the effect of binder viscosity on particle agglomeration in a low shear mixer/agglomerator

8
Ž . Powder Technology 113 2000 140–147 www.elsevier.comrlocaterpowtec The effect of binder viscosity on particle agglomeration in a low shear mixerragglomerator P.J.T. Mills a,1 , J.P.K. Seville b, ) , P.C. Knight a , M.J. Adams b a School of Chemical Engineering, UniÕersity of Birmingham, Edgbaston, Birmingham B15 2TT, UK b UnileÕer Research Port Sunlight Laboratory, Quarry Road East, Bebington, Merseyside L63 3JW, UK Received 6 May 1999; received in revised form 16 September 1999; accepted 9 December 1999 Abstract A study is reported of the effects of changing the binder viscosity in rotating drum granulation of a narrow size fraction of an irregularly shaped sand. Silicone fluids, having viscosities in the range 20–500 mPa s, were used as binders. The size distribution of granules was determined by analysis of microscope images and the granule morphology by examination of sections of granules. The compressive strength of granules was also measured. It was found that the viscosity of the binder affected both the rate of size enlargement and the mechanism of size enlargement. The growth rate increased with increase in binder viscosity up to maximum at a viscosity of about 100 mPa s. Enlargement occurred by a layering mechanism. With binders of viscosity greater than 100 mPa s, layering was not observed and growth was found to be by coalescence. Stokes number analyses of the internal deformation on impact and of the adhesion on impact of surface-wet granules were made and found to account, in part, for the effects of changing binder viscosity. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Granulation; Mixer; Drum; Viscosity; Binder; Porosity; Particle size 1. Introduction Many products of the chemical and process industries are in the form of agglomerates, each of which is made up Ž . of a large number of constituent ‘primary’ particles. This form is a convenient way of combining ingredients with different functions into a structure with desirable handling and dissolution properties. Agglomeration can be carried w x out in both low and high shear mixers 1,2 . In the former, motion is induced by the contents of the mixer flowing under gravity, while in the latter, the flow is induced by the movement of impeller blades. The rolling drum granu- ) Corresponding author. School of Chemical Engineering and IRC in Materials for High Performance Applications, The University of Birming- ham, Edgbaston, Birmingham B15 2TT, UK. Tel.: q 44-121-414-5322; fax: q 44-121-414-5377. Ž . E-mail address: [email protected] J.P.K. Seville . 1 Current address: Coca Cola N.W. Europe, 1 Queen Caroline Street, London W6 9HR, UK. lator is, in principle, one of the simplest low shear agglom- erating devices available. In order to induce the constituent particles to cohere, it is usual to add a liquid binder, the selection of which has often been carried out on a trial- and-error basis. Relatively extensive research has been carried out on the effects of the liquid content and the feed particle size distribution on agglomerate growth mechanisms and kinet- ics, particularly in the classical work of Capes and Danck- wx wx wx werts 3 , Linkson et al. 4 , Newitt and Conway-Jones 5 wx and Kapur and Fuerstenau 6 , as summarised in Table 1. The microscopic origins of agglomeration have been de- wx wx scribed by Capes 1 and Sherrington and Oliver 2 . Much Ž of the earlier work was done with low viscosity ca. 1 mPa . s aqueous binders and the literature emphasises the effect of binder surface tension on agglomeration behaviour. wx Capes and Danckwerts 3 , e.g., found that it was not possible to granulate sand in a rotating drum if the ratio of the surface tension to the size of the constituent particles y2 wx was less than 460 N m , while Aulton 7 demonstrated that agglomeration could not proceed if the solids were insufficiently wetted by the binder. More recently, the importance of the viscosity of the binder has been emphasized in a number of studies, both 0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0032-5910 00 00224-2

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Page 1: The effect of binder viscosity on particle agglomeration in a low shear mixer/agglomerator

Ž .Powder Technology 113 2000 140–147www.elsevier.comrlocaterpowtec

The effect of binder viscosity on particle agglomeration in a low shearmixerragglomerator

P.J.T. Mills a,1, J.P.K. Seville b,), P.C. Knight a, M.J. Adams b

a School of Chemical Engineering, UniÕersity of Birmingham, Edgbaston, Birmingham B15 2TT, UKb UnileÕer Research Port Sunlight Laboratory, Quarry Road East, Bebington, Merseyside L63 3JW, UK

