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agglomerator
Powder Technology 113 Ž2000. 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 b
School of Chemical Engineering, UniÕersity of Birmingham, Edgbaston, Birmingham B15 2TT, UK 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 of a large number of constituent Ž‘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 out in both low and high shear mixers w1,2x. 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 Birmingham, Edgbaston, Birmingham B15 2TT, UK. Tel.: q44-121-414-5322; fax: q44-121-414-5377. E-mail address: [email protected] ŽJ.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 agglomerating 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 trialand-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 kinetics, particularly in the classical work of Capes and Danckwerts w3x, Linkson et al. w4x, Newitt and Conway-Jones w5x and Kapur and Fuerstenau w6x, as summarised in Table 1. The microscopic origins of agglomeration have been described by Capes w1x and Sherrington and Oliver w2x. Much of the earlier work was done with low viscosity Žca. 1 mPa s. aqueous binders and the literature emphasises the effect of binder surface tension on agglomeration behaviour. Capes and Danckwerts w3x, 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 was less than 460 N my2 , while Aulton w7x 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. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 2 2 4 - 2
P.J.T. Mills et al.r Powder Technology 113 (2000) 140–147
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Table 1 Summary of published literature on tumbling drum granulation Authors
Drum diameter Žm.
Liquidr solid ratio Žvrv %.
Composition of constituent particles
Mean size Žmm.
Size distribution
Composition of binder
Surface tension ŽmN my1 .
Viscosity ŽmPa s.
Newitt and Conway-Jones w5x
0.46
Water
73
ca. 1
0.23
Water
73
ca. 1
Linkson et al. w4x
0.23
Ethanol Water
23 73
ca. 1 ca. 1
Simons et al. w13x
0.40
Narrow Narrow Narrow Wide Wide Wide Wide Wide Narrow Narrow Narrow Narrow Narrow Wide Narrow Narrow Narrow Narrow Narrow Wide Wide Narrow
ca. 1
Capes and Danckwerts w3x
218 70 29 58 18 ca. 50 ca. 20 ca. 10 165 138 97 70 49 Mixtures 214 163 96 67 48 ca. 20 ca. 10 65
73
0.30
Silica sand Silica sand Sand silt Sand silt Sand silt Calcium carbonates
Water
Kapur and Fuerstenau w6x
50–55 57–72 70 32–48 39–56 44–47 46–50 46–50 – – 64–79 60–74 68–88 – – 62 67 72 68 55 44–51 50
Silicone oil
20
20–500
Silica sands
Silica sands
Glass spheres
theoretical and observational w8–19x. It is straightforward to show that if the co-linear impact velocity between two rigid spherical particles coated with a thin layer of a viscous liquid exceeds a certain value, the dynamic force arising from the squeeze flow of the liquid film exceeds the static force due to the surface tension w19x. However, whether or not a particle impacting on a wet surface, or another wet particle, will be ‘captured’ depends not on the instantaneous force acting between them, but on the initial kinetic energy and the energy dissipated in the collision. In practice, it is difficult to apply these concepts to agglomeration processes because it is difficult to measure w20x, or to estimate theoretically, the impact velocity between particles. It is also difficult to express the energy dissipated in collisions in terms of fundamental parameters. Ennis et al. w8x considered the co-linear collision of elastic granules coated with a layer of a viscous liquid and employed the formulation of Barnocky and Davis w21x, in which the ratio of the kinetic energy of the colliding granules to the energy dissipated in the liquid layer was represented by a Stokes number. This treatment does not, however, account for dissipation within deformable granules by frictional and viscous processes w9,12,14–18,22x. This source of energy dissipation may be more important than that in a liquid layer at the surface of granules. As well as affecting the probability of coalescence, the binder viscosity, if sufficiently large, may also determine the rate of consolidation w8,12,14,16,18x and the impact strength w9,17x. The recent studies on drum granulation by Iveson et
al. w12x, Iveson and Litster w18x and Simons et al. w13x showing the effects of binder viscosity on granule compaction and growth are particularly relevant, as is the proposal by Iveson and Litster w16x of a regime map for granulation. This paper presents the results of a study of the effects of changing the binder viscosity on agglomeration of an irregularly shaped sand using a rotating drum granulator. Silicone binders were used, which had a viscosity considerably greater than that of the binders used in much previous work. Silicone fluids are expected to wet the solid well. The size of the solid used and the surface tension of the binders were such that the ratio of the surface tension to particle size was well below the limit for the formation of granules reported by Capes and Danckwerts w3x for low viscosity systems. The paper aims to explore further the influence of binder viscosity on the granule growth process and on granule physical properties.
2. Materials and methods Experiments were carried out with an irregularly shaped silica sand of sieve size range 90–180 mm. The polyŽdimethylsiloxane. silicone oils had low volatilities. At 258C, their viscosities were in the range 20–500 mPa s and their surface tension was 20 mN my1 . The stainless steel batch granulating drum had an internal diameter of 400 mm and was 100 mm deep. The front
142
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cover could be removed and a transparent viewing window incorporated. The drum revolved at 29 rpm, with its axis horizontal and included two diametrically opposed triangular baffles, each 7 mm in height, to assist the tumbling of the charge during rotation. The drum was operated under lightly loaded conditions. The binder was premixed with the solid in a planetary mixer, in batches of 100 g, to form a wet crumbly mass. The wet solid was passed through a 4.75 mm width sieve and was then charged directly to the drum without intermediate storage. The liquid to solid ratio by weight was 0.225:1, equivalent to a liquid to solid ratio by volume of approximately 0.5:1. After a period of tumbling, measured by the number of revolutions, the contents were removed from the drum. Image analysis was subsequently conducted to determine the total number of granules present, the granule size distribution Žexpressed in terms of the diameter of the circle having the same projected area as the particle., and circularity of the granules Žratio of perimeter of the granules to the perimeter of the circle with the same projected area.. The number mean granule diameter was found to be reproducible to within approximately "0.5 mm. Growth mechanisms were investigated by microscopic examination of sectioned granules formed after different mixing times. The deformation behaviours and fracture strengths of individual granules were measured by diametral compression at a velocity of 5 mm miny1 .
