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International Journal of Pharmaceutics 452 (2013) 42– 51

Contents lists available at SciVerse ScienceDirect

International Journal of Pharmaceutics

journa l h o me pag e: www.elsev ier .com/ locate / i jpharm

D hydrodynamics and shear rates’ variability in the United Statesharmacopeia Paddle Dissolution Apparatus

ouari Ameur ∗, Mohamed Bouzitaculté de Génie Mécanique, USTO-MB, 1505 El m’naouar, Oran, Algeria

a r t i c l e i n f o

rticle history:eceived 20 December 2012eceived in revised form 10 April 2013ccepted 11 April 2013vailable online 13 May 2013

a b s t r a c t

The 3D hydrodynamics and shear rates distributions within the United States Pharmacopeia Apparatus 2have been investigated in this paper. With the help of a CFD package, several geometric modifications tothe device were evaluated in this study. Specially, we examine the influence of impeller clearance, bladediameter, shape of the vessel base and shape of the lower part of blade. Increasing the impeller clearancewas observed to exacerbate the heterogeneity in shear and would likely result in greater variability indissolution measurements. Use of moderate blade diameter and dished bottom were observed to reduce

eywords:SP IIydrodynamicshear ratesomputational fluid dynamics (CFD)issolution

shear heterogeneity in the regions where tablets are most likely to visit during testing. The comparativeanalysis shows better reproducibility and accelerated dissolution rates with the modified vessel shape, thedished bottom can enhance mixing near the vessel base when compared with the flat bottom. Increasinglength of the lower edge of the paddle was observed to generate high radial pumping and to enlarge thedead zone located at the center of the vessel base.

odeling

. Introduction

In the pharmaceutical industry, drug dissolution testing is a crit-cal component of the product and process developments. Differentissolution apparatus are available; they are standardized in thenited States Pharmacopeia (USP) (United States Pharmacopeia,008). From these apparatuses, the most commonly used is thePS Dissolution Testing Apparatus 2. It has been used for decades

ince it was first officially introduced almost 40 years ago (Cohent al., 1990).

However, this apparatus presents some significant errors andest failures (Bai et al., 2011). Some published works have suggestedhat there is a considerable variability and randomness in disso-ution profiles using Apparatus 2 (Qureshi and McGilveray, 1999;osta and Lobo, 2001; Qureshi and Shabnam, 2001; Mauger et al.,003; Kukura et al., 2003; Baxter et al., 2005).

Some studies (McCarthy et al., 2003, 2004; Kukura et al., 2004;axter et al., 2005; Bai et al., 2007a; Bai and Armenante, 2008, 2009)ave shown that the fluid flow in Apparatus 2 is highly hetero-eneous, the direction and intensity of velocity vectors are highlyependent on the location within the vessel, especially at the bot-

om of the vessel where the tablet is located during dissolutionesting. This complex hydrodynamics can contribute to the pooreproducibility.

∗ Corresponding author. Tel.: +213 770343722; fax: +213 41263526.E-mail address: houari ameur@yahoo.fr (H. Ameur).

378-5173/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.ijpharm.2013.04.049

© 2013 Elsevier B.V. All rights reserved.

Kukura et al. (2004) revealed that under normal operating con-ditions, the flow in the USP Apparatus 2 exhibits large fluctuationsin the velocity field, strong enough to displace tablets along thevessel bottom. In addition, the authors showed that highly non-uniform shear rates are observed along the vessel bottom, withshear rates at the local maximum 2–3 times higher than at thecenter of the dish.

The velocity field throughout Apparatus 2 was quantified vialaser Doppler velocimetry (LDV) and CFD computer simulations byBai et al. (2007b). This study showed that the drug released by thetablet during the dissolution process is transported to the samplingpoint higher in the vessel relatively quickly (on the order of 30 s at50 rpm).

Bai and his co-workers studied the effect of agitation speed andshowed, in another work (Bai et al., 2011), that the flow pattern isnearly independent of the agitation speed in most regions of thevessel, implying that increasing the agitation speed generally pro-duced a corresponding increase in the local values of the velocity.However, the velocity profiles and flow pattern in the inner coreregion just below the impeller are much less sensitive to agitationspeed. In this region, the axial and radial velocities are especiallylow and are not significantly affected by agitation increases. Thisinner core region at the center of the vessel bottom persists irre-spective of agitation intensity.

