Measuring viscosity of pharmaceutical and cosmetic semisolids

j. Soc. Cosmet. Chem., 39, 241-258 (July/August 1988)

Measuring viscosity of pharmaceutical and cosmetic semisolids using normal stress

SHIVAJI PURWAR, JAMES K. LIM, JOHN W. MAUGER, and STEPHEN A. HOWARD, Vicks Research Center, One Far Mill Crossing, Shelton, CT 06484 (S.P.), West Virginia University School of Pharmacy, Medical Center, Morgantown, WV 26506 (J.K.L., J. W. M. ), and Ortho Pharmaceutical Corporation, Raritan, NJ 08869 (S.A.H.).

Received September 21, 1987. Presented at the 130th Annual APhA Meeting, New Orleans, April 9-14, 1983.

Synopsis

A method for measuring various viscoelastic parameters of pharmaceutical and cosmetic semisolids was reported earlier in this Journal (1). In this paper •he theoretical development of the method is described for obtaining viscosities of petrolatum USP and polyethylene glycol 1500 by pressing between parallel plates analogous to those used with the parallel plate plastometer technique. Experimental information is presented which demonstrates applicability of the slightly different mathematical approach for the proposed method as developed from tensor analysis for shear stress and rate of change of angle, 0, for the shear rate, respectively. Experimental variables tested in this study include the initial applied stress, height, and diameter of the sample plug. A 4 x 12 factorial analysis of the data indicates a dependent effect on viscosity for the initial applied stress to the sample plug, but an independent effect, within specific limits, for the plug height or diameter.

INTRODUCTION

Most semisolid systems, represented by a large number of pharmaceutical ointments and/or cosmetic creams, lotions, etc., exhibit complex flow behavior, including irre- versible shear breakdown, thixotrophy, viscoelasticity, etc., characterized by the methods of measurement. It is well known that most common viscosity measuring methods cause extensive material deformation due to high-shear stress application which results in a considerable alteration of the material structure (2-7). Consequently, the viscosity values obtained in these cases are influenced to a large extent by the level and duration of applied stress (8- 11). For these reasons, high-shear measuring methods are useful for predicting the behavior of products during the normal process of manu- facturing where significant structural breakdown occurs. However, for efficacy evaluation, quality control, the user's perception, and the conventional time- and stress-dependent viscosities obtained by high-shear methods are less meaningful. In fact, a

241

242 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS

number of pharmaceutical scientists (2,8) have in the recent past expressed concern for the lack of a suitable device for examining semisolids in their rheological "ground state," through the application of low shear largely avoiding significant changes in static structure. Low-shear methods previously available require rather complex equip- ment with elaborate procedures. A simple and readily accessible low-shear method would therefore be of distinct benefit to the investigator for fundamental studies, espe- cially for those related to material structure when the material can be examined closely under an approximately quiescent equilibrium state.

This paper reports the theoretical development of an equation that describes a method shown to be useful for evaluating the viscoelastic properties of semisolid materials (1). It also presents experimental data characterizing the simple device for day-to-day viscosity determinations. The method involves two parallel plates between which the test material is pressed. Although, a similar parallel plate plastometer is already in existence (12,13), it was basically designed with high-load capacity for engineering materials such as resins. Our device, on the other hand, with low-load capacity, is designed for semisolid materials such as petrolatum. The mathematical treatment also employs a different approach. It will be seen in the Results and Discussion section that the actual experimental data are better explained by the presently derived equation rather than by the plastometer equation (13).

GLOSSARY OF SYMBOLS

t•ii = normal component of applied stress in

S

Sii

v

Ho H

t

F

a

K1

h

J 0

'T' (2nd subscript) direction. (First subscript 'T' refers to surface.) (dynes/cm2).

= shear component of applied stress in "Xl" direction on "•" surface (x I and • do not necessarily represent cartesian coordinates but are perpendicular to each other like x, y, or z coordinates) (dynes/cm2).

= hydrostatic stress (dynes/cm2). = normal component of deviatoric stress with the same subscripts as for (dynes/

cm2). = shear strain.

= rate of shear strain (shear rate) in "Xl" and "•" direction (sec-•). = volume of sample specimen (cm3). = initial height of sample specimen (cm). = height of sample at time t, = H o - h (cm). = time (sec). = applied force (applied weight X 981 g crn/sec2). = 4WX (cm3). = (Ho '/2 - Ho•/7a)(cm•/=). = viscosity (g/cm sec or poise). = height travelled by the top plate at time t (cm). = compliance = stress/strain (cm sec2/g or cm2/dynes). = a hypothetical angle such that its change (dO) = shear strain (no units), and its

rate of change (dO/dO = shear rate (time-•).