Received 6 May 1999; received in revised form 16 September 1999; accepted 9 December 1999

Abstract

A study is reported of the effects of changing the binder viscosity in rotating drum granulation of a narrow size fraction of anirregularly shaped sand. Silicone fluids, having viscosities in the range 20–500 mPa s, were used as binders. The size distribution ofgranules was determined by analysis of microscope images and the granule morphology by examination of sections of granules. Thecompressive strength of granules was also measured. It was found that the viscosity of the binder affected both the rate of sizeenlargement and the mechanism of size enlargement. The growth rate increased with increase in binder viscosity up to maximum at aviscosity of about 100 mPa s. Enlargement occurred by a layering mechanism. With binders of viscosity greater than 100 mPa s, layeringwas not observed and growth was found to be by coalescence. Stokes number analyses of the internal deformation on impact and of theadhesion on impact of surface-wet granules were made and found to account, in part, for the effects of changing binder viscosity. q 2000Elsevier Science S.A. All rights reserved.

Keywords: Granulation; Mixer; Drum; Viscosity; Binder; Porosity; Particle size

1. Introduction

Many products of the chemical and process industriesare in the form of agglomerates, each of which is made up

Ž .of a large number of constituent ‘primary’ particles. Thisform is a convenient way of combining ingredients withdifferent functions into a structure with desirable handlingand dissolution properties. Agglomeration can be carried

w xout in both low and high shear mixers 1,2 . In the former,motion is induced by the contents of the mixer flowingunder gravity, while in the latter, the flow is induced bythe movement of impeller blades. The rolling drum granu-

) Corresponding author. School of Chemical Engineering and IRC inMaterials for High Performance Applications, The University of Birming-ham, Edgbaston, Birmingham B15 2TT, UK. Tel.: q44-121-414-5322;fax: q44-121-414-5377.

Ž .E-mail address: [email protected] J.P.K. Seville .1 Current address: Coca Cola N.W. Europe, 1 Queen Caroline Street,

London W6 9HR, UK.

lator is, in principle, one of the simplest low shear agglom-erating devices available. In order to induce the constituentparticles to cohere, it is usual to add a liquid binder, theselection of which has often been carried out on a trial-and-error basis.

Relatively extensive research has been carried out onthe effects of the liquid content and the feed particle sizedistribution on agglomerate growth mechanisms and kinet-ics, particularly in the classical work of Capes and Danck-

w x w x w xwerts 3 , Linkson et al. 4 , Newitt and Conway-Jones 5w xand Kapur and Fuerstenau 6 , as summarised in Table 1.

The microscopic origins of agglomeration have been de-w x w xscribed by Capes 1 and Sherrington and Oliver 2 . Much

Žof the earlier work was done with low viscosity ca. 1 mPa.s aqueous binders and the literature emphasises the effect

of binder surface tension on agglomeration behaviour.w xCapes and Danckwerts 3 , e.g., found that it was not

possible to granulate sand in a rotating drum if the ratio ofthe surface tension to the size of the constituent particles

y2 w xwas less than 460 N m , while Aulton 7 demonstratedthat agglomeration could not proceed if the solids wereinsufficiently wetted by the binder.

More recently, the importance of the viscosity of thebinder has been emphasized in a number of studies, both

0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved.Ž .PII: S0032-5910 00 00224-2

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( )P.J.T. Mills et al.rPowder Technology 113 2000 140–147 141

Table 1Summary of published literature on tumbling drum granulation

Authors Drum Liquidr Composition Mean size Size Composition Surface ViscosityŽ . Ž .diameter solid of constituent mm distribution of binder tension mPa s

y1Ž . Ž . Ž .m ratio vrv % particles mN m

Newitt and 0.46 50–55 Silica sand 218 Narrow Water 73 ca. 1w xConway-Jones 5 57–72 Silica sand 70 Narrow

70 Sand silt 29 Narrow32–48 Sand silt 58 Wide39–56 Sand silt 18 Wide

Kapur and 0.30 44–47 Calcium ca. 50 Wide Water 73 ca. 1w xFuerstenau 6 46–50 carbonates ca. 20 Wide