Other studies have additionally shown that small changes in thegeometry of the system can produce large effects on the systemhydrodynamic and the dissolution profiles. For example, the veloc-ity flow field and the shear strain rate near the vessel bottom are

H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51 43

Nomenclature

c impeller off-bottomed clearance (m)d blade diameter (m)ds shaft diameter (m)h dish height (m)D tank diameter (m)N impeller rotational speed (s−1)R, Z radial and vertical coordinates, respectively (m)Re Reynolds number for a Newtonian fluidV velocity (m/s)Vz axial velocity (m/s)V� tangential velocity (m/s)Vr radial velocity (m/s)

Greek letters� fluid density (kg/m3)� dynamic viscosity (Pa s)� angular coordinate (◦)

dttsc

ricab

Aw(weda

assc

nUetteesb

2

cwoa

Eq. (1); the Navier–Stokes equations are given by Eqs. (2)–(4).

∂�

∂t+ 1

r

∂(r�vr)∂r

+ 1r

∂(r�v�)∂�

+ ∂(�vz)∂z

= 0 (1)

Table 1Parameters of all geometrical configurations realized.

c/D h/D d/D

0.05 0.4 0.70.2 0.4 0.7

ω angular velocity (rad/s)

ramatically impacted by small misalignments of the impeller loca-ion (Bai and Armenante, 2008). Similarly, the exact location of theablet during the dissolution process can result in very different dis-olution profiles which may result in failure to pass the acceptanceriteria established by the FDA (Bai and Armenante, 2009).

The impeller agitation speed generally recommended for Appa-atus 2 is 50 rpm (Shah et al., 1992; FDA, 1997). However, in thendustrial practice, agitation speeds ranging from 50 to100 rpm areommonly used, with 25 rpm and 150 rpm also been employed,lthough more rarely, depending on the tablet and the drug producteing tested (Costa and Lobo, 2001; Kamba et al., 2003).

Bocanegra et al. (1990) applied LDA to measure velocities inpparatus 2 in selected regions for an agitation speed of 60 rpm,hich is a rarely used agitation speed in practice. McCarthy et al.

2004) studied the flow fields in Apparatus 2 at 25, 100 and 150 rpmith a partially validated CFD model (McCarthy et al., 2003). Kukura

t al. (2004) used the computational analysis to examine the hydro-ynamics in Apparatus 2, they predicted the shear strain rate atgitation speed of 50 and 100 rpm.

The flow field and mixing characteristics of the USP Apparatus 2re not well understood despite the data from previous work thatuggests they strongly influence test results. Thus, a comprehen-ive understanding of the hydrodynamics can provide significantontributions to aid in the evolution of this important tool.

A thorough search in the literature shows that there are still aumber of issues currently associated with dissolution testing inSP Apparatus 2, which are directly traceable to the system geom-try and the resulting hydrodynamics. Therefore, the objective ofhe present work is to investigate the effect of some parameters onhe 3D hydrodynamics and shear rates distributions within the USPnvironment. We focus on the effect of following design param-ters: impeller clearance from the tank bottom, blade diameter,hape of the vessel base and finally the shape of the lower part oflade.

. Mixing system

A standard USP Dissolution Testing Apparatus 2 vessel (Fig. 1)onsists of an unbaffled, cylindrical and hemispherical bottomed,

ith an internal diameter, D, of 100.16 mm, and an overall capacity

f 1 L. The agitation system (of the USP standard) consists of an USPpparatus 2-paddle impeller mounted on a shaft with a diameter

Fig. 1. Stirred system.

ds = 9.56 mm, the length of the top edge of the blade is 74.10 mm,the length of the bottom edge of the blade is 42.00 mm.

In this paper, some modifications to the device have been done;it concerns the effect of impeller diameter, impeller clearance,shape of the vessel base and design of the blade. The geometricparameters of all configurations realized are summarized in Table 1.

In order to investigate the effect of blade design, four cases havebeen studied. Details are given in Fig. 13.

