- Email: [email protected]
Liquid-bound granule impact deformation and coefficient of restitution
| ELSEVIER
Powder Technology 99 (1998) 234-242
Liquid-bound gr ule impact deformation and coefficient of restitution S.M. Iveson *, J.D. Litster 1 Centrefor MultiphaseProcesses, Departmentof Chemical Engineering, Universi~. of Queensland, St. l~wia, QLD 4072, Australia Received 20 August 1997; received in revised lbrm 3 June 1998
Abstract The impact behaviour of liquid.bound granules and pellets was studied using a novel but simple experimental technique. Cylindrical pellets (20 mm diameter and 25 mm long) were made from 10, 19, 31, 37 and 60 tim glass ballotini with a range of binders (water, surfactant solutions and glyceroi) and binder contents (0.,0 to 0.55 m"~binder/m "~solid). These pellets were dropped from heights of 10 to 30 cm and the amount of impact deformation measured. Impacts were mostly plastic with a coefficient of restitution less than 1%. The energy conservation model of Hawkyard [J.B. Hawkyatd, A theory for the mushrooming of flat-ended projectiles impinging on a flat rigid anvil, using energy considerations, Int. J. Mech. Sci. I I (1969) 313-333] for rigid-plastic materials was used to calculate the pellet's dynamic yield stress (Y) from the size of the deformed area. When water was used, Y increased exponentially with decreasing surface mean particle size. However, when glycerol was used, particle size had no measurable effect on Y in the range of conditions studied. Increasing binder viscosity and increasing binder surface tension both increased Y.The effect of binder content varieduincreasing the amount of a viscous binder (glycerol) increased F throughout the range of conditions studied, whereas when a low-viscosity binder (water) was used, g passed through a maximum. Hence, there are (at least) three energy dissipation mechanisms that control impact deformation. These are due to inte~article friction, capillary and viscous forces. The effect of varying binder content in a particular system cannot be predicted a priori, unless the balance between these three mechanisms is known. Measurements of granule deformation must be made at high strain rates if dynamic effects are to be accounted for. The simple technique developed has the potential for being used to characterise different formulations in order to better predict their granulation b.haviour. © 1998 Elsevier Science S.A. All rights reserved. geywo~s: Granulation: Agglomeration: Impact deformation: Coefficient of restitution: Dynamic yield stress: Viscous dis~ipatiomCapillary forces
1, Introduction Granulation is the process of agglomerating particles together into larger, semi-permanent aggregates by spraying a liquid binder onto the particles as they are agitated in a tumbling drum, fluidised bed, high shear mixer or similar device. The liquid binds the particles together by a combination of capiilary pressure, surface tension and viscous forces until more permanent bonds are formed by subsequent drying or sintering. Some advantages of agglomerated materials include improved flow properties, reduced dustiness, increased bulk density and the co-mixing of particles which would otherwise segregate. Improper granulation causes problems in down stream processes such as caking, segregation and poor tableting performance. However, in spite of its importance and over 40 years of research, it is still impos* Com~ponding author. Centre for Multiphase Processes, Department of Chemical Engineering, University of Newcastle, Callaghan, NSW 2308, Australia. Tel.: +61~2-49-215.684; Fax: +61-2-49-601-445; E-mail: [email protected] ' E-mail: j.fitstei~cheque.uq.oz.au
sible to quantitatively predict the growth behaviour of a new formulation from only a knowledge of its fundamental properties. It has long been accepted that granule deformability has a strong influence on granule growth behaviour [2,3]. During collisions, granules that deform easily will form a larger area of contact as they dissipate the collision energy. This produces a stronger bond which is more likely to survive subsequent collisions and results in successful granule coalescence. On the other hand, strong, non-deformable granules only form a small area of contact that will be easily broken apart by subsequent collisions. Coarse, narrowly sized particles produce weak, deformable granules that tend to grow quite quickly by rapid coalescence or crushing and layering [4]. In contrast, fine, widely sized particles produce strong, nondeformable granules. These systems initially grow slowly (possibly having a period of zero growth) and only grow rapidly by coalescence if their surfaces become saturated [5 ]. The earliest model of granule strength was the theory of Rumpf [ 6] who considered granules to fail by sudden rupture
0032-591019815 - see front matter © 1998 Elsevier Science S.A. All fights reserved. PIi S 0 0 3 2 - $ 9 1 0 ( 9 8 ) 0 0 1 1 5 - 6
S.M. Iveson, J.D. Litster / Powder Technology 99 (1998) 234-242
of liquid bridges across the granule diameter. Granule tensile strength (tr,) was given by the equation: t r , = S . C 1 - e ),cos(0)
e
( 1)
dp
where S is granule liquid saturation, C is a constant (C = 6 for monosized spheres), e is granule porosity, ), is liquid surface tension, 0 is the liquid-solid contact angle, and dp is surface mean particle size. This equation successfully predicts the tensile strength of compacts made from relatively coarse, narrowly sized particles with nonviscous binders [4,6,7]. However, Rumpf's equation underpredicts the strength of compacts made from fine, widely sized particles. Kristensen et al. [3] showed that interparticle friction forces are also significant. Friction forces are partially linked to capillary forces since the capillary forces causes the normal force at points of interparticle contact. However, although increasing liquid saturation increases capillary forces, it can actually decrease interparticle friction due to the lubrication effect of the liquid at interparticle contacts. Hence, the effect of liquid content can vary depending on the balance between these two forces. For instance, the strength of compacts made from glass ballotini has been found to increase with increasing liquid content, whereas the strength of compacts of fine, irregularly shaped dicalcium phosphate particles decreased with increasing liquid content [ 3]. More recently, Iveson et ai. [ 8 ] studied the effect of binder viscosity on granule consolidation rates in a tumbling drum and found that viscous forces were also important. Increasing the amount of a low-viscosity binder increased the extent of consolidation (due to the lubrication effect), whereas increasing the amount of a high-viscosity binder decreased the extent of consolidation (due to increased viscous forces). Therefore, unless the relative magnitude of viscous, capillary and interparticle friction forces is known, the effect of varying binder content in a given system cannot be predicted a priori, even qualitatively. There have been two attempts in the literature to model granule coalescence. Ouchiyama and Tanaka [2] modelled granules as surface-dry, plastic or elastic spheres. They considered the forces exerted on granules as they collided and used bulk properties of the particle-binder mixture to describe the granules. Kfistensen et al. [3] extended their work and determined that the maximum size for successful granule coalescence, 8 (i.e., the average size of granules above which coalescence will not occur due to the large torque experienced by the pair as they tumble in the granulator), was: 8 2/" - Al~r Orcr
(2)
where A is a dimensional constant independent of granule size, a is a parameter describing the nature of the deformation (a = 1/4 for plastic materials, a = 1/3 for elastic materials),
235
and tr, and icr are the critical stress and strain at failure for the wet particulate material during compressive testing. Hence a granule's ability to deform has a major influence on coalescence behaviour. Both o'er and 1~ are significantly affected by the porosity and liquid content of the wet particle compact. Critical stress may either increase or decrease with increasing liquid content and always increases with decreasing porosity (discussi, ,n above). Critical strain appears to always increase with liquid saturation regardless of whether or not capillary or frictional forces dominate (cf. limestone compacts of Schubert et al. [7], with dicalcium phosphate compacts of Holm et al. [9] ). Hence, although this model gives useful insights into coalescence behaviour, it is difficult to apply to real systems where consolidation of the tumbling granules causes their porosity and liquid saturation to change with time. This model also does not predict how different granule and liquid properties, such as binder viscosity and particle size, will affect coalescence behaviour, even though it is known that these do affect the rate of granule consolidation [ 8 ] and hence must effect granule coalescence. Ennis et al. [ 10] modelled granule coalescence based on the assumption that granules were elastic spheres with surface layers of a viscous binder. They assumed that successful coalescence occurred when the viscous dissipation in the liquid layer and elastic losses in the solid were sufficient to prevent the granules bouncing apart after impact. They derived their model in