how do agglomerates break?

www.elsevier.com/locate/powtec

Powder Technology 143–144 (2004) 110–116

How do agglomerates break?

Colin Thorntona,b,*, Lianfeng Liub

aSchool of Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UKbFormerly, School and Engineering and Applied Sciences, Aston University, Birmingham B4 7ET, UK

Available online

Abstract

Granular dynamics (DEM) simulations of a polydisperse cuboidal agglomerate impacting with a target wall are reported. The paper

focuses on identifying the physical processes that lead to fracture. It is shown that fracture is the result of the manner in which strong

interparticle forces are transmitted into the agglomerate and the consequent development of a heterogeneous distribution of primary particle

velocities. This heterogeneous velocity field produces strong velocity discontinuities along which shear weakening occurs. Consequently, the

strong velocity discontinuities become the potential fracture planes.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Granular dynamics; Agglomerates; Impact; Fracture

1. Introduction

Powders in the form of particles that are themselves

agglomerations of much smaller sized primary particles are

commonly encountered in a variety of process engineering

unit operations. Consequently, a common problem is the

attrition/fracture of agglomerates as they collide with each

other and the process equipment. Due to the small length

and time scales associated with such impact events, infor-

mation from physical experiments is normally restricted to

post-impact examinations of the fragments and debris pro-

duced. Granular dynamics simulations may be the only way

to develop an understanding of the physical behaviour of an

agglomerate during a collisional event since such simula-

tions provide complete information on the positions and

velocities of all the primary particles constituting the ag-

glomerate and the forces acting between the constituent

particles throughout the collision.

In the granular dynamics code GRANULE [1], the

primary particles are modelled as autoadhesive elastic

spheres for which the surface energy and elastic properties

are specified in order to implement contact interaction rules

based on the JKR theory of adhesion [2]. Previous agglom-

0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2004.04.035

* Corresponding author. School of Civil Engineering, University of

Birmingham, Edgbaston, B15-2TT, Birmingham, UK. Tel.: +44-121-

4144215; fax: +44-121-4143958.

E-mail address: [email protected] (C. Thornton).

erate-wall impact studies have included 2D simulations of a

random monodisperse agglomerate [3], 3D simulations of

crystalline spherical agglomerates [1], polydisperse spheri-

cal agglomerates [4,5], and small irregular-shaped agglom-

erates [6]. Other unpublished research has examined

oblique impacts of polydisperse spherical, cuboidal and

cylindrical agglomerates. In all cases, we have examined

the evolution of the wall force, kinetic energy and bond

breakage; and also examined the particle size distribution

resulting from the breakage event. It has, however, taken

considerable time and effort to identify exactly how and

why breakage occurs. This is the focus of this paper in

which we initially provide some general remarks based on

previous work and then provide visualisations that demon-

strate that the controlling physical process is the manner and

relative magnitude of the force transmission within the

agglomerate microstructure.

2. General observations

It is useful to clarify the terminology that will be adopted

to describe the observed breakage phenomena. The term

‘‘fracture’’ is reserved for breakage patterns in which clear

fracture planes (cracks) are visible. This mode produces two

or more large daughter fragments and is normally accompa-

nied by some fines production adjacent to the impact site. If

for example, due to the high impact velocity used, the large

Fig. 1. Cuboidal agglomerate before impact.

C. Thornton, L. Liu / Powder Technology 143–144 (2004) 110–116 111

daughter fragments are themselves broken into small clusters

of primary particles then the term ‘‘shattering’’ is used. An

alternative mode of breakage is one in which there is no

evidence from the simulation data of any attempted fracture

and the end products consist of one cluster centred in the

upper part of the agglomerate with the remainder of the

agglomerate reduced to small clusters of primary particles

and singlets. This type of breakage is termed ‘‘disintegra-

tion’’. If the impact velocity is sufficiently high that disin-

tegration extends throughout the agglomerate and there is no

‘‘large’’ surviving cluster then this mode is referred to as

‘‘total disintegration’’. In this case, the size distribution of the

fragments may be similar to that produced by shattering, the

distinction is the difference in the kinetic energy of the

system at the end of the impact. When shattering occurs a

significant number of small daughter fragments are projected

at relatively high speeds away from the impact location. On

the other hand, if total disintegration occurs the agglomerate

simply collapses into a heap on the target wall.

