Hydrodynamic Investigation of USP Dissolution Test ...pharxmonconsulting.com/files/119402610.pdf · available on the hydrodynamics of this apparatus. In this work, laser-Doppler velocimetry

Hydrodynamic Investigation of USP DissolutionTest Apparatus II

GE BAI,1 PIERO M. ARMENANTE,1 RUSSELL V. PLANK,2 MICHAEL GENTZLER,2 KENNETH FORD,2 PAUL HARMON2

1Department of Chemical Engineering, New Jersey Institute of Technology, Otto H. York Newark,323 M. L. King Boulevard, Newark, New Jersey 07102-1982

2Merck & Co., West Point, Pennsylvania 19486

Received 18 April 2006; revised 5 July 2006; accepted 18 August 2006

Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.20818

ABSTRACT: The USP Apparatus II is the device commonly used to conduct dissolutiontesting in the pharmaceutical industry. Despite its widespread use, dissolution testingremains susceptible to significant error and test failures, and limited information isavailable on the hydrodynamics of this apparatus. In this work, laser-Dopplervelocimetry (LDV) and computational fluid dynamics (CFD) were used, respectively,to experimentally map and computationally predict the velocity distribution inside astandard USP Apparatus II under the typical operating conditions mandated by thedissolution test procedure. The flow in the apparatus is strongly dominated by thetangential component of the velocity. Secondary flows consist of an upper and lowerrecirculation loop in the vertical plane, above and below the impeller, respectively. A lowrecirculation zone was observed in the lower part of the hemispherical vessel bottomwhere the tablet dissolution process takes place. The radial and axial velocities in theregion just below the impeller were found to be very small. This is themost critical regionof the apparatus since the dissolving tablet will likely be at this location during thedissolution test. The velocities in this region change significantly over short distancesalong the vessel bottom. This implies that small variations in the location of the tablet onthe vessel bottom caused by the randomness of the tablet descent through the liquid arelikely to result in significantly different velocities and velocity gradients near the tablet.This is likely to introduce variability in the test. � 2007 Wiley-Liss, Inc. and the American

Pharmacists Association J Pharm Sci 96:2327–2349, 2007

Keywords: dissolution; testing; pharmaceutical testing; USP dissolution test appa-ratus; hydrodynamics; laser doppler velocimetry, LDV; computational fluid dynamics,CFD; coning

INTRODUCTION

Solid dosage forms, such as tablets, are aconvenient way of administering drugs topatients. Upon ingestion, tablets disintegrate intosmaller fragments in the body compartment

where absorption by the body is initiated,typically in the stomach or the upper intestine.These fragments dissolve in the digestive juicesand can become absorbed by an epithelial layersuch as the lining of the upper intestine. Thiscomplex in vivo process is routinely simulated inin vitro dissolution tests mandated by the foodand drug administration (FDA) and specified inUnited States pharmacopoeia (USP).

Dissolution testing is routinely carried out inthe pharmaceutical industry to determine the rateof dissolution of solid dosage forms. In addition to

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 9, SEPTEMBER 2007 2327

Correspondence to: Piero M. Armenante (Telephone: 973-596-3548; Fax: 973-596-8436;E-mail: [email protected])

Journal of Pharmaceutical Sciences, Vol. 96, 2327–2349 (2007)� 2007 Wiley-Liss, Inc. and the American Pharmacists Association

being routinely used by pharmaceutical com-panies to demonstrate adequate drug releasein vivo (through in vivo/in vitro (IVIVC) correla-tion), in vitro dissolution testing is used to assistwith formulation design, process development,and especially thedemonstration of batch-to-batchreproducibility in production. Dissolution testingis one of the several tests that pharmaceuticalcompanies typically conduct on oral dosage for-mulations (e.g., tablets) to determine complianceand to release products for distribution and sales.

Although the USP lists several different dis-solution test apparatuses,1 most dissolution testsare currently conducted with USP DissolutionTest Apparatuses I and II. The USP DissolutionTest Apparatus II is the most commonly andwidely used apparatus specified by the USP,and it is the focus of the hydrodynamic studypresented in this work. The dimensions, charac-teristics, and operating conditions of USPDissolu-tion Test Apparatus II are detailed by the USP,1

and all users must conform to these prescriptionswhen conducting dissolution tests.

The USP Dissolution Test Apparatus IIcomprises a glass vessel and an agitation system.The glass vessel is a cylindrical glass tank with asemispherical bottom, and a working volume of900 mL (Fig. 1a). The agitation system consists ofa two-blade paddle impeller mounted on a shaftcentrally located in the vessel andprofiled to follow

the hemispherical portion of the vessel. In theindustrial practice, replicate dissolution tests aretypically conducted in parallel using commerciallyavailable systems containing six or more indi-vidual USP Dissolution Test Apparatus II units(Fig. 1b). These systemsallow the agitation system(motor and impellers) to be lifted above the rackholding the vessels, as shown in this figure, inorder to prepare the system for the actual test.Each vessel is filled with a prescribed amount of afluid simulating gastric or intestinal fluids, andmaintained at constant temperature of 378C byeither a water bath or a heating jacket.

The test consists of lowering the agitationsystem so that the paddles reach their predeter-mined location inside the vessels, as required bythe USP, starting the agitation so that the paddlesrotate at 50 rpm (in some instances 75 or 100 rpm),adding a single dosage form unit, such as a tablet,to each vessel simultaneously, drawing liquidsamples over time from a prescribed locationwithin the vessel, analyzing the drug concentra-tion in each sample, and determining the dissolu-tion profile over time. These profiles must bewithin a predefined range, and cannot differsignificantly from the dissolution profile that thedrug manufacturer has initially submitted to theFDAwhen the drugwas approved.Anydissolutionprofile that is found to be statistically different,according to a predefined criterion,2 from the

Figure 1. USPDissolution Testing Apparatus II: (a) paddle impeller and glass vessel;and (b) typical commercial dissolution testing systems containing seven Apparatus IIunits (Distek Premiere 5100 Bathless Dissolution System).

2328 BAI ET AL.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 9, SEPTEMBER 2007 DOI 10.1002/jps

reference profile established for that dosage formimplies failure of the test and non-compliance ofthe production batch being tested. When thisoccurs, the batch cannot be released for commer-cialization and it is often disposed of. The cost ofsuch failure is often significant given the typicalhigh value of the product.