3. Materials and methods

The USP apparatus was modeled using the CFD package CFXversion 13.0 (Ansys CFX, Inc.). CFX is a computer program formodeling fluid flow in complex geometries; it is based on thefinite volume method to solve the governing equations describ-ing the movement of fluid. The Navier–Stokes equations writtenin a rotating, cylindrical frame of references are solved. Becauseof the choice of a rotating frame, two terms are added to theequations: centrifugal and Coriolis accelerations. The equationsare written in terms of velocity components and pressure. Thesevariables are discretized on a grid of control volumes, which enablesa more precise mass conservation, and a faster convergence. Apressure-correction method of the type Semi-Implicit Method forPressure-Linked-Equations-Consistent (SIMPLEC) is used to per-form pressure–velocity coupling.

In cylindrical coordinates, the continuity equation is given by

0.4 0.4 0.50, 0.1, 0.2, 0.3, 0.4 0.70.4 0.9

0.6 0.4 0.7

44 H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51

�

�

�

wptoap

d(R

dwtiw(ii

i

Table 2Details on mesh tests.

M1 M2 M3

Number of cells 89,123 178,246 356,492

Fig. 2. Tetrahedral mesh.

(∂vr

∂t+ vr

∂vr

∂r+ v�

r

∂vr

∂�− v2

�

r+ vz

∂vr

∂z

)

= −∂p

∂r+�gr+�

(1r

∂

∂r

(r

∂vr

∂r

)− vr

r2+ 1

r2

∂2vr

∂�2− 2

r2

∂v�

∂�+ ∂2vr

∂z2

)

(2)

(∂v�

∂t+ vr

∂v�

∂r+ v�

r

∂v�

∂�+ vrv�

r+ vz

∂v�

∂z

)= −1

r

∂p

∂�+ �g�

+ �

(1r

∂

∂r

(r

∂v�

∂r

)− v�

r2+ 1

r2

∂2v�

∂�2+ 2

r2

∂vr

∂�+ ∂2v�

∂z2

)(3)

(∂vz

∂t+ vr

∂vz

∂r+ v�

r

∂vz

∂�+ vz

∂vz

∂z

)= −∂p

∂z+ �gz

+ �

(1r

∂

∂r

(r

∂vz

∂r

)+ 1

r2

∂2vz

∂�2+ ∂2vz

∂z2

)(4)

here v� , vr and vz are the tangential, radial and axial velocity com-onents, respectively. r and � are the distances in the radial andangential directions, respectively. g� , gr and gz are the componentsf the acceleration of gravity vector in the tangential, radial andxial directions, respectively. � is the dynamic viscosity, p is theressure and � is the density of fluid.

All variables describing the hydrodynamic state are written inimensionless form, the dimensionless forms of velocities, radialR) and axial (Z) coordinates are obtained as follow: V* = V/�ND;* = 2R/D and Z* = Z/D.

A pre-processor (ICEM CFD 13.0) was used to discretize the flowomain with a tetrahedral mesh (Fig. 2). An increased mesh densityas used near the impeller and the tank walls in order to capture

he boundary layer flow details. A sufficient amount of nodes defin-ng the curvature of the blades was created on the impeller edge,

hich resulted in a very refined mesh. Mesh tests were performedTable 2) by verifying that additional cells did not change the veloc-

ty magnitude in the regions of high velocity gradients around thempeller blades by more than 2.5%.

To verify the grid independency, the number of cells wasncreased by a factor of about 2 used by other researchers in CFD

V ∗max 0.4028 0.4311 0.4366

Time required (s) 8376 18,251 28,251

modeling of the mixing processes (Buwa et al., 2006; Letellier et al.,2002). The original 3D mesh of the model had 89,123 computa-tional cells. To verify the grid independency, the number of cellswas increased from 89,123 cells to 178,246 cells. The additionalcells changed the velocity magnitude in the regions of high velocitygradients by more than 3%. Thus, the number of cells was changedfrom 178,246 cells to 356,492 cells. The additional cells did notchange the velocity magnitude in the regions of high velocity gra-dients and impeller power number by more than 2.5%. Therefore,178,246 cells were employed in this study.

Constant boundary conditions have been set respecting a rotat-ing reference frame (RRF) approach. Here, the impeller is keptstationary and the flow is steady relative to the rotating frame,while the outer wall of the vessel is given an angular velocity equaland opposite to the velocity of the rotating frame (i.e. At the vesselwall and bottom (V = ωR), on the impeller (V = 0)). This approach canbe employed due to the absence of baffles. More details are givenby Ameur et al. (2011).