3. Results 3.1. Extent of granulation Microscope examination of the feed material charged to the drum showed that it consisted of loose flocs of adhering constituent particles. On drum mixing, these flocs formed small granules which themselves coalesced rapidly, within 50 drum revolutions, to give rounded millimetre-size granules, having a mean size of the order of 5 mm. It was
Fig. 1. Granulation of sand with binders of different viscosity of granule number mean diameter with number of drum revolutions.
Fig. 2. Variation of granule growth rate with binder viscosity.
not possible quantitatively to characterise the change in size and morphology of the loose flocs as they coalesced to give discrete granules. This was because the flocs adhered to each other and, consequently, discrete granules could not be identified. In contrast, the millimetre-size granules were clearly discrete and their size distribution and shape could be determined without ambiguity. On continued mixing, size enlargement occurred, the extent of which varied with the viscosity of the binder. Fig. 1 shows how the number mean diameter varied with the number of drum revolutions Žmixing or residence time. for the different binder viscosities. The dependence of number mean diameter on drum revolutions can be represented by a linear relationship, in which the gradient of the lines can be taken to be a granule growth rate. Fig. 2 shows how the granule growth rate varied with binder viscosity. It is evident that the most rapid rate of growth occurred with a binder having a viscosity of about 100 mPa s. The rate of growth was similar with the 20 and 350 mPa s binders and was small with the 500 mPa s binder. For convenience, binders of viscosity F 100 mPa s will, henceforth, be referred to as ‘lower viscosity’ binders and binders of viscosity ) 100 mPa s will be referred to as ‘higher viscosity’ binders. With the lower viscosity binders Ž20 and 100 mPa s., sub-millimetre ‘crumb’ was present. Also with these binders, material adhered to the wall of the drum. The quantity of material adhering increased with mixing revolutions; for example, with the 100 mPa s binder, this proportion had increased to 18% by weight after 300 revolutions. In contrast, with the higher viscosity binders Ž350 and 500 mPa s., there was no ‘crumb’, and no material adhered to the walls of the drum. The nature of the axial and radial components of the motion of the granules in the drum was seen visually to be affected by binder viscosity. With the binder of highest viscosity Ž500 mPa s., the speed of motion of the granules was slower than that with the lower viscosity binders. Independent of viscosity, dynamic segregation by size was evident, with the lower part of the drum containing a higher than average proportion of larger granules.
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Fig. 3. Granule size distributions after different numbers of drum revolutions: Ža. binder viscosity: 100 mPa s; Žb. binder viscosity: 500 mPa s.
Fig. 4. Photomicrographs of granules: Ža. section of a granule formed with a binder of viscosity 100 mPa s after 100 revolutions Žgranule diameter 6 mm.; Žb. granules formed with a binder of viscosity 500 mPa s after 100 revolutions Žbar s 5 mm..
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Fig. 5. Circularity as a function of number of drum revolutions for granules formed from binders with viscosities of 100 and 500 mPa s.
3.2. Size distributions Fig. 3a and b show size distributions by number, expressed in non-dimensional form by normalising with respect to the median size, for granules obtained with the 100 and 500 mPa s binders, respectively. These curves do not include the ‘crumb’ because it adhered to other agglomerates and it cannot be satisfactorily analysed. The distributions are quite narrow: with the 100 mPa s binder, 90% of the distribution lay within the range 0.7–1.3 times the mean diameter. The data appear to show ‘self-preserving’ character, but too much significance should not be attached to this observation. Self-preserving data have been reported previously for drum granulation with very low viscosity binders w3–6x. Since, theoretically, growth by both the crushing and layering and by the coalescence mechanisms can give self-preserving size distributions, this characteristic alone cannot be used to identify the dominant growth mechanism w23x.
After 100 revolutions, granules made from the lower viscosity binders had an outer layer of closely packed constituent particles, surrounding the porous centre ŽFig. 4a.. With continued mixing, the layered morphology remained, but the voids at the centre were eliminated by 300 revolutions These observations are consistent with growth by a layering mechanism in which crushed or abraded ‘crumb’ is built up on the granule surface. The granules became increasingly spherical with increasing mixing time, quantified by the measured circularities ŽFig. 5.. Granules made from the higher viscosity binders did not contain layered material at their surfaces and the circularity values were less than those of granules made with lower viscosity binders ŽFig. 5.. Incompletely coalesced dumb-bell-shaped granules were present, as illustrated in Fig. 4b. These observations are consistent with the absence of ‘crumb’ and with Žslow. growth by a coalescence mechanism. 3.4. Granule strengths
3.3. Mechanisms of growth
The force to fracture individual granules was measured by diametral crushing at a compression velocity of 5 mm miny1 . The granules deformed inelastically and fractured into fragments at a strain of between 5% and 10%. Extensive measurements were made to determine the dependence of fracture force on granule size, residence time in the mixer and binder viscosity. Typical data are shown in Fig. 6, in which the fracture force is plotted as a function of the granule size. The fracture force was found to be proportional to the granule diameter to a power of 1.6–2.0. Consequently, if the nominal fracture stress is taken to be proportional to the fracture force divided by the cross-sectional area of the granules, the nominal fracture stress is nearly independent of granule size. The data in Fig. 6 make a comparison of the effect of binder viscosity on fracture force. It is evident that the fracture force is not sensitive to binder viscosity within
In order to gain a more detailed understanding of the development of morphology and, hence, of the mechanisms of growth, granules were sectioned and examined under an optical microscope. When granules prepared after 50 drum revolutions were examined, they could be seen to be composed of partially coalesced small granules having a size of about 0.5 mm. The initial, rapid, growth thus appeared to be similar to that reported previously with binders of low viscosity, and which has been categorised as random coalescence w1–6x. With the lower viscosity binders, the degree of coalescence was such that the granules contained an appreciable volume of irregularly shaped voids of size of the order of 1 mm. Small Ž1–2 mm. granules did not, however, contain such macroscopic voids. With the higher viscosity binders, the small granules were coalesced to a greater degree, so that the volume of voids was small.
