growth kinetics and mechanism of wet granulation in a laboratory-scale high shear mixer: effect of...

Chemical Engineering Science 63 (2008) 1602–1611www.elsevier.com/locate/ces

Growth kinetics and mechanism of wet granulation in a laboratory-scale highshear mixer: Effect of initial polydispersity of particle size

Alvaro Realpe, Carlos Velázquez∗

Pharmaceutical Engineering Research Laboratory, Department of Chemical Engineering, University of Puerto Rico, P.O. Box 9046, Mayagüez, PR 00681, USA

Received 18 July 2007; received in revised form 31 October 2007; accepted 11 November 2007Available online 17 November 2007

Abstract

The effect of initial polydispersity of particle size (unimodal versus bimodal distribution) and binder characteristics on the growth kineticsand mechanism of wet granulation was studied. Wet granulation of pharmaceutical powders with initial bimodal particle size distribution (PSD)presented growth kinetics consisting of two stages: fast growth followed by slow growth. The fast stage is controlled by the amount of binderand high probability of coalescence due to the collisions of small and large particles. The second stage is characterized by slow agglomerationof powder mixtures with water content 13.6% v/w, and slow breakage of powder mixtures with water content of 9.9% and 11.7% v/w. Thewet granulation of powders with initial unimodal PSD exhibited slow growth kinetics consisting of one stage, since similar particle sizes donot promote agglomeration. The experimental results were better described by a population balance equation using a coalescence kernel thatfavors growth rate by collision between small and large particles. In general, the probability of a successful collision increased with highersize difference between particles, smaller particle size, and higher binder content.Published by Elsevier Ltd.

Keywords: Polydispersity; Particle size distribution; Wet granulation; Growth kinetics; Coalescence; Binder

1. Introduction

Wet granulation in a high shear mixer is primarily a pro-cess for particle enlargement that is used in many industriessuch as pharmaceutical, mineral processing, agriculture, food,and detergent. The process of particle enlargement via a coa-lescence mechanism improves the flow properties of the par-ticles, and decreases segregation of the ingredients, thus alsoimproving uniformity of the mixture (Cape, 1980). Granulebreakage could also occur during the wet granulation process,depending upon the viscosity and the amount of binder.

Ennis et al. (1991) developed the viscous Stokes’ (Stv) num-ber, wherein factors such as particle size and density, and binderviscosity and amount are considered to quantify the probabilityof particle coalescence and, as a consequence, granule growthrate. Ennis et al. (1990, 1991) considered the viscosity force of

∗ Corresponding author. Tel.: +1 787 8324040x2576; fax: +1 787 834 3655.E-mail address: [email protected] (C. Velázquez).

0009-2509/$ - see front matter Published by Elsevier Ltd.doi:10.1016/j.ces.2007.11.018

a liquid bridge, and modeled two colliding granules using theequation of motion:

mp

dv

dt= 3��r2

p

2xv, (1)

where mp is the granule’s mass; v is the relative velocity be-tween the two particles; rp is the granule’s radius; � is theviscosity of the binder liquid, and 2x is the distance betweencolliding granules. The analytical solution of Eq. (1) is

v = v0

[1 − 1

Stvln

(h0

x

)], (2)

where h0 is the thickness of the liquid layer on the surface ofthe particle and Stv is the viscous Stokes number given by

Stv = 8�pvorp

9�, (3)

where �p is the particle density. The particles will coalesceupon collision, if the viscous Stokes number of the particles issmaller than the critical value of the viscous Stokes’ number

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A. Realpe, C. Velázquez / Chemical Engineering Science 63 (2008) 1602–1611 1603

Fig. 1. Layering growth mechanism proposed by Tardos et al. (1997).

(St∗v), given by

St∗v =(

1 + 1

e

)ln

(h0

ha

), (4)

where e is the coefficient of restitution based upon linear ve-locity differences of the particles before and after impact; andha represents the characteristic length of the surface asperities.