terms of energies and used individual properties of the particles and binder, rather than bulk properties of the particle-liquid mass. Their work is important for two reasons: ( 1) it is the first to consider viscous dissipation, and (2) it is the first to use energies rather than forces. Experimental work measuring dynamic pendular liquid bridge strengths [ 11 ] has found that viscous forces can be much greater than capillary forces. This finding is supported by the results of computer simulations of aggregate collisions by Adams et al. [ 12 ] who found that viscous and interparticle friction energy dissipation were much greater than capillary bridge rupture energies. However, these findings are challenged by Simons et al. [13] who claim that liquid-bridge rupture (capillary) forces are most important and that these explain the results of their drum granulation experiments. Iveson et al. [8] studied the effect of liquid viscosity on the consolidation of granules in a tumbling drum. They found that increasing binder viscosity significantly decreased the rate of granule consolidation. This suggests that binder viscosity would also affect granule deformation during single impacts. Therefore there is a need for an experimental investigation to establish the effects of viscous and capillary tbrces on granule impact deformation behaviour. However, the literature contains no experimental studies of the effects of binder viscosity on granule strength. Traditionally, properties such as critical stress and strain have only been measured at slow and invariant strain rates, well below the rate of strain occurring during granule impacts. Hence, dynamic effects such as
S.M. lveson, J.D. Litster / Powder Technology 99 (1998) 234-242
236
Table 1 Properties of the glass ballotini Nominal size
x3,2 ~ (Ixm)
x4.3" (Ixm)
tr+.3" (itm)
tr4,3/x4,3" ( -- )
Dry-tapped porosity b ( -- )
Wet-tapped porosity b ( -- )
90-150 I~m 53--106 tun 44--90 ttm -53 ttm --400 Mesh
60 37 31 19 10
122 71 68 36 28
48 30 20 15 11
0.39 0.42 0.29 0.42 0.39
0.385 + 0,004 0.388 + 0.004 0.380:1:0.004 0.51 4.0.01 0,44 4. 0.01
0.373 + 0.005 0.372 + 0,004 0.367 + 0.004 0.382 + 0,005 0.385 4. 0.005
"Surface mean size (x~.,), mass mean size (x4,3) and mass-mean standard deviation (o'4,.~) measured by Malvem Mastersizer/E. t'Bulk porosities measured by tapping sample in a 30-mm diameter volumetric cylinder,
Table2 Propertiesof the liquidbinders Liquid
Density" (g/ml)
Viscosity h (Pa s)
Surface tension ( m N / m )
Water 50 wt,% Glycerol 85 wl,% Glycerol Glycerol 0,00094 M NDBS solution
0,997 !. 123 !.216 1.256 -
0,0011 0.0054 0.070 I.I -
72" 70 'm 660 63 a 3 I"
"Measuredin 2.~ml specificgravitybottle. ~'Measuredin ConlravesRheomat 115 rheometer.Shearrate was variedbetween20 and 150 s ' for glyceroland between300 and 3650 s - afor water. CMeasuredby the WilhemyPlatemethodusing2 cm squarepiecesof filterpaper. ~FromWeast [ 14]. viscous dissipation in the liquid phase have been overlooked. Furthermore, these traditional testing methods impose a predetermined rate of strain on the granule compact, whereas during real impacts, the rate of strain would vary according to the rate of energy dissipation required to dissipate the kinetic energy of the collision. This paper describes a set of simple impact experiments covering a range of binder viscosities and surface tensions. Two types of experiments were performed: ( ! ) swinging dram-granulated granules into a vertical steel plate to measure the coefficient of restitution, and (2) dropping cylindrical pellets onto a horizontal plate to measure the amount of deformation.
2. Experimental method 2, !. Materials Five sizes of glass ballotini with specific surface mean size of 10, 19, 31, 37 and 60 p,m were used. Their properties are listed in Table I. Glass ballotini were chosen because they are a well-defined system and avoid complications due to solids dissolution. The 19, 3 I, 37 and 60 Ixm baliotini were purchased from Potters Industries (Lot 4 Boundary Rd., Lavetton, Victoria, 3028, Australia) and had a density of 2.45 + 0,01 g/ml and the 10 ttm ballotini was purchased from Cataphote (POBox 2369, Jackson, MS, 39225-2369, USA) and had a density of 2.374-0.01 g/ml (measured by both water-displacement and Helium pycnometry).
Glycerol-water solutions were used to vary liquid viscosity and solutions of the surfactant sodium dodecylbenzene sulphonate (NDBS) were used to vary liquid surface tension. The properties of these solutions are listed in Table 2.
2.2. Horizontal-swing impact experiments Known amounts of glass baliotini and binder were kneaded together in a plastic bag until the binder was evenly distributed throughout the ballotini. This feed was tumbled in a 30cm diameter drum at 20 to 40 rpm for between 5 rain and an hour until granules of a suitable size were formed ( 15 to 25 mm diameter). The time of granulation depended on the binder viscosity and binder content. Typically, glycerolbound granules grew slowly and formed ellipsoidai granules with smooth surfaces whereas water-bound granules grew quickly and formed spherical granules with rough surfaces (Fig. 1 ). Granules were then placed in a specially designed 'cradle' which held them, whilst leaving their front face exposed (Fig. 2). The granule and cradle were then suspended by cotton thread from two hooks in the horizontal-swing impact equipment (Fig. 3). The frame was made from 30-mm-thick Craftwood. A 10-ram-thick, 400-mm-square, stainless-steel plate was bolted to the frame in the vertical position. Granules were released from heights of 5 or 15 cm to swing against the steel plate (giving impact velocities of 1.0 and 1.7 m/s respectively). The rebound height was measured from video footage and used to calculate the coefficient of
237
S.M. lveson, J.D. Litster / Powder Technology 99 (1998J 234-242
Fig. 1. Photo of typical water-bound and glycerol-bound granules showing their deformed face after impact.
Fig. 2. Photo of a water-bound granule held in the specially designed cradle with front face exposed.
restitution (rebound height divided by the initial release height).
The major and minor axis of the deformed face, d, and d2, were measured and the relative increase in the area of the impact face (A~/Ao) calculated from:
2.3. Vertical-drop impact experiments
CottonThread Binder and glass ballotini were again hand-mixed in a plastic bag. This feed was then weighed out into a 20-ram diameter cylindrical press (Fig. 4) to make pellets of height 25 mm, diameter (D) 20 nun and with an average porosity of 41%. These pellets were then dropped from a simple release mechanism (Fig. 5), flat-face first, onto a 10-mm-thick stainless steel plate. Fig. 6 is a side-on photo of some typical pellets after impact. The lower end is deformed greatly whilst the upper end is unaffected. The pellet face was often not parallel to the plate at impact, giving the deformed area an elliptical shape.
:
. /
G~jnule
600mm " ~ ~.. Steel Plate fi00mm
/
Craftwood Frame
-
Fig. 3. Diagram of horizontal-swing impact equipment.
238
S.M. lveson, J.D. Litster / Powder Technology 99 (1998) 234-242
3. Experimental results and analysis
~------ 40
3.1. Horizontal-swing impacts
~ 15
20 1
-~
A total of 169 granules were tested in the horizontal-swing impact tests. Glass ballotini with surface mean size of 37 Izm was granulated with three different binders: water, 50 wt,% glycerol and glycerol, with viscosities of 0.001, 0i005 and 1 Pa s respectively. Binder content was varied between 0.44 and 0.55 ml ofbinder/ml solid. This is the full range of binder contents that could be examined: any lower and well-formed granules were not produced, any higher and the granules grew too quickly and had very rough and irregular surfaces. Fig. 7 shows the coefficient of restitution measured in all the horizontal-swing impact experiments. There is a considerable amount of scatter in the results and no clear effect of binder content or binder viscosity. The low-velocity impacts (1.0 m/s) appear to have a slightly higher coefficient of restitution than the faster impacts (1.7 m/s) as would be expected for plastic materials. However, the main point to note is that the coefficient of restitution is very low (less than 1% in all but one case). Hence, in the range of conditions covered by these experiments, granule impacts were almost entirely plastic.
(variable Spacer
II-' Pellet Chamber
' 40
60
'l :I
Fig. 4, Schematicdiagramof the pellet press.
At
d,d,
Ao
D"
(3)
This is a simplistic measure of deformation which ignores the three-dimensional nature of the deformation. However, the formation of an area of contact between two colliding granules is one of the factors that control whether or not granules will coalesce. Hence this measure should provide some useful information for modeling granule coalescence bchaviour.
3.2. Vertical-dropexperiments A total of 664 cylindrical pellets were tested in the vertical impact experiments. These pellets were made from glass ballotini with surface-mean sizes of 10, 19, 31 and 60 p,m. Three different binders were used: water, glycerol and 0.00094 M NDBS solution. The surface tension of the sodium dodecylbenzene sulphonate (NDBS) solution was 31 nLN/m compared with 72 mN/m for water. Pellet binder content was
z,,/--- Pellet25 x 20
100
Dimensions in nan Not drawn to Scale
I'- 22-I TOP VIEW
SIDE VIEW
Fig. 5. Diagramof release mechanismused to drop pellets.