Fig. 6. A double logarithmic plot of compressive fracture force as a function of granule diameter for granules formed from binders with viscosities of 100 and 500 mPa s.
P.J.T. Mills et al.r Powder Technology 113 (2000) 140–147
this range. This type of fracture test is quasi-static and, hence, it can be argued that the results should not be sensitive to viscosity. Recently published results for impact strength of agglomerates show strong viscosity effects w17x. The presence of macrovoids within granules formed after a low number of revolutions was found, however, to give granules which were weaker than those formed after a large number of revolutions. The data in Fig. 6 show that the fracture force for granules made after 300 revolutions with the 100 mPa s binder was approximately 30% higher than that after 50 revolutions ŽFig. 6.. The nominal fracture stress was of the order of 15 kPa. Thus, a pile of granules resting under gravity would need to be about 1.5 m high to cause complete fracture. This suggests that complete crushing in the mixer is unlikely. However, abrasive wear can be expected to occur during oblique impacts, particularly those at low angles of incidence w24x. Note also that the wear rate of agglomerates containing a solid binder was found to correlate w24x with the reciprocal of the critical strength intensity factor determined from a fracture test.
4. Discussion 4.1. OÕerÕiew of main features The study has revealed a number of features that need to be accounted for by mechanistic models. Before attempting this, we will briefly state the main results. The primary aim of the investigation was to establish the influence of the viscosity of the binder on a small scale drum agglomeration process for a single size and type of solid. The solid used was fairly coarse and the observed behaviour is likely to be different from that with much finer solids. The results show that the viscosity affects both the rate of size enlargement and the morphology of the granules. By inference, therefore, it affects the mechanism. As has been already stated, with lower viscosity binders Žviscosity F 100 mPa s., ‘crumb’ was present and growth occurred by layering. For these binders, the growth rate increased with increasing binder viscosity. With higher viscosity binders Žviscosity ) 100 mPa s., ‘crumb’ was not present and growth occurred by coalescence. For these binders, the growth rate decreased with increasing binder viscosity. The granular motion within the drum was also affected by binder viscosity. The binder with the highest viscosity Ž500 mPa s. resulted in a granular motion within the agglomerator that was slower than that with the other binders. 4.2. Stokes number analysis of the granule strength Granules in the drum agglomerator were subjected to both slow compressive and impact loading. The relative importance of these is not established. However, the ag-
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glomeration process only occurs when granules move and interact dynamically with each other. It is reasonable, therefore, to presume that impact loading behaviour is critical. Because most impacts are oblique, frictional shearing and rolling behaviours are important. For granules to form, they must have sufficient strength to withstand the impacts without attriting excessively or breaking completely. In the collisions, energy is dissipated within the granules as they deform by friction between the constituent Žprimary. particles. Note that the friction occurs as a consequence of normal forces between the particles arising from the loading of the impacted granules, augmented by the negative capillary pressure Žproduced by the surface tension.. Provided the binder is sufficiently viscous, energy may also be dissipated by viscous flow. Capes and Danckwerts w3x found experimentally that, with binder liquids of low viscosity Žca 1 mPa s., surface tension forces dominated and that granules could only be formed provided the ratio of liquid surface tension to the size of the constituent particles was more than a critical value of 460 N my2 . For the binder used here, this corresponds to a value of 43 mm, which is considerably smaller than the size range of the particles used. The observation, that granules could be formed, indicates that the viscous forces must have been more important than surface tension forces in determining the impact strength of granules in collisions. When a granule is subjected to impact loading, the binder is forced to flow within the granule, dissipating energy. The magnitude of the energy dissipation increases with granule density, impact velocity, binder viscosity and with decrease in the size of the pores, formed by the pore space between the particles within the granule. The size of the pores is linearly related to a suitable average size of the constituent particles. Keningley et al. w14x made a simple analysis which led to the definition of a viscous Stokes number, St d , characterising the ratio of the inertial energy on impact to the viscous dissipation of energy within the granules: St d s
4r u0 d 9m
,
Ž 1.
where r , 2 u 0 , and d are the granule density, collision velocity and diameter of the constituent particles, respectively, and m is the binder liquid viscosity. We suggest that there is a critical value of the Stokes number, St )d , below which breakage and abrasive wear are not significant and above which granule breakage and abrasive wear occur, forming the ‘crumb’. In practice, there is a distribution of collision velocities. In low velocity collisions, granules will remain intact, while above a certain velocity, fragmentation will occur. Hence, both fragmentation and growth by layering will occur in parallel. With an increase in the viscosity, the probability of fragmentation is reduced and, consequently, there is an increase in the net growth rate.
P.J.T. Mills et al.r Powder Technology 113 (2000) 140–147
146
Above a certain critical viscosity, St d will always be less than St )d . Fragmentation then no longer occurs. Under these conditions, ‘crumb’ is not formed. Consequently, growth can only occur by a granule coalescence mechanism. In the present work, the critical viscosity was evidently of the order of 100 mPa s. It is also to be expected that the growth rate by coalescence should decrease with increasing binder viscosity. Coalescence requires a large amount of granule deformation, which will be opposed by binders of high viscosity. The deformation causes dilation of the packing of the constituent particles, which will cause liquid binder to be ‘sucked in’ to fill the increase in voidage. A binder of high viscosity will retard both this dilation and also the expression of liquid to the granule surface, which occurs in the subsequent consolidation of the constituent particles. 4.3. Stokes number analysis of the granular motion Considerable deformation must have occurred in the rapid coalescence stage Žwhich occurred within 50 drum revolutions.. Following this stage, with higher viscosity binders for which fragmentation did not occur, the granules presumably deformed to only a small extent in the majority of single collisions. It may be appropriate, therefore, to model these granules as surface-wet elastic spheres and thereby to determine the critical viscosity at which the flow behaviour of granules in the drum mixer is affected. A Stokes number analysis of the co-linear impact between two surface-wet, elastic granules can be used to determine whether the granules will rebound or adhere after collision. The outcome depends on the ratio of the kinetic energy of the granules to the ratio of the energy absorbed in the collision. The latter is taken to be the energy absorbed by squeezing of the viscous liquid between the granules Žcalculated from Reynolds’ lubrication equation.. In this case, the Stokes number, St D , is given by w8,19,21x: St D s
4r u0 D 9m
,
Ž 2.
