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Particuology 12 (2014) 2– 12

Contents lists available at ScienceDirect

Particuology

j o ur nal hom epag e: www.elsev ier .com/ locate /par t ic

n experimental and numerical study of packing, compression, andaking behaviour of detergent powders

ubhash C. Thakura,b, Hossein Ahmadianb, Jin Suna, Jin Y. Ooia,∗

School of Engineering, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JL, UKNewcastle Innovation Centre, Procter and Gamble Technical Centre Ltd, Newcastle upon Tyne NE12 9BZ, UK

r t i c l e i n f o

rticle history:eceived 22 April 2013eceived in revised form 21 June 2013ccepted 27 June 2013

eywords:iscrete element methodowder flowohesive materialniaxial testlasticityontact model

a b s t r a c t

This paper presents an experimental and numerical study of the packing, compression, and cakingbehaviour of spray dried detergent (SDD) powders with a two-fold aim: an experimental process ofobservation and evaluation of the packing, compression and caking behaviour of SDD powders, and anumerical approach based on discrete element modelling (DEM). The mechanical properties, includingthe stress–strain response and the corresponding porosity change as a function of consolidation stress in aconfined cylinder, the stress–strain response during unconfined shearing and the cake strength as a func-tion of consolidation stress, were evaluated and compared for different SDD powders using an extendeduniaxial tester (Edinburgh Powder Tester – EPT). The experiments using EPT showed excellent repro-ducibility in the measurement of packing, compression and caking behaviour and were therefore veryuseful for describing the handling characteristics of these powdered products including screening newproducts and different formulations. It was found that the sample with higher moisture had lower bulkporosity but higher compressibility and cake strength. The porosity, compressibility and cake strengthwere found to vary across different size fractions of the same sample. The larger sieve-cut samples had

higher initial bulk porosity, compressibility and cake strength. It is revealed that moisture plays a sig-nificant role in packing, compression, and shearing behaviour of the powder. Three-dimensional DEMmodelling using a recently developed elasto-plastic adhesive-frictional contact model showed that thecontact model is able to capture the detergent behaviour reasonably well and can be used to modelcomplex processes involving these powders.

© 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of

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. Introduction

Powder packing, compressibility, and flowability are importanteasures for industrial particulate solids, such as household and

ersonal care products, chemicals, fertilizers, coal, cements, explo-ives, dyes and pigments. The packing behaviour of a powder in aontainer is determined by its initial microstructure and the ensu-ng mechanical processes including compression, shear, vibrationnd impact, which occur during transportation, for example. Forhe manufacturing of particulate detergents, bulk porosity is anmportant variable to control since most consumer doses are mea-ured by volume and the solubility of detergent powders normally

ncrease with increasing porosity. In addition, the compressibilityf powders can influence their appearance and volume in contain-rs once they reach consumers. Caking is a phenomenon where

∗ Corresponding author.E-mail address: j.ooi@ed.ac.uk (J.Y. Ooi).

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674-2001/$ – see front matter © 2013 Chinese Society of Particuology and Institute of Process Ettp://dx.doi.org/10.1016/j.partic.2013.06.009

Sciences. Published by Elsevier B.V. All rights reserved.

ree flowing powders are transformed into lumps, aggregatesr eventually into a coherent mass. Caking of powder can havedverse effects on solubility, mixing, and dispersion resulting inoss of products, delays in launch and consumer complaints. Itan also cause storage and handling related problems includingopper/bin arching and ratholing, resulting in no flow. Accordingo an estimate by Griffith (1991), the cost of unproductive cakeroducts was in an excess of 1 billion USD in the USA alone in 1985.

The packing of porous powder is governed by inter-particle andntra-particle porosity. Several factors including particle shape,bsolute size, size distribution, and surface properties (stiffness,riction, and adhesion), affect inter-particle porosity. In additiono particle properties inter-particle porosity may also depend onize, shape, and roughness of the container as well as the methodnd intensity of deposition (Yu, 1989). It is generally accepted

hat deviation of particle shape from sphere tends to increase thenter-particle porosity of mono-sized particles (Yu & Standish,993). Porosity is found to be independent of particle size forarticle sizes above 100 �m (Yang, Zou, & Yu, 2000). For particle

ngineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

S.C. Thakur et al. / Particuo

Nomenclature

Cu coefficient of uniformityD60 diameter of particle at 60% passing (m)D10 diameter of particle at 10% passing (m)e co-efficient of restitutionf0 constant adhesion (N)fn contact normal force (N)ft contact tangential force (N)fct coulomb limiting tangential force (N)fnd normal damping force (N)fts tangential spring force (N)ftd tangential damping force (N)fhys hysteretic spring force (N)fts(n − 1) tangential spring force at previous time step (N)k1 loading stiffness parameter (N/m)k2 unloading/reloading stiffness parameter (N/m)kadh adhesive stiffness parameter (N/m)kt tangential stiffness (N/m)m* equivalent mass of the particles (kg)n non-linear index parameter�inter inter particle porosity�intra intra particle porosity�p particle porosityRi distance from the contact point to the particle cen-

tre of mass (m)�n relative normal velocity (m/s)vpores specific volume of mercury penetrating the particle

pores (L/kg)�t relative tangential velocity (m/s)w moisture content (%)ˇn normal dashpot co-efficientˇt tangential dashpot coefficient

angle of shearing resistance (◦)�fts Incremental tangential force (N)ı normal overlap (m)ımax maximum normal overlap (m)ıp plastic overlap (m)�s skeletal density or particle density (kg/m3)�b bulk density (kg/m3)� sample bulk porosity� co-efficient of friction�r coefficient of rolling friction� total applied torque (N m)