The USP Dissolution Test Apparatus II hasbeen used in the pharmaceutical industry fordecades, since this test was first officiallyintroduced almost 30 years ago.3 Nevertheless,and despite its widespread use in the industry,dissolution testing remains susceptible to signifi-cant error and test failures. A review of theliterature shows that there have been numerousreports describing high variability of testresults,4–11 even when the so called ‘‘calibratortablets’’ (i.e., tablets manufactured for the solepurpose of testing the proper operation of thedissolution test equipment) are used.5,7,10,12,13

Failures linked to dissolution testing resulted in47 product recalls during the period 2000–2002,representing 16%ofnon-manufacturing recalls fororal solid dosage forms.14–16 Irrespective of theunderlying causes (such as incorrect use of theequipment or deviation of dissolution profile fromthe standard caused by incorrect tablet formula-tion) failed dissolution tests can result in productrecalls, costly investigations, potential productiondelays, which, in turn, can have a significantlynegative financial impact.

Some of the same studies have indicated thatthehydrodynamics ofApparatus II appears to playa major role in the poor reproducibility of dissolu-tion testing data and the inconsistency of dissolu-tion results. This is hardly surprising consideringthat Apparatus II is a small, unbaffled vesselwith a hemispherical bottom provided with aslowly rotating paddle, in which a tablet (oranother dosage form) is dropped. This system canbe expected to be associated with a complexhydrodynamics resulting in fluid velocities whosedirections and intensities are highly dependent onthe location within the vessel. To complicate theissue farther, tablets have often been reported toland at different locations at the bottom of thevessel after they are dropped in the vessel at thebeginning of a test,making the dissolution processeven more susceptible to hydrodynamic factors.

Until recently, limited information has beenavailable on the hydrodynamics of the dissolutionapparatus and the effects of operating andgeometric variables on the velocity distributionin the system. Such information is critical to

advance the fundamental understanding of thedissolution rate process, enhance the reliabilityof dissolution testing, and eliminate artifactsassociated with test methods, especially sincedissolution measurements have often beenreported to be inconsistent and poorly repro-ducible. A literature review shows that a fewinvestigators have conducted hydrodynamic stu-dies. Bocanegra et al.9 measured the flow field bylaser Doppler anemometry (LDA), the first experi-mental measurement of this kind in dissolutionvessels. These researchers generated data only forvery limited regions of the vessel. More recently,Kukura et al.12 obtained experimental flowpatterns using particle image velocimetry (PIV)and laser-induced fluorescence (LIF), and com-puted the velocity flow field using computationalfluid dynamics (CFD). However, they presentedvery limited quantitative comparison between theexperimental data and the predictions. Otherresearchers also made an effort to determine theflow field inside the USP Apparatus II vesselthrough CFD. Kukura et al.17 and Baxter et al.13

predicted the flow pattern and shear effects withCFD. McCarthy et al.18,19 predicted the flow fieldwith CFD and compared the CFD predictions withthe limited experimental results from previousresearch.9

This overview shows that our current knowl-edge on the hydrodynamics of dissolution testingsystems is still greatly incomplete, and that thereis a significant need for work aimed at fullyquantifying the hydrodynamics in the USP Appa-ratus II both computationally and experimentally.Therefore, the primary objective of this work is toquantify the hydrodynamics in a standard USP IIdissolution vessel by experimentally mapping (vialaser Doppler velocimetry) and computationallypredicting (via CFD) the velocity distributioninside the vessel under the typical operatingconditions mandated by the dissolution test pro-cedure. A detailed comparison of the numericalpredictions against the experimental data is alsoprovided, and it appears to be favorable.

EXPERIMENTAL APPARATUS AND METHOD

Dissolution Vessel and Agitation System

A standard USP Apparatus II dissolution vesselconsisting of an unbaffled, cylindrical, trans-parent, glass tank with a hemispherical bottom,and having an internal diameter, T, of 100.16 mm

HYDRODYNAMICS OF USP II APPARATUS 2329

DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 9, SEPTEMBER 2007

and an overall capacity of 1 L was used in allexperiments (Fig. 2a). The agitation systemconsisted of a standard USP II two-blade paddleimpeller mounted on a shaft. The exact geometryof each component of the impeller was obtained bymeasuring the actual dimensions with a caliper,which were found to be as follows: shaft diameter,9.53 mm; length of the top edge of the blade,74.10 mm; length of the bottom edge of the blade,42.00 mm; height of the blade, 19.00 mm; andthickness of the blade, 5.00 mm. This impellerwas provided by the Merck researchers and had aslightly larger diameter shaft at the blade,resembling a collar, as opposed to the uniformshaft diameter, including the portion at the blade,typical of the USP design. The radius of this collarwas only 1.6 mm larger than that of the rest of theshaft. The experiments and the computationalresults were obtained with this impeller in orderto insure exact conformity to the Merck system.However, the geometric differences betweenthis system and the typical USP system are sominimal that the result obtained here areexpected to be equally valid for the USP impellerwith no collar.

Since only thehydrodynamics of the systemwasof interest here, the dissolution vessel and paddlewere not assembled in a full dissolution systemsimilar to that shown in Figure 1b. Instead, theimpeller was connected to a 1/8-HP motor con-trolled by an external controller (G.K.Heller Corp,Model 202P6518) which was used here to rotate at

a constant agitation speed of 50 rpm, the conven-tional operating condition specified in the USP forthe test. The corresponding impeller tip speed was0.194 m/s and the impeller Reynolds number was4939. The motor-impeller system was mounted ona bracket above the vessel so that the impeller wascentered in the vessel and the impeller clearanceoff the vessel bottom was 25 mm, as mandatedby USP. The vessel was filled with 900 mL ofdeionized water, as in the typical case for this test.