where D is the granule diameter. There is a critical value of the Stokes number, St )D above which rebound will occur and below which granules will adhere. With low viscosity liquids, the magnitude of St D will be much larger than St )D , and the granular flow will be insensitive to changes in viscosity. With an increase in viscosity, the magnitude of St D will become comparable to St )D , and the granular motion will be affected by the magnitude of the binder viscosity. In the present work, this condition occurred with a binder having a viscosity of 500 mPa s. To utilise Eq. Ž2. in a predictive manner, it is necessary to estimate the magnitude of St )D . Estimates of St )D show it to have a magnitude of order unity w8,19,21x. As suggested by Ennis et al. w8x, 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 mm granules and taking St )D s 1, the critical viscosity for granule adhesion is found to be about 3000 mPa s. Thus, the prediction of the Stokes number analysis that the granular flow will be affected by binders having viscosities approaching this magnitude is in agreement with experiment.
5. Conclusions A study has been made of changing the binder viscosity in the range 20–500 mPa s in the rotating drum granulation 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 in diameter occurred very rapidly by a coalescence mechanism, independent of binder viscosity. Thereafter, enlargement was much slower and the behaviour depended upon the viscosity of the liquid. With the liquids of viscosity F 100 mPa s, classified here as lower viscosity binders, the degree of size enlargement increased with increase in viscosity. A crushing and layering mechanism operated, in which ‘crumb’ accumulated both on the exterior of the granules and on the drum wall. It appears that the ‘crumb’ was formed by abrasive wear at the granule contact surfaces under dynamic loading conditions. With liquids of viscosity 350 and 500 mPa s, classified here as higher viscosity binders, the extent of size enlargement decreased with an increase in viscosity. There was no ‘crumb’ present and growth occurred by coalescence. The effect of increasing the viscosity was to retard the coalescence process. A Stokes number analysis was made of the viscous dissipation of energy within deforming granules during collisions. It provided a qualitative explanation for the change in kinetics and mechanism in size enlargement which occurred with binders of viscosity above 100 mPa s. A second Stokes number analysis was made of the collision of granules containing the higher viscosity binders, in which the granules were modelled as elastic surface-wet spheres. It was concluded that the slower speed of granular motion observed with the highest viscosity binder could be accounted for by dissipation of impact energy by viscous flow of the liquid squeezed between granules.
Acknowledgements The authors acknowledge the earlier contributions of two University of Surrey, UK, undergraduates, David Marshall and Christian Bracken in the planning of this work, and of Dr. Stefaan Simons Žnow of University College London, UK. who carried out some of the preliminary
P.J.T. Mills et al.r Powder Technology 113 (2000) 140–147
experiments. They also acknowledge useful comments made by the referees. The experimental work was carried out in the Department of Chemical and Process Engineering at the University of Surrey and supported by a joint grant from the EPSRC Specially Promoted Programme in Particulate Technology ŽGRrG56256. and Unilever Research Port Sunlight Laboratory, UK.
References w1x C.E. Capes, Particle Size Enlargement, Elsevier, New York, 1980. w2x P.J. Sherrington, R. Oliver, Granulation, Heydon & Son, London, 1981. w3x C.E. Capes, P.V. Danckwerts, Trans. Inst. Chem. Eng. 43 Ž1965. T116. w4x P.B. Linkson, J.R. Glastonbury, G.J. Duffy, Trans. Inst. Chem. Eng. 51 Ž1973. 251. w5x D.M. Newitt, J.M. Conway-Jones, Trans. Inst. Chem. Eng. 36 Ž1958. 422. w6x P.C. Kapur, W. Fuerstenau, Trans. AIME 229 Ž1964. 348. w7x M.F. Aulton, Proc. Int. Conf. Fluid. Technol. Pharm. Manuf., Powder Advisory Centre, London, 1982, p. 1.
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w8x B.J. Ennis, G. Tardos, R. Pfeffer, Powder Technol. 65 Ž1991. 257. w9x M.J. Adams, C. Thornton, G. Lian, First international particle technology forum, AIChE Ž1994. 220. w10x A.A. Adetayo, J.D. Litster, S.E. Pratsinis, B.J. Ennis, Powder Technol. 82 Ž1995. 37. w11x J.D. Litster, R. Sarwono, Powder Technol. 88 Ž1996. 165. w12x S.M. Iveson, J.D. Litster, B.J. Ennis, Powder Technol. 88 Ž1996. 15. w13x S.J.R. Simons, J.P.K. Seville, M.J. Adams, Proc. 6th. Int. Symp. Agglom., Nagoya Ž1993. 117. w14x S.T. Keningley, P.C. Knight, A.D. Marson, Powder Technol. 91 Ž1997. 95. w15x G.I. Tardos, M. Irfan Kkan, P.R. Mort, Powder Technol. 94 Ž1997. 245. w16x S.M. Iveson, J.D. Litster, AIChE J. 44 Ž1998. 1510. w17x S.M. Iveson, J.D. Litster, Powder Technol. 99 Ž1998. 234. w18x S.M. Iveson, J.D. Litster, Powder Technol. 99 Ž1998. 243. w19x J.P.K. Seville, U. Tuzun, R. Clift, The Processing of Particulate Solids, Chapman & Hall, London, 1997, p. 116. w20x D.J. Parker, A.E. Dijkstra, T.W. Martin, J.P.K. Seville, Chem. Eng. Sci. 52 Ž1997. 2011. w21x G. Barnocky, R.H. Davis, Phys. Fluids 31 Ž1988. 1324. w22x A.A. Adetayo, J. Ennis, AIChE J. 43 Ž1997. 927. w23x P.C. Kapur, Adv. Chem. Eng. 10 Ž1978. 55. w24x M.A. Mullier, J.P.K. Seville, M.J. Adams, Powder Technol. 65 Ž1991. 321.
