Powder Technology 198 (2010) 101–107

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Measuring the hydrophobicity of lubricated blends of pharmaceutical excipients

Marcos Llusa a, Michael Levin b, Ronald D. Snee c, Fernando J. Muzzio a,⁎a Department of Chemical and Biochemical Engineering, Rutgers University, USAb Metropolitan Computing Corporation, New Jersey, USAc Tunnell Consulting, King of Prussia, PA, USA

⁎ Corresponding author.E-mail address: fjmuzzio@yahoo.com (F.J. Muzzio).

0032-5910/$ – see front matter © 2009 Elsevier B.V. Aldoi:10.1016/j.powtec.2009.10.021

a b s t r a c t

a r t i c l e i n f o

Article history:Received 12 December 2008Received in revised form 29 October 2009Accepted 31 October 2009Available online 5 November 2009

Keywords:WettabilityLubricationDissolutionMagnesium stearate

This paper discusses how the hydrophobicity of lubricated pharmaceutical formulations is affected byprocess variables such as shear rate and strain. Hydrophobicity is a critical property that affects thedissolution of powder formulations, tablets and capsules as well as the performance of tablet coating andgranulation operations. In this paper, hydrophobicity is measured using a modified Washburn method.Results show that, in the absence of lubricant, the hydrophobicity of powders does not change substantiallyas a function of shear rate or strain. However, when magnesium stearate is present (concentrations studiedhere range between 0.5% and 2%), hydrophobicity increases as a function of strain, shear rate and lubricantconcentration. Observed changes range over several orders of magnitude, readily explaining common“overlubrication” observations of delayed drug dissolution.

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© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Lubricants are added to pharmaceutical formulations to improvepowderflowability [1], to facilitate tablet ejection and tominimize tabletdefects [2]. However, most lubricants are hydrophobic compounds andcan alter blend hydrophobicity (also known as wettability). The latterblend property affects the performance of post-lubrication steps of atablet manufacturing process, such as compaction or tablet coating, andproperties of the final product such as tablet and capsule dissolution andtablet strength [3]. In addition, blend hydrophobicity affects a granula-tion process: high substrate hydrophobicity may lead to inadequatebinder distribution which in turn means weak, porous granules. As aresult, granule flow and tablet mechanical properties can be compro-mised [4–6]. Drug dissolution from tablets is probably the most studiedparameter because itmeasures thedrug release rate and ultimately drugbioavailability. There aremanyparameters in the lubricationprocess andin the formulation that affectdissolution anddrugbioavailability. Amongthe formulation parameters, there is selection of excipients and otheradditives [7–9]. Among the lubrication parameters, there is type andconcentration of lubricant [10–12]. In addition, there are interactionsbetween lubricant and the additives that help dissolution [13]. Finally,there are lubricant mixing variables. In those latter studies, drugdissolution is typically correlated with the type of blender (i.e. scale,shape, intensifier bars, etc.), its operation method (i.e. fill level, speed ofrotation, etc.) [14–18] and mixing time [20,21,22]. Well known resultsshow that as the mixing time for magnesium stearate increases, there isan increase in the disintegration time and a decrease in drug dissolutionfor tablets.

Here, we add a new facet to the lubricant mixing studies, becausewe correlate powder hydrophobicity with fundamental processingvariables such as strain and shear rate rather than blender parametersandmixing time. This is useful for two reasons: First, lubricated blendsare not only exposed to shear rate and strain in a blender but also insome subsequent process steps such as flow in feed frames. It is moremeaningful to analyze the contribution of these units towardshydrophobicity and dissolution using fundamental variables ratherthan blender variables. Second, if we can characterize the contributionof each piece of equipment, processing conditions (i.e. mixingprotocols) and process scale-up towards blend hydrophobicity andthen correlate it with drug dissolution, we are making an importantcontribution towards Quality by Design. This type of study will helpoptimize lubrication and consequently granulation, powder flow,tableting and coating (i.e. by developing a method to measurehydrophobicity online). The aim of this paper is to study thecorrelation between processing variables and blend hydrophobicityfor lubricated blends using the Washburn method and an instrumentthat uniformly exposes a blend to specific shear rate and amounts ofstrain. This equipment has been successfully used to study the effectsof these variables on different properties of lubricated blends andtablets (i.e. density, flow, etc.) [3].