_l
-i
S.M. lveson, J.D. Litster l Powder Technology 99 (1998) 234-242
0.015
37 l~m Glass Ballotinl Oe Water, Low & High Velocitly V• 50 wt% Glycerol, Low & High Velocity E l • Glycerol, Low & High Velocity O
C: 0
== 0.010
v 0 0
i
v v
"~ 0.005
8
! 0.000
45
Ig. 8 lil :°°" o
e
§
50
55
Granule Moisture (ml liquid/100ml solid)
Fig. 7. Coefficient of restitution vs. granule binder content for all the horizontal-swing impact experiments. Granules were released from heights of 5 and 15 cm giving impact velocities of 1.0 and 1.7 m/s respectively.
varied between 0.39 and 0.54 ml liquid/ml solid. At lower binder contents pellets were too crumbly and at higher binder contents pellets were too 'sloppy' to be handled. Pellets were released from heights of 10, 20 or 30 cm (giving impact velocities of 1.4, 2.0 and 2.4 m/s respectively assuming that friction losses during release and fall were negligible). The results of the vertical drop impact tests were analysed with the model developed by Hawkyard [ 1] for the impact of cylindrical slugs against a rigid target. This mode: uses a conservation of energy approach and assumes the material is rigid plastic with a strain-rate independent dynamic yield stress. The non-elastic assumption is justified by the low coefficient of restitution measured in the swing-impact tests. However, as will be shown, binder viscosity has a significant effect on the amount of impact deformation which suggests that the assumption of strain rate independence may be inaccurate (since viscous effects are inherently strain rate dependant). Nevertheless, this model is a useful starting place for analysis.
239
Most workers studying impact deformation use the reduction in length of the impacting cylinder as a measure of deformation (e.g., [ 1,15 ] ). This was not possible in this case because the pellets often landed at an angle to the vertical and there was no clearly defined final length of the pellet (see Fig. 6). Instead the increase in impact area was used. The deformed face was elliptical in shape, so the major and minor axes were measured and used to calculate the area. For a cylinder of initial area Ao, dynamic yield stress Y, impact velocity Uo and density p, Hawkyard's [1 ] model predicts the deformed contact area A~ will satisfy: ~pU"
LAt-l+ln
(4)
Hence, plotting I/2pU 2 vs. Ao/ A ~- 1+ ln ( A ~/ Ao ) , should give a straight line with slope Y. The dynamic yield stress calculated from the slope of these plots was used to compare the effects of varying particle and liquid properties. A typical example is shown in Fig. 8. There is a clear linear dependence between the two groups. Increasing the velocity of impact increases the amount of deformation. However, the intercept 19 pm Ballotiniwith 0.441 ml/ml Water
~
~ ~ / & & &A
4
0.
~
3
I 0.01
I 0.02
I 0.03
" 0.04
0.05
A0/AI-I+In(AI/A0)
Fig. 8. Plot of l/2pU 2 vs. A . / A s - 1 +In(A~/A.) for pellets of 19 gm ballotini with 0.441 ml water/ml solid. The slope gives the dynamic yield stress.
240
S.M. Iveson. J.D. Litster / Powder Technology 99 (1998) 234--242
does not pass through the origin ~,spredicted by Hawkyard's model. There are two probable reasons for this. Firstly, the pellets did have a small elastic component which would tend to shift the intercept upwards. Secondly, the calculated pellet impact velocities used in these plots may be too high due to frictional losses as the pellets drop from the release mechanism.
1000
i
|
Si,e.Binder i
• 31pm.Water o31pm, Q~y O31pm, NDBS &19pro, Water AI9pm, NDBS
G. W w
m "a 100, o >.
| I | | I
I
E
3.2.1. Effect of liquid content and viscosity Fig. 9 shows the dynamic yield stress vs. liquid content for pellets made from 19 and 31 I~mballotini with water, glycerol or surfactant binders. Using glycerol as the binder liquid (increasing binder viscosity from 0.001 to 1 Pa s) greatly decreased the amount of pellet deformation. This is due to the increase in viscous dissipation as the more viscous binder is squeezed between particles during deformation. The effect of binder content is complex. At low moistures, increasing the amount of water increased the yield stress. However, as water content increased further, the effect reversed and the yield stress dropped. There is a significant range of water contents from 0.45 to 0.50 ml/ml in which the effect of varying water content is minimal. In contrast, when glycerol was used as a binder, the yield stress increased steadily as binder content was increased throughout the range of conditions studied. This variable influence of binder content may be explained by the balance between three forces: interparticle friction, capillary and viscous forces. These forces all resist granule deformation, however, the influence of binder content on these three forces varies. Increasing binder content can reduce interparticle friction due to the lubrication effect [ 3 ]. Increasing binder content increases capillary forces up to the saturation point [4,6], after which granule strength decreases rapidly when the droplet state is reached. Increasing binder content should increase viscous forces since there is a larger amount of binder that needs to be squeezed out from in between particles when deformation occurs. For systems where viscous forces ate small (e.g., water binders), increasing binder content initially causes an increase in capillary forces and hence increases the yield strength of the pellet (cf. the increase in strength when a dry powder is initially moistened). However, eventually, as more binder is added, the reduction in interparticle friction due to lubrication becomes mote significant than any increase in capillary forces and pellet strength decreases (ultimately the system becomes a slurry with no strength). The location of this maximum in yield stress depends on the balance between interparticle friction and capillary forces, which will vary with particle size and roughness [ 3 ]. For systems where viscous forces dominate (e.g., glycerol binder), the increase in viscous forces with increasing binder content outweighs the reduction in interparticle friction. Hence granule yield stress increases. Eventually these systems too would also become slurries and their yield stress would drop, however, this occurs outside the range of binder contents that could be studied.
C
o
' 10 0.38
I 0.42
I
Sirfactant
0.4S 0.SO Binder Content (ml/ml)
J 0.S4
Fig, 9. The dynamic yield stress vs. binder content tor pellets made from 19 and 31 gm ballotini with water, glycerol (Gly.) or surfactant (NDBS) solutions. Error bars show the 95% confidence interval on the yield stress determined from the slope of the plot of 112pU" vs. A,IA~ - 1 + ln(A~/A,).
Hence, the effect of binder content on granule dynamic yield stress cannot be predicted beforehand, even qualitatively, unless the relative magnitude of friction, capillary and viscous forces is known. There is a range of binder contents in which increasing the amount of a viscous binder increases yield stress whereas increasing the amount of a nonviscous binder decreases yield stress. A similar effect was seen by Iveson et at. [ 8] on the minimum porosity reached by tumbling granules--increasing the amount of water increased the extent of consolidation, whereas increasing the amount of glycerol decreased the extent of consolidation.
3.2.2. Effect of liquid surface tension The effect of binder surface tension was studied using 0.00094 M NDBS solutions (surface tension 31 mN/m). Fig. 9 shows that lowering the surface tension decreased the dynamic yield stress of both the 19 and 31 I~m ballotini. This is because lowering binder surface tension reduces the capillary forces holding particles together. Glycerol also has a lower surface tension than water (63 vs. 72 raN/m). However, the expected decrease in yield stress due to its lower surface tension was swamped by the opposing effect of increasing viscosity. This finding is consistent with the measurements of dynamic pendular bridge strength by Ennis et al. [ 11 ], the computer simulations of aggregate collisions by Adams et al. [12] and the granule consolidation studies of Iveson et al. [ 8] which all found that viscous effects can be much greater than capillary forces in dynamic situations.
3.2.3. Effect of particle size In Fig. 9, increasing particle size decreased the pellet yield stress. This is seen more clearly in Fig. 10 which plots yield stress vs. particle size for both water and glycerol binders across a range of particle sizes and binder contents. For water, the yield stress was related to the specific surface mean particle size (dp) according to the equation:
Y=Kexp(-Bdo)
(5)
S.M. h,eson, £D. Litswr / Powder Technology 99 (1998) 234--242 1000
i i Ii t l • . . ,,,.
A ¢1 0,,e v
i i
. . . . . . . . . . . .
.
== • 0A41 rri,'rrt Water
•o .~_ >,, .o
& 0.490 rrUmlWater
100
t
c
-'---~..
0 0.441 rrV~ Glycerol
"'-~.
&0.490 rrgml Glycerol
o 10
I 10
Specific
I .... 20
Surface
;
;
1
!