Recently, the importance of Ennis’ theory has inspired re-searchers (Mackaplow et al., 2000; Mill et al., 2000; Adetayoet al., 1995; Badawy and Hussain, 2004) to further study the ef-fects of particle size, binder viscosity, and amount on the growthkinetics and mechanism of wet granulation. For instance, Millet al. (2000) found that the growth rate of sand in a low shearmixer increases with an increase in the amount of a low viscos-ity binder (up to maximum 100 mPa s), such as silicone. Theyalso found that growth rate decreases with an increase in theamount of binder with viscosity higher than 100 mPa s.

Badawy and Hussain (2004) determined in experiments withanhydrous lactose that the growth rate increases with a decreasein initial particle size, in accordance with Ennis’ theory, assmaller particles present low kinetic energy that is dissipatedeasily in the binder layer. Ennis et al. (1991) and Adetayo et al.(1995) observed a sequential two-stage mechanism during thewet granulation of fertilizers with a wide size distribution, whileMill et al. (2000) failed to observe the sequential two-stagemechanism during the granulation of materials with a narrowsize distribution.

Powders with bimodal particle size distribution (PSD) or awide size distribution contain many small and large particlesthat favor coalescence between them by the layering mecha-nism or adhesion of fine particles to large particles as suggestedby Litster and Waters (1988, 1990), and Tardos et al. (1997)(Fig. 1). Hounslow et al. (2001) and Boerefijn and Hounslow(2005) also developed size-dependent agglomeration ker-nels that mathematically favored the coalescence of smalland large particles. On the contrary, it is believed that pow-ders with unimodal PSD or a narrow size distribution havesimilar size particles which do not favor the preferentialcoalescence between small and large particles. However,the effect of initial polydispersity of particle size (uni-modal PSD or narrow size distribution and bimodal PSDor wide size distribution) on the mechanism and growthkinetics of wet granulation has not been studied suffi-ciently enough to increase the fundamental understandingof particle agglomeration.

The main objective of this investigation is to study the ef-fect of initial polydispersity of particle size (unimodal versusbimodal distribution) on growth kinetics and the mechanism ofwet granulation. The effect of interactions between factors suchas initial particle size and the amount and viscosity of binderswere also studied. PSD was determined by means of image pro-cessing and analysis (Realpe and Velázquez, 2006; Velázquezet al., 2006) to avoid granule breakage and/or agglomerationduring sieving/shaking process.

2. Experimental methods

2.1. Materials and equipment

Pharmaceutical powders such as lactose anhydrous suppliedby Sheffield Products and lactose monohydrate manufac-tured by FOREMOST FARMS USA #55-0072 and supplied byMutchler Inc. (PR) were used in the wet granulation experi-ments. Fig. 2 shows the three PSD used in the wet granulationexperiments, designated as PSD1 (fine size powders), PSD2(medium size powders), and PSD3 (coarse size powders). Thethree levels of PSD were obtained by screening lactose monohy-drate and anhydride using the following sieve trays Tyler’s 270,230, 200, 170, 140, 70, 50, and 40 mesh US Standard. Powdersrecollected at each level were combined to prepare unimodaland bimodal distribution (PSD1, PSD2, and PSD3) and mea-sured by means of image processing and analysis (Realpe andVelázquez, 2006; Velázquez et al., 2006).

A viscometer (Brookfield LVDV-III+) was used to measurethe viscosity of Povidone–water mixtures at room temperature.Three different amounts of solid Povidone (0%, 5%, and 9%)were dissolved in water at room temperature to obtain homoge-neous binder solutions with viscosities of 1, 2.49, and 4.85 cp,respectively. The Povidone (Plasdone K-29/32) was manufac-tured by ISP Technologies INC.

Fig. 3 depicts a schematic of a laboratory-scale high shearmixer. A Ryobi� 12-in drill press was used as an impeller

Fig. 2. Initial particle size distributions for wet granulation.

1604 A. Realpe, C. Velázquez / Chemical Engineering Science 63 (2008) 1602–1611

Fig. 3. Laboratory-scale high shear mixer.

motor, rotating vertically, at a speed fixed at 560 rpm. Twostainless steel blades were attached to the impeller axis. Liq-uid binder was added to the powder mixture at a rate of161.7 ml/min using a peristaltic pump through a nozzle.