Ning et al. [4] reported simulations of polydisperse

spherical agglomerates impacting a target wall and observed

that fracture did not occur in any of their simulations. In

contrast, Thornton et al. [5] presented results of agglomerate

wall collisions for a polydisperse spherical agglomerate

which rebounded, fractured or shattered depending on the

magnitude of the impact velocity. Further simulations were

performed on polydisperse spherical agglomerates by Mis-

hra and Thornton [7] who examined the effect of micro-

structure on the breakage behaviour. From these simulations

it was shown that, for ‘‘compact’’ agglomerates (as opposed

to fractal agglomerates) ‘‘dense’’ agglomerates always frac-

ture and ‘‘loose’’ agglomerates always disintegrate. This is

true irrespective of the strength of the bonds between the

primary particles, when compared at the corresponding

Weber Number WfV2/C where V is the impact velocity

and C is the bond interface energy. It was also found that

either fracture or disintegration, or both, might occur for

agglomerates with an intermediate packing density. It was

demonstrated that, for agglomerates with intermediate pack-

ing densities, the mode of failure could change from

disintegration to fracture by either increasing the contact

density or changing the location on the agglomerate surface

that is used as the impact site.

When an agglomerate impacts a target wall the forces

generated at the interface propagate through the agglomer-

ate. The force transmission can only occur via the interpar-

ticle contacts. Consequently, the manner in which the force

propagation occurs depends on the microstructure, i.e. the

number and locations of contacts within the agglomerate. A

generic feature of compact particle systems is that the force

transmission is not uniformly distributed but tends to be

focussed along discrete chains of particles, which align with

the direction of compression [8,9].

From computer generated images of the force propagation

through agglomerates during impact, it has been observed

that fracture only occurs if strong force transmission path-

ways are established in the region adjacent to the impact site

and then propagate into the system. The ability to establish

such strong propagation pathways depends on the local

microstructure at the impact site and on the stability of the

particles composing the potential pathways. Dense systems

enable the establishment of strong force transmission path-

ways due to the highly constrained nature of the individual

primary particles. In loose systems, with fewer contacts, the

individual particles are less constrained and therefore tend to

be displaced as the force attempts to propagate from the

target wall. This results in irrecoverable deformation of the

microstructure adjacent to the impact site and strong atten-

uation of the magnitude of the force transmitted through the

agglomerate. It has been observed that when this happens

disintegration occurs rather than fracture, even when the

bonds are strong and the impact velocity is high [5,7].

3. Fracture of crystalline agglomerates

The above observations do not fully explain how fracture

occurs. Kafui and Thornton [1] simulated a crystalline (face-

centred cubic) agglomerate impacting a target wall. The

agglomerate was orientated so that there were vertical

contiguous columns of particles orthogonal to the wall.

Contact with the wall was established over a diamond-

shaped area, which was dictated by the orientation of the

four sets of dense (triangular) packed planes. As a result of

the impact, forces were transmitted exclusively along the

vertical columns of particles immediately above the contact

area and particles in these columns were decelerated.

Particles in the adjacent dense packed planes, outside the

vertical projection of the contact area, and elsewhere,

experienced no deceleration. Consequently, strong velocity

discontinuities were created between the adjacent loaded

and unloaded dense-packed planes. This produced a local-

ised shear deformation and resulted in the breaking of one

set of the three sets of contacts between the particles in the

Fig. 2. Cuboidal agglomerate at t = 11 As.

C. Thornton, L. Liu / Powder Technology 143–144 (2004) 110–116112

adjacent dense-packed planes as the wall force increased to

a maximum value. The bond breaking propagated upwards

from the wall as the kinetic energy reduced to a minimum

value. Then during unloading, as the kinetic energy in-

creased, a second set of contacts was broken between the

adjacent loaded and unloaded dense-packed planes, propa-

gating downwards from the top of the agglomerate. With

further recovery of kinetic energy, some bonds were broken

in the third set of contacts leading to fracture along some of

the shear induced weakened planes just prior to the end of

the impact. It was shown that, during deceleration of the

agglomerate, a complete set of shear induced weakened

planes was created and that there was an impact velocity,

which produced a complete set of fracture planes. Subsets of

this fracture pattern were observed at lower impact veloc-

ities. Higher impact velocities did not produce extra fracture

planes but the residual fragments were weakened due to

Fig. 3. Evolution of the total norma

internal bond breakage and this resulted in shattering at high

impact velocities.