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iameters smaller than 100 �m, the ratio of inter-particle forceo the weight of particles can be greater than unity (Krupp, 1967),esulting in different packing behaviour. Higher inter-particleorce ratios cause formation of chain-like structure leading toigh porosity (Yang et al., 2000). For cohesionless powders, as thepread of the particle size distribution (PSD) increases, the porosityecreases because the smaller particles fill the pores between

arger particles. The effect of PSD on porosity of cohesive materials not very well understood and is influenced by the complexdhesive forces that exist. In addition, the intra-particle porosityf a powder may depend on chemical composition, and shrinkager puffing effect due to drying (Hecht & King, 2000a, 2000b).

The powder compressibility may result from particle

earrangement, breakage of loosely bonded agglomerates intorimary particles, failure of the particle during elasto-plasticeformation, and fragmentation of the primary particles (Heckel,961; Hersey & Rees, 1970). These mechanisms do not happen

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logy 12 (2014) 2– 12 3

n sequence and usually overlap each other (Hersey & Rees,970). For agglomerated cohesive powders subjected to increasingonsolidation stress, particles are likely to undergo rearrangementnd loosely bonded agglomerate may break without excessiveeformation at the particle contacts. The rearrangement ofhe particle will depend on the particle shape (Cho, Dodds, &antamarina, 2006; Güden, Celik, Hizal, Altindis , & Cetiner, 2008),ize and size distribution (Hersey & Rees, 1970), rolling andtatic friction (Sheng, Lawrence, Briscoe, & Thornton, 2004), anddhesion (Mehrotra, Chaudhuri, Faqih, Tomassone, & Muzzio,009). The breakage of an agglomerate will also depend on bondtrength. As the consolidation stress is increased, elasto-plasticeformation of the particles leads to squashing and reduction in

ntra- and inter-particle porosity. On further application of stress,ragmentation of the primary particle may occur and excessiveeformation may lead to work hardening.

The cake strength of powder at an applied consolidation stress isffected by particle size, size distribution, friction, shape, humidity,oisture content, plastic deformation and adhesion at the parti-

le contact etc. Several experiments including shear cells (Jenike,nnular, and Peschl), tensile test, creep test, penetration test, cak-ng index test, blow test, and uniaxial test have been used for the

easurement of caking propensity (Cleaver, 2008). Each tester hasts own advantages and disadvantages, which were explained bychwedes (2003). Uniaxial test has widely been used to study theaking or shear behaviour of powders (Bell, Catalano, Zhong, Ooi,

Rotter, 2007; Enstad & Ose, 2003; Freeman & Fu, 2011; Parrella,arletta, Boerefijn, & Poletto, 2008; Röck, Ostendorf, & Schwedes,006; Williams, Birks, & Bhattacharya, 1971; Zhong, Ooi, & Rotter,005) in industrial practice because of its simplicity and rapidity inonducting a test. Repeatability of measurement is one of the majoroncerns for uniaxial testers. An extended uniaxial tester, the Edin-urgh Powder Tester (EPT), has been developed at the Universityf Edinburgh, with a focus on robustness, repeatability and speedor industrial solids measurement (Bell et al., 2007).

The discrete element method (DEM) has increasingly been usedo model discrete phenomena including powder packing (Dong,ang, Zou, & Yu, 2006; Yang et al., 2000; Yang, Zou, Dong, An,

Yu, 2007; Yen & Chaki, 1992), compaction (Morgeneyer et al.,005; Redanz & Fleck, 2001; Samimi, Hassanpour, & Ghadiri, 2005;heng et al., 2004), and powder flow (Baxter, Abouchakra, Tüzün,

Mills Lamptey, 2000; David, García-rojo, Herrmann, & Luding,007; Luding et al., 2004; Mehrotra et al., 2009; Moreno-Atanasio,ntony, & Ghadiri, 2005). To date the DEM modelling of cohesiveowders has been less successful in producing quantitative predic-ions.

The major objective of this paper is to study packing, compres-ion, and caking behaviour of spray dried detergent powders usinghe EPT, and to model the full spectrum of the loading regimes fromompression to shear failure using DEM. The EPT is used to measurehe mechanical properties including the stress–strain response andhe corresponding porosity change as a function of consolidationtress in a confined cylinder. In addition, the stress strain responseuring unconfined shearing and the cake strength as a functionf consolidation stress is evaluated. The physical properties of theowders, which may affect the mechanical properties, are alsoeasured. These include moisture content, particle size, size dis-

ribution, shape, inter- and intra-porosity. DEM modelling is thensed to simulate the packing, compression and shear behaviour,hich is compared with the experiments for one example deter-

ent powder. The simulations utilised a recently developed contact

odel that uses hysteretic non-linear loading and unloading paths

o model the elasto-plastic permanent contact deformation and andhesion parameter which is a function of the maximum contactverlap (Thakur, Morrissey, Sun, Chen, & Ooi, 2011).

4 S.C. Thakur et al. / Particuology 12 (2014) 2– 12

Table 1Distribution of moisture content (%) across different size fractions (n = 3).