Although this is a laboratory-scale high shear mixer,the down-scaling of the wet granulation process allows anacceptable-mixed process without significant spatial variationin PSD and, therefore, obtains reliable measurements. Thespatial variation of PSD (or PSD uniformity) in a granulatoris modeled by the term (∇ • (�n)) in the population balanceequation (Randolph and Larson, 1971):

�n

�t+ ∇ • (�n) − B + D = 1

V

(∑Qin × nin −

∑Q × n

),

(5)

∇ • (�n) = �(vxn)

�x+ �(vyn)

�y+ �(vzn)

�z, (6)

where n is the number density function; t is the time; v is particlevelocity; B and D are the birth and death rates, respectively; Vis the mixer volume; and Qin and Q are flow rates.

In order to obtain an acceptable mixing quality, the poor mix-ing zone in the granulator located near the wall and bottom ofthe vessel had to be reduced. This was achieved by reducing thespace between the blades and the vessel wall, and by position-ing the blades equidistantly in the vessel as shown in Fig. 3b.

2.2. Granulator characterization

The granulator was tested to determine the spatial variationof PSD and, therefore, the experiment reproducibility. Foursamples were taken from four different zones of the granulator(Fig. 4), dried at room temperature, and analyzed by means ofimage processing and analysis to determine their PSD (Realpeand Velázquez, 2006; Velázquez et al., 2006). Fig. 5 shows acumulative mass percentage similar for the top and bottom ofthe mixer. Furthermore, the low standard deviation for the massmedian diameter (Table 1) indicates granule size measurementsare similar at four positions inside the mixer. Mass mediandiameter is the diameter in which exactly one-half of the mass

Fig. 4. Zones inside the granulator.

Fig. 5. Cumulative mass percentages for the four different zones inside thegranulator.

Table 1Study of repeatability

Vessel zones Mass median diameter (�m)

Top zone 1 808Top zone 2 820Bottom zone 3 823Bottom zone 4 821

Mean 818 �mS.D. 6.78 �mR.S.D. 0.83%

S.D. = standard deviation; R.S.D. = relative standard deviation.

is composed of smaller particles, and the other half of the massis composed of larger particles.

2.3. Granulation process

Approximately 90 g of lactose monohydrate and 345 g oflactose anhydride were mixed for 5 min in a high shear mixer,operating at 560 rpm. Homogenization of the powder mixture


Table 2Experimental design

Factors Particle size distribution (mm) (Fig. 2) Binder viscosity (cp) Amount of binder (% vliquid/wsolid)

Levels PSD1 PSD2 PSD3 1 2.49 4.85 9.9 11.7 13.6

is ensured using an NIR spectrometer; the dry powders weremixed until the spectrum no longer changed significantly withrespect to the previous one. Water was then added to the lactosemixture by means of a peristaltic pump through a nozzle andthe powder mixture was granulated. The granulator was stoppedafter the first minute to extract samples from different pointsinside the mixer to measure PSD, and to collect off-line spectra.This experimental procedure was repeated at 2, 4, 6, 8, 10, and12 min.

2.4. Experiment design

The experiments to study wet granulation behavior using lac-tose anhydrous and monohydrate were carried out following theSplit-Plot experimental design (Montgomery, 2001) consistingof three factors and three levels for each factor, plus two repli-cates, as shown in Table 2. The Split-Plot design consists offactorial experiments, not completely randomized.

3. Results and discussion

3.1. Effect of initial polydispersity of particle size (unimodalversus bimodal) on the mechanism and growth rate of wetgranulation

A normalized number distribution (NND) was used to showthe change in PSD over time, as indicated in Figs. 6–8. The two-stage coalescence mechanism was observed in the wet gran-ulation of pharmaceutical powders at 13.6% binder with bothinitial unimodal and bimodal PSD. The bimodal PSD showedfast growth followed by slow growth while the unimodal PSDshowed an opposite mechanism, slow growth followed by fastgrowth as observed in Fig. 9 through the evolution of the massmedian diameter of the particles during wet granulation.

The initial bimodal PSD (Figs. 6 and 7) first exhibits a faststage of granule growth. This stage is controlled by both thebinder amount added during the first 30 s and the high probabil-ity of collision between small and large particles that increasesthe growth rate. For large particles with a few porous, the binderis spread over the surface and it is immediately available for co-alescence with the fine particles as observed by Adetayo et al.(1995) and Litster and Waters (1988, 1990).