Laser-Doppler Velocimetry (LDV) System

Laser-Doppler velocimetry (LDV) is a non-intru-sive experimental method used to determine thelocal velocity distribution (including its fluctuat-ing component) in a fluid inside any transparentpiece of equipment. LDV has been proved to bea very valuable experimental method in fluidmechanic studies and was extensively used byseveral investigators to quantify the flow charac-teristics of mixing vessels and reactors.20–23 Inthis project, a Dantec 55� series LDV apparatus(Dantec Measurement Technology USA, Mah-wah, NJ) was used to determine the velocity flowfield and turbulence intensity inside the vessel(Fig. 3). The LDV system comprised a 750 mWargon-ion laser (Ion Laser Technology, Inc.)producing a single multicolored laser beam pas-sing through an optical filter to generate a mono-chromatic green beam (wavelength: 512 nm).The resulting beam passed through a beam

Figure 2. (a) Basic geometry ofUSPDissolutionApparatus II vessel and impeller; and(b) iso-surfaces at different vertical positions.

2330 BAI ET AL.


splitter from which two beams emerged, one ofwhich was passed through a Bragg cell to lowerthe frequency by 40MHz and distinguish betweenpositive and negative velocity measurements. Thebeams then passed through a beam expandersystem and a final focusing lens with a focallength of 330 mm. This lens made the beamsconverge so that they intersected each other toform a small control volume in the interrogationregion where the velocity was to be measured. Inan actual measurement, the beams were made toconverge inside the USP II vessel.

TheUSP II vesselwas suspended fromabracketspecifically built so that the vessel could be placedin an external Plexiglas square tank filled withwater, in order to minimize optical distortionduring LDV measurements. The water in theUSP vessel was seeded with trace amounts ofneutrally buoyant 1.5 mm silver coated particles(TSI, Inc., Minneapolis, MN) that could follow thefluid flow pattern very closely.

The motor-impeller-vessel assembly wasmounted on an x-y-z traversing system that couldposition the vessel at any desired location in frontof the LDV system, thus enabling the velocity tobe measured anywhere in the vessel. The lightscattered by the particles was collected by aphotodetector assembly placed next to the tankat a 908 orientation with respect to the laser, andconnected to a data acquisition system. The timeinterval for each measurement was typically 60 s.In most cases, some 600–2500 instantaneousvelocity data points were collected at any locationand for the selected velocity component, fromwhich the local average velocity and turbulenceintensity could be calculated. Data analysis wasperformed to generate the local velocity com-ponents in the direction parallel to that of theplane of the two laser beams. Appropriate rotation

of the laser beam assembly and translation ofthe vessel-motor assembly yielded the velocitycomponents in all three directions at any location.

Ten iso-surfaces at different vertical (z) posi-tions were selected along the height of the vesselwhere LDV velocity measurements were made(Fig. 2b). The horizontal plane where the cylind-rical and hemispherical portions of the dissolutionvessel intersect was taken as the iso-surfaceat z¼ 0. The iso-surfaces at z¼�6.75 mm,z¼�15.75 mm, and z¼�25.75 mm are the planeson which the top edge of the impeller blade, themiddle of the impeller blade and the bottomedge ofthe impeller blade lie, respectively.

On the iso-surfaces above the impeller, LDVmeasurements were made at seven evenly spacedradial locations between the shaft and the vesselwall. However, because of the hemisphericalshape of the vessel bottom and the presence ofthe impeller blades, fewer measurement locationswere used in the impeller region and the bottomregion. At each measurement location, threevelocity components (tangential, axial, and radial)were obtained by LDV.

Numerical CFD Simulation

Numerical simulations of the velocity distributionand turbulence levels inside the USP II dissolutiontest apparatus were conducted using a commercialmesh generator (Gambit 2.1.6)24 coupled with acomputational fluid dynamic (CFD) package(Fluent 6.2.16).25 The full 3608-tank geometrywas incorporated in the simulations.

Mesh Generation and Mesh Quality

Figure 4 shows the mesh used in the CFDsimulations. In order to save computation time

Figure 3. Laser-Doppler velocimetry (LDV) apparatus used in this work.



and effectively increase the simulation conver-gence, a structured Cooper-type hex mesh wascreated in the cylindrical portion of the vessel andin the upper section of the hemispherical vesselbottom above section A-A in Figure 4c. Anunstructured, tetrahedral mesh was generatedin the lower section of the hemispherical bottom tofollow the curved shape more closely. Accordingly,the liquid volume was computationally parti-tioned into two sub-volumes. The meshes in eachsub-volume were created starting from the samestarting face (Fig. 4a), that is, the horizontal crosssection of the vessel located where the lower edgeof the impeller blade lies (section A-A in Fig. 4c).On this starting face, the curves resulting fromthe intersection of the horizontal plane withvertical solid surfaces such as the vessel wall(resulting in a circle) or the impeller blade edge(resulting in a rectangle) were identified. Thesecurves were partitioned into small elements byspecifying points on them fromwhich the grid linestarted. This approach resulted in the generationof a larger number of smaller cells in the regionsnear the impeller and the tank wall in order tocapture the steep velocity gradients in thoseregions. From the pre-meshed starting surface(Fig. 4a), a hex grid was generated with a Cooper-scheme approach, by extending and projectingthe pre-meshed surface both upward, up to theliquid-air interface (Fig. 4b), and downwards,reaching down to the iso-surface 12.35 mm below

the lower edge of the impeller. A much finertetrahedron mesh was created below thisiso-surface, in order to capture the flow near thevessel bottom.

The mesh typically contained 80262 cells,219590 faces, and 62472 nodes. Simulations witha mesh containing 258310 cells were also run, inorder to evaluate the effect of grid number to thenumerical solution. The twoCFDpredictions werenot appreciably different. In fact, the resultswith the coarser mesh matched the LDV datamarginally better.

Significant attentionwas paid to the generationof a high quality mesh, since this determinedwhether the simulation converged to a stablesolution or not. The average EquiAngle Skewparameter (one of the most important parametersto determine the quality of themesh) was typicallyin the range 0.3–0.4 (0-best; 1-worst) and was nolarger than 0.809 for any individual cell. The sizevariationwas very smooth in the complete domain.There was no hex cell with a high aspect ratio inthe domain. The cell elements were fine enoughto capture the high gradient of the geometry in thearea of impeller blade and the bottom of the vessel.