30
40
50
60
"
M e a n P a r t i c l e S i z e (microns)
Fig. ! 0. Dynamic yield stress vs. surface mean particle size for glass ballotini with water and glycerol L;nders.
where K = 120 4- 70 kPa and B = 0.035 4- 0.02 Ixm-Decreasing particle size decreases the average pore size between particles and increases the volume density of interparticle contacts. This increases both capillary and interparticle friction forces and thus explains why, when water was used as the binder, decreasing particle size increased the yield stress. However, when glycerol was used as the binder, particle size did not have any significantly measurable effect on deformation in the range of conditions examined (Fig. 10). Using glycerol, viscous forces should dominate (Section 3.2.2). According to lubrication theory, viscous forces are inversely proportional to gap distance when squeezing a thin film between two plates [10]. Hence, the decrease in average pore-size was expected to increase the viscous forces and hence increase the yield stress. Thus the observed non effect of particle size was surprising. This non effect is possibly due to the low accuracy when measuring small amounts of deformation (i.e., high yield stresses). This problem has the potential to be overcome in future work by: ( 1 ) increasing the accuracy of measurement (e.g., computer image analysis of the deformed area); and (2) increasing the velocity of impact to increase the amount of deformation (e.g., by 'firing' the pellets at a target).
4. Discussion In the range of conditions investigated, granule impacts were almost entirely plastic. This restricts the range of applicability of the coalescence model of Ennis et al. [ 10] which assumed that granules were hard, elastic spheres. This will only apply in systems where granules dry quickly (e.g., in fluidised beds) or consolidate sufficiently to become strong enough to resist further deformation (e.g., some cases in high shear mixers or after long residence times). More recent coalescence modeling by Ennis and Adetayo [16] has acknowledged this limitation by including an empirical parameter for granule deformability. The present authors have also proposed a granule growth regime map based on the granule dynamic yield stress [ 17].
241
This work demonstrates that viscous dissipation in the binder phase can have a significant effect on impact deformation. Hence, although the model of Ennis et al. is limited in applicability, it is significant because it was the first to consider viscous forces. The earlier work of Ouchiyama and Tanaka [ 2 ] was correct in considering the plastic deformation of granules, but considered only capillary and frictional forces. Any general model of granule coalescence must consider all three forces and be based on dynamic energy dissipation, not just low strain rate static conditions. The effect of particle size (dp) and binder surface tension (y) on dynamic yield stress ( 10 are similar to their effect on the theoretical granule tensile strength (or,) predicted by Rumpf's model (Eq. ( 1 ) )---decreasing d r and increasing y increase both Y and ~. This suggests that granule dynamic yield stress is directly related to granule tensile strength. However, Rumpf's model was a static model which considered only capillary forces. Hence, this model needs to be extended to include interparticle friction and viscous effects. Granule deformation is affected by (at least) three energy dissipation mechanisms, due to interparticle friction, viscous and capillary forces. Unless the balance between these three mechanisms is known, the effect of binder content cannot be predicted beforehand, even quolitatively. This, in part, answers the debate in the literature as to whether viscous or capillary forces are most important. Clearly both can dominate in different situations. ~ : : n viscous binders are used with relatively coarse particles, viscous forces dominate whereas capillary force can dominate when low viscosity binders are used. Hence any general model of granule impact deformation must consider all three of these forces. So far, only the computer simulations of Adams et al. [12] have done so, although whether or not these simulations can predict the complicated effects of binder content remains to be seen. The importance of viscous forces means that experimental testing of granule compacts must be done at high enough strain rates to measure dynamic effects. Conventional methods use only relatively slow and invariant strain rates. Hence new testing procedures will need to be developed, perhaps based on the impact experiment used here. This method is crude, but has the potential to be improved by better controlling and measuring the impact conditions and dimensions of deformation.
5. Conclusions For the first time, the impact deformation of liquid-bound granules and compacts has been measured experimentally using a novel but simple technique. Deformation was measured as the increase in impact area and this was used to calculate the dynamic yield stress (Y) based on the energy conservation model for rigid plastic materials proposed by Hawkyard [ l ]. In the range of conditions covered, impacts were almost entirely plastic with only a very small elastic component (coefficient of restitution less than 1% ).
242
S.M. lveson, J.D. Litster/ Powder Technology 99 (1998) 234-242
~ e n water was used as the binder, Y was related to surface-mean particle size (alp) according to the equation: YffiK e x p ( - B d p )
where K = 120 4- 70 kPa and B - 0.035 4- 0.02 ttm- ~. However, when glycerol was used as the binder, particle size did not have a ~asurably significant effect on Y in the range of c o n ~ o n s examined. Increasing binder surface tension and viscosity both increased ¥. The effect of binder content varied. For highviscosity binders, increasing binder content increased Y throughout the range of conditions measured, whereas for low-viscosity binders, Y passed through a maximum. These results show that there are three energy-dissipation mechanisms that can affect impact deformation, due to interparticle friction, capillary and viscous forces. The effect of binder content on yield stress cannot be predicted a priori unless the balance between these three forces is known. Dynamic effects can dominate when viscous binders are used. This exposes a weakness in conventional measurements of granule properties which use relatively low and invariant strain rates and fail to account for dynamic effects. Any general model of granule deformation and coalescence must take into account both the plastic nature of granules and the importance of dynamic effects such as viscous dissipation. It must include the effects of interparticle friction, capillary and viscous forces and should be able to predict the variable effect of binder content.
Acknowledgements This work has been funded by an Australian Postgraduate Award scholarship and an Australian Research Council Grant (A89600426),
References [1] J.B. Hawkyard, A theory for the mushrooming offlat-ended projectiles impinging on a flat rigid anvil, using energy considerations, Int. J. Mech. Sci. 11 (1969) 313-333. [2] N. Ouchiyama, T. Tanaka, The probability of coalescence in granulation kinetics, I&EC Process Des. Dev. 14 (1975) 286-289. [ 3 ] H.G. Kristensen, P. Holm, T. Schaefer, Mechanical properties of moist agglomerates in relation to granu|ation mechanisms: Part 1. Deformability of moist, densified agglomerates; Part 2. Effects of particle size distribution, Powder Technol. 44 (1985) 227-247. [4] D.M. Newitt, J.M. Conway-Jones, A contribution to the theory and practice of granulation, Trans. I. Chem. Eng. 36 (1958) 422-441. [ 5 ] P.B. Linkson,LR. Glastonbury, G.J. Duffy, The mechanism of granule growth in wet pelletisation, Trans. lnstn. Chem. Engrs. 51 (1973) 251-259. [6] H. Rumpf, The strength of granules and agglomerates, in: W.A. Knepper (Ed.), AIME, Agglomeration, lnterscience, New York, 1962, pp. 379-418. [7l H. Schubert, W. Herrmann, H. Rumpf, Deformation behaviour of agglomerates under tensile stress, Powder Technol. I 1 (1975) 121131. [8 ] S.M. Iveson, J.D. Litster, B.J. Ennis, Fundamental studies of granule consolidation: Part 1. Effects of binder viscosity and binder content, Powder Technol. 88 (1996) 15-20. [9] P. Holm, T. Schaefer, H.G. Kristensen, Granulation in high speed mixers: Part V. Power consumption and temperature changes during granulation, Powder Technol. 43 (1985) 213-223. [ 10l B.J. Ennis, G.I. Tardos, R. Pfeffer, A microlevel-based characterization of granulation phenomena, Powder Technol. 65 ( ! 991 ) 257-272. [ 11 ] BJ. Ennis, J. Li, G.I. Tardos, R. Pfeffer, The influence of viscosity on the strength of an axially strained pendular liquid bridge, Chem. Eng. Sci. 45 (1990) 3071-3088. [ 12] M.J. Adams, C. Thornton, G. Lian, Agglomerate Coalescence, First International Particle Technology Forum, Vol. I, August 17-19, Denver, USA, 1994, pp. 220-224. [ 13l S.J.R. Simons, J.P.K. Seville, M.J. Adams, Mechanisms of agglomeration, 6th Int. Symp. Agglomeration, Nov. 15-17, Nagoya, Japan, 1993, pp. ! 17-122. [ 14] R.C. Weast (Ed.), CRC Handbook of Chemistry and Physics, 62nd Edn., CRC Press, Boca Raton, Florida, 1981-1982. [ 15] G.I. Taylor, The use of flat-ended projectiles for determining dynamic yield stress: 1. Theoretical considerations, Proc. R. Soc. London, Ser. A 194 (1948) 289-299. [161 B.J. Ennis, A.A. Adetayo, Unifying approach to modelling granule coalescence mechanisms, AIChE J. 43 (4) (1997) 927-934. [171 S.M. Iveson, J.D. Litster, A growth regime map for liquid-bound granules, AIChE J. 44 (7) (1998) 1510-1518.