In our study, the turbulence model used is the SST model. Thismodel has the option of specifying how we model the transitionturbulence: it is the fully turbulent, specified intermittency (requir-ing acquired knowledge), the gamma model or the gamma thetamodel.

“Water-liquid” with a predefined viscosity(1.003 × 10−3 kg/m s) at room temperature (20 ◦C) was cho-sen as the material for the vessel volume. The liquid height is keptequal to the vessel volume. A cylinder of 8.5 mm height with a13 mm diameter was set up at the vessel base. This cylindricalvolume was then intersected with 4 quarters of the vessel base todefine the new fluid volume of the vessel. Following the introduc-tion of the compact, this allowed the viscosity of the liquid to beset to that of water at 37 ◦C (0.6943 × 10−3 kg/m s) (Visawanth andNatarajan, 1989). The inclusion of the compact complicated themeshing process in the hemispherical region of the vessel. Meshingwas facilitated by ensuring that individual edges of the top circularface quarters of the compact were meshed in exactly the samemanner as the bottom circular face quarters of the paddle.

The steep gradients in velocity and pressure involved in theregions of interface between fluid and solid components can com-plicate solution convergence. To solve this problem, we haveintroduced meshing boundary layers at all interfaces betweensolid and fluid on the vessel volume (McCarthy et al., 2003). Thisfeature allows the user to define the thickness of the first layerof grid cells at the interface, the ratio of the thickness of sub-sequent layers, and the total number of boundary layers at theinterface.

Simulations were considered converging when the scaled resid-uals for each transport equation were below 10−7. The velocitieshad converged to either a single value. Most simulations requiredabout 2000 iterations for convergence. Computations were carriedout using Pentium(R) Core i7 with 8.0 GB of RAM and convergencewas typically achieved after 4–5 h.

4. Results and discussion

Computational analysis is used to examine the hydrodynamicenvironment within the USP Apparatus 2. But before any investi-gation, we have seen necessary to check the validity of the CFD

H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51 45

mrsbir

ccae

-0.04 0.00 0.0 4 0.0 8 0.1 2 0.1 6 0.2 0 0.2 4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

V *

Z* c/D = 0 .05c/D = 0 .2c/D = 0 .4c/D = 0 .6

In this paper, we try to test some design parameters in order

Fig. 3. Tangential velocity for N = 25 rpm, Z = 25 mm.

odel and the numerical method used. For this purpose, we haveeferred to the work published by Bai et al. (2011). We note theame geometrical configuration as that reported by Bai et al. haseen realized for the validation of our numerical results. As shown

n Fig. 3, where the tangential velocity is presented along the vesseladius, the comparison shows a satisfactory agreement.

The reasonable comparison remarked on this figure providesonfidence that the present CFD model (CFX 13.0) can accurately

apture the mixing features within the device. The computationsre then used to obtain data that cannot be easily measured withxperiments.

Fig. 4. Streamlines for N = 150

z

Fig. 5. Axial velocity for N = 25 rpm, � = 0◦ , R* = 0.4, d/D = 0.7, h/D = 0.4.

4.1. Effect of impeller clearance

The previous published works available in the literature showthat the shear environment within the USP Apparatus 2 is highlynon-uniform. This distribution of shear forces is a direct cause ofdissolution testing variability. This variability is large enough tocause for type II dissolution test failures, i.e. failures are a result ofvulnerability of the dissolution method rather than a problem witha dosage form (Kukura et al., 2004).

to eliminate this potential source of failures that is unrelated toproduct quality. One of the simplest changes that can be made tothe system is the alteration of agitator clearance. For this purpose,

rpm, d/D = 0.7, h/D = 0.4.

46 H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51

r N = 1

fc

cftdtfw

Fig. 6. Shear strain rates fo

our geometrical configurations have been realized and which are:/D = 0.05, 0.2, 0.4 and 0.6, respectively.