4. Fracture of polydisperse agglomerates

Thornton et al. [5] observed that, for a polydisperse

spherical agglomerate, there was a certain velocity that

maximised the number of fracture planes and that lower

velocities produced fracture patterns, which approximated to

subsets of the complete fracture pattern. However, they

reported that elucidation of the detailed evolution of the

physical processes leading to fracture were extremely diffi-

cult to confirm for 3D polydisperse spherical agglomerates.

Fig. 1 shows a polydisperse cuboidal agglomerate con-

sisting of 10,000 autoadhesive elastic primary particles of

five different sizes in the range 16 to 24 Am. The interface

energy is 1.0 J m� 2. In order to create the agglomerate, the

primary particles were initially randomly generated within a

defined cuboidal region with no interparticle contacts. A

centripetal gravity field was introduced to bring the particles

together. In order to ensure a dense agglomerate, the

interface energy was gradually introduced only after a

compact system had been established. The centripetal grav-

ity field was gradually removed and replaced by a vertical

gravity field before simulating any impacts with the wall. As

a result of this method of preparation, the edges of the

agglomerate are curved and the faces are nonplanar.

As shown in Fig. 1, the agglomerate is oriented so that it

impacts with the wall along the leading edge. The angle

between the contact normal with the wall and the vector

connecting the contact point with the centre of mass of the

agglomerate is 30j. A vertical velocity of 1.0 m s� 1 was

specified for all the primary particles in order to simulate a

non-collinear normal impact with the wall, which resulted in

breakage of the agglomerate as shown in Fig. 2. Fig. 2

shows a thin central section (approximately three particles

l force generated at the wall.

Fig. 6. Velocity field after 1.64 As.Fig. 4. Force transmission (t = 1.125 As).


wide) of the agglomerate in order to clearly illustrate the

fracture mode. The advantage of this configuration is that,

although the particle arrangement is three-dimensional, the

overall behaviour is essentially two-dimensional making

visualisations of the mechanisms much easier to identify.

The evolution of the total normal force generated at the

wall is shown in Fig. 3. The wall force increases to 6.5 mN,

drops and then increases to a maximum value of 7.3 mN

after 1.64 As. There is then a sudden drop in the force to

about 3 mN after which the force reduces further with

Fig. 5. Force transmission (t = 1.892 As).

significant fluctuations until, at t = 65 As, the force is

approximately 1 AN corresponding to the self-weight of

the agglomerate.

Fig. 4 illustrates the force transmission through the

agglomerate when the wall force is 6.5 mN. The lines show

the location and orientation of the (resultant) contact forces.

The thickness of the lines indicates the magnitude of the

force, scaled to the current maximum. For clarity, only a thin

central section of the agglomerate is shown. Fig. 4 shows

that the large forces generated at the contacts with the wall

propagate vertically upwards. Fig. 5 shows the force trans-

mission after 1.89 As, just after the wall force has reached its

Fig. 7. Velocity field after 1.89 As.




maximum value. The figure shows that there is a significant

but smaller wall force propagating towards the lower right

hand side of the agglomerate at this stage.

Figs. 6–9 show the velocity field as it evolves during the

impact. In the figures, the velocities are represented by

green vectors originating from the particle centres. In order

to indicate the direction of the vectors, the leading end of

each vector is coloured red. It can be seen that, as a

consequence of the large forces transmitted vertically up-

wards into the agglomerate, the primary particles in the

region into which these forces propagate are decelerated but

continue to move downwards in a vertical direction. Par-


ticles in the lower right hand side of the agglomerate do not

experience such a rapid deceleration and, consequently, a

heterogeneous velocity field is created which results in an

inclined velocity discontinuity between the loaded and

unloaded regions. The relative shear motion along the

velocity discontinuity results in some breakage of contacts

and thereby a weakened plane is created. As a result of the

secondary, inclined, contact force seen in Fig. 5, there is a

rotation of the velocity field in the lower right hand region

of the agglomerate that increases the shear weakening along

Fig. 11. Cuboidal agglomerate face impact.