Size fractions Sample A Sample B

M RSD (%) M RSD (%)

Bulk 2.29 2.39 4.74 2.70>500 �m 2.55 4.99 4.96 4.24500–250 �m 2.30 3.30 4.43 2.50<250 �m 2.12 4.30 4.17 4.80

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. Materials and physical properties measurement

.1. Materials

In this study, spray dried detergent (SDD) powders were inves-igated, which constitute 60–70% of the commercially availableetergent washing powders and are the most common detergentowders sold worldwide with billions of dollars sales. Two SDDowders produced with a low moisture content (Sample A) and aigh moisture content (Sample B) were selected, covering a rangef unconfined yield (cake) strength. The chemical composition andoisture content of spray dried powders vary across different size

ractions. Therefore, the spray dried powders were separated intohree different size fractions, <250 �m (small size), 250–500 �mmedium size), and >500 �m (large size). Tests were conducted onulk samples covering all particle size range as well as differentize fractions.

.2. Measurement of powder physical properties

Before any measurement on the specimen is made, it is vitalhat a representative sample is obtained. In this study the samplesbtained from a spray dried tower was first mixed in a rotary mixero get a homogenous sample and also to reduce the bulk powderown to a 5 kg batch. The powder is then further sampled down tohe 1 kg size using a split sampler. Finally, the powder is sampledown to required sizes using a Pascal turntable sample divider, apinning sample divider. The rotation speed and vibration levels in

Pascal turntable sample divider were chosen to provide a uniformow of powder. Since spray dried powders are sensitive to moisturend humidity, the powders were packed and sealed in air tightontainers for further testing.

The powder moisture content, particle size and size distribu-ion, inter- plus intra-particle pore, and shape were characterised,sing moisture balance, mechanical sieve analysis, gas pycnome-ry, mercury porosimetry, and scanning electron microscope (SEM).

oisture content by weight was measured using an oven-dryingethod. A temperature of 105 ◦C and heating time of 24 h was

sed. The moisture content and its distribution across different sizeractions are shown in Table 1. The moisture contents of Sample Bere higher than those of Sample A for all size fractions. Addition-

lly for both samples, the larger size fractions had higher moistureontents than the smaller size fractions. This could be due to thegglomeration of primary particles into larger sizes with highernternal moisture. It should be noted that the moisture content isot free and mobile surface moisture; but rather moisture after theowders have gone through drying process in a spray drying tower.

The size distributions of the SDD powders were measured usingibrating mechanical sieves following the ASTM D6913 procedure.

he amplitude and frequency of vibration were set to minimisereakage of agglomerates and to ensure thorough sieving of theample. The full size distributions of particle size on weight basisre shown in Fig. 1. The median particle sizes D50 of Sample A and

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Fig. 1. Particle size distribution of the spray dried detergent powders.

ample B were approximately 480 and 390 �m respectively. Bothowders have a similar coefficient of uniformity, Cu, (D60/D10) of.6.

Inter- and intra-particle porosity was characterised using mea-urements from gas pycnometry and mercury porosimetry. A gasycnometer, Accupyc II 1340 (Micromeritics, USA), was used toeasure skeletal density (solid density), based on a gas displace-ent method to measure volume accurately. Helium gas is used as

t obeys the ideal gas law and is able to penetrate small pores (ASTM5550, 2006) due to its small atomic number. However Heliumoes not permeate any closed pores. The average values of skeletalensity from five runs are 1919 and 1910 kg/m3 for Sample A andample B respectively. There was no significant difference betweenkeletal density measurements across different size fractions.

Pore size characterisation of the spray dried samples was con-ucted using mercury porosimetry (AutoPore IV, Micromeritics,SA). The instrument provides a wide range of information, e.g.

he pore size distribution, the total pore volume (inter- and intra-article pores) or porosity, the skeletal and envelope density. The

nstrument characterises a material’s porosity by applying variousevels of pressure to a sample immersed in mercury. The pressureequired to intrude mercury into the sample’s pores is inverselyroportional to the size of pores and given by the Washburn’squation (Washburn, 1921).

A Hitachi TM 1000 SEM was used in this study for visual inspec-ion of particles. The SEM photographs of three different sizeractions of Sample A and Sample B are shown in Figs. 2 and 3,espectively. A significant amount of pore openings can be seen onhe surface of the particles. No discernible difference in shape andexture of respective size fractions of Sample A and Sample B wasound. It can be seen from Figs. 2 and 3 that the larger particles areot individual but agglomerates of primary particles.

.3. Measurement of powder mechanical properties

The EPT was employed to measure the packing, compression,nd shear behaviour of the SDD powders. The main differencesetween EPT and some previous uniaxial tester lies in the attentiono mechanical details, the level of care directed to the consolida-ion as well as failure load application, and the strategic intentBell et al., 2007). The diameter of the EPT sample mould is 40 mmnd the height can be up to 80 mm. The height of the specimen iseasured continually with a built-in linear variable voltage trans-

ormer (LVDT) displacement transducer of an accuracy of 0.1 mmttached to the loading piston. The powder compressibility can

hen be evaluated from the measurement.

The photographic illustration of the EPT test procedure is shownn Fig. 4. In the EPT, the powder sample is poured into the consoli-ation cylinder. The sample is loaded by applying a constant weight

S.C. Thakur et al. / Particuology 12 (2014) 2– 12 5

Fig. 2. SEM photographs of different size Sample A: (a) passing through 250 �m, (b) between 250 and 500 �m, and (c) retained on 500 �m.