Fig. 4(a) shows the 2D velocity fields along the blade (angularoordinate � = 0◦) and at the blade mediator (� = 90◦), respectivelyor the four cases studied (c/D). It can be observed that for any loca-ion c/D, the fluid was ejected radially from the impeller and was

irected in one of two ways. Either the fluid flowed up the walloward the top surface and then back down the impeller shaft,orming a recirculation zone above the impeller, or the materialas directed down to the dish center and was pulled up through

Fig. 7. Flow fields for N = 150 rpm, h/D = 0.4, c/D

50 rpm, h/D = 0.4, d/D = 0.7.

the center of the dish back to the paddle, forming a second recir-culation zone below the impeller. Recirculation regions markingthe secondary flow, first reported in the device by Bocanegra et al.(1990), exist both above and below the impeller.

Fig. 4(b) presents the streamlines velocity in a 3D view; wecan remark that the structures of fluid flows below the impeller

are more complicated than those above the impeller. Fluid veloc-ities directly below the paddle at the convergence point (centerof paddle) appear to be involved in a local “vortex” flow, as it isin this region that dissolution from a solid (or particulate) drug

= 0.4: (a) 2D view, � = 90◦; (b) 3D view.

H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51 47

0.0 0.2 0.4 0.6 0.8 1.0-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

Vz*

R*

d/D = 0.5d/D = 0.7d/D = 0.9

Fh

daml

aiabbrtdfi

icbaosmir

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

d/D = 0 .5d/D = 0 .7d/D = 0 .9

R*

Shear Strain Rate [s-1]

In this section, the effects of impeller diameter are investigated.

ig. 8. Axial velocity for N = 25 rpm, Z* = 0 (just below the blade), � = 0◦ , c/D = 0.4,/D = 0.4.

elivery system is likely to occur. With increasing clearance (c/D)nd because of the shape of dish (hemispherical shape), the vortexarked below the center of paddle get intensified giving rise to a

arger dead zone.If the paddle is very close to the vessel base (c/D = 0.05), it results

type of breaking flow in this region, where the recirculation zones very small in size (Fig. 4(a)). However, with increasing clear-nce (for c/D = 0.2 and 0.4) the lower recirculation zone is larger,ut the excessive clearance cannot ensure mixing near the vesselase (c/D = 0.6). Even for a small volume (c/D = 0.2), the low velocityegion below the impeller could create issues during dissolutionesting including the formation of a cone of material for dense,isintegrating tablets. It is likely that these issues would be magni-ed as this low-flow region increased in size.

This phenomenon is demonstrated by the profiles of axial veloc-ty given in Fig. 5. At the same plane with the blade (angularoordinate � = 0◦) and for a radial position between the impellerlade and the vessel wall R* = 0.4, the axial velocity is presentedlong the vessel height for difference clearances c/D. As it can bebserved, the axial velocity component is at its highest in the areawept by the impeller, the positive values indicate the upward

otion of flow (up to the free surface of liquid) and negative ones

ndicate the downward motion (downward to the vessel base). Noecirculation zone is marked below the paddle if the clearance is

Fig. 9. Shear strain rates for N = 1

Fig. 10. Shear strain rates for N = 150 rpm, Z* = 0 (just below the blade), � = 0◦ ,c/D = 0.4, h/D = 0.4.

very small, but the lower part of vessel is badly disturbed. Increas-ing clearance can enhance the axial circulation up to the free surfaceof liquid, but the great distance from the vessel base can permit theformation of a dead zone near the dish.

The shear (deformation) rate of the fluid is a physically relevantquantity to many dissolution tests that can be difficult to measureexperimentally. This measure is directly related to the shear forcesexerted by the fluid motion. Fig. 6 shows the distribution of shearforces at the bottom of the tank. The most striking observation fromthis figure is the presence of a circular low-shear region at the centerof the bottom of the device. This region is approximately the size ofa typically dosage form. Outside of that small area, the shear forcesrise rapidly. On the other hand, when the impeller is very close tothe vessel base, the highest shear rates are limited at the blade tip.This heterogeneity distribution of shear rates can be reduced byincreasing clearance.

4.2. Effect of impeller diameter

The blade diameter is changing as follows: d/D = 0.5, 0.7 and 0.9.As a first step of examination, the 2D velocity fields are plotted

along the plane corresponding to the angular coordinate � = 90◦

50 rpm, c/D = 0.4, h/D = 0.4.

