A novel nucleation apparatus for regime separated granulation
W.J. Wildeboer a,1, E. Koppendraaier b, J.D. Litster a,⁎, T. Howes a, G. Meesters b
a Particle and System Design Centre, Division of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australiab Delft University of Technology, Delft, The Netherlands
Granulation and control of granulation processes have becomeincreasingly significant in a range of formulation industries,including pharmaceuticals, agricultural chemicals, mineral pro-cessing, food technology and detergents. Granulation of powdersis generally desirable to assist with dust minimization, handlingand storage and more importantly, the delivery of active in-gredients in pharmaceuticals and detergents. Granulation is de-fined as agglomeration by agitation in the presence of a binderliquid. Thus for granulation to occur there is generally some formof agitation of a powder, during and after the addition of a liquidbinder. Current well-known granulation processes include the useof fluidized beds, flat bed, pan or disc, drum and mixer gran-ulators, all of which use agitation to encourage granulation. Thedesired results of granulation processes are to produce granuleswith the required physical properties andwith a narrow size range.Current granulators produce granuleswith awide size distributionresulting in segregation and large recycle streams of granules
outside the required size range. Further, due to the complexinternal mechanisms, current granulators are difficult to designand to scale up rationally [1]. Ennis and Litster [2] separated theinternal granulation mechanisms in three rate processes, thesebeing wetting and nucleation, consolidation and coalescence andbreakage and attrition.
Extending this idea, we propose the concept of a regimeseparated granulator in which key regimes are physically sep-arated so that they can be controlled to a much greater extent thanis now possible. Fig. 1 illustrates this concept.Most combinationsof desired product qualities could be achieved in two-stagegranulation where the first stage gives controlled nuclei formationand the second stage gives controlled growth and consolidation.Acombination drop controlled nucleation and layered growth givespotential for very narrow granule size distributions.
Hapgood and co-workers [3,4] demonstrated the criticalimportance of the nucleation and liquid binder distributionprocess in determining the size and spread of the final granulesize distribution. They described several nucleation regimes,including the drop controlled regime in which there is a one toone correspondence between the drop size distribution and thegranule size distribution. A key parameter in determining thenucleation regime was the dimensionless spray flux. Their workhelped quantify and explain earlier experimental studies on the
Fig. 2. Stability region for mono-sized droplet formation according to Sakai andHoshino [19].
97W.J. Wildeboer et al. / Powder Technology 171 (2007) 96–105
effect of powder flux and spray nozzle parameters on granulesize distributions [5–7].
Monosized drops can be produced from a showerheadarrangement using an acoustically vibrated jet [8]. Schaafsmaet al. [9] used a similar approach with a single vibrated nozzle influidized bed granulation. In this paper, we completely separatethe nucleation zone of a granulator by passing a thin powder layeron a conveyor belt, an approach described qualitatively by Rumpf[10] but which has received little attention since. By using amonosized drop generator as the spray nozzle and independentcontrol of the powder speed on the belt, it should be possible toguarantee an extremely narrow nuclei granule size distribution.
2. Theory
A liquid flowing through a circular orifice may drip or form alaminar, wavy or turbulent jet, depending on the nozzle flow[11,12]. The disintegration of a laminar liquid jet is sensitive tonatural as well as imposed disturbances. Natural disturbancesmay exist out of all sorts of background noise such as velocityrelaxation, whereas imposed disturbances may consist ofmechanical vibration or electrical forces [13]. Investigationsby Sakai et al. [13] show that for low viscosity liquids, thesurface waves imposed by disturbances grow following theRayleigh equation [14,15]. Weber [16] generalized Rayleigh'slinear stability analysis to the case of viscous fluids. He alsoconsidered the effects of air drag on the moving jet at high jetvelocities. Drop formation using high viscosity liquids has beenextensively studied by Goedde and Yuen [17].