2. Materials and methods

2.1. Formulations

The materials used in all experiments reported here are a mixtureof lactose (Fast Flo Lactose, ∼100 µm, spherical particles, ForemostFarm, Newark, NJ), microcrystalline cellulose (Avicel PH 102, ∼90 µm,

Fig. 1. Couette shear instrument to expose the formulations to controlled shear conditions.A: Internal cylinder with pins. B: External cylinder with pins. C: Assembled unit with lid.

Nomenclature

m Mass of fluid that penetrates the column in the Washburn method (g).t Time (s).η Viscosity of the solution used in the Washburn method (Pa s).ρ Density of the solution used in the Washburn method (g/l).γ Surface tension of the solution used in the Washburn method (N/m=kg/s2).C Geometric factor that is constant as long as the column packing and the particle size remain constant.θ Contact angle between fluid and surface of particles.Φ The term (Cρ2γ cosθ/η) from the Washburn equation is represented here as Φ for notation simplicity and called hydrophobicity.

Φ is the slope of the lines in Fig. 4.MgSt Magnesium stearate (lubricant).API Active Pharmaceutical Ingredient.df Degrees of freedom.

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needle-like particles, FMC, Rothschild, WI) and different amounts ofmagnesium stearate (∼20 µm, monohydrate, irregular particles,Mallinckrodt, Product Code: 5712, St. Louis, MO).

Four mixtures are prepared with the following proportions onmass basis:

• Mixture 1: Lactose (60%), Avicel (40%), MgSt (0%).• Mixture 2: Lactose (59.5%), Avicel (40%), MgSt (0.5%).• Mixture 3: Lactose (59%), Avicel (40%), MgSt (1%).• Mixture 4: Lactose (58%), Avicel (40%), MgSt (2%).

2.2. Controlled shear environment: modified Couette system

The geometry of the controlled shear environment is based on anannular Couette rheometer used for liquids. The device consists oftwo concentric aluminum cylinders 4.3 in tall (11 cm) and a gap of0.75 in (1.9 cm) that allows a powder volume of approximately 0.6 l.The internal cylinder (Fig. 1–A) has a diameter of 6.5 in (16.51 cm).The internal cylinder can rotate at any speed in the range of 1 to245 rpm whereas the external cylinder is stationary. Both cylindersare made of aluminum and they are supplemented with equallyspaced interlocking pins that create a homogeneous shear field in theflow region (Fig. 1-B). The controlled shear environment has a lid anda seal (Fig. 1–C).

2.3. Procedure to prepare formulations under controlled shear conditions

Prior to exposing the samples to the controlled shear environment,a pre-blend of the ingredients in the desired proportions must beprepared. The practice of pre-blending the sample is adopted becausethe controlled shear environment is not an effective mixer. Dispersionis the main axial macro-mixing mechanism in the device; convectionalong the axis of rotation is very slow. If it is loaded with the ingre-dients in an unmixed stratified state, it takes a long time to achievelubricant homogeneity throughout the unit, and during this time, thematerial is experiencing shear under inhomogeneous conditions.Homogeneity is critical because if ingredients are not pre-blended,some parts of the blend will have a high concentration of lubricantand others will have a low concentration of lubricant while beingsheared, making the lubrication process uneven; unless this isavoided, misleading results are obtained.

The procedure to prepare the pre-blends in a small V-blender(4 qt) is described in Fig. 2. In a first step, only the excipients are pre-blended; the second step is the mixing of the lubricant and the pre-blend of excipients. The loading pattern for lubricant and excipientsis top–bottom. Both blending steps consist of a short mixing time(50 rev), using the blender at a moderate rotational speed (10 rpm).The small scale of the blender and the mild mixing conditions (speedand time) minimize exposure of the lubricant to shear and are not

enough to cause complete homogenization of the lubricant. There-fore, as shown in a previous publication [3] for blends with a 1% and2% MgSt content, after mixing the lubricant in the V-blender andeven processing the blend in the shear cell for a low number ofrevolutions, lubricant homogeneity (measured by RSD) is in therange of 5–7%. For larger shear exposure, lubricant RSD values arebetween 1% and 2%.