46–50 ca. 10 WideCapes and 0.23 – Silica sands 165 Narrow Water 73 ca. 1

w xDanckwerts 3 – 138 Narrow64–79 97 Narrow60–74 70 Narrow68–88 49 Narrow– Mixtures Wide Ethanol 23 ca. 1

Linkson et 0.23 – Silica sands 214 Narrow Water 73 ca. 1w xal. 4 62 163 Narrow

67 96 Narrow72 67 Narrow68 48 Narrow55 ca. 20 Wide44–51 ca. 10 Wide

Simons et 0.40 50 Glass spheres 65 Narrow Silicone oil 20 20–500w xal. 13

w xtheoretical and observational 8–19 . It is straightforwardto show that if the co-linear impact velocity between tworigid spherical particles coated with a thin layer of aviscous liquid exceeds a certain value, the dynamic forcearising from the squeeze flow of the liquid film exceeds

w xthe static force due to the surface tension 19 . However,whether or not a particle impacting on a wet surface, oranother wet particle, will be ‘captured’ depends not on theinstantaneous force acting between them, but on the initialkinetic energy and the energy dissipated in the collision. Inpractice, it is difficult to apply these concepts to agglomer-

w xation processes because it is difficult to measure 20 , or toestimate theoretically, the impact velocity between parti-cles. It is also difficult to express the energy dissipated incollisions in terms of fundamental parameters.

w xEnnis et al. 8 considered the co-linear collision ofelastic granules coated with a layer of a viscous liquid and

w xemployed the formulation of Barnocky and Davis 21 , inwhich the ratio of the kinetic energy of the collidinggranules to the energy dissipated in the liquid layer wasrepresented by a Stokes number. This treatment does not,however, account for dissipation within deformable gran-

w xules by frictional and viscous processes 9,12,14–18,22 .This source of energy dissipation may be more importantthan that in a liquid layer at the surface of granules. Aswell as affecting the probability of coalescence, the binderviscosity, if sufficiently large, may also determine the rate

w xof consolidation 8,12,14,16,18 and the impact strengthw x9,17 . The recent studies on drum granulation by Iveson et

w x w x w xal. 12 , Iveson and Litster 18 and Simons et al. 13showing the effects of binder viscosity on granule com-paction and growth are particularly relevant, as is the

w xproposal by Iveson and Litster 16 of a regime map forgranulation.

This paper presents the results of a study of the effectsof changing the binder viscosity on agglomeration of anirregularly shaped sand using a rotating drum granulator.Silicone binders were used, which had a viscosity consid-erably greater than that of the binders used in muchprevious work. Silicone fluids are expected to wet the solidwell. The size of the solid used and the surface tension ofthe binders were such that the ratio of the surface tensionto particle size was well below the limit for the formation

w xof granules reported by Capes and Danckwerts 3 for lowviscosity systems. The paper aims to explore further theinfluence of binder viscosity on the granule growth processand on granule physical properties.

2. Materials and methods

Experiments were carried out with an irregularly shapedŽsilica sand of sieve size range 90–180 mm. The poly di-

.methylsiloxane silicone oils had low volatilities. At 258C,their viscosities were in the range 20–500 mPa s and theirsurface tension was 20 mN my1.

The stainless steel batch granulating drum had an inter-nal diameter of 400 mm and was 100 mm deep. The front

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cover could be removed and a transparent viewing windowincorporated. The drum revolved at 29 rpm, with its axishorizontal and included two diametrically opposed triangu-lar baffles, each 7 mm in height, to assist the tumbling ofthe charge during rotation. The drum was operated underlightly loaded conditions. The binder was premixed withthe solid in a planetary mixer, in batches of 100 g, to forma wet crumbly mass. The wet solid was passed through a4.75 mm width sieve and was then charged directly to thedrum without intermediate storage. The liquid to solid ratioby weight was 0.225:1, equivalent to a liquid to solid ratioby volume of approximately 0.5:1.

