique to one particular system.Therefore, they are largely unsuitable for predicting the breakage of particles in other systems.
Salman et al. 46 use a numerical model for calculating the particle trajectory in dilute-phase pipe transport.In their model, they consider a dilute system where inter-particle collisions are neglected and fragmentation is only considered upon impact with pipe walls.They use this model, coupled with single-particle impact studies, to predict particulate breakage in pneumatic conveying.The results are validated with experimental observations on a small-scale pneumatic conveying system consisting of a horizontal pipe with a 90°bend (see Figure 10).In this figure, model results are represented as lines, and experimental data as points.The figure shows that high velocities lead to a dramatic increase in particle breakage.Specifically, they found negligible breakage in the horizontal pipe due to a very low impact angle.This is consistent with single-particle impact studies under different impact angles (e.g. Figure 6).Therefore, particle breakage at the bend can be reduced by decreasing the impact angle.This can be achieved by using long radius bends and by reducing the conveying velocity.This study shows that single-particle impact data can be used for predicting particulate breakage on a process level in dilute systems.

Conclusions
Analysis of the breakage of single particles and agglomerates is used to model and predict failure on a process level.Observation of failure forms shows that spherical particles of a wide range of materials can be classified into distinct failure regimes with respect to impact velocity.Specifically, many materials are observed to fail very similarly at a high impact velocity.Low-and medium-impact velocity forms contain some similarities and differences due to different material properties.The quantitative analysis of single-particle impact can be achieved by fitting breakage rates by a 2-parameter Weibull distribution.These two parameters can be used to successfully model the single-impact breakage rate under normal and oblique impact conditions.These single-impact studies can be used to explain breakage observations on a process level.For example, the amount of breakage in a pneumatic conveying system can be predicted using Weibull distribution parameters from single particle impact studies.
In granulation, breakage has been shown to exist.Specifically, in f luidised bed granulation by obser ving Relationship between the number of unbroken fertiliser particles and mean air velocity for 3.2-mm, 5.15-mm and 7.1-mm particles in a pneumatic conveying rig [40]  the changing mean size distribution after spraying, and in high-shear granulation by tracer and impeller speed studies.In both processes, breakage has been incorporated into population balance models in order to improve the evolving granule size distribution.More detailed information on breakage from tracer studies has enabled breakage functions to be deduced with the aim of improving model descriptions of the process.

Fig. 2
Fig. 2 Normal low impact velocity regime failure patterns of several materials

Fig. 3
Fig. 3 Intermediate impact velocity regime failure patterns of several materials

Fig. 4
Fig. 4 High impact velocity regime failure patterns of several materials

Fig. 5 Fig. 6
Fig.5 Typical relationship between particle impact velocity and number of unbroken particles (7-mm diameter spherical fertiliser particles under normal impact)

Fig. 7
Fig.7 Comparison between model and experimental results for the change in mean size for liquid-to-solid ratios of (a) 0.05 (b), 0.1, and (c) 0.2 in f luidised bed granulation[35]

Fig. 10
Fig.10 Relationship between the number of unbroken fertiliser particles and mean air velocity for 3.2-mm, 5.15-mm and 7.1-mm particles in a pneumatic conveying rig[40]