The controlled shear environment is loaded to full capacity (∼0.6 l)with pre-blend and one of the shear treatment conditions indicated inTable 1 is applied. Table 1 displays the shear rates in rows (with thecorresponding rotational speeds of the cylinder in rpm), the strain(expressed also as number of revolutions) in columns. A sparse

Fig. 2. Illustration of the pre-blending process in a V-blender: first, excipients are mixed in a blender operated at 10 rpm for 5 min, then MgSt is mixed for an additional 5 min at10 rpm.

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diagonal design (marked with ‘X’) is used to examine the effect ofshear rate for similar amounts of strain, and the effect of strain atconstant shear rates. In the experiments reported here, strain variesovermore than two orders of magnitude from ∼270 to ∼53,000, whileshear rate varies from 0.9 s−1 (at 2 rpm) to 109 s−1 (at 245 rpm). Thisrange comprises typical values for most industrial units, ranging fromsmall tumblers without intensifier bars in the low end, to “high shear”mixer-granulators on the high end.

2.4. Washburn technique for measuring hydrophobicity

Washburn described the phenomenon of liquid rising into thelattice of a powder bed due to capillary action [19] and developed atechnique that measures the speed at which a fluid permeatesthrough a powder bed to study the hydrophobicity (or contact angle)of many types of materials. In his paper, he shows that the volume ofthe fluid that penetrates the powder bed is a linear function of thesquare root of time. This can be alternatively expressed as the linearrelationship between mass of fluid squared and time (Eq. (1)) with aslope given by (η/Cρ2γ cosθ) [20]. This technique has been thoroughlyused for drugs and pharmaceutical excipients [21].

t =η

Cρ2γ cosθm2 ð1Þ

For notation simplicity, the term (η/Cρ2γ cosθ) is represented asΦin this paper. When the blend is very hydrophobic fluid permeatesslowly through the bed. The contact angle between the fluid andthe particles is high, the cosine of this angle is almost zero, and Φ hasvery large values. When the blend is slightly hydrophobic, fluidspermeate through the blend rather quickly. The contact anglebetween the fluid and the particles is lower, the cosine of this angleadopts an intermediate value and the slope Φ has lower values. C is aproportionality constant that depends on the packing. In order to keeppacking constant between experiments, controlled tapping of thecolumn filled with formulation was performed.

In the present study, the powder (50 g) is poured into achromatographic column (Chromaflex SZ 233) with the bottommade of sintered glass (Fig. 3-A) and densified during 1 min using thetap density tester (VanKel, Model 50-1200). The bottom of thecolumn is immersed into a large container of solution saturated withall soluble blend components (i.e. lactose) with the level of liquidbarely above the sintered glass (Fig. 3-B). The column is held by asupport beam positioned on a scale (Adventurer Pro, Ohaus)connected to a computer with a data collecting system (BalanceTalk, Labtronics, Inc.), as shown in Fig. 3-C. The scale is tared and the

Table 1Grid showing the shear rates and strain conditions used in the Couette shear cell(controlled shear environment).

10 rev(267)

80 rev(2136)

320 rev(8544)

2000 rev(53,400)

2 rpm (0.9 s−1) X X40 rpm (17.8 s−1) X X X160 rpm (71.2 s−1) X X X245 rpm (109 s−1) X X

system collects weigh data as the fluid permeates into the powderbed. This data is plotted as time versus mass of solution squared, andas a result, straight lines (Fig. 4-A, B, C, and D) are obtained.

2.5. Design of experiment and general analysis of the effect of variableson hydrophobicity

The current experiment is designed to determine the effect ofshear rate, strain, and lubricant concentration on blend hydropho-bicity. The combinations of levels of shear rate and strain analyzed(Table 1) correspond to those found in the majority of industrialequipment, and they form an incomplete factorial model. For each ofthese ten “shear treatments”, the effect of 4 lubricant concentrationsis tested on blend hydrophobicity, generating a total of forty experi-mental conditions. Additionally, each condition is tested twice. Theexperiments are randomized, which means that the conditions arenot tested in any pre-determined order, and the repetitions are notperformed in sequence.

The statistical analysis is performed with the Minitab software,using a General Linear Model (GLM) which takes into account theimbalance in the data sheet generated by the fact that not all thecombinations of revolutions and rpm are studied. The analysis is doneon the natural logarithmic scale.