For any disturbance to result in breakup of a laminarcylindrical jet of low viscosity into droplets, Plateau [18] foundthat the disturbance wavelength λ has to be larger than thecircumference of the liquid jet.
kzpdj ð1ÞThis restriction can be expressed in terms of the dimension-
less wave number:
kaV1 ð2Þ
where a is the jet radius and k=2π/λ. Therefore:
ka ¼ pdj fuj
ð3Þ
in which dj, f and uj are the jet diameter, disturbance frequencyand jet velocity respectively. In the literature, the jet radius,diameter and velocity in Eq. (3) are often substituted by theinternal diameter d of the nozzle and the average liquid velocityu in the nozzle. The same simplifications are made here.
The stability of the production of mono-sized drops byimposed disturbances is further affected by the operatingconditions and physical properties of the liquid. Sakai andHoshina [19] provide an in-depth experimental study of theeffects of these conditions and properties on the stability ofmono-sized drop formation. Four empirical relations weredetermined marking the boundaries of an operational envelope
Table 1Physical properties of chalcopyrite and limestone powder
Properties a Chalcopyrite Limestone
True density ρs 3.78 2.77Tap density ρt 1.70 1.47d4,3 (μm) 118 57dmass,50 (μm) 63 5.3Nucleation ratio K (–) 1.39 1.62a The true density was measured with a helium picnometer (Micromeritics
Accupyc 1330). Tap density was measured according to the ASTM B527-93standard. Size properties were measured with a Malvern Mastersizer/E. Thenucleation ratios were determined from nuclei formed from a single drop in atapped powder bed. Nuclei were excavated from the bed and their diametermeasured with calipers.
in terms of disturbance frequencies and nozzle flow velocities.The upper and lower disturbance frequency limits are given by:
fL;H ¼ lRemWen ð4Þwhere for fL, the lower frequency limit, l, m and n are 0.11,−0.066 and 0.17. For fH, the high frequency limit, the constantsare 0.18, 0.031 and 0.12. Re and We are the Reynolds andWeber number, respectively. The upper and lower nozzle flowvelocity limits are given by:
uL;H ¼ ogqd
Ohp ð5Þ
where o and p are 3 and −0.96 for the low and 300 and −0.33for the high velocity limits respectively. Oh is the Ohnesorgenumber which is defined as We0.5/Re.
For water flowing through a nozzle with inner diameter of0.66 mm, the operation envelope for the production of mono-sized drops based on Eqs. (4) and (5) is given in Fig. 2.
In Fig. 2, the vertically dotted lines indicate transitionsbetween dripping, laminar flow and wavy jets. Rayleigh typebreakup and production of mono-sized droplets is only possiblewithin the laminar flow region. Within the non-uniform region,jet-breakup is unstable and droplets of different size are pro-duced. Within the uniform region, all droplets possess the samesize and originate from one disturbance wavelength. In thesatellite region, satellite drops are formed from the ligaments thatare created when the main drop detaches from the liquid jet. At
Fig. 3. Schematic of nuclei formed in a powder bed with two different nozzleconfigurations.
relative high dimensionless wave numbers, the satellite dropsformed in this region are negligible. This theory for breakup of asingle laminar jet has been applied successfully to multiplenozzle arrangements [8,20–22] which are very similar to thedroplet generator developed in this work.
An important aspect of the design and operation of thenucleation apparatus is the ratio of nuclei and dry powderproduced. This ratio is optimal when the surface coverage ofnuclei on the powder bed is maximized. Fig. 3a and b showschematic diagrams of multi-line nuclei patterns on a powderbed when ideally nuclei are formed from single droplets.
In both figures, l is the distance between the centers of theouter nozzles, dn is the nucleus size, Δx is the spacing betweenthe centers of two nozzles,Δy is the spacing between the centersof two nuclei in the direction of powder motion, vb is thepowder bed velocity and z is the direction of powder motion.The nuclei diameters are related to the drop diameters by:
dn ¼ffiffiffiffiK
pdd ð6Þ
where K is the nucleation ratio.It is clear that the pattern of nuclei shown in Fig. 3a, where
the nozzles are positioned within a nucleus diameter, results in
Fig. 4. A complete operational map for the production of limestone nuclei usingwater as binder liquid, an internal nozzle diameter of 0.66 mm and a maximumpowder bed velocity of 1.13 m s−1.
Fig. 5. Photograph of the experimental nucleation setup.