THEORY

Viscosity is defined by Newton as the proportionality constant between shear stress and shear rate:

MEASURING VISCOSITY OF SEMISOLIDS 243

Syy -- - 5 YY

I ' ' ! Top Plate

•\• H,2 Sample Specimen

r , ........ of Volume V i m I I I

I I

i • "' 1• Bottom ' Plate Figure I. Diagram illustrating deformation of sample plug between pressing parallel plates; r -- plug radius; H = plug height.

q- -- •l 0 <1)

where T is the shear stress, i•, the shear rate, and qq, the viscosity.

Shear stress. Since normal stress is used in our study, it is necessary to resolve its shear components using a three-dimensional tensor analysis (14). Based on this analysis, if normal stress, O'yy, is applied in the direction of the y-coordinate (Figure 1), then

O O O S O O S,= O O 0 O'yy 0 = 0 S 0 -'[- 0 Syy 0 0 0 0 0 0 S 0 0

Stress Tensor Hydrostatic Stress

where S - O + O'yy + O _ gyy 3 3

Deviatoric Stress

and Syy = O'yy - S = O'yy - (O'yy) 2 3 = '•'O'yy Also, the sum of the deviatoric stress in the x, y, z direction remains zero.

(2)

Sxx --I- Syy -1 t- Szz = 0 (2A)


y

-Syy

Sxx Sxx

Figure 2. Shear stress due to normal stress.

x

This indicates that 2/3 of the applied normal stress is used as deviatoric stress, causing the deformation of sample shape, while the remaining • of the applied stress is ex- pended as the hydrostatic stress.

This analysis provides normal deviatoric stresses in the x, y and z directions. However, in pure shear, an element experiencing a compression in one direction (y) and a tension in the perpendicular directions (x or z) (Figure 2) behaves as though it were subjected to pure shear stress •re,• on planes indicated by side "h" (15). This shear stress equals normal stress Syy in magnitude (14, 15) and causes a change in angle 0. Since no normal stress acts on side "h" of the element, the sides do not change length with deformation. Although Figure 2 represents the analysis in two dimensions, it can be shown that in a three-dimensional system, Syy splits into two equal parts in the yx and yz planes, sharing half of the magnitude in each direction.

Shear rate. Shear rate is usually defined as du•/dly (Figure 3), where du• is the difference in x components of the velocities of the two layers at dly distance apart. In terms of angle 0 (Figures 1-3), the same shear rate could be defined as d0/dt with units of time -• (14,15).

In a three-dimensional system, angle 0 represents only V2 of the actual strain (12), since


y

dU x '•yx

X

Figure 3. Diagram illustrating shear rate based on plug deformation, producing a change of angle 0.

in a two-dimensional system this angle would have doubled with the same magnitude of applied stress. Thus, in our case, the rate of change of angle 0 is:

or

dO 1.

dt -

2 d0 •-• = 3e,• (3)

EQUATION FOR THE SYSTEM

If three identical cylindrical sample plugs of radius r, height H, and volume V, are pressed between two lubricated plates by a normal force F, then the shear stress for each sample becomes

're.= •Syy = cry,,, = • = • V (4) where (V/H) refers to the cross-sectional area of the sample. For shear rate, the angle 0 in the coordinate form (Figure 1) gives (substituting r with X/•/XH for the cylindrical geometry)

tan = - = ß

r •


which after differentiating provides

From simple coordinates (Figure 1)

=•] • 'dH

(•) r2 + H2/4 4V + XH 3 sec 2 = = r 2 4V

substituting in this Equation 5 and rearrangement provides HX/2

d0 = 6•' ß dH 4V + XH 3

(5)

dO H •/2 dH or 2'--= 12X/-•-V' '-- (6)

dr 4V + XH 3 dr

which is equivalent to/• by Equation 3. Substituting Equations 4 and 6 into Equation 1 and using (-)ve sign for compressive stress yields

2 FH H 1/2 dH = •1' 12X/•' '--

9 V 4V + XH 3 dt

Designating the quantity 4V/X = a (constant for a given sample size), and rearrangement gives

fo r F fi•,rl •_( 1 ) dH -- ß ß .