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o the consolidation cell and the force is recorded by the load cellttached to the consolidation plunger. After the sample is loadedor 1 min, the consolidation plunger is automatically lifted off leav-ng the consolidated sample. The mould is then manually slid downhe pedestal, exposing a free standing column of consolidated

owder sample. The sample is then failed by a motor driven testiston and the stress–strain response during the unconfined axial

oading to failure can be recorded. The loading piston travels with apeed of 0.4 mm/s. The speed of the piston is so chosen that the test

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Fig. 4. (a) Edinburgh Powder Tester, (b) compression,

50 �m, (b) between 250 and 500 �m, and (c) retained on 500 �m.

an be conducted rapidly, and at the same time unconfined yieldtrength is not compromised. Watanabe and Groves (1964) foundhat unconfined strength of detergent samples was unaffected ifhe piston speed was varied in a range of 0.084–0.43 mm/s.

The friction between the particles and boundary may affect

he compressibility of the powders in uniaxial tests (Enstad &se, 2003). In the EPT, boundary effect is minimised by allowing

he powder sample to compress from both the top and bottom.urther to minimise any effect of boundary friction, the sample

(c) unconfined sample, and (d) crushed sample.

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Table 2Initial sample porosity (%) measurements for Sample A and Sample B powders.

Size fractions Sample A Sample B

M RSD (%) M RSD (%)

All fractions (n = 3) 72.5 0.36 69.6 0.35>500 �m (n = 1) 77.7 – 75.2 –500–250 �m (n = 1) 75.4 – 72.8 –<250 �m (n = 1) 72.2 – 69.8 –

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ffpfpotppA which is indeed consistent with the proposition of increasinginter-particle porosity with increasing moisture content. However,the intra-particle porosity for Sample A was 5.2% higher than thatof Sample B which masked the higher inter-particle porosity in

Table 3Breakdown of bulk porosity (%) for the SDD powder sample (250–500 �m).

Types of porosity Sample A Sample B

S.C. Thakur et al. / Pa

spect ratio (sample height at 1 kPa stress to diameter ratio) duringonfined compression is kept in a narrow range of 1.3–1.4. Duringnconfined compression, the sample aspect ratio is kept between.2–1.4 which was found to give very good test reproducibility

n unconfined strength measurement. Previous studies have pro-osed an aspect ratio of tan (45◦ + ˚/2) or larger, where = anglef shearing resistance of the powder, to minimise the effect ofnd plate friction (Bishop & Green, 1965; Rock & Schwedes, 2005;illiams et al., 1971). Williams et al. (1971) argued that for lower

alues of aspect ratio, the failure of the sample can take placenly when part of the specimen slips along one of the end platens,hich would require extra work to be done causing an increase

n unconfined yield strength. However, the present study foundhat even with aspect ratio between 1.2 and 1.4 which is muchmaller than tan (45◦ + ˚/2), the failed sample did not intersecthe end platen (see Fig. 4(d) for a typical failure). A higher aspectatio would also increase the effect of wall friction and cause areater density variation across the height of the specimen whichan compromise measurement reproducibility.

It is further proposed that these highly repeatable bulk mea-urements can be used for DEM model calibration. These arehe (vertical) stress–strain and the stress–porosity response dur-ng confined compression as well as the (vertical) stress–strainesponse during unconfined compression including the peaknconfined strength.

. Results and discussion

.1. Experimental results

.1.1. PackingThe EPT was used to measure the bulk porosity of the powder

nder compression. The initial bulk porosity was measured cor-esponding to a small applied initial stress of 1 kPa (approx). Thiselps to reduce the variability of the fill porosity measurement andive a stable measurement of the initial height of the specimen with

level surface. The height and weight of the specimen were usedo calculate the average value of the bulk density (�b). The sampleulk porosity (�) can then be calculated using �b, moisture contentw), and the particle density (�s) as follows:

= 1 − �b

�s(1 + w). (1)

However, in this study the particle density was measured for theowder with moisture, therefore the moisture was not considered

n porosity calculation, and porosity was simply calculated as:

= 1 − �b

�s. (2)

The porosity comprises of the inter-particle pores as well as thepen and closed intra-particle pores. However, the skeletal den-ity measurement of the SDD samples before and after milling wasound to be similar, indicating insignificant closed pores in the sam-les. The average bulk porosity of Sample A and Sample B for fullize fraction and different sieve cut fractions are shown in Table 2.he bulk porosities of the larger sieve cut fractions for both samplesere higher compared to those of the smaller sieve cut fractions.s it can be seen from the SEM images (Figs. 2 and 3) the larger

ractions are agglomerates of the primary particles. In addition tohe intra and inter-particle porosity, the inter-agglomerate poros-ty also contributes to the total porosity leading to a higher porosity

or the larger fractions.