Fig. 14. Particle velocity field.Fig. 12. Force transmission.


the velocity discontinuity. Finally, as can be seen in Fig. 10,

the particles in the region above the impact point come to

rest but, due to the continued movement of the lower right

hand side of the agglomerate, fracture occurs along the

previously shear weakened velocity discontinuity, as can be

seen in Fig. 2.

To further illustrate the significance of the force trans-

mission on agglomerate fracture, the same cuboidal agglom-

erate was reoriented in order to simulate a face impact with

Fig. 13. Particle acceleration field.

the wall, as shown in Fig. 11. Again, the initial velocity

attributed to all the primary particles was 1 m s� 1 in the

vertical downward direction. Fig. 12 shows a typical side

view of the force transmission through the agglomerate, Fig.

13 shows the corresponding acceleration field and Fig. 14

shows the subsequent velocity field. In each case, a thin

internal slice, approximately three particles wide, is used to

aid the visualisation.

It can be seen from Fig. 12 that the strong forces tend to

be inclined to the vertical direction, some to the left and

some to the right of the centre of the agglomerate. It

Fig. 15. Final fracture mode (velocity field).


should be noted that the forces in contact with the wall are

not uniform but there are large forces generated at the

centre due to the curvature of the faces of the agglomerate,

as seen in Fig. 11. The two arrows superimposed on the

figure indicate the average direction for the two groups of

force transmission pathways. Fig. 13 demonstrates that the

two-pronged force transmission pattern results in a hetero-

geneous acceleration field with a strong discontinuity along

the centreline. (The fact that most of the vectors are

pointing upwards indicates that the particles are decelerat-

ing.) As a result of the acceleration field shown in Fig. 13,

the particle velocities rotate, with the vertical component

decreasing and outwards horizontal components develop-

ing, as indicated in Fig. 14. Fig. 14 shows that, except for

the region adjacent to the wall, there are two distinct, more

or less uniform, velocity regions separated by a strong

vertical velocity discontinuity along the centreline. Conse-

quently, this velocity discontinuity subsequently becomes

the fracture plane as a result of bond breakage (a) initially

due to the localised high shear strain and (b) subsequently

due to the outward movement of the two adjacent trans-

lating regions.

Similar visualisations to those shown in Figs. 12–14

were observed when the agglomerate was examined by

viewing from the front. Therefore, when viewed from

above as shown in Fig. 15, the final fracture mode

consisted of two nonplanar, near vertical cracks each

passing through the centre of the agglomerate. The figure

shows a thin horizontal section through the agglomerate in

order to assist the visualisation. As a result of the impact,

the agglomerate broke into four large daughter fragments,

whose translational movement is clearly indicated in the

figure, plus some small debris was produced adjacent to

the wall, around the perimeter of the impacting face of the

agglomerate.

5. Conclusion

Fracture occurs as a result of strong force transmission

into the agglomerate that creates a heterogeneous velocity

field. This produces shear weakening along velocity dis-

continuities that subsequently become the potential fracture

planes. If, for whatever reason, strong forces are unable to

propagate into the agglomerate then fracture does not

occur and the breakage mechanism is one of progressive

disintegration.

Acknowledgements

The work reported above was carried out at Aston

University and part of it was first presented at the AIChE

2000 Annual Meeting, Los Angeles, November, 2000 but

was not included on the corresponding CD-Rom.

References

[1] K.D. Kafui, C. Thornton, Powder Technol. 109 (2000) 113.

[2] K.L. Johnson, K. Kendall, A.D. Roberts, Proc. R. Soc. Lond., A 324

(1971) 301.

[3] C. Thornton, K.K. Yin, M.J. Adams, J. Phys., D. Appl. Phys. 29 (1996)

424.

[4] Z. Ning, R. Boerefijn, M. Ghadiri, C. Thornton, Adv. Powder Technol.

8 (1997) 15.

[5] C. Thornton, M.T. Ciomocos, M.J. Adams, Powder Technol. 105

(1999) 74.

[6] C. Thornton, M. Nasrullah, Proc. AIChE 2000 Annual Meeting, Los

Angeles, CD-Rom, 2000.

[7] B.K. Mishra, C. Thornton, Int. J. Miner. Process. 61 (2001) 1107.

[8] C. Thornton, KONA Powder and Particle 15 (1997) 81.

[9] C. Thornton, S.J. Antony, Philos. Trans. R. Soc. Lond., A 356 (1998)

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how do agglomerates break?

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