Powder Technology 99 (1998) 234-242
Liquid-bound gr ule impact deformation and coefficient of restitution S.M. Iveson *, J.D. Litster 1 Centrefor MultiphaseProcesses, Departmentof Chemical Engineering, Universi~. of Queensland, St. l~wia, QLD 4072, Australia Received 20 August 1997; received in revised lbrm 3 June 1998
Abstract The impact behaviour of liquid.bound granules and pellets was studied using a novel but simple experimental technique. Cylindrical pellets (20 mm diameter and 25 mm long) were made from 10, 19, 31, 37 and 60 tim glass ballotini with a range of binders (water, surfactant solutions and glyceroi) and binder contents (0.,0 to 0.55 m"~binder/m "~solid). These pellets were dropped from heights of 10 to 30 cm and the amount of impact deformation measured. Impacts were mostly plastic with a coefficient of restitution less than 1%. The energy conservation model of Hawkyard [J.B. Hawkyatd, A theory for the mushrooming of flat-ended projectiles impinging on a flat rigid anvil, using energy considerations, Int. J. Mech. Sci. I I (1969) 313-333] for rigid-plastic materials was used to calculate the pellet's dynamic yield stress (Y) from the size of the deformed area. When water was used, Y increased exponentially with decreasing surface mean particle size. However, when glycerol was used, particle size had no measurable effect on Y in the range of conditions studied. Increasing binder viscosity and increasing binder surface tension both increased Y.The effect of binder content varieduincreasing the amount of a viscous binder (glycerol) increased F throughout the range of conditions studied, whereas when a low-viscosity binder (water) was used, g passed through a maximum. Hence, there are (at least) three energy dissipation mechanisms that control impact deformation. These are due to inte~article friction, capillary and viscous forces. The effect of varying binder content in a particular system cannot be predicted a priori, unless the balance between these three mechanisms is known. Measurements of granule deformation must be made at high strain rates if dynamic effects are to be accounted for. The simple technique developed has the potential for being used to characterise different formulations in order to better predict their granulation b.haviour. © 1998 Elsevier Science S.A. All rights reserved. geywo~s: Granulation: Agglomeration: Impact deformation: Coefficient of restitution: Dynamic yield stress: Viscous dis~ipatiomCapillary forces
1, Introduction Granulation is the process of agglomerating particles together into larger, semi-permanent aggregates by spraying a liquid binder onto the particles as they are agitated in a tumbling drum, fluidised bed, high shear mixer or similar device. The liquid binds the particles together by a combination of capiilary pressure, surface tension and viscous forces until more permanent bonds are formed by subsequent drying or sintering. Some advantages of agglomerated materials include improved flow properties, reduced dustiness, increased bulk density and the co-mixing of particles which would otherwise segregate. Improper granulation causes problems in down stream processes such as caking, segregation and poor tableting performance. However, in spite of its importance and over 40 years of research, it is still impos* Com~ponding author. Centre for Multiphase Processes, Department of Chemical Engineering, University of Newcastle, Callaghan, NSW 2308, Australia. Tel.: +61~2-49-215.684; Fax: +61-2-49-601-445; E-mail: [email protected] ' E-mail: j.fitstei~cheque.uq.oz.au
sible to quantitatively predict the growth behaviour of a new formulation from only a knowledge of its fundamental properties. It has long been accepted that granule deformability has a strong influence on granule growth behaviour [2,3]. During collisions, granules that deform easily will form a larger area of contact as they dissipate the collision energy. This produces a stronger bond which is more likely to survive subsequent collisions and results in successful granule coalescence. On the other hand, strong, non-deformable granules only form a small area of contact that will be easily broken apart by subsequent collisions. Coarse, narrowly sized particles produce weak, deformable granules that tend to grow quite quickly by rapid coalescence or crushing and layering [4]. In contrast, fine, widely sized particles produce strong, nondeformable granules. These systems initially grow slowly (possibly having a period of zero growth) and only grow rapidly by coalescence if their surfaces become saturated [5 ]. The earliest model of granule strength was the theory of Rumpf [ 6] who considered granules to fail by sudden rupture
0032-591019815 - see front matter © 1998 Elsevier Science S.A. All fights reserved. PIi S 0 0 3 2 - $ 9 1 0 ( 9 8 ) 0 0 1 1 5 - 6
S.M. Iveson, J.D. Litster / Powder Technology 99 (1998) 234-242
of liquid bridges across the granule diameter. Granule tensile strength (tr,) was given by the equation: t r , = S . C 1 - e ),cos(0)
e
( 1)
dp
where S is granule liquid saturation, C is a constant (C = 6 for monosized spheres), e is granule porosity, ), is liquid surface tension, 0 is the liquid-solid contact angle, and dp is surface mean particle size. This equation successfully predicts the tensile strength of compacts made from relatively coarse, narrowly sized particles with nonviscous binders [4,6,7]. However, Rumpf's equation underpredicts the strength of compacts made from fine, widely sized particles. Kristensen et al. [3] showed that interparticle friction forces are also significant. Friction forces are partially linked to capillary forces since the capillary forces causes the normal force at points of interparticle contact. However, although increasing liquid saturation increases capillary forces, it can actually decrease interparticle friction due to the lubrication effect of the liquid at interparticle contacts. Hence, the effect of liquid content can vary depending on the balance between these two forces. For instance, the strength of compacts made from glass ballotini has been found to increase with increasing liquid content, whereas the strength of compacts of fine, irregularly shaped dicalcium phosphate particles decreased with increasing liquid content [ 3]. More recently, Iveson et ai. [ 8 ] studied the effect of binder viscosity on granule consolidation rates in a tumbling drum and found that viscous forces were also important. Increasing the amount of a low-viscosity binder increased the extent of consolidation (due to the lubrication effect), whereas increasing the amount of a high-viscosity binder decreased the extent of consolidation (due to increased viscous forces). Therefore, unless the relative magnitude of viscous, capillary and interparticle friction forces is known, the effect of varying binder content in a given system cannot be predicted a priori, even qualitatively. There have been two attempts in the literature to model granule coalescence. Ouchiyama and Tanaka [2] modelled granules as surface-dry, plastic or elastic spheres. They considered the forces exerted on granules as they collided and used bulk properties of the particle-binder mixture to describe the granules. Kfistensen et al. [3] extended their work and determined that the maximum size for successful granule coalescence, 8 (i.e., the average size of granules above which coalescence will not occur due to the large torque experienced by the pair as they tumble in the granulator), was: 8 2/" - Al~r Orcr
(2)
where A is a dimensional constant independent of granule size, a is a parameter describing the nature of the deformation (a = 1/4 for plastic materials, a = 1/3 for elastic materials),
235
and tr, and icr are the critical stress and strain at failure for the wet particulate material during compressive testing. Hence a granule's ability to deform has a major influence on coalescence behaviour. Both o'er and 1~ are significantly affected by the porosity and liquid content of the wet particle compact. Critical stress may either increase or decrease with increasing liquid content and always increases with decreasing porosity (discussi, ,n above). Critical strain appears to always increase with liquid saturation regardless of whether or not capillary or frictional forces dominate (cf. limestone compacts of Schubert et al. [7], with dicalcium phosphate compacts of Holm et al. [9] ). Hence, although this model gives useful insights into coalescence behaviour, it is difficult to apply to real systems where consolidation of the tumbling granules causes their porosity and liquid saturation to change with time. This model also does not predict how different granule and liquid properties, such as binder viscosity and particle size, will affect coalescence behaviour, even though it is known that these do affect the rate of granule consolidation [ 8 ] and hence must effect granule coalescence. Ennis et al. [ 10] modelled granule coalescence based on the assumption that granules were elastic spheres with surface layers of a viscous binder. They assumed that successful coalescence occurred when the viscous dissipation in the liquid layer and elastic losses in the solid were sufficient to prevent the granules bouncing apart after impact. They derived their model in terms of energies and used individual properties of