3. Results

3.1. General analysis of the effect of variables on hydrophobicity Φ

Table 2 compiles the Φ values, which are the slopes of the lines inFig. 4-A to D, for all the combinations of shear rate, strain, andlubricant concentration examined. This section presents a statisticaland a graphical analysis of these data. Before proceeding to theanalysis of this data, it is necessary to provide an explanation aboutthe variability observed between replicas. The formulation withoutmagnesium stearate shows large variation between replicas and theycan be different by a factor of up to six. However, all thehydrophobicity Φ values are very low as fluid permeates the powderbed very fast, regardless of the shear treatment of the formulation. Iflubricant is not added, the hydrophobicity Φ of the formulation is notexpected to change and it is natural that hydrophobicity Φ valuesare very low. Therefore, a relatively larger variation among thesevalues is admissible. On the other hand, for formulations withmagnesium stearate, hydrophobicity is larger and increases evenmore under shear treatment. For these samples, the hydrophobicityvalues of replicas are within a factor of two. There is only one casewhere the hydrophobicity of replicas differs by a factor of 10 or more(2% MgSt and 160 rpm — 2000 rev). In this case, the hydrophobicityvalues measured byWashburnmethod are very high and almost haveno physical meaning because the flow of fluid in the powder column isalmost undetectable. The Washburn technique cannot measure thevalue ofΦ for the blends with 1% and 2% magnesium stearate that areprepared in the controlled shear environment operating at 245 rpmfor 2000 rev because the solution does not permeate the powder bedat all. Therefore, in the statistical analysis, these conditions are notincluded. In conclusion, we accept a larger variability (up to 6 times)for replicas with very low hydrophobicity (0% MgSt) than for replicaswith some MgSt (up to 2 times). The number of measurements

Fig. 3. A: Chromatographic column, loadedwith the powder, in the tap density tester. B:Chromatographic column submerged in the solution container. C: Setting to measureand record the increase in weigh of the chromatographic column.

Fig. 4. A: Plot of the experimental data as time versus mass of fluid squared (lubricantconcentration: 0%). B: Plot of the experimental data as time versusmass of fluid squared(lubricant concentration: 0.5%). C: Plot of the experimental data as time versus mass offluid squared (lubricant concentration: 1%). D: Plot of the experimental data as timeversus mass of fluid squared (lubricant concentration: 2%).

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(65 values) used for statistical analysis still gives enough degrees offreedom to run and determine the effects of shear rate (df=3), strain(df=3), lubricant concentration (df=3) and all their possibleinteractions.

The results of the ANOVA test (Table 3) show that, for a sig-nificance p level of 0.05, shear rate (pb0.001), strain (p=0.001) andlubricant concentration (pb0.001) affect blend hydrophobicity. Theeffect of each of these three variables is represented in the three plotsin Fig. 5, which represents the mean hydrophobicity in naturallogarithmic scale (y-axis) versus the different levels for each variable.The plots show that strain (revolutions) and magnesium stearateconcentration can drastically increase blend hydrophobicity whilelarger shear rates (plot in upper left corner) increase hydrophobicitybut in a more moderate manner. Table 3 also shows that there is asignificant interaction between lubricant concentration and strain(pb0.001) and this effect is illustrated in Fig. 6. This figure representsthe mean hydrophobicity in natural logarithmic scale (y-axis) versusmagnesium stearate concentrations. Each curve is for blends exposedto different amounts of strain (number of revolutions) and exposure

Table 2Hydrophobicity values Φ (given by the slope of the lines in Fig. 5-a to d) obtained foreach combination of shear rate, strain (rows) and lubricant concentration (columns).

0% MgSt 0.5% MgSt 1% MgSt 2% MgSt

2 rpm — 10 rev 0.022, 0.041 0.136, 0.124 0.137, 0.103 0.356, 0.35140 rpm — 10 rev 0.025, 0.075 0.128, 0.224 0.117, 0.146 0.475, 0.4412 rpm — 80 rev 0.078, 0.114 0.142, 0.172 0.213, 0.265 2.798, 2.26240 rpm — 80 rev 0.024, 0.024 0.171, 0.309 0.203, 0.397 2.0, 1.377160 rpm — 80 rev 0.141, 0.102 0.267, 0.192 0.569, 0.627 3.315, 3.90940 rpm — 320 rev 0.029, 0.189 0.734, 1.691 3.521, 2.774 17.05, 43.77160 rpm — 320 rev 0.070, 0.084 2.203, 2.107 8.815, 8.351 90.5, 75.31245 rpm — 320 rev 0.024, 0.077 4.280, 6.951 5.7, 10.317 123.8, 92.33160 rpm — 2000 rev 0.212, 0.145 35.328, 39.9 128.89, 217.97 10,912, 758.78245 rpm — 2000 rev 0.046, 0.058 34.328, 23.66 NA, NA NA, NA

Table 3ANOVA test shows that shear rate, strain and MgSt concentration affect hydrophobicitysignificantly (pb0.001). It also shows that the interaction between strain (revolutionsof the shear cell) and MgSt concentration is also significant.