CFD Approach

The control volume technique used by the solverinvolved the discretization of the computationaldomain into a finite number of contiguous controlvolumes. The conservation equations of mass andmomentum were solved for each of these controlvolumes. All simulations were carried out on aDell Precision 650 Workstation, equipped withtwo Intel XEON 2.8 Gigahertz processors and2 gigabytes of random access memory (RAM). Atypical simulation required 40000 iterations andabout 30 h of CPU time to achieve conversion.

To account for the turbulent effects during thenumerical simulations, CFD simulations wereconducted using different turbulence models, thatis, the k-o model with low Reynolds numbercorrection, RNG k-e model, and Realizable k-emodel,26,27 or with no turbulencemodel at all, thatis, assuming laminar flow. After preliminaryresults were obtained, as describe below, the k-omodel with low Reynolds number correction wasselected and used throughout this work.

The standard k-o model is an empirical modelbased on model transport equations for theturbulence kinetic energy (k) and the specificdissipation rate (o), which can also be thought ofas the ratio of e to k.26,27 The k-o model has been

Figure 4. Mesh used in CFD simulation: (a) startingface on iso-surface at A-A; (b) top face on iso-surface atB-B; (c) axial, side view of mesh.

2332 BAI ET AL.


modified over the years, and production termshave been added to both the k and o equations,resulting in improved accuracy for free shearflows, lower sensitivity to boundary conditions,and better performance at lower Reynolds num-bers. However, good convergence is not easilyachieved. The governing equations for the stan-dard k-o model are as follows:

@

@tðrkÞ þ @

@xiðrkuiÞ ¼

@

@xjGk

@k@xj

� �þGk � Yk þ Sk

ð1Þ

@

@tðroÞ þ @

@xiðrouiÞ ¼

@

@xjGo

@o@xj

� �þGo � Yo þ So

ð2Þ

Because of the relatively low impeller rotationalspeed resulting in a low impeller Reynoldsnumber (Re¼ 4939), large portions of the domainwere dominated by transitional flow. A lowReynolds number correction of the standard k-omodel was applied to improve the velocity predic-tions in these flow regions.25

Boundary Conditions and Frame of Reference

The no-slip condition in the appropriate frame ofreference was assumed at all solid surfaces. Theair–water interface was always assumed to beflat, since the agitation speed in this work was lowenough (50 rpm) to prevent the formation of avortex, as visually confirmed in the experiments.The air–water interface was modeled as africtionless surface, and the normal gradients ofall variables were zero at this interface.

A single reference frame approach was used inthe CFD simulation in which the vessel wall wasassumed to be rotating, and the impeller wasstationary, although the appropriate body forceswere included in the computation to account forthe non-inertial characteristics of the rotatingreference frame.

As mentioned above, the LDV apparatus candetermine only the average velocity (separately foreach component) at a given location, bymeasuringthe instantaneous local velocities at that locationover a period of time, typically 60 s, duringwhich the impeller rotates but the measurementlocation relative to the (fixed) vessel does not. Theinstrument then determines the time-averagedvelocity component at that location aswell as otherstatistics. By contrast, the CFD simulations

produce time-invariant three-dimensional flowpredictions where the velocities vary with posi-tion, including the azimuthal position. However,since the dissolution vessel is unbaffled, theCFD-predicted flow can also be viewed as a time-dependent flow in which the velocity at a givenfixed location is a function of its azimuthal positionrelative to the rotating impeller. Therefore, inorder to compare the LDV data with the CFDpredictions, the CFD-predicted velocities at agiven axial and radial position but differentazimuth must be averaged along the circum-ference passing through that point in order togenerate anaverageazimuthal velocity that canbecompared with the time-averaged velocity of theLDV at the same axial and radial position.

In this work, for each velocity component,the CFD-predicted velocities at eight differentazimuth positions at the same radial location on agiven iso-surface were averaged to give a singlevalue of the azimuth ensemble-averaged velocitycomponent at that location. The ensemble-averagelocal velocity component values so obtained couldbe compared with the time-averaged velocitymeasurements obtained experimentally with theLDV.

RESULTS

Selection of Turbulence Model for CFD Simulations

In a preliminary study, the results of simulationsbased on the use of two different turbulencemodels (the RNG k-e model and the Standard k-o model with Low Reynolds-Number correction)and those obtained with no turbulence model (i.e.,laminar flow model) were compared with the LDVdata collected on two different iso-surfaces(z¼ 50 mm, z¼�31.75 mm) located above andbelow the impeller, respectively. Figure 5 showsthat the results based on the turbulence modelswere of the same order of magnitude, indicatingthat this approach was somewhat robust.

The k-o simulations were generally in betteragreement with the LDV data than those with anyother turbulence model or in the absence of anyturbulence model. For example, the highest LDVtangential velocity at z¼ 50 mm was 43% of theimpeller tip speed and was observed at relativeradial position of 0.41. The k-o simulationspredicted that the peak tangential velocity wasalso 43% of the impeller tip speed, but at relativeradial position of 0.47. By contrast, the RNG k-e



simulations predicted a peak velocity of 46% atrelative radial position of 0.68. On the iso-surfaceat z¼�31.75 mm, the agreement between theLDV data and the k-o simulations was even betternot only in the core region closer to the shaft, butalso in the region extending beyond 2r/T¼ 0.27,that is, where the velocity profiles flatten out.

As for the axial velocities, the shape and themagnitude of the velocity profiles predicted by k-esimulations were appreciably different from theLDV data, especially for z¼ 50 mm. The k-osimulations predicted not only better velocitymagnitudes but also shapes of the velocity profilesthat were more similar to the LDV data.

Finally, the radial velocities on the iso-surfaceat z¼ 50 mmwere all very small (less than 3.5% ofthe impeller tip speed), although the k-o predic-tion were much closer to the LDV data. Similarly,for z¼�31.75 mm, the k-o model predicted abetter shape of the velocity profile than RNG k-emodel, even though the LDV data showed that thevelocities were typically much smaller than 9% ofthe impeller tip speed.

In a separate series of simulations conducted fora slightly different geometry of the dissolutionsystem than that used in this work anotherturbulence model was additionally tested, namelytheRealizable k-emodel. The results obtainedwiththis model were only marginally better than thoseobtained with the standard k-e model (results notshown).

In the rest of the study, all simulations wereconducted using the k-o turbulence model withlowReynolds number correction. Similarly, all the

simulation results presented here were obtainedusing this model.