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 b
School of Chemical Engineering, UniÕersity of Birmingham, Edgbaston, Birmingham B15 2TT, UK 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 of a large number of constituent Ž‘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 out in both low and high shear mixers w1,2x. 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 Birmingham, Edgbaston, Birmingham B15 2TT, UK. Tel.: q44-121-414-5322; fax: q44-121-414-5377. E-mail address: [email protected] ŽJ.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 agglomerating 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 trialand-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 kinetics, particularly in the classical work of Capes and Danckwerts w3x, Linkson et al. w4x, Newitt and Conway-Jones w5x and Kapur and Fuerstenau w6x, as summarised in Table 1. The microscopic origins of agglomeration have been described by Capes w1x and Sherrington and Oliver w2x. Much of the earlier work was done with low viscosity Žca. 1 mPa s. aqueous binders and the literature emphasises the effect of binder surface tension on agglomeration behaviour. Capes and Danckwerts w3x, 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 was less than 460 N my2 , while Aulton w7x 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. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 2 2 4 - 2
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Table 1 Summary of published literature on tumbling drum granulation Authors
Drum diameter Žm.
Liquidr solid ratio Žvrv %.
Composition of constituent particles
Mean size Žmm.
Size distribution
Composition of binder
Surface tension ŽmN my1 .
Viscosity ŽmPa s.
Newitt and Conway-Jones w5x
0.46
Water
73
ca. 1
0.23
Water
73
ca. 1
Linkson et al. w4x
0.23
Ethanol Water
23 73
ca. 1 ca. 1
Simons et al. w13x
0.40
Narrow Narrow Narrow Wide Wide Wide Wide Wide Narrow Narrow Narrow Narrow Narrow Wide Narrow Narrow Narrow Narrow Narrow Wide Wide Narrow
ca. 1
Capes and Danckwerts w3x
218 70 29 58 18 ca. 50 ca. 20 ca. 10 165 138 97 70 49 Mixtures 214 163 96 67 48 ca. 20 ca. 10 65
73
0.30
Silica sand Silica sand Sand silt Sand silt Sand silt Calcium carbonates
Water
Kapur and Fuerstenau w6x
50–55 57–72 70 32–48 39–56 44–47 46–50 46–50 – – 64–79 60–74 68–88 – – 62 67 72 68 55 44–51 50
Silicone oil
20
20–500
Silica sands
Silica sands
Glass spheres
theoretical and observational w8–19x. It is straightforward to show that if the co-linear impact velocity between two rigid spherical particles coated with a thin layer of a viscous liquid exceeds a certain value, the dynamic force arising from the squeeze flow of the liquid film exceeds the static force due to the surface tension w19x. However, whether or not a particle impacting on a wet surface, or another wet particle, will be ‘captured’ depends not on the instantaneous force acting between them, but on the initial kinetic energy and the energy dissipated in the collision. In practice, it is difficult to apply these concepts to agglomeration processes because it is difficult to measure w20x, or to estimate theoretically, the impact velocity between particles. It is also difficult to express the energy dissipated in collisions in terms of fundamental parameters. Ennis et al. w8x considered the co-linear collision of elastic granules coated with a layer of a viscous liquid and employed the formulation of Barnocky and Davis w21x, in which the ratio of the kinetic energy of the colliding granules to the energy dissipated in the liquid layer was represented by a Stokes number. This treatment does not, however, account for dissipation within deformable granules by frictional and viscous processes w9,12,14–18,22x. This source of energy dissipation may be more important than that in a liquid layer at the surface of granules. As well as affecting the probability of coalescence, the binder viscosity, if sufficiently large, may also determine the rate of consolidation w8,12,14,16,18x and the impact strength w9,17x. The recent studies on drum granulation by Iveson et
al. w12x, Iveson and Litster w18x and Simons et al. w13x showing the effects of binder viscosity on granule compaction and growth are particularly relevant, as is the proposal by Iveson and Litster w16x of a regime map for granulation. This paper presents the results of a study of the effects of changing the binder viscosity on agglomeration of an irregularly shaped sand using a rotating drum granulator. Silicone binders were used, which had a viscosity considerably greater than that of the binders used in much previous work. Silicone fluids are expected to wet the solid well. The size of the solid used and the surface tension of the binders were such that the ratio of the surface tension to particle size was well below the limit for the formation of granules reported by Capes and Danckwerts w3x for low viscosity systems. The paper aims to explore further the influence of binder viscosity on the granule growth process and on granule physical properties.
2. Materials and methods Experiments were carried out with an irregularly shaped silica sand of sieve size range 90–180 mm. The polyŽdimethylsiloxane. silicone oils had low volatilities. At 258C, their viscosities were in the range 20–500 mPa s and their surface tension was 20 mN my1 . The stainless steel batch granulating drum had an internal diameter of 400 mm and was 100 mm deep. The front
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cover could be removed and a transparent viewing window incorporated. The drum revolved at 29 rpm, with its axis horizontal and included two diametrically opposed triangular baffles, each 7 mm in height, to assist the tumbling of the charge during rotation. The drum was operated under lightly loaded conditions. The binder was premixed with the solid in a planetary mixer, in batches of 100 g, to form a wet crumbly mass. The wet solid was passed through a 4.75 mm width sieve and was then charged directly to the drum without intermediate storage. The liquid to solid ratio by weight was 0.225:1, equivalent to a liquid to solid ratio by volume of approximately 0.5:1. After a period of tumbling, measured by the number of revolutions, the contents were removed from the drum. Image analysis was subsequently conducted to determine the total number of granules present, the granule size distribution Žexpressed in terms of the diameter of the circle having the same projected area as the particle., and circularity of the granules Žratio of perimeter of the granules to the perimeter of the circle with the same projected area.. The number mean granule diameter was found to be reproducible to within approximately "0.5 mm. Growth mechanisms were investigated by microscopic examination of sectioned granules formed after different mixing times. The deformation behaviours and fracture strengths of individual granules were measured by diametral compression at a velocity of 5 mm miny1 .