After a period of tumbling, measured by the number ofrevolutions, the contents were removed from the drum.Image analysis was subsequently conducted to determinethe total number of granules present, the granule size

Ždistribution expressed in terms of the diameter of the.circle having the same projected area as the particle , and

Žcircularity of the granules ratio of perimeter of the gran-ules to the perimeter of the circle with the same projected

.area . The number mean granule diameter was found to bereproducible to within approximately "0.5 mm. Growthmechanisms were investigated by microscopic examinationof sectioned granules formed after different mixing times.

The deformation behaviours and fracture strengths ofindividual granules were measured by diametral compres-sion at a velocity of 5 mm miny1.

3. Results

3.1. Extent of granulation

Microscope examination of the feed material charged tothe drum showed that it consisted of loose flocs of adher-ing constituent particles. On drum mixing, these flocsformed small granules which themselves coalesced rapidly,within 50 drum revolutions, to give rounded millimetre-sizegranules, having a mean size of the order of 5 mm. It was

Fig. 1. Granulation of sand with binders of different viscosity of granulenumber mean diameter with number of drum revolutions.

Fig. 2. Variation of granule growth rate with binder viscosity.

not possible quantitatively to characterise the change insize and morphology of the loose flocs as they coalescedto give discrete granules. This was because the flocsadhered to each other and, consequently, discrete granulescould not be identified. In contrast, the millimetre-sizegranules were clearly discrete and their size distributionand shape could be determined without ambiguity.

On continued mixing, size enlargement occurred, theextent of which varied with the viscosity of the binder.Fig. 1 shows how the number mean diameter varied with

Ž .the number of drum revolutions mixing or residence timefor the different binder viscosities. The dependence ofnumber mean diameter on drum revolutions can be repre-sented by a linear relationship, in which the gradient of thelines can be taken to be a granule growth rate. Fig. 2shows how the granule growth rate varied with binderviscosity. It is evident that the most rapid rate of growthoccurred with a binder having a viscosity of about 100mPa s. The rate of growth was similar with the 20 and 350mPa s binders and was small with the 500 mPa s binder.For convenience, binders of viscosity F100 mPa s will,henceforth, be referred to as ‘lower viscosity’ binders andbinders of viscosity )100 mPa s will be referred to as‘higher viscosity’ binders.

Ž .With the lower viscosity binders 20 and 100 mPa s ,sub-millimetre ‘crumb’ was present. Also with thesebinders, material adhered to the wall of the drum. Thequantity of material adhering increased with mixing revo-lutions; for example, with the 100 mPa s binder, thisproportion had increased to 18% by weight after 300revolutions. In contrast, with the higher viscosity bindersŽ .350 and 500 mPa s , there was no ‘crumb’, and nomaterial adhered to the walls of the drum.

The nature of the axial and radial components of themotion of the granules in the drum was seen visually to beaffected by binder viscosity. With the binder of highest

Ž .viscosity 500 mPa s , the speed of motion of the granuleswas slower than that with the lower viscosity binders.Independent of viscosity, dynamic segregation by size wasevident, with the lower part of the drum containing ahigher than average proportion of larger granules.

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Ž . Ž .Fig. 3. Granule size distributions after different numbers of drum revolutions: a binder viscosity: 100 mPa s; b binder viscosity: 500 mPa s.

Ž . Ž .Fig. 4. Photomicrographs of granules: a section of a granule formed with a binder of viscosity 100 mPa s after 100 revolutions granule diameter 6 mm ;Ž . Ž .b granules formed with a binder of viscosity 500 mPa s after 100 revolutions bars5 mm .

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Fig. 5. Circularity as a function of number of drum revolutions forgranules formed from binders with viscosities of 100 and 500 mPa s.

3.2. Size distributions

Fig. 3a and b show size distributions by number, ex-pressed in non-dimensional form by normalising with re-spect to the median size, for granules obtained with the100 and 500 mPa s binders, respectively. These curves donot include the ‘crumb’ because it adhered to other ag-glomerates and it cannot be satisfactorily analysed. Thedistributions are quite narrow: with the 100 mPa s binder,90% of the distribution lay within the range 0.7–1.3 timesthe mean diameter. The data appear to show ‘self-preserv-ing’ character, but too much significance should not beattached to this observation. Self-preserving data havebeen reported previously for drum granulation with very

w xlow viscosity binders 3–6 . Since, theoretically, growth byboth the crushing and layering and by the coalescencemechanisms can give self-preserving size distributions, thischaracteristic alone cannot be used to identify the domi-

w xnant growth mechanism 23 .