Velocity Distribution Profiles

Figures 6–8 show, respectively, the tangential,axial, and radial velocity profiles obtained fromLDV measurements and the results of the CFDsimulations based on the k-o model with lowReynolds-Number correction. The LDV measure-ments on z¼�6.75 mm and below were limited tolocations between the hemispherical vessel walland the impeller.

Figure 6 shows that all the tangential velocities,irrespective of the iso-surfaces where they wereobtained, were oriented in the same direction asthe impeller rotation, indicating a strong tangen-tial flow, as in the case of other unbaffledsystems.22,23,28–32 Everywhere in the vessel theexperimental tangential velocities were alwaysmuch stronger than the other components, withpeak tangential velocities ranging between 40%and50%of the tip speed onall iso-surfaceswith theexception of the iso-surfaces at z¼�25.75mmandz¼�6.75 mm, where the maximum velocity was38%–36% of the tip speed, respectively. Thesevelocity peaks were achieved at a radial distance2r/T& 0.41 on iso-surfaces at z¼�0.75 mm andabove; at a radial location very close to theblade tipon iso-surface at z¼�15.75 mm (middle of theimpeller blade); and at radial locations very closeto the vessel wall on iso-surfaces at z¼�25.75mmand below. On the iso-surface at z¼�6.75 mm,where the top edge of the impeller blade is located,

Figure 5. Comparison between experimental LDV velocity data and CFD predictionson iso-surface z¼ 50 mm and z¼�31.75 mm using different turbulence models.

2334 BAI ET AL.


only two LDV measurements could be obtained.Significant although not complete agreement canbe observed between the experimental data andthe numerical results. Especially relevant is thegoodagreement between theLDVandCFDresults

for the tangential velocities at or below theimpeller. This is the most critical region for theoperation of the USP II apparatus, because ofthe presence of the solid dosage form somewhereon the bottom of the vessel. This is also the most

Figure 6. Comparison between LDV data and CFD predictions for tangentialvelocities on different iso-surfaces.



difficult region where LDV measurements can bemade because of the increasing curvature ofthe vessel with respect to the observation planeof the laser, that is, where the laser beams enterthe vessel.

In the upper region of the vessel, that is, forz��0.75 mm, the fluid in the inner core (2r/

T< 0.4) rotates with the shaft in solid bodyrotation, as indicated by the linear increase ofthe velocity with 2r/T (Fig. 6). In the outer region(2r/T> 0.4), the velocity profiles are much flatter,and decrease slowlywith the radial position beforedropping rapidly at the tank wall, where the fluidvelocity is expected to go to zero. LDV data could

Figure 7. Comparison between LDV data and CFD predictions for axial velocities ondifferent iso-surfaces. Positive values indicate upwards velocities.

2336 BAI ET AL.


not be taken too close to the wall because of theoptical distortion produced by the round glasswall.

On the iso-surface z¼�15.75mm, that is, in themiddle of the impeller blade, the CFD profilematches closely the LDV measurements, showing

that the peak tangential velocity occurs nearthe impeller tip and decreases toward the wall.For z¼�6.75 mm, where the top edge of theimpeller blade lies, the CFD simulation showsthat the tangential velocity is higher near theimpeller blade than near the wall, while the LDV

Figure 8. Comparison between LDV data and CFD prediction for radial velocities ondifferent iso-surfaces. Positive values indicate velocities directed outwards, that is, awayfrom the center of the vessel and toward the wall.



measurements, although supporting the simula-tions, show aflat velocity profile and lower velocitymagnitudes.

In the region below the impeller (z¼�25.75 mm, z¼�31.75 mm, z¼�37.75 mm,z¼�43.75 mm), both the LDV measurementsand the CFD simulations show that the radiallocation where the peak velocity occurs is closer tothe vessel wall, which is the opposite of what wasobserved in the region above the vessel (Fig. 6).This can be attributed to the proximity of theimpeller and to the curvature of the vessel wall,creating a fluid region where the local tangentialvelocity follows more closely that of the impeller.

Figure 7 presents the results for the axialvelocities. These velocities are relatively smallcompared to the tangential velocities, with themagnitude of the LDV axial velocities in the 0%–20%range of the tip speed, and those from theCFDsimulations in the range at 0%–15% of the tipspeed. On most iso-surfaces, the LDV measure-ments and CFD the simulations producedsimilar axial velocity profiles, although deviationsoccurred. In general, the CFD simulationspredicted slightly higher absolute velocity magni-tudes than the LDV measurements.

The velocities on the iso-surfaces above theimpeller (z¼�0.75 mm, z ¼25 mm, z¼ 50 mm,z¼ 65 mm) or at the impeller top blade(z¼�6.75 mm) are directed downwards near thecenter of the vessel and upwards near the vesselwall, creating a weak but clearly detectable top-to-bottom recirculation loop. The reverse is true inthe region at or below the impeller (z¼�43.75mm,z¼�37.75 mm, z¼�31.75 mm, z¼�25.75 mm,and z¼�15.75 mm), where the flow near the wallis directed downwards. This is the result of the jetemanating radially from the impeller, impingingon the vessel wall, and then creating two weakrecirculation loops above and below the impeller.This is typical of most radial (paddle-like)impellers, although in the USP II vessel thehemispherical bottom, the absence of baffles, andthe relatively large size of the impeller withrespect to the vessel diameter produce an evenweaker flow in the region below the impeller.

On the iso-surface at z¼ 65 mm, the LDVmeasurements show a flat velocity profile withalmost zero velocity magnitude in the region0.13< 2r/T< 0.68, while the CFD simulationsshow negative velocities (Fig. 7). The discrepancybetween these curves is an indication that therecirculation loop in the portion above theimpeller actually ‘‘closes’’ below the iso-surface at

z¼ 65mm (i.e., the flow converges back toward theshaft), while theCFD simulation predicts that thisrecirculation effect occurs at a higher verticallocation. For z¼�25.75 mm, z¼�6.75 mm,z¼�0.75 mm, z¼�15.75 mm, the LDV and CFDprofiles are similar, but translated vertically withrespect to each other.