54• dt = HX/2 (7) 1 + H3/a

The above expression may be integrated between the limits of H o (sample height at time 0) and H (sample height at time t) with the use of the following series expansion:

1 - 1 - x + x 2 - x 3 -I- ........

l+x

such that H 3 --l<x=

a

or

H3X H3X

4V 4Xr2H

or H < 2r

which provides

where K 1 = (Ho

27v F

7a ]

7a/1 -- • (8)


It should be noted that only the first two terms in the series are used for integration purposes. It can be shown that an error of less than 1% is introduced when the height- to-diameter ratio (H/2r) of the sample is within 0.60 and less than 2% error when the ratio is within 0.75.

INCOMPRESSIBILITY OF MATERIAL

Soft poly. meric solids have a bulk modulus of around 3 x 10 •ø,, dynes/cm 2 (16,17), indicating that such materials would require almost a ton (1000 kg) of pressure to cause as little as 1% volumetric change. Since the proposed method is an open system re- quiring the equivalent of approximately 100 g of pressure for necessary deformation, volumetric change was neglected in the above derivation.

MATERIALS AND METHODS

ISOTROPICITY OF MATERIAL

Small quantities of PEG 1500 (Lot #1305, Ruger Chemical Co., Inc., NJ) and petrolatum (Lot #710683, Ruger Chemical Co., Inc., NJ) were melted and congealed for examination under the polarizing microscope (Nikon Microflex EFM with photomicro- graphic attachment, imposed with polarizer and analyzer, Nippon, Kogaky, Tokyo, Japan (Figure 4). These materials were found to be crystalline and hence anisotropic.* .On this basis some deviation from ideal behavior was expected since the use of tensor :analysis requires the material to be isotropic.

APPARATUS ß

A complete description of the main apparatus has been presented earlier (1). It consists of two horizontal parallel plates pressing the test material with a known stress, analogous to that reported for the parallel plate plastometer technique (12). A guide rod and a guide plate together with the use of three equal-sized sample plugs ensured the smooth descent of the top plate during measurements. Several substitutes of bottom plates were kept ready for quick changes. Teflon © was used to minimize friction between moving parts of the device. The entire unit, which includes the main apparatus, an LVDT unit (linear variable differential transformer; Schaevitz Eng., Type 1000 HR, S/N 5519, CAS Series, Pennsauken, NJ), a chart recorder (Sargent-Welch, Model SRG), and a Brookfield helipath stand, is shown in Figure 5. The applied stress is represented by the total weight of the top plate with guide rod, plunger of the LVDT unit, and any added weights.

METHOD

With the aid of an open-end 5-ml disposable Monoject syringe, the samples were drawn from the test material, previously melted, and set in preparation trays. A column of

* We agree with the reviewer's comment that "The existence of anisotropic materials dispersed in an isotropic phase does not necessarily make the material behave in an anisotropic manner." However, whether the material could still behave as truly isotropic is also not certain.


:'..• ..•.•<>. '•f•'•'g? .'wx: 5..;5•.. .... a"•:'•. •-.'.•37•"3.1•.. •" ? :?•evv. .. ,, • .... •.. •.. ½:. ß :..½.. •a... •. • • :.• "•

Figure 4. Polarized photomicrograph of PEG 1500 (top) and petrolatum (bottom). Magnification 100 X


material was ejected and plugs of the same measured size were sliced from the middle section, with the initial and end portions discarded. Three of these plugs (used to prevent tilting of the top plate during pressing) were carefully placed on the prelubricated bottom plate, approximately equidistant from each other. The underside of the top plate was also prelubricated with a thin film of mineral oil. A fourth sample plug was used simply to monitor the material temperature by an Electronic Digital Ther- mometer (Fisher Scientific Co). The top plate bearing the LVDT plunger and desired weights was carefully positioned above the sample plugs with the aid of the Brookfield helipath stand (Figure 5). Actual contact of the top plate with the sample plugs at the start of the run was monitored visually and marked aproximately on the chart recording.

The LVDT unit was precalibrated, usually at the rate of 0.04 cm/sec, or 25 sec/cm, which was equivalent to 0.0082 crrdchart division.

SHAPE OF SAMPLE DEFORMATION

Preliminary studies on the deformation shape of samples using PEG 1500 provided some interesting observations. After heating the material in siliconized trays (Ekco Houseware Co., IL) over a water bath to remove entrapped air, it was left undisturbed to equilibrate for a period of two weeks. The uniform cylindrical samples drawn from the congealed material were found to deform as a frustum of a cone when pressed together between the two parallel plates, with the lower end expanding faster than the upper end. Such deformation was later traced to the material's top surface rather than to

Figure 5. Apparatus with accessories used to measure viscoelastic parameters. Key: (A) Main apparatus; (B) Linear variable differential transformer (LVDT) unit; (C) Chart recorder; (D) Brookfield helipath; (E) Electronic digital thermometer.