48 H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51

Fig. 11. Streamlines for N = 150 rpm, d/D = 0.7.

tes for

(sltwaidi

F

Fig. 12. Shear strain ra

Fig. 7(a)). High velocity magnitudes can be observed in the areawept by the paddle and two recirculation loops are formed at thisevel. The increase in blade diameter yields higher radial pumping;he two recirculation loops are then pushed away to the verticalall of vessel. Another remark that can be discussed is the size

nd location of the eddy flow formed below the paddle. This eddy

s larger in size and located near the vessel base when the bladeiameter is small (d/D = 0.5); however, this eddy becomes smaller

n size and gets pushed upward with the increase of d/D.

ig. 13. The different geometries realized to testing the effect of blade design.

N = 150 rpm, d/D = 0.7.

An examination of velocities across a 3D visualization (Fig. 7(b))indicates that the increase in blade diameter yields higher radialpumping; the well-stirred region is then enlarged.

To give an insight on the magnitude of axial velocity whenchanging the blade diameter, Fig. 8 is presented. For a location justbelow the paddle and for a position corresponding to the angu-lar coordinate (� = 0◦), the axial component of velocity is presentedalong the vessel radius. The profiles plotted in this figure show thevolume immediately below the region swept by the paddle wingsis dominated by negative axial velocity (toward the base of thevessel). Outside of this area (between the paddle wings and wall)the fluid velocity has a positive axial component. The magnitudeof axial velocity increases with respect to the increase of bladediameter.

The distribution of shear rates can provide valuable informa-tion regarding the impact that hydrodynamics can have on themeasured dissolution rate. Figs. 9 and 10 show the distribution ofshear forces within the fluid.

Evaluation of the shear rates along the dish of the vessel was par-ticularly useful as this represented the region in which the tabletwould spend most of the time during testing. Fig. 9 shows the con-tour plots of the shear rates distribution along the dish, as viewed,

H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51 49

0 rpm

atdoiit

faredlbw

4

rdt

Fc

Fig. 14. Streamlines for N = 15

circular low-shear region was observed in the bottom center ofhe device. Outside of this small region, the shear rate increasedramatically. Another remark is that very weak shear rates arebserved close to the vessel base with a small ratio of d/D. Thisssue can be remedied by increasing d/D; however, the excessivencrease of d/D can permit the formation of a larger dead zone athe center of vessel base.

The shear as a function of radial position is calculated for dif-erent ratio d/D and presented in Fig. 10. The data corresponds to

position just below the impeller and along the blade (� = 0◦). Theesults show a steep change in shear intensity that a tablet mayxperience if moved, even slightly, from the center of the dish. Thisramatic change in shear intensity can have strong effects on disso-

ution rates. The intensity of shear rates increases with increasinglade diameter, and it decays slowly when closing to the vesselall.

.3. Effect of the curvature of vessel bottom

The low velocity region in the bottom center of the USP appa-atus results in the formation of a cone of material, particularly inosage forms with dense recipients. Beckett et al. (1996) reportedhat much of the variability in dissolution testing with the USP

0.0 0.2 0.4 0.6 0.8 1.0-0.050.000.050.100.150.200.250.300.350.400.450.500.550.600.65

R*

V*Case 1Case 2Case 3Case 4

ig. 15. Mean velocity for N = 150 rpm, � = 0, Z* = 0 (just below the blade), h/D = 0.4,/D = 0.4, d/D = 0.7.

, h/D = 0.4, c/D = 0.4, d/D = 0.7.

Apparatus 2 is attributable to the cone formation of fluid near thevessel base. To remedy this issue, the PEAK vessel was developedby VanKel Industries Inc. The PEAK vessel has an inverted conemolded into the bottom, designed to eliminate the potential forcone formation.

In this paper, we try to test the effect of dish shape on the fluidflows and distribution of shear rates. To this end, we have realizedfive geometrical configurations, one with a flat bottom (h/D = 0)and four others with a dished bottom: h/D = 0.1, 0.2, 0.3 and 0.4,respectively.

Fig. 11 presents the velocity fields in the plane of the paddle(angular coordinate � = 0◦) and for � = 90◦. We can remark that thematerial ejected from the impeller either moves up the wall to thetop before returning down a channel midway between the shaft andwall, or the fluid gets pushed down along the wall before movingup to the impeller in the center of the device.