The bulk porosity of the full size fraction of Sample A was foundo be higher than that of Sample B (see Table 2). Indeed the bulkorosities of different size fractions of Sample A were consistently

B: n = number of measurements; initial porosity taken at a consolidation stress of kPa.

igher than the corresponding fractions of Sample B. This waseemed counterintuitive considering that both samples have sim-

lar shape, morphology and gradation, except a higher moistureontent for Sample B. One might speculate that a higher mois-ure content (Sample B) could lead to a more-open structure and aigher porosity resulting from higher adhesive forces at the parti-le contacts (assuming that moisture is at the contacts). It shoulde noted that the microstructure of spray dried powder comprisesorous primary particles and agglomerates of these primary par-icles. Such a microstructure cannot be easily defined by a singlealue of bulk porosity. Therefore, a combination of measurementssing mercury porosimetry and gas pycnometry was used to esti-ate porosity between the particles (inter-porosity) and porosity

nside the particles (intra-particle porosity). Inter-particle porosityas calculated as:

inter = 1 − �b

�s(1 − �p), (3)

here �inter is the inter-particle porosity, and �p is the particleorosity which was calculated as:

p = vpores

(vpores + (1/�s)), (4)

here, vpores = specific volume (mL/g) of mercury penetrating thearticle pores.

The fraction of total void space in a sample contributed by par-icle porosity is termed as intra-particle porosity and expressed as:

intra = �p(1 − �). (5)

Because of difficulty in separating inter- and intra-particles forull size fraction samples, inter- and intra-porosity was estimatedor the 250–500 �m narrow size fractions assuming that the intra-orosity measurement will be valid for other size fractions andull size fraction. The assumption is reasonable since intra-particleorosity relates to primary particles and should be independentf size of agglomerates (i.e. different size fractions). Table 3 showshe breakdown of the total porosity for 250–500 �m for the SDDowders in terms of inter- and intra-particle porosity. The inter-article porosity of Sample B was 2.6% higher than that of Sample

M RSD (%) M RSD (%)

Bulk porosity 75.4 – 72.8 –Intra particle porosity 21.38 0.85 16.19 3.45Inter particle porosity 54.02 – 56.61 –

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ample B and led to a higher overall porosity for the Sample A.he higher amount of intra-particle porosity for Sample A can bettributed to the way the samples were processed in the spray dry-ng tower. Sample A was exposed to slightly higher temperature inhe spray drying tower causing puffing or shrinking and leading to

ore porous primary particles.

.1.2. Confined compression and decompressionThe compression process was studied by plotting the axial

tress–strain measurements and the porosity-stress measure-ents. Fig. 5(a) shows the axial strain for three specimens of

ample A and Sample B as a function of the consolidation stress andig. 5(b) shows the corresponding porosity variation as a functionf consolidation stress. Sample B exhibited a higher overall com-ressibility than Sample A despite the fact that the initial (bulk)orosity of Sample B was lower. In Fig. 5(b), the powder com-ression process can be divided into two stages; stage I relatingo particle rearrangement (mostly compression of inter-porosity),nd stage II when the elasto-plastic deformation causing squashingf both inter- and intra-particle porosity began to dominate. It cane seen that at the onset of consolidation the porosity decreasedharply (stage I). During stage II as the consolidation progressed, theorosity varied linearly with a flatter slope compared to stage I. Theteeper slope of the porosity stress curve for Sample B indicatesarger particle rearrangement during stage I, and larger elasto-lastic deformation for stage II. The larger particle rearrangementf Sample B can be resulting from higher (2.6% for 250–500 �mize) inter-particle porosity compared to Sample A (Table 3). Thearger elasto-plastic deformation in stage II for sample B may berising from higher moisture increasing the plasticity at contactsOkasanen & Zografi, 1990) and agglomerate breakage due to weak-ning of the solid bridges (Yan & Barbosa-Canovas, 1997, 2001).

Once the desired consolidation stress was reached, the sampleas unloaded and the sample height was recorded to calculate the

onsolidated porosity (denoted by points on X-axis, see Fig. 5(b)).one of the powders returned to the initial porosity upon unloading

ndicating substantial plastic deformation arising from the particleearrangement, breakage, and plastic deformation at the contacts.s can be seen from Fig. 5(b) the maximum difference in poros-

ty measurements for each of the powders at any specific appliedtress was less than 0.5% (see error bars) indicating a high level ofeproducibility.

Fig. 6(a) shows axial stress–strain behaviour and Fig. 6(b) showsorresponding porosity change as a function of consolidation stressor different sieve-cut fractions of Samples A and B. While com-aring different size fractions of the sample, the larger sieve-cutraction compresses more, which could be related with compres-ion of larger inter-agglomerate pore, breakage of the large sizegglomerates, and larger plastic deformation. It has been foundn literature that as the size of the agglomerate (food powder)ncreased a higher volume reduction for large size agglomeratesuring compression in a cylindrical mould was found (Yan &arbosa-Canovas, 1997). The particle size effect on breakage wasxplained by the larger particles having more edges or corners onheir surface than the smaller ones, resulting in more abrasion andhipping. While comparing compression behaviour of correspond-ng sieve-cut samples of two SDD powders, sample A compressesess showing a similar trend to the full size fraction.

In addition, a larger gradient in porosity-stress curve (for bothtage I and stage II) is found for Sample B. For example, the decrease

n bulk porosity for 250–500 �m sample B was 0.2% and 0.5% higherhan the same size fraction sample A for stage I and stage II, respec-ively. This again indicates larger particle rearrangement in stage Ind larger elasto-plastic deformation in stage II for Sample B.

sE

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logy 12 (2014) 2– 12 7

.1.3. Unconfined compression and flow functionThe unconfined stress–strain behaviour for all samples was

btained but the results are presented only for full size rangeDD powders. Fig. 7 shows typical stress–strain behaviour duringnconfined compression for four different (20–80 kPa) consolida-ion stresses. The peak stress at which the sample fails (denotedy drop down in stress) is known as the unconfined yield strength.ery often in literature only the unconfined yield strength as a func-

ion of consolidation stress is reported. However, the area under thenconfined stress–strain curve is related to the energy requiredo fail the sample and needs to be captured in the DEM simula-ions. It can be seen that both the unconfined strength and the areander the curve increase with increasing consolidation stress foroth samples.