Finally, Figure 8 presents the results for theradial velocities. In the upper portion of thevessel (iso-surfaces at z¼�0.75 mm, z¼ 25 mm,z¼ 50 mm, z¼ 65 mm), both the LDV measure-ments and CFD simulations show that the magni-tude of the radial velocities is very small (less than2.5% of the impeller tip speed), that is, a very weakradial flow. As for the impeller region, on theiso-surface at z¼�6.75 mm, the LDV measure-ments show an almost zero radial velocity magni-tude, that is, no radial flow. However, the CFDsimulation shows positive (i.e., outward) radialvelocities. For z¼�15.75 mm, the reverse is true,that is, a positive radial velocity with a relativelyhigh velocity magnitude of 22% of the impeller tipspeed was measured with the LDV. This isreasonable because in this region the impellerblade should push the fluid toward the wall. TheCFD simulation also shows positive velocities, buttheir magnitudes are only about half of the LDVmeasurements. All this means that the radialvelocity is over predicted by CFD near the upperedge of the blade and is under predicted it in themiddle of the impeller and near its lower edge,which implies that there is a small discrepancybetween CFD predictions and LDV data about theexact location where the impeller produces theexpected outward directed radial jet. Apparently,CFD predicts this point to be slightly higher thanwhat actually observed experimentally. However,the phenomenon is adequately predicted by theCFD simulations. This change in radial flow mustoccur over a very small vertical distance in thesmall gap between the impeller blade and thevessel wall. Therefore, in this region, even a smallerror in the prediction of the location where thisflow reversal occurs can produce a larger discre-pancy with the experimental data.

Below the impeller, the radial velocity istypically negative, although still small. This isalso expected since the flowmust be negative nearthe vessel wall in this region, as the curvatureof the vessel redirects the radial flow generatedby the impeller inwards and toward the bottom ofthe vessel. This is what both the LDV measure-ments and CFD prediction show for loweriso-surfaces.

2338 BAI ET AL.


As already mentioned, difference between theslightly larger diameter shaft at the blade used inthis work instead of the more commonly useduniform shaft diameter is so small that the resultsobtained here are expected to be equally valid forthe USP impeller with no collar at the impellerblade.

Velocity Magnitude and Velocity Vectors

Figure 9 shows the contours of the CFD-predictedvelocity magnitude on a vertical cross section

through the impeller shaft for different orienta-tions of the impeller. Figure 10 presents thesame contours plots of the velocity magnitude oniso-surfaces at different vertical (axial) locations.Additional plots show the velocity vectors on avertical cross section through the impeller shaftat different orientations of the impeller (Fig. 11),an expanded view of the velocity vectors inimpeller region (Fig. 12), an expanded view ofvelocity vectors near vessel bottom region for twodifferent impeller orientations (Fig. 13), and,finally, the velocity vectors on the iso-surfaces at

Figure 9. CFDpredictions of the velocitymagnitude on vertical cross sections throughthe impeller shaft for different impeller orientations (m/s).



different vertical locations (Fig. 14). In some ofthese figures, the greater vector density in thelower portion of the vessel is an artifact caused bythe greater concentration of computational cellsin that region (Fig. 4).

A full picture of the three-dimensional flow inthe USP II vessel emerges by looking at all thesefigures and by combining them with the velocityprofiles previously discussed (Figs. 6–8). The topportion of the vessel is dominated by a strong

Figure 10. CFD predictions of velocity magnitude on different iso-surfaces (m/s).

2340 BAI ET AL.


tangential flow. A much weaker circulation loopcaused by the impeller rotation is also present onthe vertical cross section in the upper region of thevessel. The radial jet generated by the rotatingimpeller near the top edge of the blade impinges onthe wall, producing an axial upward flow near thevesselwall. Thisflow is confined in theouter regionof the vessel (2r/T>� 0.7; Figures 11 and 12). The

CFD simulation predicts that this loop closes veryhigh in the tank, as indicated by the relativelystronger radial flow near the air–liquid interface(Fig. 11). In themiddle inner core region above theimpeller (�0.3< 2r/T<�0.7), the flow is directeddownwards. It should be remarked that this regiondoes not extend all the way to the center of thevessel to include the shaft. Instead, the innermost

Figure 11. CFD predictions of velocity vectors colored by velocity magnitude onvertical cross section through the impeller shaft at different orientations (m/s).



core region (2r/T<�0.3) is characterized by verylowaxial and radial velocities (Figs. 7 and8) andbytangential velocities increasing proportionally tothe radial position (Fig. 6). In other words, theinner core rotates almost as a solid body.

The fluid region around the impeller isobviously dominated by the impeller rotation(Fig. 12). The fluid velocity near the blade tipmatches the tip speed. However, the fluid velocitydecays rapidly, both radially and axially, awayfrom the blade tip. For example, the velocitieson the upper edge of the blade near the bladetip (z¼�6.75 mm) are very similar to the tipspeed, but the velocities on the iso-surface atz¼�0.75 mm, which is only 6 mm above the topedge of the blade, show a significant decay in thevelocitymagnitude (Figs. 11 and12).Anevenmore

Figure 12. CFD predictions of velocity vectorscolored by velocity magnitude on vertical cross sectionsthrough the impeller shaft for the impeller region (m/s).

Figure 13. CFD predictions of velocity vectors colored by velocity magnitude on verticalcross section through the impeller shaft at different orientations, for the bottomregion (m/s).

2342 BAI ET AL.


dramatic drop in velocity occurs in the radialdirection, as it can be seen by moving away fromthe blade tip and towards the wall in Figure 12.

The radial jet generated by the impellerproduces a complex flow in the gap between theblade tip and the vessel wall (Fig. 12). The radialflow is rapidly converted to amore axially orientedflow, which is predicted by the CFD to be directedupwards only near the top edge of the blade.Anywhere else in the gap, the flow is predicted tobe oriented downwards. By looking at this figure,one can easily appreciate that even a minor errorin the prediction of the vertical location wherethe flow switches direction from upwards todownwards can result in a significant discrepancybetween the CFD results and the experimentalLDV data. As already mentioned, this observationpartially justifies the differences between the LDVand CFD results in this region.