99W.J. Wildeboer et al. / Powder Technology 171 (2007) 96–105
the maximum attainable surface area coverage of nuclei.However, when the breakup times of the jets show slightvariations due to small differences between or fouling of thenozzles, merging of nuclei is likely to occur. Further, there isno flexibility in the operation because small changes of thebreakup frequency or powder bed velocities will immediatelyresult in merging of nuclei as well. A nozzle design givingmore flexibility of operation is obtained when the nozzlesare mounted one nucleus diameter or further apart, representedby:
D xzdn ð7Þ
Fig. 3b shows the nuclei coverage of this situation.Decreasing disturbance frequency and increasing powder bedvelocity will now lead to larger gap distances between the nucleiin the direction of powder motion.
Fig. 6. Schematic of sonic mono-sized drop
Within the uniform drop region shown in Fig. 2, the dropdiameter dj can be easily calculated from the volumetric flowrate of the jet and the disturbance frequency:
dd ¼ 3d2u2f
� �1=3
¼ 3p2ka
� �1=3
d ð8Þ
where d is the internal nozzle diameter. Combining Eqs. (6) and(8) gives the relation between produced nucleus diameter andnozzle diameters as a function of nucleation ratio and operatingconditions:
dnd
¼ K1=2 3p2ka
� �1=3
ð9Þ
From Eq. (9), the appropriate internal nozzle diameter can bedetermined by choosing the required nuclei diameter anddimensionless wave number that ensures uniform production ofdroplets.
For nozzle configurations resulting in nuclei patterns on thepowder bed as shown in Fig. 3b, the optimal spacing betweennucleiΔy, in the direction of powder motion z, is obtained whenthe rate of production of nuclei multiplied by the nuclei size,equals the powder bed velocity:
dn fvb
¼ 1 ð10Þ
Combining Eqs. (9) and (10) gives the relation for optimalspacing of any nucleus size in the direction of powder motion:
f ¼ 2v3b3K3=2u
� �1=2
d ð11Þ
The design of the nucleation apparatus in this paper is basedon the nucleation of limestone with water as binder liquid. Thenucleation ratio of limestone and water is 1.62 (Table 1).Choosing a required nucleus diameter of 1.5 mm and operating
let generator (dimensions are in mm).
Fig. 7. (a) Arrangement of multiple nozzles on the nozzle plate. (b) Enlarged photograph of typical nozzle tip with inner diameter of 0.66 mm.
Fig. 8. Settings of experiments (+), plotted in Sakai and Hoshino (1980) stabilitymap for production of mono-sized droplets.
at a dimensionless wave number of 0.8 results in a requiredinner nozzle diameter of 0.66 mm (Eq. (11)). To prevent overlapof nuclei between the nozzles, the centers of the nozzles have tobe positioned more than 1.5 mm apart (Eq. (7)).
The nuclei production rate at a fixed dimensionless wavenumber, increases linearly with increasing disturbance frequen-cy. The maximum production rate is determined by the fastestobtainable powder bed velocity and corresponding disturbancefrequency giving optimal nuclei spacing (Eq. (11)). Themaximum speed of the conveyer belt is 1.13 m s−1.
The operation map shown in Fig. 4 is obtained from plottingEqs. (4), (5) and (11) using these conditions.
The skewed parallelogram is the stability region according toSakai and Hoshino [19]. As wave number decreases, thenucleus size increases (Eq. (8)). For a given wave number, as jetvelocity decreases, the spacing between nuclei increases. Thebold dotted line indicates the closest spacing of different sizednuclei at maximum powder bed velocity (Eq. (11)). Operatingthe nucleation apparatus above this line, will inevitably result inmerging of nuclei in the direction of powder motion. The filleddot indicates the operating conditions corresponding to adimensionless wave number of 0.8, where nuclei of 1.5 mm areformed with the closest possible spacing at maximumproduction rate. Within the region of the parallelogram belowthe bold dotted line, the required belt speed for optimal spacingbetween nuclei may be calculated from Eq. (11).