3. Results 3.1. Extent of granulation Microscope examination of the feed material charged to the drum showed that it consisted of loose flocs of adhering constituent particles. On drum mixing, these flocs formed small granules which themselves coalesced rapidly, within 50 drum revolutions, to give rounded millimetre-size granules, having a mean size of the order of 5 mm. It was
Fig. 1. Granulation of sand with binders of different viscosity of granule number mean diameter with number of drum revolutions.
Fig. 2. Variation of granule growth rate with binder viscosity.
not possible quantitatively to characterise the change in size and morphology of the loose flocs as they coalesced to give discrete granules. This was because the flocs adhered to each other and, consequently, discrete granules could not be identified. In contrast, the millimetre-size granules were clearly discrete and their size distribution and shape could be determined without ambiguity. On continued mixing, size enlargement occurred, the extent of which varied with the viscosity of the binder. Fig. 1 shows how the number mean diameter varied with the number of drum revolutions Žmixing or residence time. for the different binder viscosities. The dependence of number mean diameter on drum revolutions can be represented by a linear relationship, in which the gradient of the lines can be taken to be a granule growth rate. Fig. 2 shows how the granule growth rate varied with binder viscosity. It is evident that the most rapid rate of growth occurred with a binder having a viscosity of about 100 mPa s. The rate of growth was similar with the 20 and 350 mPa s binders and was small with the 500 mPa s binder. For convenience, binders of viscosity F 100 mPa s will, henceforth, be referred to as ‘lower viscosity’ binders and binders of viscosity ) 100 mPa s will be referred to as ‘higher viscosity’ binders. With the lower viscosity binders Ž20 and 100 mPa s., sub-millimetre ‘crumb’ was present. Also with these binders, material adhered to the wall of the drum. The quantity of material adhering increased with mixing revolutions; for example, with the 100 mPa s binder, this proportion had increased to 18% by weight after 300 revolutions. In contrast, with the higher viscosity binders Ž350 and 500 mPa s., there was no ‘crumb’, and no material adhered to the walls of the drum. The nature of the axial and radial components of the motion of the granules in the drum was seen visually to be affected by binder viscosity. With the binder of highest viscosity Ž500 mPa s., the speed of motion of the granules was slower than that with the lower viscosity binders. Independent of viscosity, dynamic segregation by size was evident, with the lower part of the drum containing a higher than average proportion of larger granules.
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Fig. 3. Granule size distributions after different numbers of drum revolutions: Ža. binder viscosity: 100 mPa s; Žb. binder viscosity: 500 mPa s.
Fig. 4. Photomicrographs of granules: Ža. section of a granule formed with a binder of viscosity 100 mPa s after 100 revolutions Žgranule diameter 6 mm.; Žb. granules formed with a binder of viscosity 500 mPa s after 100 revolutions Žbar s 5 mm..
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Fig. 5. Circularity as a function of number of drum revolutions for granules formed from binders with viscosities of 100 and 500 mPa s.
3.2. Size distributions Fig. 3a and b show size distributions by number, expressed in non-dimensional form by normalising with respect to the median size, for granules obtained with the 100 and 500 mPa s binders, respectively. These curves do not include the ‘crumb’ because it adhered to other agglomerates and it cannot be satisfactorily analysed. The distributions are quite narrow: with the 100 mPa s binder, 90% of the distribution lay within the range 0.7–1.3 times the mean diameter. The data appear to show ‘self-preserving’ character, but too much significance should not be attached to this observation. Self-preserving data have been reported previously for drum granulation with very low viscosity binders w3–6x. Since, theoretically, growth by both the crushing and layering and by the coalescence mechanisms can give self-preserving size distributions, this characteristic alone cannot be used to identify the dominant growth mechanism w23x.
After 100 revolutions, granules made from the lower viscosity binders had an outer layer of closely packed constituent particles, surrounding the porous centre ŽFig. 4a.. With continued mixing, the layered morphology remained, but the voids at the centre were eliminated by 300 revolutions These observations are consistent with growth by a layering mechanism in which crushed or abraded ‘crumb’ is built up on the granule surface. The granules became increasingly spherical with increasing mixing time, quantified by the measured circularities ŽFig. 5.. Granules made from the higher viscosity binders did not contain layered material at their surfaces and the circularity values were less than those of granules made with lower viscosity binders ŽFig. 5.. Incompletely coalesced dumb-bell-shaped granules were present, as illustrated in Fig. 4b. These observations are consistent with the absence of ‘crumb’ and with Žslow. growth by a coalescence mechanism. 3.4. Granule strengths
3.3. Mechanisms of growth
The force to fracture individual granules was measured by diametral crushing at a compression velocity of 5 mm miny1 . The granules deformed inelastically and fractured into fragments at a strain of between 5% and 10%. Extensive measurements were made to determine the dependence of fracture force on granule size, residence time in the mixer and binder viscosity. Typical data are shown in Fig. 6, in which the fracture force is plotted as a function of the granule size. The fracture force was found to be proportional to the granule diameter to a power of 1.6–2.0. Consequently, if the nominal fracture stress is taken to be proportional to the fracture force divided by the cross-sectional area of the granules, the nominal fracture stress is nearly independent of granule size. The data in Fig. 6 make a comparison of the effect of binder viscosity on fracture force. It is evident that the fracture force is not sensitive to binder viscosity within
In order to gain a more detailed understanding of the development of morphology and, hence, of the mechanisms of growth, granules were sectioned and examined under an optical microscope. When granules prepared after 50 drum revolutions were examined, they could be seen to be composed of partially coalesced small granules having a size of about 0.5 mm. The initial, rapid, growth thus appeared to be similar to that reported previously with binders of low viscosity, and which has been categorised as random coalescence w1–6x. With the lower viscosity binders, the degree of coalescence was such that the granules contained an appreciable volume of irregularly shaped voids of size of the order of 1 mm. Small Ž1–2 mm. granules did not, however, contain such macroscopic voids. With the higher viscosity binders, the small granules were coalesced to a greater degree, so that the volume of voids was small.