Source df F p

Rpm 3 6.32 0.001Revolutions 3 137.58 b0.001% MgSt 3 320.01 b0.001Rpm % MgSt 9 1.50 0.174Revolutions % MgSt 9 13.85 b0.001Error 48

Fig. 6. The lines in the plot indicate an ordinal interaction between lubricantconcentration and strain (revolutions). The combination of larger strain and largerlubricant concentration boosts blend hydrophobicity.

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to larger strain yields higher hydrophobicity mean values. Thesecurves have an upward trend, but they are not parallel and they do notcross, which indicates the existence of an ordinal interaction betweenlubricant concentration and strain. Larger magnesium stearateconcentrations and larger exposure to shear lead, by themselves, tomore hydrophobic blends. An ordinal interaction between these twovariables suggests that a treatment (i.e. amount of strain) has amore intense effect in one condition (i.e. lubricant concentration)than another. In other words, when two independent variables arecombined, a larger than expected effect (on hydrophobicity) isproduced (i.e. the combination is greater than the sum of its parts).It is important to quantify this interaction to avoid conditions that cannegatively affect product properties.

In addition to the previous statistical analysis, a single graphicalrepresentation illustrates the effect of the three variables on theterm Φ. The average value for each of the forty conditions tested(Table 2) is plotted in Fig. 7. This figure presents the value of the

Fig. 5. (ln scale for mean values) Upper left: plot shows that higher shear rates (or rpmof the shear cell) increase the mean blend hydrophobicity. Upper right: plot shows thatlarger strain (or revolutions of the shear cell) notoriously increases mean blendhydrophobicity. Bottom: plot shows that larger magnesium stearate concentrationsincrease blend hydrophobicity.

term Φ as a function of the lubricant concentration, and each curvecorresponds to one of the ten shear treatments indicated in Table 1.The solid line curves at the bottom correspond to the minimum levelof strain (10 rev), and different shear rates (2 rpm and 40 rpm). Thedashed line curves correspond to a larger amount of strain (80 rev),and different shear rates (2 rpm, 40 rpm, and 160 rpm). The curveswith dot lines correspond to a larger amount of strain (320 rev), anddifferent shear rates (40 rpm, 160 rpm, and 245 rpm). Finally, theblurry lines on top correspond to blends prepared using 2000 rev andtwo different shear rates (160 rpm and 245 rpm). It is observed that,as strain (revolutions) increases, the value for hydrophobicity (termΦ) follows an upward trend. A more detailed look at the groups oflines for a specific amount of strain, which are represented here withdifferent line patterns, shows that the lowest hydrophobicity valuescorrespond to the lowest shear rate used in the preparation processand that hydrophobicity increases for larger shear rates.

Fig. 7 also shows that blend hydrophobicity for any shear treat-ment increases as a function of lubricant concentration, and mostcurves increase from left to right. In general, there is a steep increasein blend hydrophobicity when lubricant concentration goes from 0%to 0.5% (difference between lubricated and un-lubricated blends), anda slower and constant increase when lubricant concentration goesfrom 0.5% to 2%.

Fig. 7. Effect of lubricant content (x-axis), strain or revolutions of the shear cell (shownby the pattern of the curves) and shear rate or rpm of the shear cell on blendhydrophobicity. Larger strain increases hydrophobicity Φ and for equivalent strain(i.e. curve with the same pattern), larger shear rate increases hydrophobicity.

106 M. Llusa et al. / Powder Technology 198 (2010) 101–107

3.2. Effect of shear rate and strain for lubricated and un-lubricatedblends

The previous analysis shows that there is an interaction betweenlubricant concentration and strain. In order to investigate the effects oflubricant concentration and processing variables in more depth weperformed an analysis of the effects of processing variables (sheartreatment) on blend hydrophobicity for each lubrication concentration.The data on blend hydrophobicity is plotted for each lubricant con-centration and it is subsequently analyzed using statistics. The figuresplot the average value of the term Φ as a function of strain (number ofrevolutions) using curves that correspond todifferent shear rates (speedof the cylinder of the controlled shear environment).