3.3. Mechanisms of growth

In order to gain a more detailed understanding of thedevelopment of morphology and, hence, of the mecha-nisms of growth, granules were sectioned and examinedunder an optical microscope. When granules prepared after50 drum revolutions were examined, they could be seen tobe composed of partially coalesced small granules havinga size of about 0.5 mm. The initial, rapid, growth thusappeared to be similar to that reported previously withbinders of low viscosity, and which has been categorised

w xas random coalescence 1–6 . With the lower viscositybinders, the degree of coalescence was such that thegranules contained an appreciable volume of irregularly

Žshaped voids of size of the order of 1 mm. Small 1–2.mm granules did not, however, contain such macroscopic

voids. With the higher viscosity binders, the small granuleswere coalesced to a greater degree, so that the volume ofvoids was small.

After 100 revolutions, granules made from the lowerviscosity binders had an outer layer of closely packed

Žconstituent particles, surrounding the porous centre Fig..4a . With continued mixing, the layered morphology re-

mained, but the voids at the centre were eliminated by 300revolutions These observations are consistent with growthby a layering mechanism in which crushed or abraded‘crumb’ is built up on the granule surface. The granulesbecame increasingly spherical with increasing mixing time,

Ž .quantified by the measured circularities Fig. 5 .Granules made from the higher viscosity binders did not

contain layered material at their surfaces and the circular-ity values were less than those of granules made with

Ž .lower viscosity binders Fig. 5 . Incompletely coalesceddumb-bell-shaped granules were present, as illustrated inFig. 4b. These observations are consistent with the absence

Ž .of ‘crumb’ and with slow growth by a coalescencemechanism.

3.4. Granule strengths

The force to fracture individual granules was measuredby diametral crushing at a compression velocity of 5 mmminy1. The granules deformed inelastically and fracturedinto fragments at a strain of between 5% and 10%. Exten-sive measurements were made to determine the depen-dence of fracture force on granule size, residence time inthe mixer and binder viscosity. Typical data are shown inFig. 6, in which the fracture force is plotted as a functionof the granule size. The fracture force was found to beproportional to the granule diameter to a power of 1.6–2.0.Consequently, if the nominal fracture stress is taken to beproportional to the fracture force divided by the cross-sec-tional area of the granules, the nominal fracture stress isnearly independent of granule size.

The data in Fig. 6 make a comparison of the effect ofbinder viscosity on fracture force. It is evident that thefracture force is not sensitive to binder viscosity within

Fig. 6. A double logarithmic plot of compressive fracture force as afunction of granule diameter for granules formed from binders withviscosities of 100 and 500 mPa s.

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( )P.J.T. Mills et al.rPowder Technology 113 2000 140–147 145

this range. This type of fracture test is quasi-static and,hence, it can be argued that the results should not besensitive to viscosity. Recently published results for impact

w xstrength of agglomerates show strong viscosity effects 17 .The presence of macrovoids within granules formed after alow number of revolutions was found, however, to givegranules which were weaker than those formed after alarge number of revolutions. The data in Fig. 6 show thatthe fracture force for granules made after 300 revolutionswith the 100 mPa s binder was approximately 30% higher

Ž .than that after 50 revolutions Fig. 6 .The nominal fracture stress was of the order of 15 kPa.

Thus, a pile of granules resting under gravity would needto be about 1.5 m high to cause complete fracture. Thissuggests that complete crushing in the mixer is unlikely.However, abrasive wear can be expected to occur duringoblique impacts, particularly those at low angles of inci-

w xdence 24 . Note also that the wear rate of agglomeratesw xcontaining a solid binder was found to correlate 24 with

the reciprocal of the critical strength intensity factor deter-mined from a fracture test.