Although the nozzle is designed for the production of1.5 mm nuclei operating at a dimensionless wave number of0.8, smaller or larger nuclei may still be produced. Operating atdimensionless wave numbers of 1 and 0.5 would theoreticallyresult in nuclei of 1.41 and 1.77 mm, respectively. It should bekept in mind that nuclei sizes obtained at different dimension-less wave numbers should not exceed the gap distance betweenthe centers of the nozzles.
3. Experimental
Fig. 5 shows a photograph of the nucleation apparatus. Theapparatus comprises a mono-sized droplet generator (1), a
variable speed conveyer belt (2) to transport powder through thespray zone and a GFG-813 Function Generator (3) to imposesine-wave disturbances to the droplet generator. The imposeddisturbances are monitored with an oscilloscope (4). Binderliquid is supplied to the droplet generator by gravitational flowfrom a highly placed liquid reservoir and regulated using asimple flow valve.
The mono-sized droplet generator is positioned 5 cm abovethe center of the conveyer belt with the row of nozzles per-pendicular to the direction of belt motion. This height is justbelow the point of jet disintegration so that gravitational andaerodynamic effects on the produced droplets are minimized. Bypositioning the droplet generator above the center of the belt, thelast quarter of the belt has reached constant speed before passingthe nozzle, and has time to come to a halt when the belt is turnedoff after passing the spray. Fig. 6 shows a more detaileddescription of the mono-sized droplet generator.
A side-view of the droplet generator (Fig. 6a), shows areservoir (3) with a fluid inlet (1) mounted midway on the side.The reservoir functions as a buffer zone to remove any
Fig. 9. Mono-sized drop formation at different dimensionless wavenumbers of(a) 0.29, (b) 0.42, (c) 0.47, (d) 0.61, (e) 0.71, (f) 0.76, (g) 0.81, (h) 0.87, (i) 0.9,(j) 0.95. Size intervals on the ruler are in mm.
Fig. 11. Example of mono-sized drop production using the multiple nozzledroplet generator operated at a dimensionless wave number of 0.9.
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turbulence from the liquid. A 25 mm diameter piezoelectricoscillator (8) number 2312709 of RS-components Australia ismounted in a hole in the center of the top lid of the reservoir asshown in Fig. 6b. Further, the top lid is equipped with a ventvalve (2) to remove any air from the reservoir. Information onhow to use piezoelectric oscillators is described in ElectronicsAustralia (1996). The bottom lid (5) of the reservoir holds thenozzle plate (9). Both lids are sealed with rubber rings (6). Thenozzle plate shown in Fig. 6c holds 17 nozzles (7) in a lineconfiguration. A center to center spacing of 7 mm was used toprevent possible interference between the jets and to be able tonucleate a large variety of powders using different dimensionlesswave numbers. The nozzles were manufactured from hypoder-mic needles with inner diameter of 0.66 mm. After shorteningthe needles to 10 mm the edges were polished. Fig. 7a shows aphoto of the nozzle arrangement on the nozzle plate. Fig. 7b is anenlarged photograph showing an excellently circular and burrfree nozzle tip. All nozzles were soldered on the nozzle platesuch that half of the nozzle is visible below the nozzle plate.
Fig. 10. Droplet size obtained using different wave numbers at constant nozzleflow velocity of 1.81 m·s−1.
A series of experiments were performed using a singlenozzle plate with the nozzle positioned in the center, to comparethe operation of the droplet generator with drop productiontheory. The operating conditions of the experiments aresummarized in Fig. 8 and shown as + signs.
A ruler was mounted next to the single jet for size reference.The production of droplets was filmed using a S-VHS videorecorder connected to a JVC TK-S350 video camera. By light-ing the produced droplets using appropriate frequencies with anIEC xenon stroboscope model XE-H, static images were ob-tained. The images were digitized by retrieving them from thevideo using a frame grabber and analyzed with image analysissoftware.