Fig. 8 shows the relationship between unconfined strength andonsolidation stress, otherwise known as flow function. The repro-ucibility of EPT was tested for full size range SDD bulk samples. Theelative standard deviation (RSD) at 37 kPa of consolidation stressor Sample A and Sample B (3 tests each on fresh samples) wereound to be 4.8% and 2.8%, respectively. Whilst three data pointsould not usually be considered sufficient for rigorous statistical

nalysis, the low RSD indicates that the reproducibility of EPT isery high.

The Sample B displayed higher unconfined strength at the sameonsolidation stress. The most plausible explanation is that mois-ure increases stickiness and plasticity of the contact leading toigher unconfined strength. Higher plastic deformation has beenbserved for Sample B during confined compression (see Fig. 5). Forhe different sieve-cut fractions of Sample B, larger sieve-cut frac-ions showed higher unconfined strength compared to small sieveut fractions (for the larger than 500 �m fraction consolidated at7 kPa, the unconfined strength exceeded the 45 kPa limit of the

oad cell). The plausible explanation for lower strength associatedith finer particles is that the fine fractions contain a dispropor-

ionate amount of anticaking agents which reduces the adhesionetween particles and that fine fractions have a slightly lower mois-ure content compared to the coarser fractions. In contrast, theoarser particles have higher moisture content and have shownreviously to deform more plastically (see Fig. 6(a)) compared tomall size particles, which may probably give rise to higher con-act area and therefore higher adhesion. This is consistent withrevious findings that small increase in moisture content (0.6%)roduced significant increase in cake strength (64%) of SDD pow-ers (Watanabe & Groves, 1964).

.2. DEM simulation

.2.1. Elasto-plastic adhesive contact modelA DEM contact model based on the physical phenomena

bserved in adhesive contact experiments has been proposedJones, 2003). When two particles or agglomerates are pressedogether, they undergo elastic and plastic deformations and theull-off (adhesive) force increases with an increase of the plasticontact area. A non-linear contact model that accounts for both thelasto-plastic contact deformation and the contact-area dependentdhesion is proposed. However, the linear version of the contactodel is used in this study (Fig. 9(b)). The schematic diagram of

ormal force-overlap (fn − ı) for this model is shown in Fig. 9.This contact model has been implemented through the API in

DEM® v2.3, a commercial DEM code developed by DEM Solutionstd (2010). The total contact normal force is sum of hysteretic

pring force, fhys, and normal damping force, fnd, and is given byq. (6):

n = (fhys + fnd)u, (6)

8 S.C. Thakur et al. / Particuology 12 (2014) 2– 12

Fig. 5. (a) Confined stress–strain and (b) porosity–stress behaviour of full size range Sample A and Sample B.

Fig. 6. (a) Confined stress–strain and (b) porosity–stress behaviour of different sieve cut fractions of Sample A and Sample B.

Fig. 7. Unconfined stress–strain of (a) Sample A and (b) Sample B.

Fig. 8. Flow functions (a) for uncut Sample B and Sample A, and (b) for different size fractions of Sample B and Sample A. COV denotes coefficient of variation, the absolutevalue of which is the RSD.

S.C. Thakur et al. / Particuology 12 (2014) 2– 12 9

rmal

wt

wptsd

f

wi

ˇ

wr

og

f

f

wsb

�

wtg�

f

ˇ

T

am

f

w

mb

�

wfutT

3

imicptFifbAommd

s(catgpaTs

Fig. 9. Non-linear (a) and linear (b) no

here, u is the unit normal vector pointing from the contact pointo the particle centre and fhys is given by Eq. (7):

fhys =

⎧⎪⎨⎪⎩

f0 + k1ın if k2(ın − ınp)≥k1ın;

f0 + k2(ın − ınp) if k1ın > k2(ın − ın

p) > −kadhın;

f0 − kadhın if kadhın≥k2(ın − ınp);

(7)

here f0 is constant adhesion, ı is normal total overlap, ıp is normallastic overlap, k1 is the virgin loading stiffness parameter, k2 ishe unloading/reloading stiffness parameter, kadh is the adhesivetiffness parameter, and n is the non-linear index parameter. Theamping force is given by Eq. (8):

nd = −ˇnvn, (8)

here �n is the magnitude of the relative normal velocity, and ˇn

s the normal dashpot coefficient expressed as:

n =√

4m∗k1

1 + (/ ln e)2, (9)

ith the equivalent mass of the particles m*, and the coefficient ofestitution e defined in the simulation.