the particles and binder, rather than bulk properties of the particle-liquid mass. Their work is important for two reasons: ( 1) it is the first to consider viscous dissipation, and (2) it is the first to use energies rather than forces. Experimental work measuring dynamic pendular liquid bridge strengths [ 11 ] has found that viscous forces can be much greater than capillary forces. This finding is supported by the results of computer simulations of aggregate collisions by Adams et al. [ 12 ] who found that viscous and interparticle friction energy dissipation were much greater than capillary bridge rupture energies. However, these findings are challenged by Simons et al. [13] who claim that liquid-bridge rupture (capillary) forces are most important and that these explain the results of their drum granulation experiments. Iveson et al. [8] studied the effect of liquid viscosity on the consolidation of granules in a tumbling drum. They found that increasing binder viscosity significantly decreased the rate of granule consolidation. This suggests that binder viscosity would also affect granule deformation during single impacts. Therefore there is a need for an experimental investigation to establish the effects of viscous and capillary tbrces on granule impact deformation behaviour. However, the literature contains no experimental studies of the effects of binder viscosity on granule strength. Traditionally, properties such as critical stress and strain have only been measured at slow and invariant strain rates, well below the rate of strain occurring during granule impacts. Hence, dynamic effects such as
S.M. lveson, J.D. Litster / Powder Technology 99 (1998) 234-242
236
Table 1 Properties of the glass ballotini Nominal size
x3,2 ~ (Ixm)
x4.3" (Ixm)
tr+.3" (itm)
tr4,3/x4,3" ( -- )
Dry-tapped porosity b ( -- )
Wet-tapped porosity b ( -- )
90-150 I~m 53--106 tun 44--90 ttm -53 ttm --400 Mesh
60 37 31 19 10
122 71 68 36 28
48 30 20 15 11
0.39 0.42 0.29 0.42 0.39
0.385 + 0,004 0.388 + 0.004 0.380:1:0.004 0.51 4.0.01 0,44 4. 0.01
0.373 + 0.005 0.372 + 0,004 0.367 + 0.004 0.382 + 0,005 0.385 4. 0.005
"Surface mean size (x~.,), mass mean size (x4,3) and mass-mean standard deviation (o'4,.~) measured by Malvem Mastersizer/E. t'Bulk porosities measured by tapping sample in a 30-mm diameter volumetric cylinder,
Table2 Propertiesof the liquidbinders Liquid
Density" (g/ml)
Viscosity h (Pa s)
Surface tension ( m N / m )
Water 50 wt,% Glycerol 85 wl,% Glycerol Glycerol 0,00094 M NDBS solution
0,997 !. 123 !.216 1.256 -
0,0011 0.0054 0.070 I.I -
72" 70 'm 660 63 a 3 I"
"Measuredin 2.~ml specificgravitybottle. ~'Measuredin ConlravesRheomat 115 rheometer.Shearrate was variedbetween20 and 150 s ' for glyceroland between300 and 3650 s - afor water. CMeasuredby the WilhemyPlatemethodusing2 cm squarepiecesof filterpaper. ~FromWeast [ 14]. viscous dissipation in the liquid phase have been overlooked. Furthermore, these traditional testing methods impose a predetermined rate of strain on the granule compact, whereas during real impacts, the rate of strain would vary according to the rate of energy dissipation required to dissipate the kinetic energy of the collision. This paper describes a set of simple impact experiments covering a range of binder viscosities and surface tensions. Two types of experiments were performed: ( ! ) swinging dram-granulated granules into a vertical steel plate to measure the coefficient of restitution, and (2) dropping cylindrical pellets onto a horizontal plate to measure the amount of deformation.
2. Experimental method 2, !. Materials Five sizes of glass ballotini with specific surface mean size of 10, 19, 31, 37 and 60 p,m were used. Their properties are listed in Table I. Glass ballotini were chosen because they are a well-defined system and avoid complications due to solids dissolution. The 19, 3 I, 37 and 60 Ixm baliotini were purchased from Potters Industries (Lot 4 Boundary Rd., Lavetton, Victoria, 3028, Australia) and had a density of 2.45 + 0,01 g/ml and the 10 ttm ballotini was purchased from Cataphote (POBox 2369, Jackson, MS, 39225-2369, USA) and had a density of 2.374-0.01 g/ml (measured by both water-displacement and Helium pycnometry).
Glycerol-water solutions were used to vary liquid viscosity and solutions of the surfactant sodium dodecylbenzene sulphonate (NDBS) were used to vary liquid surface tension. The properties of these solutions are listed in Table 2.
2.2. Horizontal-swing impact experiments Known amounts of glass baliotini and binder were kneaded together in a plastic bag until the binder was evenly distributed throughout the ballotini. This feed was tumbled in a 30cm diameter drum at 20 to 40 rpm for between 5 rain and an hour until granules of a suitable size were formed ( 15 to 25 mm diameter). The time of granulation depended on the binder viscosity and binder content. Typically, glycerolbound granules grew slowly and formed ellipsoidai granules with smooth surfaces whereas water-bound granules grew quickly and formed spherical granules with rough surfaces (Fig. 1 ). Granules were then placed in a specially designed 'cradle' which held them, whilst leaving their front face exposed (Fig. 2). The granule and cradle were then suspended by cotton thread from two hooks in the horizontal-swing impact equipment (Fig. 3). The frame was made from 30-mm-thick Craftwood. A 10-ram-thick, 400-mm-square, stainless-steel plate was bolted to the frame in the vertical position. Granules were released from heights of 5 or 15 cm to swing against the steel plate (giving impact velocities of 1.0 and 1.7 m/s respectively). The rebound height was measured from video footage and used to calculate the coefficient of
237
S.M. lveson, J.D. Litster / Powder Technology 99 (1998J 234-242
Fig. 1. Photo of typical water-bound and glycerol-bound granules showing their deformed face after impact.
Fig. 2. Photo of a water-bound granule held in the specially designed cradle with front face exposed.
restitution (rebound height divided by the initial release height).
The major and minor axis of the deformed face, d, and d2, were measured and the relative increase in the area of the impact face (A~/Ao) calculated from:
2.3. Vertical-drop impact experiments
CottonThread Binder and glass ballotini were again hand-mixed in a plastic bag. This feed was then weighed out into a 20-ram diameter cylindrical press (Fig. 4) to make pellets of height 25 mm, diameter (D) 20 nun and with an average porosity of 41%. These pellets were then dropped from a simple release mechanism (Fig. 5), flat-face first, onto a 10-mm-thick stainless steel plate. Fig. 6 is a side-on photo of some typical pellets after impact. The lower end is deformed greatly whilst the upper end is unaffected. The pellet face was often not parallel to the plate at impact, giving the deformed area an elliptical shape.
:
. /
G~jnule
600mm " ~ ~.. Steel Plate fi00mm
/
Craftwood Frame
-
Fig. 3. Diagram of horizontal-swing impact equipment.
238
S.M. lveson, J.D. Litster / Powder Technology 99 (1998) 234-242
3. Experimental results and analysis
~------ 40
3.1. Horizontal-swing impacts
~ 15
20 1
-~
A total of 169 granules were tested in the horizontal-swing impact tests. Glass ballotini with surface mean size of 37 Izm was granulated with three different binders: water, 50 wt,% glycerol and glycerol, with viscosities of 0.001, 0i005 and 1 Pa s respectively. Binder content was varied between 0.44 and 0.55 ml ofbinder/ml solid. This is the full range of binder contents that could be examined: any lower and well-formed granules were not produced, any higher and the granules grew too quickly and had very rough and irregular surfaces. Fig. 7 shows the coefficient of restitution measured in all the horizontal-swing impact experiments. There is a considerable amount of scatter in the results and no clear effect of binder content or binder viscosity. The low-velocity impacts (1.0 m/s) appear to have a slightly higher coefficient of restitution than the faster impacts (1.7 m/s) as would be expected for plastic materials. However, the main point to note is that the coefficient of restitution is very low (less than 1% in all but one case). Hence, in the range of conditions covered by these experiments, granule impacts were almost entirely plastic.
(variable Spacer
II-' Pellet Chamber
' 40
60
'l :I
Fig. 4, Schematicdiagramof the pellet press.
At
d,d,
Ao
D"
(3)
This is a simplistic measure of deformation which ignores the three-dimensional nature of the deformation. However, the formation of an area of contact between two colliding granules is one of the factors that control whether or not granules will coalesce. Hence this measure should provide some useful information for modeling granule coalescence bchaviour.
3.2. Vertical-dropexperiments A total of 664 cylindrical pellets were tested in the vertical impact experiments. These pellets were made from glass ballotini with surface-mean sizes of 10, 19, 31 and 60 p,m. Three different binders were used: water, glycerol and 0.00094 M NDBS solution. The surface tension of the sodium dodecylbenzene sulphonate (NDBS) solution was 31 nLN/m compared with 72 mN/m for water. Pellet binder content was
z,,/--- Pellet25 x 20
100
Dimensions in nan Not drawn to Scale
I'- 22-I TOP VIEW
SIDE VIEW
Fig. 5. Diagramof release mechanismused to drop pellets.