4. Discussion

4.1. OÕerÕiew of main features

The study has revealed a number of features that needto be accounted for by mechanistic models. Before at-tempting this, we will briefly state the main results. Theprimary aim of the investigation was to establish theinfluence of the viscosity of the binder on a small scaledrum agglomeration process for a single size and type ofsolid. The solid used was fairly coarse and the observedbehaviour is likely to be different from that with muchfiner solids. The results show that the viscosity affects boththe rate of size enlargement and the morphology of thegranules. By inference, therefore, it affects the mechanism.As has been already stated, with lower viscosity bindersŽ .viscosity F100 mPa s , ‘crumb’ was present and growthoccurred by layering. For these binders, the growth rateincreased with increasing binder viscosity. With higher

Ž .viscosity binders viscosity )100 mPa s , ‘crumb’ wasnot present and growth occurred by coalescence. For thesebinders, the growth rate decreased with increasing binderviscosity. The granular motion within the drum was alsoaffected by binder viscosity. The binder with the highest

Ž .viscosity 500 mPa s resulted in a granular motion withinthe agglomerator that was slower than that with the otherbinders.

4.2. Stokes number analysis of the granule strength

Granules in the drum agglomerator were subjected toboth slow compressive and impact loading. The relativeimportance of these is not established. However, the ag-

glomeration process only occurs when granules move andinteract dynamically with each other. It is reasonable,therefore, to presume that impact loading behaviour iscritical. Because most impacts are oblique, frictional shear-ing and rolling behaviours are important. For granules toform, they must have sufficient strength to withstand theimpacts without attriting excessively or breaking com-pletely. In the collisions, energy is dissipated within thegranules as they deform by friction between the constituentŽ .primary particles. Note that the friction occurs as aconsequence of normal forces between the particles arisingfrom the loading of the impacted granules, augmented by

Žthe negative capillary pressure produced by the surface.tension . Provided the binder is sufficiently viscous, en-

ergy may also be dissipated by viscous flow. Capes andw xDanckwerts 3 found experimentally that, with binder

Ž .liquids of low viscosity ca 1 mPa s , surface tensionforces dominated and that granules could only be formedprovided the ratio of liquid surface tension to the size ofthe constituent particles was more than a critical value of460 N my2 . For the binder used here, this corresponds to avalue of 43 mm, which is considerably smaller than thesize range of the particles used. The observation, thatgranules could be formed, indicates that the viscous forcesmust have been more important than surface tension forcesin determining the impact strength of granules in colli-sions.

When a granule is subjected to impact loading, thebinder is forced to flow within the granule, dissipatingenergy. The magnitude of the energy dissipation increaseswith granule density, impact velocity, binder viscosity andwith decrease in the size of the pores, formed by the porespace between the particles within the granule. The size ofthe pores is linearly related to a suitable average size of the

w xconstituent particles. Keningley et al. 14 made a simpleanalysis which led to the definition of a viscous Stokesnumber, St , characterising the ratio of the inertial energyd

on impact to the viscous dissipation of energy within thegranules:

4ru d0St s , 1Ž .d 9m

where r, 2u , and d are the granule density, collision0

velocity and diameter of the constituent particles, respec-tively, and m is the binder liquid viscosity. We suggestthat there is a critical value of the Stokes number, St) ,d

below which breakage and abrasive wear are not signifi-cant and above which granule breakage and abrasive wearoccur, forming the ‘crumb’. In practice, there is a distribu-tion of collision velocities. In low velocity collisions,granules will remain intact, while above a certain velocity,fragmentation will occur. Hence, both fragmentation andgrowth by layering will occur in parallel. With an increasein the viscosity, the probability of fragmentation is reducedand, consequently, there is an increase in the net growthrate.

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Above a certain critical viscosity, St will always bed

less than St). Fragmentation then no longer occurs. Underd

these conditions, ‘crumb’ is not formed. Consequently,growth can only occur by a granule coalescence mecha-nism. In the present work, the critical viscosity was evi-dently of the order of 100 mPa s. It is also to be expectedthat the growth rate by coalescence should decrease withincreasing binder viscosity. Coalescence requires a largeamount of granule deformation, which will be opposed bybinders of high viscosity. The deformation causes dilationof the packing of the constituent particles, which willcause liquid binder to be ‘sucked in’ to fill the increase invoidage. A binder of high viscosity will retard both thisdilation and also the expression of liquid to the granulesurface, which occurs in the subsequent consolidation ofthe constituent particles.