The opposite case is observed for initial mono-dispersed uni-modal PSD (Fig. 8). The first stage of granule growth is slow,due to the high concentration of similar sized particles, whichdoes not favor coalescence. In this case, particles slowly enlargeover the first 8 min of wet granulation. This enlargement trans-forms the distribution from mono-dispersed unimodal (standarddeviation, S.D. = 0.034 mm) PSD to poly-dispersed unimodal

Fig. 6. Effect of initial bimodal PSD (coarse size powders, PSD3) on thegrowth rate of wet granulation at initial 13.6% v/w and 1 cp viscosity.

Fig. 7. Effect of initial bimodal PSD (medium size powders, PSD2) on thegrowth rate of wet granulation at initial 13.6% v/w and 1 cp viscosity.

(S.D. = 0.189 mm) PSD. The poly-dispersed volume ratio be-tween small to large particles was approximately 150. The sizeof small particles was obtained on the 10% of the total num-ber of particles, while the size of large particles was obtainedon the 90%. This volume ratio is higher than the 112 observedfor the initial bimodal PSD (Figs. 6 and 7) with a 0.071 mmS.D. This change to poly-dispersed unimodal PSD caused thesecond stage to be fast, similar to that seen in the bimodal dis-tribution which is governed by the high probability of collisionbetween small and large particles.


Fig. 8. Effect of initial unimodal PSD (fine size powders, PSD1) on thegrowth rate of wet granulation at initial 13.6% v/w and 1 cp viscosity.

Fig. 9. The evolution of mass median diameter in wet granulation at 13.6% v/wand 1 cp viscosity.

The strength of the liquid bridge formed between similarsize particles is weaker than that between small and large parti-cles due to high bending, stretching, and the gravitational forceyielded by the particles with the highest weight. The increasedstrength of the liquid bridge between small and large particlesand the lower kinetic energy of small particles allow the parti-cles to remain in contact for enough time to permit the smallparticle to join the larger one by diffusion through binder layers.The preferential coalescence between small and large particlesis supported by a layering mechanism or coalescence of coarseand fine particles (Fig. 1) described by the Stokes’ number ifsizes between colliding particles are different (Tardos et al.,1997) and by size-dependent agglomeration kernels developedby Hounslow et al. (2001) and Boerefijn and Hounslow (2005).

The nucleation mechanism for fine narrow PSD could oc-cur over first stage of slow growth of wet granulation by pen-etration of liquid drops into the fine powder bed. These nucleitake time to consolidate and become surface wet to facilitatecoalescence. These observations agree with the initial “induc-tion phase” as described by Iveson and Litster (1998), andIveson et al. (2001).

The gradient of each line in Fig. 9 is shown in Table 3, andrepresents the granule growth rate, similar to that calculated byMill et al. (2000). For wet granulation of powders with initialbimodal PSD, the growth rate increases with decreasing particlesize, as indicated in Table 3. These results are consistent withEnnis’ theory (Ennis et al., 1991).

3.2. Effect of initial particle size on granule growth rate inwet granulation

Fig. 9 shows how mass median diameter increased over timefor all three size ranges of powders (PSD1, PSD2, and PSD3)at 13.6% v/w and 1 cp viscosity. The figure depicts how parti-cle growth rate increases with a decrease in initial particle size,as indicated by the mass median diameter in Table 3. ThroughFig. 9 and Table 3, we can see that fine powders with initialunimodal PSD exhibit a faster growth rate in the second stageof wet granulation than the growth rate observed in the firststage of wet granulation with medium-sized and coarse pow-ders. This phenomenon occurs due to a mono-dispersed uni-modal PSD becoming a poly-dispersed unimodal PSD over thefirst 8 min, favoring agglomeration of particles. The unimodalPSD grows larger in size than the initial bimodal PSD after8 min, since it reaches a volume ratio of 150, which is higherthan the 112 reached by the initial bimodal PSD. The initialunimodal PSD consists of fine particles with high surface areafavoring agglomeration of particles.