For a flat bottomed vessel and a very small clearance, the fluidflow is limited below the paddle. Increasing the curvature of thevessel base can create better circulation in this area. The vesselwall also experiences high deformation relative to the interior ofthe tank. The lowest shear is found at the center of vessel bottombelow the impeller (Fig. 12).

The comparative analysis show better reproducibility and accel-erated dissolution rates with the modified vessel shape. The dishedbottom can enhance mixing near the vessel base when comparedwith the flat bottom. When comparing the four cases of dished bot-tom, it seems that the last one with hemispherical shape can givebetter performance by increasing the size of the well-stirred region(Fig. 12).

4.4. Effect of curvature of the lower part of the blade

In this section, we examine the impact of another geometricparameter; it concerns the design of the lower part of the blade.Four configurations are realized for this purpose and which aresummarized in Fig. 13. A thorough hydrodynamic evaluation of thissystem would be valuable to determine if the issues identified inthe standard configuration are remedied through the use of themodified impeller.

Fig. 14 presents the flow fields generated for Cases 1 and 4, theplots are given on the plane of the blade (� = 0◦) and at the mediator

(� = 90◦), respectively. Large variations in the flow structure withthe blade design were evident, particularly in the vicinity of thepaddle tips. A low velocity domain was evident directly below thecenter of the rotating paddle. For the Case 1, the flow eddy formed

50 H. Ameur, M. Bouzit / International Journal of Pharmaceutics 452 (2013) 42– 51

Fig. 16. 3D streamlines for N = 150 rpm, h/D = 0.4, c/D = 0.4, d/D = 0.7.

150 r

bba

blsw

ctdHtad

rcht

Fig. 17. Shear strain rates for N =

elow the paddle at � = 90◦ (Case 1) is going downward to the vesselase when increasing the length of lower edge of paddle (Case 4),nd this due to the increase of radial pumping.

Fig. 15 gives an insight on the variations of mean velocity justelow the blade and for � = 0◦. As observed, increased length of the

ower edge of the paddle generates higher velocities in the areawept by the blade (Fig. 15) and it enlarges the size of the vortexhich is located near the vessel base (Fig. 16).

In the context of dissolution, the magnitude of the strain ratesontrols the boundary layer thickness of fluid at the surface ofhe tablet that influences the mass transfer of material from theosage form into the bulk fluid, as reported by Kukura et al. (2004).igh strain rates lead to thinner boundary layer, promoting faster

ransport. If transport through this layer is limited, then high vari-bility in strain rates has the potential to lead to inconsistentissolution performance.

In comparison between the four cases studied (Fig. 17), we

emark that, for any case, the lower shear rates are located at theenter of dish where the tablet is most likely to rest. On the otherand, the heterogeneity of shear forces becomes significant withhe increase of length of the lower edge of blade.

pm, h/D = 0.4, c/D = 0.4, d/D = 0.7.

5. Conclusion

Computational analysis is used to investigate the 3D flow fieldsgenerated within the USP Apparatus 2. The predicted results aidin understanding the underlying hydrodynamics and shear rateswithin the device, and help explain many of the problems encoun-tered with dissolution testing in the USP II. The results obtainedby testing several design parameters can be summarized as thefollowing:

The USP Apparatus 2 shows highly non-uniform distribution ofshear rates within the media. Very low shear rates are located in acircular area at the center of vessel base.

When the paddle is placed very close to the vessel base, thatproduces a type of a breaking flow in this area and the upperpart of the vessel is not disturbed. A better mixing is achievedwith increased impeller clearance, however, the excessive clear-ance results in a larger dead zone near the dish.

Very weak shear rates are observed close to the vessel base witha small ratio d/D. This issue is remedied by increasing d/D; however,the excessive increase of d/D permits the formation of a larger deadzone at the center of vessel base.

urnal

dpwt

nryi

R

A

B

B

B

B

B

B

B

B

H. Ameur, M. Bouzit / International Jo

The shape of the vessel base has shown an important effect: theished bottom improves mixing near the vessel base when com-ared with the flat bottom. It was also found that the vessel baseith a hemispherical shape gives better performance by increasing

he size of the well-stirred region.The impeller design tested in this paper has also shown a sig-

ificant influence on the hydrodynamics and distribution of shearates. The increasing length of the lower part of the paddle canield high heterogeneity near the vessel base, and this is due to thencrease of the radial pumping.

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