The contact tangential force, ft, is similarly given by the sumf tangential spring force, fts, and tangential damping force, ftd., asiven by Eq. (10):

t = (f ts + f td). (10)

The tangential spring force is expressed in incremental terms:

ts = f ts(n−1) + �f ts, (11)

here fts(n − 1) is the tangential spring force at the previous timetep, and �fts is the increment of the tangential force and is giveny:

f ts = −ktıt, (12)

here kt is the tangential stiffness, and ıt is the increment of theangential spring. The tangential damping force is product of tan-ential dashpot coefficient, ˇt, and the relative tangential velocity,t, as given by Eq. (13):

td = −ˇtvt . (13)

The dashpot coefficient ˇt is given by:√4m∗kt

t =1 + (/ ln e)2

. (14)

The total tangential force is limited by Coulomb friction law.hat is, if the friction force is greater than maximum shear force

mt

t

contact force–displacement function.

llowed by shear slider, the tangential force is set equal to theaximum frictional value, fct:

ct ≤ �|fhys + kadhın|, (15)

here � is the coefficient of friction.For the torque calculation, the default EDEM rolling friction

odel is adopted in this study. The total applied torque, �i, is giveny:

i = −�r |fhys|Riωi, (16)

here �r is the coefficient of rolling friction, Ri is the distancerom the contact point to the particle centre of mass and ωi is thenit angular velocity vector of the object at the contact point. Fur-her details about the contact model can be found in the paper byhakur, Morrissey, et al. (2013).

.2.2. Model implementationThere are several challenges in modelling cohesive powder at

ndividual particle level. First, it is computationally prohibitive toodel each and every individual particle and the cohesion aris-

ng from several different phenomena including van der Waals,apillary bridge, and electrostatic forces separately. Second, realarticles are not spherical and can have surface asperities and con-act occurs not at a single point but through multiple asperities.inally, it is very difficult to measure input parameters includ-ng adhesive force, contact stiffness, coefficient of restitution etc.or cohesive powders. For example, enormous scatter in data haseen reported in measurement of adhesive pull-off force usingFM measurement (Heim et al., 2005; Tykhoniuk et al., 2007). Inur approach, the focus is on an intermediate scale between theicro- and macro-scales, aiming at a phenomenological contactodel that can reproduce the bulk cohesive strength, stress history

ependency, and other behaviour evidenced in bulk experiments.As a first step towards calibration of DEM model parameter, a

implified linear version of the contact model, i.e., parameter n = 1Luding, 2008; Walton & Braun, 1986) is used (see Fig. 9(b)). Theohesive contact model was only applied to particle-particle inter-ctions. The particle-geometry interactions were modelled usinghe Hertz-Mindlin (no-slip) contact model and hence no particle-eometry adhesion was permitted. For this investigation, the DEMarameters were estimated to match primarily the compressionnd the unconfined strength of Sample B retained on 500 �m sieve.he DEM input parameters used are presented in Table 4. An exten-ive parametric study is underway to develop a robust calibration

ethodology which should permit a rigorous model calibration in

he near future.The geometric similarity between the experiments and simula-

ions was maintained by using the same diameter mould. In order to

10 S.C. Thakur et al. / Particuol

Table 4Simulation parameters.

Number of particles 3500Loading spring stiffness, k1 (N/m) 1 × 106

Unloading spring stiffness, k2 (N/m) 4 × 106

Adhesive force, f0 (N) –0.004Adhesive parameter stiffness, kadh (N/m) 2 × 106

Particle static friction, �sf 0.6Particle rolling friction, �rf 0.001Wall friction, �wf 0.4Top and bottom platen Friction, �Pf 0.4Coefficient of restitution, e 0.4DEM time step, ts (s) 4.6 × 10−6

prnl3s(aotdettac

d

(qtiraptm(swsttrttr

3

fbiwpitibpippam

ffc

Fig. 10. Paired particle with aspect ratio of 1.5.

redict the mechanical behaviour of real adhesive frictional mate-ial which is neither spherical nor smooth, it is important thaton-spherical shape is considered to mimic the geometric inter-

ocking that exists. In this simulation, the cylinder was filled with500 non-spherical particles, each consisting of two overlappingpheres of 2 mm diameter giving a particle aspect ratio of 1.5Fig. 10). It should be noted that the DEM particles in this studyre mesoscopic representation of the detergent powders. A studyn numerical scaling of DEM parameters in uniaxial test has shownhat if the DEM input parameters are scaled properly, size indepen-ent bulk stress–strain results can be obtained (Thakur, Ahmadian,t al., 2013). Therefore, particle size larger than realistic size par-icles is used. The particle size distribution can have an effect onhe bulk behaviour but is not considered in this simulation where

detergent powder with a narrow size range has been chosen foromparison.

Each simulation consists of three stages: (1) filling the cylin-rical mould to form the initial packing used for all stress levels;

eeoo

Fig. 11. Snapshots of uniaxial test simulations: (1) filling, (2) c

ogy 12 (2014) 2– 12

2) confined consolidation to the required stress level and subse-uent unloading; and (3) unconfined compression of the sampleo failure after the removal of the mould. The process is visualisedn Fig. 11. The random rainfall method was adopted to provide aandom packing of particles. To ensure that the system reached

quasi-static state, loading only commenced when the kinetic tootential energy ratio was less than 10−5 with a constant coordina-ion number. The confined consolidation process was conducted by

oving the top platen downward at a constant speed of 10 mm/sstrain rate ≈ 0.14 s−1) to apply a vertical compression. After con-olidating the sample to the desired stress, the load on the assemblyas released by moving the top platen upward at the same con-

tant speed. The lateral confining walls were then removed andhe unconfined sample was allowed to relax for a short period ofime (0.1 s). This allowed the kinetic energy generated from theemoval of the confining wall and upward retreat of the top plateno dissipate. The sample was then crushed to failure by moving theop platen downward again at a constant rate of 5 mm/s (strainate ≈ 0.1 s−1).