However, for fine powders with initial unimodal PSD at 9.9%and 11.7% v/w, a stage of rapid growth was not evident dur-ing wet granulation. Instead, a one-stage mechanism of slowgranule growth was predominant. A slow growth rate at lowbinder content is due to the high cohesive force of small par-ticles produced by the large contact surface, leading to stronggranules that the material, itself, cannot is hard to deform,thereby decreasing agglomeration. The addition of liquid allowsthe agglomerate to deform due to decreased particle–particle in-teractions. These results are in agreement with results reportedby Jægerskou et al. (1984) that ball growth may occur if toomuch liquid is added, or if granulation times are too long.

3.3. Effect of binder content on granule growth and themechanism of wet granulation

Fig. 10 depicts the effect of the amount of binder on particlegrowth. A change in the amount of binder can alter the mech-anism and growth rate in the second stage of wet granulation.For powders with initial bimodal PSD, the mechanism changesfrom a particle agglomeration at 13.6% v/w of binder, to a parti-cle breakage mechanism at 9.9% and 11.7% v/w of binder. Forpowder mixtures with initial unimodal PSD, variations in theamount of binder can also change the number of stages fromtwo (slow and fast) at 13.6% v/w of initial binder, to one for9.9% and 11.7% v/w of initial binder, as observed in Fig. 11.

The initial fast growth for bimodal PSD is maintained by highliquid content added during the first 30 s and by the high prob-ability of collisions between small and large particles, as these


Table 3Effect of particle size on granule growth rate at 13.6 % v/w and 1 cp viscosity

Mass median diameter (mm) PSD Stage Growth rate (mm/min) Ratio: fast/low

0.46 PSD3: bimodal First: fast 0.160 8.0Second: slow 0.020

0.37 PSD2: bimodal First: fast 0.311 11.96Second: slow 0.026

0.13 PSD1: unimodal First: slow 0.038 16.7Second: fast 0.634

Fig. 10. Effect of binder content (1 cp viscosity) on the growth rate of wetgranulation of coarse size powders (PSD3) with bimodal PSD.

Fig. 11. Effect of binder content (1 cp viscosity) on the growth rate of wetgranulation of fine size powders (PSD1) with unimodal PSD.

collisions facilitate coalescence. However, the second stage ischaracterized by either a slow breakage mechanism, due to thelow moisture content (9.9% and 11.7% v/w) and binder evap-oration (Fig. 12) induced by high shear force, or by slow ag-glomeration of particles, due to the decreasing size differencebetween particles.

There is a minimum critical amount of liquid on the gran-ule surface required to trigger the second stage of slow growth.

Fig. 12. Change in binder content (1 cp viscosity) during wet granulation ofcoarse size powders (PDS3) with bimodal PSD at 9.9% v/w.

This minimum amount of liquid is the least required to forma liquid layer on the granule surface to increase the probabil-ity of coalescence between particles. Above this critical min-imum value, there is therefore a high probability of only onestage of fast growth. The end of the first stage of fast granulegrowth is related to the end of the addition of binder, and thebeginning of slow granule growth or breakage without a signif-icant change in particle size. These observations are consistentwith results obtained by Holm et al. (1984), Lindberg (1984),Schæfer et al. (1990), and Mackaplow et al. (2000). Although,fast granule growth may continue if too much liquid is addedinitially (Fig. 6).

Fig. 11 also shows the effect of the amount of binder at1 cp viscosity on the growth of particles with unimodal PSD.The agglomeration mechanism was always the predominantphenomenon during wet granulation with three different levelsof moisture content. Variations in the amount of binder can alsochange the stage number, from one stage at 9.9% and 11.7% v/wof binder, to two stages at 13.6% v/w of binder.

3.4. Effect of binder viscosity on granule growth and themechanism of wet granulation

Binder viscosity was modified by dissolving differentamounts of Povidone in water. Fig. 13 demonstrates the effectof binder viscosity on the growth kinetics and mechanism ofwet granulation of coarse size powders with initial bimodal


Fig. 13. Effect of binder viscosity on the growth rate of wet granulation ofcoarse size powders (PSD3) with initial bimodal PSD at 11.7% v/w.