Fig. 8-A shows that in the absence of lubricant all the hydropho-bicity values are very similar. The Φ values are very similar and in therange 0.01–1. On the other hand, when lubricant is present, sheartreatment changes the hydrophobicity significantly. Fig. 8-B, C, and Dpresent the results for a 0.5%, 1%, and 2% MgSt concentration. Ingeneral, the termΦ increases as a function of strain, and such increaseis ∼104 fold after the blend is exposed to 2000 rev of the controlledshear environment. An explanation of these changes in hydrophobic-ity is based on the surface modification of excipient particles by MgSt.When lubricant is included in the formulation, the surface of excipientparticles is chemically modified (by lubrication deposition) adoptingthe hydrophobic character of the lubricant. In the absence of lubricant,this chemical surface modification of excipients surface cannot occur.Only physical modification of particle surfaces (i.e. roughness) couldeventually occur. Therefore, without lubricant, hydrophobicity of theexcipients is not modified by shear rate or strain, at least in an extentthat can be measured by the Washburn method. Single factor ANOVAtests are run using the hydrophobicity data sets for each lubricantconcentration. For simplicity we did not discriminate shear rate andstrain in this statistical analysis and considered the conditions inTable 1 as different processing conditions. The number of conditionsused in the statistical analysis of the 0% and 0.5% magnesium stearateconcentration data sets gives enough degrees of freedom (df=9) torun a one-factor ANOVA and determine the effects of shear treatment.For the analysis of the 1% and 2% magnesium stearate concentrationdata sets, less information is available (16 values) because after2000 rev there is either very high or no measurements available forhydrophobicity (df=7). The results of these one-factor ANOVA tests(Table 4) show that without magnesium stearate, even for asignificance p level of 0.05, shear treatment does not affect blendhydrophobicity. On the other hand when magnesium stearate ispresent, the ANOVA tests for the data set for each lubricant con-centration indicate that at a significance p level of 0.001, sheartreatment affects blend hydrophobicity.

4. Conclusions

This paper presents a method to examine the effect of lubricantcontent, shear rate and strain on the hydrophobicity of solid formula-tions. A new controlled shear environment allows to uniformly exposeblends to controlled combinations of shear rate and strain and blendhydrophobicity is measured using the Washburn method. The entireprocedure is highly reliable and gives reproducible results. Thisprocedure provides a tool towards building predictive methods for

Fig. 8. A: The hydrophobicity of blends with 0% magnesium stearate does not increaseas a function of strain (revolutions) or shear rate (rpm). B: The hydrophobicity of ablend with 0.5% magnesium stearate increases as a function of strain (revolutions) andshear rate (indicated by the color of the curves). C: The hydrophobicity of a blend with1% magnesium stearate increases as a function of strain (revolutions) and shear rate(indicated by the color of the curves). D: The hydrophobicity of a blend with 2%magnesium stearate increases as a function of strain (revolutions) and shear rate(indicated by the color of the curves). (For interpretation of the references to color inthis figure legend, the reader is referred to the web version of this article.)

Table 4ANOVA tests are run using the hydrophobicity values for each of the different lubricantconcentrations. When the observed F value is larger than a critical F (which isestablished at a certain confidence level of 0.001 in most cases here) it indicates thatshear treatment (any combination of shear rate and strain) affects hydrophobicity. Onlyin the absence of lubricant is hydrophobicity not affected.

Observed F Critical F

0% 2.344 F.05,9,10=3.020.5% 14.431 F.001,9,10=8.121% 19.092 F.001,7,8=12.42% 30.427 F.001,7,8=12.4

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dissolution, drug release, and other properties of products (i.e. tabletstrength, coating, etc.). It is useful also for developing mixing protocols,performing process scale-up and assessing the shear conditions ofmanufacturing equipment.

The results show that, as expected, the hydrophobicity of lubri-cated blends increases as a function of strain, shear rate, and lubricantconcentration. In addition, they show that the effect of strain on thehydrophobicity of lubricated blends is larger than the effect of shearrate. The latter conclusion is an important design and scale-up con-sideration which is communicated here for the first time.

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