A series of experiments using the multiple nozzle plate wereperformed to determine whether the produced droplets from thedifferent jets weremono-sized. The experiments were performedat a constant nozzle flow velocity of 0.93 m s−1 and disturbancefrequencies of 406, 387, 362 and 315 Hz, corresponding to wavenumbers of 0.9, 0.85, 0.8 and 0.7, respectively. A ruler wasmounted next to the outer jet for size reference. The multiple jetswere back-lit with a MVS-7000 machine vision flat panelstroboscope. Photos of the multiple jets were taken in a darkroom with a 35 mm SLR still camera using a focal length of50 mm, an exposure of 0.7 s and an aperture of f 22. During theexposure, a single flash of the stroboscope was used to light upand freeze the jets. The photos were then scanned and analyzedusing image analysis software.
Nucleation experiments were performed using chalcopyriteand limestone powders. Chalcopyrite powder was chosen torepresent A-type powders according to the Geldart fluidizationregimes. Limestone powder is much finer and more cohesiveand represents the C-type powders. Some physical properties ofthese materials are listed in Table 1.
The aims of these experiments were to investigate the effectsof powder bed velocity on the spacing between the nuclei in thedirection of powder motion and on the formation of nuclei in thenucleation apparatus. Droplet production of the multiple jetswas carried out at a wave number of 0.9. The nozzle flowvelocity and disturbance frequency were 0.93 m·s−1 and406 Hz, respectively. Three nucleation experiments were then
Fig. 13. Percentage of limestone nuclei originating from various amounts ofdrops.
Fig. 12. Limestone nuclei produced at powder bed velocities of (a) 0.7 m·s−1 and (b) 1.13 m·s−1. Theoretical expected nuclei size is 1.45 mm. The photos showfootprints of fully penetrated drops.
performed with both powders using powder bed velocities of0.7, 1 and 1.13 m·s−1.
The experimental procedure consists of a few simple steps.First the droplet generator is set to the required operatingconditions. Then the middle of the prepared powder bed ispositioned under the droplet generator. Directly after this thepowder belt is switched on. The conveyer belt is switched offbefore the end of the powder bed containing the formed nucleireaches the edge of the conveyer belt. After each experiment,photos of the nuclei formed in the powder bed were taken with a35 mm SLR camera using a focal length of 50 mm. The aperturesize and exposure time were regulated by the still camera. Thephotos were scanned and analyzed using image analysissoftware.
4. Results and discussion
The operation of the developed mono-sized drop generatorwas tested using one nozzle over the range of operatingconditions pointed out in Fig. 8. The results of theseexperiments confirm the formation of mono-sized droplets forall settings chosen within the operation envelope proposed bySakai and Hoshino [19] (Fig. 2). Fig. 9 shows photographs ofdroplets produced during the experiments at increasingdimensionless wave numbers. The photos were taken justbelow the point of jet disintegration.
Fig. 9 illustrates that droplet sizes are inversely proportionalto the dimensionless wave number. It also clearly illustrates thedecrease of droplet spacing with increasing dimensionless wavenumber. The formation of mono-sized drops at low wavenumbers due to merging of satellite drops with main drops isdemonstrated by the white circles in Fig. 9a–e.
The above results are represented quantitatively in Fig. 10,where the measured drop diameters and expected theoreticaldiameters (Eq. (8)) of all tests at different dimensionless wavenumbers, using a constant nozzle flow velocity of 1.81 m·s−1,are plotted. In the case of Fig. 9a–e, droplet sizes weremeasured after coalescence and further away from the nozzle.The error bars indicate the 95% probable measurement error ofthe drop size measurements.
Fig. 10 shows that the measured drop sizes compare wellwith the theoretically expected drop sizes. This indicates theproper functioning of the droplet generator, and further showsthat the drop size can be effectively controlled by altering thedimensionless wave number. A photograph of the jets at adimensionless wave number of 0.9 is shown in Fig. 11.
In all tests, the disturbance was applied using the maximumamplitude output of the piezoceramic oscillator. When operat-ing at smaller dimensionless wave numbers, the disturbanceamplitude-wavelength ratio decreases, which could explain theslightly larger observed variation of droplet sizes at the smallerdimensionless wave numbers. Using a piezoceramic oscillatorcapable of producing larger amplitude outputs could result inless variation of droplet sizes at lower dimensionless wavenumbers.