Fig. 6. A double logarithmic plot of compressive fracture force as a function of granule diameter for granules formed from binders with viscosities of 100 and 500 mPa s.
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this range. This type of fracture test is quasi-static and, hence, it can be argued that the results should not be sensitive to viscosity. Recently published results for impact strength of agglomerates show strong viscosity effects w17x. The presence of macrovoids within granules formed after a low number of revolutions was found, however, to give granules which were weaker than those formed after a large number of revolutions. The data in Fig. 6 show that the fracture force for granules made after 300 revolutions with the 100 mPa s binder was approximately 30% higher than that after 50 revolutions ŽFig. 6.. The nominal fracture stress was of the order of 15 kPa. Thus, a pile of granules resting under gravity would need to be about 1.5 m high to cause complete fracture. This suggests that complete crushing in the mixer is unlikely. However, abrasive wear can be expected to occur during oblique impacts, particularly those at low angles of incidence w24x. Note also that the wear rate of agglomerates containing a solid binder was found to correlate w24x with the reciprocal of the critical strength intensity factor determined from a fracture test.
4. Discussion 4.1. OÕerÕiew of main features The study has revealed a number of features that need to be accounted for by mechanistic models. Before attempting this, we will briefly state the main results. The primary aim of the investigation was to establish the influence of the viscosity of the binder on a small scale drum agglomeration process for a single size and type of solid. The solid used was fairly coarse and the observed behaviour is likely to be different from that with much finer solids. The results show that the viscosity affects both the rate of size enlargement and the morphology of the granules. By inference, therefore, it affects the mechanism. As has been already stated, with lower viscosity binders Žviscosity F 100 mPa s., ‘crumb’ was present and growth occurred by layering. For these binders, the growth rate increased with increasing binder viscosity. With higher viscosity binders Žviscosity ) 100 mPa s., ‘crumb’ was not present and growth occurred by coalescence. For these binders, the growth rate decreased with increasing binder viscosity. The granular motion within the drum was also affected by binder viscosity. The binder with the highest viscosity Ž500 mPa s. resulted in a granular motion within the agglomerator that was slower than that with the other binders. 4.2. Stokes number analysis of the granule strength Granules in the drum agglomerator were subjected to both slow compressive and impact loading. The relative importance of these is not established. However, the ag-
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glomeration process only occurs when granules move and interact dynamically with each other. It is reasonable, therefore, to presume that impact loading behaviour is critical. Because most impacts are oblique, frictional shearing and rolling behaviours are important. For granules to form, they must have sufficient strength to withstand the impacts without attriting excessively or breaking completely. In the collisions, energy is dissipated within the granules as they deform by friction between the constituent Žprimary. particles. Note that the friction occurs as a consequence of normal forces between the particles arising from the loading of the impacted granules, augmented by the negative capillary pressure Žproduced by the surface tension.. Provided the binder is sufficiently viscous, energy may also be dissipated by viscous flow. Capes and Danckwerts w3x found experimentally that, with binder liquids of low viscosity Žca 1 mPa s., surface tension forces dominated and that granules could only be formed provided the ratio of liquid surface tension to the size of the constituent particles was more than a critical value of 460 N my2 . For the binder used here, this corresponds to a value of 43 mm, which is considerably smaller than the size range of the particles used. The observation, that granules could be formed, indicates that the viscous forces must have been more important than surface tension forces in determining the impact strength of granules in collisions. When a granule is subjected to impact loading, the binder is forced to flow within the granule, dissipating energy. The magnitude of the energy dissipation increases with granule density, impact velocity, binder viscosity and with decrease in the size of the pores, formed by the pore space between the particles within the granule. The size of the pores is linearly related to a suitable average size of the constituent particles. Keningley et al. w14x made a simple analysis which led to the definition of a viscous Stokes number, St d , characterising the ratio of the inertial energy on impact to the viscous dissipation of energy within the granules: St d s
4r u0 d 9m
,
Ž 1.
where r , 2 u 0 , and d are the granule density, collision velocity and diameter of the constituent particles, respectively, and m is the binder liquid viscosity. We suggest that there is a critical value of the Stokes number, St )d , below which breakage and abrasive wear are not significant and above which granule breakage and abrasive wear occur, forming the ‘crumb’. In practice, there is a distribution of collision velocities. In low velocity collisions, granules will remain intact, while above a certain velocity, fragmentation will occur. Hence, both fragmentation and growth by layering will occur in parallel. With an increase in the viscosity, the probability of fragmentation is reduced and, consequently, there is an increase in the net growth rate.