Table 4Effect of binder viscosity on granule growth rate at 11.7% v/w and coarsesize powders (PSD3)

Mass mediandiameter (mm)

Viscosity(cp)

Stage Growth rate(mm/min)

0.46 1 Second: slow −0.00090.46 2.49 Second: slow −0.00160.46 4.85 Second: slow −0.0042

Fig. 14. Bimodal breakage: (a) many small particles and a few large particlesand (b) many small particles and one large particle.

PSD at 11.7% v/w of binder. The granulation exhibited a two-stage mechanism: initial fast agglomeration followed by slowbreakage of particles. The growth rate in the first stage in-creases with increase in binder viscosity, while the growth ratein the second stage decreases with increase in binder viscosity(Table 4 and Fig. 13).

The initial fast granule growth rate agrees with results re-ported by Hoornaert et al. (1998) when they observed that a vis-cous binder (water with polyvinylpyrrolidone) produced largerinitial granules.

The large granule size in the first stage, obtained by an in-crease in binder viscosity, is the result of increasing viscousforces, as indicated by Eq. (7) (Ennis et al., 1990, 1991). Itcould also result from the droplet size obtained during binderatomization, achieved by changing surface tension. However,Holm et al. (1983) found that granule size in a high shear mixerappears almost independently of atomized binder droplet size:

Fvis = 3��v0r2p

4h. (7)

Fig. 15. Breakage mechanism during wet granulation of coarse size powders(PSD3) with initial bimodal PSD at 11.7% v/w and 1 cp viscosity.

Fig. 16. Effect of binder viscosity on wet granulation of fine size powders(PSD1) with initial unimodal PSD at 11.7% v/w.

These results are also in agreement with the Stokes number(Eq. (2)). As previously stated, the probability of coalescenceincreases by increasing the viscosity of the binder covering theparticles. The viscous forces of the binder layer increase as theviscosity increases, as predicted by Eq. (7), favoring the dis-sipation of kinetic energy by preventing rebound and allowingthe granules to stay in contact long enough for coalescence tooccur.

A decrease in granule growth rate during the second stageis due to the increase in binder viscosity by dissolution of lac-tose in the binder (Schaasfsma et al., 1998), which acts as aresistance to the motion of the particle. This favors the binarybreakage of particles by high shear. Schaasfsma et al. (1998)suggest that the deviation between the experimental and sim-ulated results in their experiment with a fluid bed granulatorwas caused by an increase in binder viscosity during wet gran-ulation due to the dissolution of lactose in the binder solu-tion. Thus, the second stage is characterized by slow breakagemechanism, also due to a low binder content (11.7% v/w). This


combination could yield rigid granules that could be more eas-ily broken by blade impacts. Each granule undergoes bimodalbreakage to produce many small particles and a few large par-ticles (Fig. 14a), or many small particles and one large particle(Fig. 14b). This hypothesis is supported by a noted decreasein the number of large particles and an increase in small andmedium size particles, as shown in Fig. 15. Similar bimodalbreakage was also suggested by Hounslow et al. (2001).

Fig. 16 depicts the effect of binder viscosity, in this case, forinitial unimodal PSD. The agglomeration mechanism of twostages (medium-fast and slow growth) is predominant, and themass median size increased with an increase in binder viscosityduring wet granulation. Still, the mechanism of the two stagesin wet granulation of powders with unimodal PSD is less pro-nounced than for powders with bimodal PSD.

Fig. 17. Effect of interaction of the factors on granule rate (a) particle sizeversus binder viscosity and (b) moisture content and binder viscosity.

Table 5Goodness of fit for kernels, relative to the experimental data

Kernel structure Reference Average residuals

Unimodal Bimodal BimodalPSD1 PSD2 PSD3

(l + �)3 Smoluchowski (1917) 9.6083 × 10−2 6.0243 × 10−1 4.0120 × 10−1

(l × �) Golovin variation 8.7336 × 10−2 6.0247 × 10−1 4.0140 × 10−1

(l + �)2 ×√(

1l3

+ 1�3

)Equipartition of kinetic energy. Boerefijn and Hounslow (2005) 8.7284 × 10−2 1.6876 × 10−1 1.7822 × 10−1

3.5. Effect of the interaction of factors on granule growth ofwet granulation

The effect of interactions between particle size and amountand viscosity of binder on the growth rate during the first stageof wet granulation was analyzed. Fig. 17a indicates that growthrate increases with increase in binder viscosity at all moisturecontent. Particle size, on the other hand, has negligible effect atlow moisture (zero slope), while a significant negative slope athigh moisture content (13.6%) is observed. This indicates a lowinteraction between particle size and moisture content at lowmoisture content. Fig. 17b confirms that moisture content is asignificant factor on the growth rate and interaction betweenmoisture content and binder viscosity is significant at moisturecontent higher than 11.7% and negligible otherwise.