The production of limestone nuclei from single droplets withthe developed nozzle operating at a dimensionless wavenumberof 0.9 and disturbance frequency of 406 Hz on powder bedsmoving at velocities of 0.7, 1 and 1.13 m·s−1, should result in1.45 mm nuclei with gap distances of 0.27, 1.02 and 1.34 mm,
Fig. 14. Example of droplet merging and runnel formation before nucleating on a moving limestone powder bed.
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respectively. Fig. 12 shows random sections of limestone nucleiformed on a powder bed moving at 0.7 and 1.13 m·s−1.
Most of the measured nuclei sizes in Fig. 12a and b arenoticeably larger than the theoretical expected size of 1.45 mm.The gap distances between the nuclei are also larger thanexpected and increase when neighboring nuclei become larger.When counting the number of nuclei on a single row, noticeablyless nuclei are found than the expected numbers of 20 and 12 forFig. 12a and b, respectively. From these observations one mustconclude that most of the formed nuclei do not originate from asingle drop. Further it can be observed that some nuclei are notperfectly positioned on lines parallel to the direction of powdermotion. This phenomenon will be discussed together with thenucleation results of chalcopyrite powder below.
Analyzing the nuclei sizes of the whole photograph of eachlimestone nucleation experiment, showed that the nuclei sizescould be grouped in a number of discrete narrow size ranges.This observation suggests that the nuclei are formed from amultiplicity of droplets. Fig. 13 shows the measured limestonenuclei sizes of all nucleation experiments.
The discrete size ranges are grouped according to the numberof droplets fromwhich the nuclei originate. The bars indicate thenumber percentage of nuclei originating from a particular integernumber of binder liquid drops. The values above the bars are themean nuclei sizes in mm and the 95% size range in which the
Fig. 15. Chalcopyrite nuclei produced at powder bed velocities of (a) 0.7 m
measurements were found. Fig. 13 shows that the variation innuclei sizes are highest using a belt speed of 0.7 m·s−1. Thedistribution of sizes at belt speeds of 1 and 1.13 m·s−1 show lessvariation in nuclei sizes. The narrowest distributed nuclei areobtained at a belt speed of 1.13 m·s-1.
To investigate why nuclei are formed from multiple ratherthan single droplets, the landing zone of droplets on a limestonepowder bed was filmed using a microscope connected to a videocamera. Fig. 14 shows drop deformation due to the momentumchange experienced during the period after landing on thepowder bed. This deformation and deformation of a droplet onimpact while landing on the powder bed cause coalescencebetween neighboring droplets. Due to the coalescence of thedroplets, a runnel from merged binder liquid droplets is formedin which the outline of the individual droplets can still beidentified. Surface tension then pulls the runnel back to a singledrop which penetrates the bed to form a nuclei. At higherpowder bed velocity, the drops a separated further on the bedsurface and are therefore less likely to coalescence with aneighboring drop or drops. Thus smaller and more narrowlydistributed nuclei are formed.
The production of chalcopyrite nuclei operating at adimensionless wave number of 0.9 and disturbance frequencyof 406 Hz on powder beds moving at velocities of 0.7, 1 and1.13 m·s−1, should result in 1.35 mm nuclei with gap distances
·s−1and (b) 1.13 m s−1. Theoretical expected nuclei size is 1.35 mm.
Fig. 17. Comparison of drop penetration in (a) chalcopyrite and (b) limestonepowder beds. Distances between the needle tip and droplets are indicated inmillimeters.
of 0.37, 1.11 and 1.44 mm respectively. Fig. 15 shows randomsections of nuclei formed on a powder bed moving at 0.7 and1.13 m·s−1.
Again, the obtained nuclei sizes and spacings are larger thenthe expected values. Also counting the nuclei in a single rowyields a lower number of nuclei then expected. Therefore, most ofthe chalcopyrite nuclei must also be formed from more than asingle drop according to the samemechanism of drop coalescencethat occurred in the limestone nucleation experiments. Grooves inthe powder bed left behind by runnels of binder liquid,demonstrated in the white rectangle in Fig. 15a, confirm this.
The complete size analysis of the nucleation experiments atpowder bed velocities of 1 and 1.13 m s−1 are shown in Fig. 16.