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Above a certain critical viscosity, St d will always be less than St )d . Fragmentation then no longer occurs. Under these conditions, ‘crumb’ is not formed. Consequently, growth can only occur by a granule coalescence mechanism. In the present work, the critical viscosity was evidently of the order of 100 mPa s. It is also to be expected that the growth rate by coalescence should decrease with increasing binder viscosity. Coalescence requires a large amount of granule deformation, which will be opposed by binders of high viscosity. The deformation causes dilation of the packing of the constituent particles, which will cause liquid binder to be ‘sucked in’ to fill the increase in voidage. A binder of high viscosity will retard both this dilation and also the expression of liquid to the granule surface, which occurs in the subsequent consolidation of the constituent particles. 4.3. Stokes number analysis of the granular motion Considerable deformation must have occurred in the rapid coalescence stage Žwhich occurred within 50 drum revolutions.. Following this stage, with higher viscosity binders for which fragmentation did not occur, the granules presumably deformed to only a small extent in the majority of single collisions. It may be appropriate, therefore, to model these granules as surface-wet elastic spheres and thereby to determine the critical viscosity at which the flow behaviour of granules in the drum mixer is affected. A Stokes number analysis of the co-linear impact between two surface-wet, elastic granules can be used to determine whether the granules will rebound or adhere after collision. The outcome depends on the ratio of the kinetic energy of the granules to the ratio of the energy absorbed in the collision. The latter is taken to be the energy absorbed by squeezing of the viscous liquid between the granules Žcalculated from Reynolds’ lubrication equation.. In this case, the Stokes number, St D , is given by w8,19,21x: St D s
4r u0 D 9m
,
Ž 2.
where D is the granule diameter. There is a critical value of the Stokes number, St )D above which rebound will occur and below which granules will adhere. With low viscosity liquids, the magnitude of St D will be much larger than St )D , and the granular flow will be insensitive to changes in viscosity. With an increase in viscosity, the magnitude of St D will become comparable to St )D , and the granular motion will be affected by the magnitude of the binder viscosity. In the present work, this condition occurred with a binder having a viscosity of 500 mPa s. To utilise Eq. Ž2. in a predictive manner, it is necessary to estimate the magnitude of St )D . Estimates of St )D show it to have a magnitude of order unity w8,19,21x. As suggested by Ennis et al. w8x, 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 mm granules and taking St )D s 1, the critical viscosity for granule adhesion is found to be about 3000 mPa s. Thus, the prediction of the Stokes number analysis that the granular flow will be affected by binders having viscosities approaching this magnitude is in agreement with experiment.
5. Conclusions A study has been made of changing the binder viscosity in the range 20–500 mPa s in the rotating drum granulation 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 in diameter occurred very rapidly by a coalescence mechanism, independent of binder viscosity. Thereafter, enlargement was much slower and the behaviour depended upon the viscosity of the liquid. With the liquids of viscosity F 100 mPa s, classified here as lower viscosity binders, the degree of size enlargement increased with increase in viscosity. A crushing and layering mechanism operated, in which ‘crumb’ accumulated both on the exterior of the granules and on the drum wall. It appears that the ‘crumb’ was formed by abrasive wear at the granule contact surfaces under dynamic loading conditions. With liquids of viscosity 350 and 500 mPa s, classified here as higher viscosity binders, the extent of size enlargement decreased with an increase in viscosity. There was no ‘crumb’ present and growth occurred by coalescence. The effect of increasing the viscosity was to retard the coalescence process. A Stokes number analysis was made of the viscous dissipation of energy within deforming granules during collisions. It provided a qualitative explanation for the change in kinetics and mechanism in size enlargement which occurred with binders of viscosity above 100 mPa s. A second Stokes number analysis was made of the collision of granules containing the higher viscosity binders, in which the granules were modelled as elastic surface-wet spheres. It was concluded that the slower speed of granular motion observed with the highest viscosity binder could be accounted for by dissipation of impact energy by viscous flow of the liquid squeezed between granules.
Acknowledgements The authors acknowledge the earlier contributions of two University of Surrey, UK, undergraduates, David Marshall and Christian Bracken in the planning of this work, and of Dr. Stefaan Simons Žnow of University College London, UK. who carried out some of the preliminary
P.J.T. Mills et al.r Powder Technology 113 (2000) 140–147
experiments. They also acknowledge useful comments made by the referees. The experimental work was carried out in the Department of Chemical and Process Engineering at the University of Surrey and supported by a joint grant from the EPSRC Specially Promoted Programme in Particulate Technology ŽGRrG56256. and Unilever Research Port Sunlight Laboratory, UK.
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w8x B.J. Ennis, G. Tardos, R. Pfeffer, Powder Technol. 65 Ž1991. 257. w9x M.J. Adams, C. Thornton, G. Lian, First international particle technology forum, AIChE Ž1994. 220. w10x A.A. Adetayo, J.D. Litster, S.E. Pratsinis, B.J. Ennis, Powder Technol. 82 Ž1995. 37. w11x J.D. Litster, R. Sarwono, Powder Technol. 88 Ž1996. 165. w12x S.M. Iveson, J.D. Litster, B.J. Ennis, Powder Technol. 88 Ž1996. 15. w13x S.J.R. Simons, J.P.K. Seville, M.J. Adams, Proc. 6th. Int. Symp. Agglom., Nagoya Ž1993. 117. w14x S.T. Keningley, P.C. Knight, A.D. Marson, Powder Technol. 91 Ž1997. 95. w15x G.I. Tardos, M. Irfan Kkan, P.R. Mort, Powder Technol. 94 Ž1997. 245. w16x S.M. Iveson, J.D. Litster, AIChE J. 44 Ž1998. 1510. w17x S.M. Iveson, J.D. Litster, Powder Technol. 99 Ž1998. 234. w18x S.M. Iveson, J.D. Litster, Powder Technol. 99 Ž1998. 243. w19x J.P.K. Seville, U. Tuzun, R. Clift, The Processing of Particulate Solids, Chapman & Hall, London, 1997, p. 116. w20x D.J. Parker, A.E. Dijkstra, T.W. Martin, J.P.K. Seville, Chem. Eng. Sci. 52 Ž1997. 2011. w21x G. Barnocky, R.H. Davis, Phys. Fluids 31 Ž1988. 1324. w22x A.A. Adetayo, J. Ennis, AIChE J. 43 Ž1997. 927. w23x P.C. Kapur, Adv. Chem. Eng. 10 Ž1978. 55. w24x M.A. Mullier, J.P.K. Seville, M.J. Adams, Powder Technol. 65 Ž1991. 321.