4.3. Stokes number analysis of the granular motion

Considerable deformation must have occurred in theŽrapid coalescence stage which occurred within 50 drum

.revolutions . Following this stage, with higher viscositybinders for which fragmentation did not occur, the gran-ules presumably deformed to only a small extent in themajority of single collisions. It may be appropriate, there-fore, to model these granules as surface-wet elastic spheresand thereby to determine the critical viscosity at which theflow behaviour of granules in the drum mixer is affected.A Stokes number analysis of the co-linear impact betweentwo surface-wet, elastic granules can be used to determinewhether the granules will rebound or adhere after collision.The outcome depends on the ratio of the kinetic energy ofthe granules to the ratio of the energy absorbed in thecollision. The latter is taken to be the energy absorbed bysqueezing of the viscous liquid between the granulesŽ .calculated from Reynolds’ lubrication equation . In this

w xcase, the Stokes number, St , is given by 8,19,21 :D

4ru D0St s , 2Ž .D 9m

where D is the granule diameter. There is a critical valueof the Stokes number, St) above which rebound will occurD

and below which granules will adhere. With low viscosityliquids, the magnitude of St will be much larger thanD

St) , and the granular flow will be insensitive to changes inD

viscosity. With an increase in viscosity, the magnitude ofSt will become comparable to St) , and the granularD D

motion will be affected by the magnitude of the binderviscosity. In the present work, this condition occurred witha binder having a viscosity of 500 mPa s.

Ž .To utilise Eq. 2 in a predictive manner, it is necessaryto estimate the magnitude of St). Estimates of St) show itD D

w xto have a magnitude of order unity 8,19,21 . As suggestedw xby Ennis et al. 8 , the average granule velocity may be

taken to be equal to the peripheral velocity of the drum.

Applying the above analysis to the collision of 5 mmgranules and taking St) s1, the critical viscosity forD

granule adhesion is found to be about 3000 mPa s. Thus,the prediction of the Stokes number analysis that thegranular flow will be affected by binders having viscositiesapproaching this magnitude is in agreement with experi-ment.

5. Conclusions

A study has been made of changing the binder viscosityin the range 20–500 mPa s in the rotating drum granula-tion of a coarse size fraction of an irregularly shaped solid.The charge to the granulator was a pre-mixed wet floc.Size enlargement of the floc to form granules ca. 5 mm indiameter occurred very rapidly by a coalescence mecha-nism, independent of binder viscosity. Thereafter, enlarge-ment was much slower and the behaviour depended uponthe viscosity of the liquid. With the liquids of viscosityF100 mPa s, classified here as lower viscosity binders,the degree of size enlargement increased with increase inviscosity. A crushing and layering mechanism operated, inwhich ‘crumb’ accumulated both on the exterior of thegranules and on the drum wall. It appears that the ‘crumb’was formed by abrasive wear at the granule contact sur-faces under dynamic loading conditions.

With liquids of viscosity 350 and 500 mPa s, classifiedhere as higher viscosity binders, the extent of size enlarge-ment decreased with an increase in viscosity. There was no‘crumb’ present and growth occurred by coalescence. Theeffect of increasing the viscosity was to retard the coales-cence process.

A Stokes number analysis was made of the viscousdissipation of energy within deforming granules duringcollisions. It provided a qualitative explanation for thechange in kinetics and mechanism in size enlargementwhich occurred with binders of viscosity above 100 mPa s.

A second Stokes number analysis was made of thecollision of granules containing the higher viscositybinders, in which the granules were modelled as elasticsurface-wet spheres. It was concluded that the slowerspeed of granular motion observed with the highest viscos-ity binder could be accounted for by dissipation of impactenergy by viscous flow of the liquid squeezed betweengranules.

Acknowledgements

The authors acknowledge the earlier contributions oftwo University of Surrey, UK, undergraduates, David Mar-shall and Christian Bracken in the planning of this work,

Žand of Dr. Stefaan Simons now of University College.London, UK who carried out some of the preliminary

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experiments. They also acknowledge useful commentsmade by the referees. The experimental work was carriedout in the Department of Chemical and Process Engineer-ing at the University of Surrey and supported by a jointgrant from the EPSRC Specially Promoted Programme in

Ž .Particulate Technology GRrG56256 and Unilever Re-search Port Sunlight Laboratory, UK.

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