3.6. Modeling of experimental data by population balanceequation: agglomeration kernels proposed in the literature

As indicated above, the particle coalescence that occurs dur-ing the process of wet granulation is favored by the collision ofsmall and large particles, as demonstrated by the higher granulegrowth rate for powders with bimodal PSD than for powderswith unimodal PSD. Table 5 shows three size-dependent ker-nels published in the literature used to predict our experimen-tal results of slow granule growth for both unimodal and bi-modal distributions. The coalescence kernels were divided intothree types: (1) kernels that favor growth rate by collision be-tween small and large particles (Boerefijn and Hounslow, 2005;Adetayo and Ennis, 1997); (2) kernels that favor growth rate bycollision between particles of similar size (Golovin variation);and (3) kernels without any preferential effect on growth rateby collision of particles of any size (Smoluchowski, 1917).

Table 5 also shows the residuals obtained for each kernelby fitting the parameters with experimental data. The param-eter estimation was performed using Parsival�, a commercialsoftware designed to solve a large class of integro-differentialequations using a discretization technique. A detailed descrip-tion is provided by Wulkow et al. (2001). The Hounslow’skernel describes the experimental data obtained from the wetgranulation of fine and medium size powders, although the fitdoes not describe the first peak in the curve for wet granulationof coarse size powders toward the endpoint of the granulation.As anticipated, the Golovin variation and Smoluchoski kernelsdo not describe the granule agglomeration produced by the


Fig. 18. Comparison of simulations of coalescence kernels published in theliterature versus the experimental data (bimodal PSD3).

collision of different-sized particles, as observed in Fig. 18,which only depicts results at 12 min of granulation.

4. Conclusions

Initial PSD shape, whether unimodal or bimodal, has a strongeffect upon granule growth rate and the mechanism by whichwet granulation occurs. A sequential mechanism consisting oftwo stages was observed during the wet granulation of powderswith bimodal PSD, for three binder contents. The first stageof rapid granule growth is controlled by the amount of binderand by the high probability of coalescence resulting from thecollision of small and large particles. The second stage exhibitsslow agglomeration when binder content is 13.6% v/w, and slowbreakage when binder content is 9.9% or 11.7% v/w.

Wet granulation of pharmaceutical powders with initial uni-modal PSD at 9.9% and 11.7% v/w binder content exhibitedslow granule growth rate in two stages, stages which were lesspronounced than the two stages for powders with bimodal PSD.In contrast, wet granulation of pharmaceutical powders withinitial unimodal PSD at 13.6% v/w binder content exhibitedtwo pronounced stages, due to the enlargement of particles thatoccurred during the first stage (the first 8 min) of wet granula-tion. This enlargement transforms the distribution shape from amono-dispersed, unimodal PSD to a poly-dispersed, unimodalPSD. A volume ratio between small and large particles of ap-proximately 150 was necessary to obtain fast granule growth inthe second stage. The experimental results were best predictedby a population balance equation using a coalescence kernelthat favors growth rate by collision between small and largeparticles.

In general, the binder content, PSD shape, and interactionbetween particle size and binder content were the factors withthe strongest effect upon granule growth rate and the mecha-nism of wet granulation, whereas binder viscosity and initialparticle size affected granule growth rate moderately. Variationin the three factors is explained by the viscous Stokes’ (Stv)

number, developed by Ennis et al. (1991), wherein the probabil-ity of successful coalescence between particles is increased bysmaller particle size, higher binder viscosity, and higher bindercontent.

Acknowledgments

We are grateful to Angel Zapata and Efren Gregory for theircollaboration during the equipment setup. Thanks to the NSF-EPSCoR and INDUNIV for their financial support.

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