Yet again the nuclei possess less variation in the amount ofdroplets from which they originate at the highest powder bedvelocity of 1.13 m s−1.
An interesting phenomenon is observed at a belt speed of0.7 m s−1, which was not observed when nucleating limestone atthe same operating conditions. The runnels of binder liquidformed due to the deformation of droplets after landing on thepowder bed penetrated the bed before the runnel could springback due to the binder liquid surface tension. An example of thisphenomenon is pointed out within the white ellipse in Fig. 15a.This observation stresses the importance of further investigationof the difference in nucleation behaviour between the two powdermaterials. To gain more insight into the formation of nuclei, thepenetration of a droplet into limestone and chalcopyrite powderbeds was monitored adapting the technique used by Hapgood [4].
Fig. 17a and b show the initial phase of 3 mm dropspenetrating in chalcopyrite and limestone powder beds atintervals of 0.04 s, where the first image is taken between 0 and0.04 s after contact.
The height of the needle tip above the powder beds was keptconstant in both experiments and therefore the distance betweenthe needle tip and droplet is a good indication for the rate ofpenetration of the droplets.
Fig. 17a and b show that the rate of penetration of a dropletinto a chalcopyrite powder bed is higher than for limestone.
Fig. 16. Percentage of chalcopyrite nuclei originating from various amounts ofdrops.
Therefore, the droplet is bound earlier to the powder bed. Thisexplains the lack of time for the runnels of binder liquid on achalcopyrite powder bed to form spherical droplets, resulting inthe formation of long stretched nuclei as shown in Fig. 15a. Thetimes required for the droplets to completely sink into thechalcopyrite and limestone powder beds were 0.6 and 0.95 s,respectively.
The difference in penetration rates between the two materialsalso explains why limestone nuclei occasionally are off-line withthe direction of powder motion, whereas this is not the case forchalcopyrite nuclei. Due to the slower penetration of binder liquiddroplets into a limestone powder bed immediately after impact,the binder liquid droplet is less firmly bound to the powder bedsurface. Therefore, small irregularities on the surface of themoving powder bed allow the droplet to roll across the bed beforesinking into the powder bed and nucleate.
5. Conclusions
The nucleation apparatus presented in this chapter is the firstapparatus where the nucleation mechanism is completelyseparated from all other granulation mechanisms. Due to theisolation of the nucleation process, complex influences of theother granulation mechanisms on the nucleation process areavoided. The apparatus is remarkably easy to design and operate,based on a sound theory of mono-disperse droplet formationunder the influence of mechanical disturbances and thenucleation ratio of a particular powder-binder liquidcombination.
Nucleation experiments with chalcopyrite and limestonepowders using water as the binder liquid resulted in theproduction of nuclei with very narrow size distributions.Investigation of the resulting nuclei size distributions showedthat the nuclei were formed from multiplicities of the generateddroplets. This phenomenon was studied by observing the initialstage of droplet impact on the powder bed and the behaviour for ashort time period thereafter. These studies indicated that runnelsof binder liquid were formed due to droplet deformation onimpact and coalescence with neighboring droplets. These runnelsthen contract to give larger droplets (and therefore larger nuclei)than would otherwise be predicted. Further, the effects ofdifferent powder bed velocities and nuclei formation dynamics
105W.J. Wildeboer et al. / Powder Technology 171 (2007) 96–105
on the resulting nuclei were studied. It was shown that a lowervariation of nuclei sizes is obtained when the powder bedvelocity is increased, and when powder-binder liquid combina-tions are used that have faster penetration times.
Nomenclature
a Jet radius (m)d Inner diameter of nozzle (m)dd Droplet diameter (m)dj Jet diameter (m)dn Diameter of nucleus (m)F Disturbance frequency (Hz)K Nucleation ratio (–)ka Dimensionless wavenumber (–)l, m, n, o, p Empirical constants (–)Oh Ohnesorge number (–)Re Reynolds number (–)U Liquid velocity inside nozzle (m·s−1)uj Jet velocity (ms−1)vb Conveyer belt speed (ms−1)vbmax Maximum conveyer belt speed (ms−1)We Weber number (–)
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