_l
-i
S.M. lveson, J.D. Litster l Powder Technology 99 (1998) 234-242
0.015
37 l~m Glass Ballotinl Oe Water, Low & High Velocitly V• 50 wt% Glycerol, Low & High Velocity E l • Glycerol, Low & High Velocity O
C: 0
== 0.010
v 0 0
i
v v
"~ 0.005
8
! 0.000
45
Ig. 8 lil :°°" o
e
§
50
55
Granule Moisture (ml liquid/100ml solid)
Fig. 7. Coefficient of restitution vs. granule binder content for all the horizontal-swing impact experiments. Granules were released from heights of 5 and 15 cm giving impact velocities of 1.0 and 1.7 m/s respectively.
varied between 0.39 and 0.54 ml liquid/ml solid. At lower binder contents pellets were too crumbly and at higher binder contents pellets were too 'sloppy' to be handled. Pellets were released from heights of 10, 20 or 30 cm (giving impact velocities of 1.4, 2.0 and 2.4 m/s respectively assuming that friction losses during release and fall were negligible). The results of the vertical drop impact tests were analysed with the model developed by Hawkyard [ 1] for the impact of cylindrical slugs against a rigid target. This mode: uses a conservation of energy approach and assumes the material is rigid plastic with a strain-rate independent dynamic yield stress. The non-elastic assumption is justified by the low coefficient of restitution measured in the swing-impact tests. However, as will be shown, binder viscosity has a significant effect on the amount of impact deformation which suggests that the assumption of strain rate independence may be inaccurate (since viscous effects are inherently strain rate dependant). Nevertheless, this model is a useful starting place for analysis.
239
Most workers studying impact deformation use the reduction in length of the impacting cylinder as a measure of deformation (e.g., [ 1,15 ] ). This was not possible in this case because the pellets often landed at an angle to the vertical and there was no clearly defined final length of the pellet (see Fig. 6). Instead the increase in impact area was used. The deformed face was elliptical in shape, so the major and minor axes were measured and used to calculate the area. For a cylinder of initial area Ao, dynamic yield stress Y, impact velocity Uo and density p, Hawkyard's [1 ] model predicts the deformed contact area A~ will satisfy: ~pU"
LAt-l+ln
(4)
Hence, plotting I/2pU 2 vs. Ao/ A ~- 1+ ln ( A ~/ Ao ) , should give a straight line with slope Y. The dynamic yield stress calculated from the slope of these plots was used to compare the effects of varying particle and liquid properties. A typical example is shown in Fig. 8. There is a clear linear dependence between the two groups. Increasing the velocity of impact increases the amount of deformation. However, the intercept 19 pm Ballotiniwith 0.441 ml/ml Water
~
~ ~ / & & &A
4
0.
~
3
I 0.01
I 0.02
I 0.03
" 0.04
0.05
A0/AI-I+In(AI/A0)
Fig. 8. Plot of l/2pU 2 vs. A . / A s - 1 +In(A~/A.) for pellets of 19 gm ballotini with 0.441 ml water/ml solid. The slope gives the dynamic yield stress.
240
S.M. Iveson. J.D. Litster / Powder Technology 99 (1998) 234--242
does not pass through the origin ~,spredicted by Hawkyard's model. There are two probable reasons for this. Firstly, the pellets did have a small elastic component which would tend to shift the intercept upwards. Secondly, the calculated pellet impact velocities used in these plots may be too high due to frictional losses as the pellets drop from the release mechanism.
1000
i
|
Si,e.Binder i
• 31pm.Water o31pm, Q~y O31pm, NDBS &19pro, Water AI9pm, NDBS
G. W w
m "a 100, o >.
| I | | I
I
E
3.2.1. Effect of liquid content and viscosity Fig. 9 shows the dynamic yield stress vs. liquid content for pellets made from 19 and 31 I~mballotini with water, glycerol or surfactant binders. Using glycerol as the binder liquid (increasing binder viscosity from 0.001 to 1 Pa s) greatly decreased the amount of pellet deformation. This is due to the increase in viscous dissipation as the more viscous binder is squeezed between particles during deformation. The effect of binder content is complex. At low moistures, increasing the amount of water increased the yield stress. However, as water content increased further, the effect reversed and the yield stress dropped. There is a significant range of water contents from 0.45 to 0.50 ml/ml in which the effect of varying water content is minimal. In contrast, when glycerol was used as a binder, the yield stress increased steadily as binder content was increased throughout the range of conditions studied. This variable influence of binder content may be explained by the balance between three forces: interparticle friction, capillary and viscous forces. These forces all resist granule deformation, however, the influence of binder content on these three forces varies. Increasing binder content can reduce interparticle friction due to the lubrication effect [ 3 ]. Increasing binder content increases capillary forces up to the saturation point [4,6], after which granule strength decreases rapidly when the droplet state is reached. Increasing binder content should increase viscous forces since there is a larger amount of binder that needs to be squeezed out from in between particles when deformation occurs. For systems where viscous forces ate small (e.g., water binders), increasing binder content initially causes an increase in capillary forces and hence increases the yield strength of the pellet (cf. the increase in strength when a dry powder is initially moistened). However, eventually, as more binder is added, the reduction in interparticle friction due to lubrication becomes mote significant than any increase in capillary forces and pellet strength decreases (ultimately the system becomes a slurry with no strength). The location of this maximum in yield stress depends on the balance between interparticle friction and capillary forces, which will vary with particle size and roughness [ 3 ]. For systems where viscous forces dominate (e.g., glycerol binder), the increase in viscous forces with increasing binder content outweighs the reduction in interparticle friction. Hence granule yield stress increases. Eventually these systems too would also become slurries and their yield stress would drop, however, this occurs outside the range of binder contents that could be studied.
C
o
' 10 0.38
I 0.42
I
Sirfactant
0.4S 0.SO Binder Content (ml/ml)
J 0.S4
Fig, 9. The dynamic yield stress vs. binder content tor pellets made from 19 and 31 gm ballotini with water, glycerol (Gly.) or surfactant (NDBS) solutions. Error bars show the 95% confidence interval on the yield stress determined from the slope of the plot of 112pU" vs. A,IA~ - 1 + ln(A~/A,).
Hence, the effect of binder content on granule dynamic yield stress cannot be predicted beforehand, even qualitatively, unless the relative magnitude of friction, capillary and viscous forces is known. There is a range of binder contents in which increasing the amount of a viscous binder increases yield stress whereas increasing the amount of a nonviscous binder decreases yield stress. A similar effect was seen by Iveson et at. [ 8] on the minimum porosity reached by tumbling granules--increasing the amount of water increased the extent of consolidation, whereas increasing the amount of glycerol decreased the extent of consolidation.
3.2.2. Effect of liquid surface tension The effect of binder surface tension was studied using 0.00094 M NDBS solutions (surface tension 31 mN/m). Fig. 9 shows that lowering the surface tension decreased the dynamic yield stress of both the 19 and 31 I~m ballotini. This is because lowering binder surface tension reduces the capillary forces holding particles together. Glycerol also has a lower surface tension than water (63 vs. 72 raN/m). However, the expected decrease in yield stress due to its lower surface tension was swamped by the opposing effect of increasing viscosity. This finding is consistent with the measurements of dynamic pendular bridge strength by Ennis et al. [ 11 ], the computer simulations of aggregate collisions by Adams et al. [12] and the granule consolidation studies of Iveson et al. [ 8] which all found that viscous effects can be much greater than capillary forces in dynamic situations.
3.2.3. Effect of particle size In Fig. 9, increasing particle size decreased the pellet yield stress. This is seen more clearly in Fig. 10 which plots yield stress vs. particle size for both water and glycerol binders across a range of particle sizes and binder contents. For water, the yield stress was related to the specific surface mean particle size (dp) according to the equation:
Y=Kexp(-Bdo)
(5)
S.M. h,eson, £D. Litswr / Powder Technology 99 (1998) 234--242 1000
i i Ii t l • . . ,,,.
A ¢1 0,,e v
i i
. . . . . . . . . . . .
.
== • 0A41 rri,'rrt Water
•o .~_ >,, .o
& 0.490 rrUmlWater
100
t
c
-'---~..
0 0.441 rrV~ Glycerol
"'-~.
&0.490 rrgml Glycerol
o 10
I 10
Specific
I .... 20
Surface
;
;
1
!