The flow in the region below the impeller is themost complex and themost important for thiswork(Fig. 13 combinedwithFigures 6–8). These figuresshow that the flow is relatively strong in thetangential direction, even in the region below theimpeller, but that the radial and axial componentsare generally weak, and are affected by thepresence of a second vertical recirculation loophaving a stronger pulsating component generatedby the passing of the paddle. After the paddlehas passed, the flow becomes extremely weak(Fig. 13).

The striking feature of the flow in the regionbelow the impeller is that this vertical recircula-tion loop is not able to penetrate the inner coreregion located just at the center under the impeller(Figs. 9, 11 and 13). The net result is that the flowin this core is nearly stagnant in the vertical planeand it is dominated by weak tangential velocities(although stronger than the other components) onthe order of 5% of the tip speed or less. This weaklyswirling but otherwise nearly stagnant core regionextends all the way from the vessel bottom to thelower edge of the impeller. As the impeller rotates,the stagnant core region expands (Fig. 13, y-plane)and contracts (Fig. 13, x-plane). The axialvelocities change rapidly with time and locationwhen moving across the vertical boundaries forthis core region, while remaining very weak.

Figure 13 also shows that small changes inposition near the bottom of the vessel areassociated with large changes in the velocitymagnitude. For example, by moving by a distanceof only 2–5 mm, the velocity in the plane of theimpeller can vary from near 0 to 1/3 of the tipspeed, andpossiblyhigher. It is obvious that such achange in local velocity can have a dramatic effecton the localmass transfer rate at a specific locationon the surface of the tablet and hence on the localdissolution rate of a solid tablet. Even moreimportantly, the initial location of a dissolvingtablet on the bottom of the vessel (e.g., inside thesemi-quiescent region under the shaft or outsideit) can produce significant differences in thevelocity profiles and velocity gradients experi-enced by the tablet, with a possible significantimpact on the dissolution or erosion rate.

The CFD simulations cannot be expected toprovide a full description of such a complex flow,with such small velocities, in such a small region.However, the CFD results obtained here consis-tently capture the main features of the flow,including the fact that the flow under the impelleris dominated by a weak tangential flow and has

Figure 14. CFD predictions of velocity vectorscolored by velocity magnitude on different iso-surfaces.



near zero radial and axial components. This isconfirmed not only by the LDV results, but also bythe robustness of the predictions in this region,which are relatively similar irrespective of theturbulence model used.

Turbulence Kinetic Energy (k) andTurbulent Dissipation Rate (e)

Figures 15 and 16 show plots of the turbulencekinetic energy and turbulent dissipation rate,respectively, on vertical cross sections throughthe impeller shaft at different orientations.Appreciable turbulence levels and dissipationrates are present only in the impeller region,and especially near the blade tip. As the rotatingimpeller moves away from a given location in theimpeller region, both turbulence and energydissipation rate decay rapidly. Low values of kand e are predicted anywhere else in the vessel.The turbulence kinetic energy is weak even in the

region below the impeller where tablet dissolutionoccurs. Some higher values of energy dissipationrate appear along the vessel bottom, but not in thecenter where the tablet is usually located during atest.

Strain Rate

Figures 17 and 18 present contour plots of thestrain rate, respectively, on a full vertical crosssection of the vessel and, magnified, in the bottomregion. As one can expect, the strain rate is highnear the impeller blades and near the walls,where the velocity must eventually become zeroand the velocity gradients are large. However, thestrain rate is significantly higher at the wall inthe region near the vessel bottom than at thewall in the cylindrical section the vessel. Thisphenomenon can be attributed not only to theproximity to the impeller, but also to the presence

Figure 15. CFD predictions of the turbulence kineticenergy on vertical cross sections through the impellershaft at different orientations (m2/s2).

Figure 16. CFD predictions of the energy dissipationrate on vertical cross sections through the impeller shaftat different orientations (m2/s3).

2344 BAI ET AL.


in this bottom region of steep velocity gradientsresulting from the rapid variation in velocitymagnitude over short distances, as indicated inthe previous section.

The strain rate is not uniform in the regionbelow the impeller. Figure 18 shows that the strainrate changes by more than an order of magnitudeas one moves along to the hemispherical wallwhere the tablet is located during the dissolutiontest.

DISCUSSION

This is possibly the first study aimed at com-pletely characterizing the hydrodynamics of aUSP Dissolution Apparatus II through CFDsimulations and a detailed point-by-point

comparison of the CFD predictions with experi-mental LDV data obtained for the entire dissolu-tion vessel. Some of the results of this work can becompared with those of the few investigationsavailable to date.

The results found here can be partially com-paredwith those ofBocanegra et al.,9who obtainedLDA data for only a few selected locations inthe dissolution vessel. The tangential velocitiesfound here at two iso-surfaces (z¼�43.75mmandz¼ 25 mm) agree well with the experimentalresults of those authors.

A different group of investigators12,13,17

conducted a series of experimental studies usingPIV and compared their data with CFD predic-tions. Because of the nature of their experimentaldata, these authors only produced a qualitativecomparison between data and numerical predic-tions. However, their velocity plots appear tocompare favorably with the detailed resultsobtained here.

Finally, another group of investigators18,19 useda CFD approach similar to that used here, butgenerated no experimental data of their own.Instead, they used the limited experimental dataof Bocanegra et al.9 to partially validate theirapproach.A comparison of the results ofMcCarthyet al.19 with those obtained here shows that thebasic features of the flow field in the vessels, suchas the main recirculation patterns and the jetflowing inwards near the vessel bottom, aresimilar. However, some differences can be foundin the finer flow structures. For example, the flowthat was predicted and experimentally validatedhere for the innermost core in the upper region ofthe vessel is weaker than that which McCarthyet al. obtained. Their results also show inter-mediate recirculation patterns near thewall in theupper portion of the vessel, which were neitherpredicted nor experimentally measured here. Inthis regard, the results of Kukura et al.12,17 andBaxter et al.13 are more similar to those foundhere. A more interesting difference between theresults of McCarthy et al.19 and those of thepresent work is in the finer flow structure belowthe impeller. McCarthy et al.19 found a strongerand much more structured ‘‘wavy’’ flow below theimpeller than that numerically predicted here orreported by Kukura et al.12,17 and Baxter et al.13

Our experimental results seem to confirm that theflow below the impeller is indeed very weak in anydirection other than tangential, and that the CFDpredictions generally overestimate the intensity ofsuch a flow. It should be stressed that the k-o

Figure 17. CFD predictions of strain rate on verticalcross sections through the impeller shaft at differentorientations (1/s).



model with low Reynolds number correction wasused here to model turbulence effects. This modelis probably superior to other standard turbulencemodels routinely used in simulations.26,27 How-ever, it is unclear what turbulence modelMcCarthy et al.19 used in their work.