.2.3. Simulation resultsSample B with particle size range 500–2000 �m is chosen

or DEM model calibration. The compression and decompressionehaviour (stress–strain and change in porosity–stress) is shown

n Fig. 12. The predicted stress–strain response matches very wellith the experimental stress–strain behaviour of Sample B witharticle size range 500–2000 �m. However, there is a discrepancy

n porosity–stress behaviour with the DEM predicting a lower ini-ial porosity. This can be attributed to the highly irregular shape,ntra-particle porosity, and surface asperities of Sample B as showny the SEM photographs (see Fig. 3(c)), which have not beenroperly accounted for in the DEM model. This warrants further

nvestigation into the interaction between inter- and intra-particleorosity on packing and compressibility behaviour of cohesiveowder. However, when change in porosity is plotted againstpplied consolidation stress, the results show reasonable agree-ent between the simulation and the experiments (see Fig. 12(b)).Fig. 13(a) and (b) compares simulation and experimental results

or the unconfined loading response (to failure) and the flowunction, respectively. The computed peak unconfined strengthompares reasonably well at 37 kPa consolidation stress. How-

ver, the initial stiffness in DEM simulation was steeper than thexperiments. Furthermore, overconsolidation behaviour was notbserved in the simulations. This could be due to the fragile naturef the SDD powders undergoing breakage during shearing. From

onfined consolidation, and (3) unconfined compression.

S.C. Thakur et al. / Particuology 12 (2014) 2– 12 11

Fig. 12. Confined stress–strain (a) and porosity–stress behaviour (b) (simulation vs. experiments).

nd flo

Fpc

4

scppctts

spiurcTs

theipl

ilpep

stdtpcfls

blcmctp

saso

Fig. 13. Unconfined stress–strain behaviour (a) a

ig. 13(b), the flow function result from DEM simulations com-ares reasonably well to experimental results, especially at higheronsolidation stresses (40–60 kPa).

. Conclusions

The packing, compression and flowability behaviour of twopray-dried powders manufactured at two different moistureontents have been studied using the EPT uniaxial tester. The EPTrovided highly reproducible measurements of the confined com-ression (giving the porosity-stress function) and the unconfinedompression to failure (giving the flow function) of the powders:hese can be very useful in describing the handling characteris-ics of these powdered products including screening new products,tudying formulation changes and the effect of anticaking agent.

Comparing the two manufactured powders, the low moistureample had higher intra-particle porosity and lower inter-particleorosity, resulting in a higher overall porosity. However the higher

ntra-particle porosity did not lead to a higher compressibilitynder load. For the high moisture sample, the higher moisture gaveise to higher inter-particle porosity and a higher plasticity at theontacts under load, resulting in a higher overall compressibility.he higher plasticity at the contacts eventually led to a higher caketrength for the high moisture sample.

For different sieve-cut samples, it was found that moisture con-ent was not uniformly distributed, with the larger size fractionsaving higher moisture contents, most probably due to the agglom-

ration of primary particles into larger sizes enclosing highernternal moisture. The larger size fractions showed higher totalorosity compared to the smaller size fractions. It is noted that the

arger fractions are agglomerates of the primary particles. Thus the

mofr

w function (b) for simulation and experiments.

nter-agglomerate porosity also contributed to the total porosityeading to a higher porosity for the larger fractions. Higher initialorosity, and high moisture associated with large size fractionsxplains why large size fractions always showed a higher com-ressibility than the smaller size fractions.

Additionally, the larger size fractions also showed higher caketrength than the full size range in each of the two powders. This hashe practical implication that if the detergent powder segregatesuring the handling and transport operation, the coarser frac-ion may dominate the overall caking behaviour of the detergentowders. In addition, the powders with higher inherent moistureontent can have a higher cohesivity and may therefore cause moreowability problems especially when subjected to significant con-olidation stresses.

The filling and, confined compression/decompression, followedy the unconfined loading to failure, in an EPT test have been simu-

ated with DEM using a recently developed elasto-plastic adhesiveontact model. The simulation results are in reasonably good agree-ent with the experimental results for the flow function and

ompression behaviour but less so for other observed features. Fur-her development of contact model is underway to improve theredictive capabilities.

This study is the first step towards using DEM to model cohe-ive powders for industrial scale applications. More simulationsre required to study the effects of several DEM input parametersuch as particle size, shape, particle size distribution, friction etc.n the bulk response. However, this first step demonstrated the

odel’s capability to predict the pertinent macroscopic behaviour

f a cohesive powder under compression and shear and its potentialor modelling complex industrial processes involving these loadingegimes.

1 rticuol

A

iDPa

R

A

B

B

B

C

C

D

D

D

E

F

G

G

H

H

H

H

H

J

K

L

L

M

M

M

O

P

R

R

R

S

S

S

T

T

T

T

W

W

W

W

Y

Y

Y

Y

Y

Y

2 S.C. Thakur et al. / Pa

cknowledgements

The support from the EU Marie Curie Initial Training Networks gratefully acknowledged. The authors would also like to thankr Luis Martindejuan, Dr Graham Calvert, Mr Simon Greener, Johnaul Morrissey, and Prof Jian-Fei Chen for many useful discussionsnd Miss Tara Aziz for technical assistance.

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