30
40
50
60
"
M e a n P a r t i c l e S i z e (microns)
Fig. ! 0. Dynamic yield stress vs. surface mean particle size for glass ballotini with water and glycerol L;nders.
where K = 120 4- 70 kPa and B = 0.035 4- 0.02 Ixm-Decreasing particle size decreases the average pore size between particles and increases the volume density of interparticle contacts. This increases both capillary and interparticle friction forces and thus explains why, when water was used as the binder, decreasing particle size increased the yield stress. However, when glycerol was used as the binder, particle size did not have any significantly measurable effect on deformation in the range of conditions examined (Fig. 10). Using glycerol, viscous forces should dominate (Section 3.2.2). According to lubrication theory, viscous forces are inversely proportional to gap distance when squeezing a thin film between two plates [10]. Hence, the decrease in average pore-size was expected to increase the viscous forces and hence increase the yield stress. Thus the observed non effect of particle size was surprising. This non effect is possibly due to the low accuracy when measuring small amounts of deformation (i.e., high yield stresses). This problem has the potential to be overcome in future work by: ( 1 ) increasing the accuracy of measurement (e.g., computer image analysis of the deformed area); and (2) increasing the velocity of impact to increase the amount of deformation (e.g., by 'firing' the pellets at a target).
4. Discussion In the range of conditions investigated, granule impacts were almost entirely plastic. This restricts the range of applicability of the coalescence model of Ennis et al. [ 10] which assumed that granules were hard, elastic spheres. This will only apply in systems where granules dry quickly (e.g., in fluidised beds) or consolidate sufficiently to become strong enough to resist further deformation (e.g., some cases in high shear mixers or after long residence times). More recent coalescence modeling by Ennis and Adetayo [16] has acknowledged this limitation by including an empirical parameter for granule deformability. The present authors have also proposed a granule growth regime map based on the granule dynamic yield stress [ 17].
241
This work demonstrates that viscous dissipation in the binder phase can have a significant effect on impact deformation. Hence, although the model of Ennis et al. is limited in applicability, it is significant because it was the first to consider viscous forces. The earlier work of Ouchiyama and Tanaka [ 2 ] was correct in considering the plastic deformation of granules, but considered only capillary and frictional forces. Any general model of granule coalescence must consider all three forces and be based on dynamic energy dissipation, not just low strain rate static conditions. The effect of particle size (dp) and binder surface tension (y) on dynamic yield stress ( 10 are similar to their effect on the theoretical granule tensile strength (or,) predicted by Rumpf's model (Eq. ( 1 ) )---decreasing d r and increasing y increase both Y and ~. This suggests that granule dynamic yield stress is directly related to granule tensile strength. However, Rumpf's model was a static model which considered only capillary forces. Hence, this model needs to be extended to include interparticle friction and viscous effects. Granule deformation is affected by (at least) three energy dissipation mechanisms, due to interparticle friction, viscous and capillary forces. Unless the balance between these three mechanisms is known, the effect of binder content cannot be predicted beforehand, even quolitatively. This, in part, answers the debate in the literature as to whether viscous or capillary forces are most important. Clearly both can dominate in different situations. ~ : : n viscous binders are used with relatively coarse particles, viscous forces dominate whereas capillary force can dominate when low viscosity binders are used. Hence any general model of granule impact deformation must consider all three of these forces. So far, only the computer simulations of Adams et al. [12] have done so, although whether or not these simulations can predict the complicated effects of binder content remains to be seen. The importance of viscous forces means that experimental testing of granule compacts must be done at high enough strain rates to measure dynamic effects. Conventional methods use only relatively slow and invariant strain rates. Hence new testing procedures will need to be developed, perhaps based on the impact experiment used here. This method is crude, but has the potential to be improved by better controlling and measuring the impact conditions and dimensions of deformation.
5. Conclusions For the first time, the impact deformation of liquid-bound granules and compacts has been measured experimentally using a novel but simple technique. Deformation was measured as the increase in impact area and this was used to calculate the dynamic yield stress (Y) based on the energy conservation model for rigid plastic materials proposed by Hawkyard [ l ]. In the range of conditions covered, impacts were almost entirely plastic with only a very small elastic component (coefficient of restitution less than 1% ).
242
S.M. lveson, J.D. Litster/ Powder Technology 99 (1998) 234-242
~ e n water was used as the binder, Y was related to surface-mean particle size (alp) according to the equation: YffiK e x p ( - B d p )
where K = 120 4- 70 kPa and B - 0.035 4- 0.02 ttm- ~. However, when glycerol was used as the binder, particle size did not have a ~asurably significant effect on Y in the range of c o n ~ o n s examined. Increasing binder surface tension and viscosity both increased ¥. The effect of binder content varied. For highviscosity binders, increasing binder content increased Y throughout the range of conditions measured, whereas for low-viscosity binders, Y passed through a maximum. These results show that there are three energy-dissipation mechanisms that can affect impact deformation, due to interparticle friction, capillary and viscous forces. The effect of binder content on yield stress cannot be predicted a priori unless the balance between these three forces is known. Dynamic effects can dominate when viscous binders are used. This exposes a weakness in conventional measurements of granule properties which use relatively low and invariant strain rates and fail to account for dynamic effects. Any general model of granule deformation and coalescence must take into account both the plastic nature of granules and the importance of dynamic effects such as viscous dissipation. It must include the effects of interparticle friction, capillary and viscous forces and should be able to predict the variable effect of binder content.
Acknowledgements This work has been funded by an Australian Postgraduate Award scholarship and an Australian Research Council Grant (A89600426),
References [1] J.B. Hawkyard, A theory for the mushrooming offlat-ended projectiles impinging on a flat rigid anvil, using energy considerations, Int. J. Mech. Sci. 11 (1969) 313-333. [2] N. Ouchiyama, T. Tanaka, The probability of coalescence in granulation kinetics, I&EC Process Des. Dev. 14 (1975) 286-289. [ 3 ] H.G. Kristensen, P. Holm, T. Schaefer, Mechanical properties of moist agglomerates in relation to granu|ation mechanisms: Part 1. Deformability of moist, densified agglomerates; Part 2. Effects of particle size distribution, Powder Technol. 44 (1985) 227-247. [4] D.M. Newitt, J.M. Conway-Jones, A contribution to the theory and practice of granulation, Trans. I. Chem. Eng. 36 (1958) 422-441. [ 5 ] P.B. Linkson,LR. Glastonbury, G.J. Duffy, The mechanism of granule growth in wet pelletisation, Trans. lnstn. Chem. Engrs. 51 (1973) 251-259. [6] H. Rumpf, The strength of granules and agglomerates, in: W.A. Knepper (Ed.), AIME, Agglomeration, lnterscience, New York, 1962, pp. 379-418. [7l H. Schubert, W. Herrmann, H. Rumpf, Deformation behaviour of agglomerates under tensile stress, Powder Technol. I 1 (1975) 121131. [8 ] S.M. Iveson, J.D. Litster, B.J. Ennis, Fundamental studies of granule consolidation: Part 1. Effects of binder viscosity and binder content, Powder Technol. 88 (1996) 15-20. [9] P. Holm, T. Schaefer, H.G. Kristensen, Granulation in high speed mixers: Part V. Power consumption and temperature changes during granulation, Powder Technol. 43 (1985) 213-223. [ 10l B.J. Ennis, G.I. Tardos, R. Pfeffer, A microlevel-based characterization of granulation phenomena, Powder Technol. 65 ( ! 991 ) 257-272. [ 11 ] BJ. Ennis, J. Li, G.I. Tardos, R. Pfeffer, The influence of viscosity on the strength of an axially strained pendular liquid bridge, Chem. Eng. Sci. 45 (1990) 3071-3088. [ 12] M.J. Adams, C. Thornton, G. Lian, Agglomerate Coalescence, First International Particle Technology Forum, Vol. I, August 17-19, Denver, USA, 1994, pp. 220-224. [ 13l S.J.R. Simons, J.P.K. Seville, M.J. Adams, Mechanisms of agglomeration, 6th Int. Symp. Agglomeration, Nov. 15-17, Nagoya, Japan, 1993, pp. ! 17-122. [ 14] R.C. Weast (Ed.), CRC Handbook of Chemistry and Physics, 62nd Edn., CRC Press, Boca Raton, Florida, 1981-1982. [ 15] G.I. Taylor, The use of flat-ended projectiles for determining dynamic yield stress: 1. Theoretical considerations, Proc. R. Soc. London, Ser. A 194 (1948) 289-299. [161 B.J. Ennis, A.A. Adetayo, Unifying approach to modelling granule coalescence mechanisms, AIChE J. 43 (4) (1997) 927-934. [171 S.M. Iveson, J.D. Litster, A growth regime map for liquid-bound granules, AIChE J. 44 (7) (1998) 1510-1518.