In general, the CFD predictions obtained hereagreed reasonably well with the LDV data. This isimportant to validate the CFD results obtained inthis work, and draw more wide-ranging con-clusions basedon them. Inaddition, theagreementindicates that the turbulence model used in thiswork, that is, the k-o model with low Reynoldsnumber correction, is appropriate for this kind ofsystems.

The hydrodynamics of the USP Apparatus II isdominated by two main features. The first is thatanywhere in the system the main flow is stronglytangential, as in all unbaffled systems, withlimited axial and radial components. Secondaryflows are also present, but they form two smallerrecirculation loops above and below the impeller.This has implications for the axial homogeneity ofthe vessel, although the small size of the vesselimplies that blending is likely to occur relativelyrapidly.

The second important hydrodynamic feature isthat the central core region between the bottom ofthe vessel and the lower edge of the impeller ischaracterized by exceedingly small radial and

Figure 18. CFD predictions of the strain rate on vertical cross sections through theimpeller shaft at different orientations for the bottom region (1/s).

2346 BAI ET AL.


axial velocities and turbulence levels. This zonerotates with the impeller, and it is surrounded byanother zone, also below the impeller, with muchhigher radial and axial velocities. This analysiscan qualitatively explain the effect of ‘‘coning’’ atthe center of the vessel bottom. Coning is oftenobserved when a tablet disintegrates rapidlyduring the dissolution test, and the resultinggranules form a rotating cone of loosely aggregat-ing particles under the impeller.

The high degree non-uniformity in the flow fieldnear the vessel bottom can introduce a degree ofuncertainty in the dissolution test. A tablet that isdropped into the gently agitated liquid in thevessel, as ina typical dissolution test,may landatarandom location on the vessel bottom, and thus beexposed to very different flow fields depending onits final position. The velocities in this region,albeit small, change significantly over short dis-tance along the vessel bottom. This implies thatsmall variations in the location of the tablet on thevessel bottom caused by the randomness of thetablet descent through the liquid are likely toresult in significantly different velocities at thetablet location. The strain rate, which is anotherimportant factor that can affect the tablet dissolu-tion rate, also changes significantly along thevessel bottom. The dramatic changes of bothvelocities and strain ratewithin a very small spacecan likely introduce variability in the dissolutiontest. Therefore, the vessel hydrodynamics and theinitial location of the tablet after being droppedinto the vessel can possibly affect the dissolutiontest results.

CONCLUSIONS

The following conclusions can be drawn from thiswork:

a. The LDV measurements and the CFDvelocity predictions are, in general, in sub-stantial agreement

b. All tangential velocities, irrespective ofwhere in the vessel they are obtainedfrom, are oriented in the same direction asthe impeller rotation, indicating a strongtangential flow. The highest tangentialvelocity is typically between 40% and 50%of the impeller tip speed on all iso-surfaces,both above and below the impeller.

c. The axial velocities are all significantlysmaller than the tangential velocities, with

magnitudes typically ranging between 0%and 15% of the tip speed. This impliesthat top-to-bottom recirculation in theUSP II apparatus is weak, as in mostunbaffled vessels. The radial velocities areeven smaller than the tangential and axialvelocities.

d. The flow in the region below the impeller iscomplex, and it is strongly dominated bythe tangential component while the radialand axial components are very weak. Thepresence of a vertical recirculation loophaving a pulsating component generatedby the passing of the impeller blades canbe observed. When this pulsating effectdecays, the flow is extremely weak.

e. In the region below the impeller, the verticalrecirculation loop is not able to penetratethe inner core region located just underthe shaft. The flow in this core is nearlyquiescent in the vertical plane and isdominated by the tangential velocity. Thisweakly swirling but otherwise nearly stag-nant core region extends all the way fromthe vessel bottom to the lower edge ofthe impeller. At its vertical boundaries, theaxial velocities change rapidly with time andlocation, while remaining weak. This canexplain the ‘‘coning’’ effect often observed atthe center of the vessel bottom.

f. The strain rate is not uniform in the regionbelow the impeller, but it changes by morethan an order of magnitude by moving alongthe hemispherical bottom. This is likely tohave an impact on themass transfer rate andhence the dissolution rate, depending on theexact location of a tablet, or its deviationfrom it.

In conclusion, the hydrodynamics near thevessel bottom, where the tablet is located, cancontribute to high variability in dissolutiontesting.

NOMENCLATURE

D impeller diameter (m)k turbulence kinetic energy (m2/s2)Gk the generation of k due to mean velocity

gradients (kg/m �s3)Go generation of o (kg/m3 �s2)N impeller rotational speed (rotations/s)



r radial coordinate of LDVmeasurement point,(m or mm)

Re impeller Reynolds number (¼r �N �D2/m),dimensionless

Sk user-defined source term of k (kg/m �s3)So user-defined source term of o (kg/m3 �s2)T vessel diameter (m or mm)u velocity (m/s)Yk dissipation of k (kg/m�s3)Yo dissipation of o (kg/m3 �s2)z vertical location of iso-surface (m or mm)

Greek Symbols

Gk effective diffusivity of k (kg/m �s)Go effective diffusivity of o (kg/m �s)e turbulent dissipation rate (m2/s3)m liquid viscosity (kg/m �s)r liquid density (kg/m3)o specific dissipation rate (s�1)

ACKNOWLEDGMENTS

This work was supported through a grant fromMerck & Co. West Point, PA, whose contributionis gratefully acknowledged. The authors also wishto thank Dr. Scott Reynolds for his contributionand support.

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Hydrodynamic Investigation of USP Dissolution Test ...pharxmonconsulting.com/files/119402610.pdf · available on the hydrodynamics of this apparatus. In this work, laser-Doppler velocimetry