0.4

0.3

I i I I I , I i I I I I

2 7 12 17 22 27 32 37 42 õ2' 62

Time (t) sec

Figure 6. Typical chart recordings for distance traveled by top plate vs. time for petrolatum. Each plot represents a single run.

a gravitational effect. With the top layer of the prepared material removed, the sample plugs were observed to deform in a uniform fashion. Thus, in this as well as the previous study (1), samples were drawn only from the middle layer of the prepared material, excluding the top and the bottom layers.

RESULTS AND DISCUSSION

TESTING THE EQUATION

Original curves representing the extent of material deformation of petrolatum plugs, 0.7-cm high and 1.2-cm in diameter, tested with a total load of 81.31 g (23.51 X 103 dynes/cm 2) for the top plate, metallic rod, and LVDT plunger, are presented in Figure

E o 3

z

2 7 12 17 22 27 32 7 42 52

Time (t} sec Figure 7. Compliance calculated using Equation 8 œor the data depicted in Figure 6.


6. Points were selected along these curves for the values of height traveled "h," and the "H" (height remaining to be traveled) was calculated by the relationship H = (H 0 - h). Compliance values (ratio of strain/stress represented by the quantity on the left-hand side of Equation 8) were calculated for each point and plotted against time (Figure 7; subsequent Figures 8, 9, 11, and 12 were plotted similarly). The appearance of the initial curved portion of the compliance curve which represents the viscoelastic behavior of the material was discussed before, and the equation was accordingly modi- fied (1). In this paper, data only from the terminal linear portion of the plot representing the linear flow of the dashpot unit of the Maxwell model (1) has been used to determine the viscosity values. On this basis, the viscosity for petrolatum from the reciprocal of the linear slope was found to be around 2.45 x 10 6 poise.*

EFFECT OF VARYING INITIAL STRESS

Experimental data showing the effect of various stress levels on the viscosities for petrolatum and PEG 1500 are presented in Table I. The viscosity values based on triplicate runs using three sample plugs for each run were calculated from the reciprocal of the terminal linear slopes of the compliance curves (Figure 8). The ANOVA test using a 4 x 12 factorial design with three replications for the compliance data indicate significant differences (or = 0.05) in viscosity values with application of different stress levels, consistent with the non-Newtonian nature of these materials.

In Figure 8, the compliance curves obtained with the higher stress levels were seen to deviate from linearity with time in the terminal region. This could be explained by the fact that within the same time period, the "effective" stress is reduced relatively rapidly with the higher stress levels. The "effective" stress here is defined as dynamic stress at any given point of time after starting the run, and can be computed from the sample dimensions at that time. For example, with the largest stress, i.e., 38 x 10 3 dynes cm -2, the initial stress had decreased by approximately 80% to 7.6 x 103 dynes cm -2 within 60 seconds (Figure 8), as compared to a decrease of less than 30% to 16.9 x 10 3 dynes cm -2 with the smallest stress, i.e., 23.5 x 10 3 dynes cm -2 within the same time period. Thus, in spite of starting with a higher stress value of 38 x 10 3 dynes cm -2, the "effective" stress of 7.6 x 10 3 dynes cm -2 in the former case becomes much too small within 60 seconds, as compared to 16.9 x 10 3 dynes cm -2 in the latter case where it started with a lower stress of 23.5 x 10 3 dynes cm -2.

Although such stress change is inherently accounted for in Equation 8 by virtue of integration over time, the point of emphasis here is that in the case of the higher initial stress, the "effective" stress eventually becomes too small too quickly to maintain the desired uniform deformation, ultimately approaching a zero flow. This situation is analogous to the yield value with conventional instruments where a minimum level of stress

* Equation 8 is based on the assumption of small sample deformation such that, as 0 •> 0, tan 0 • 0, a condition usually valid with stress application in the linear viscoelastic range. The data in this paper have been collected in the non-linear viscoelastic range with rather large sample deformation for the purpose of determining whether the results with this device are independent of such parameters as sample height and diameter. Consequently, the viscosity values shown here and in the tables elsewhere should not be consid- ered "ground state" viscosities as was the case in the previous publication (1). In that publication, the values were obtained in the linear viscoelastic range and were stress-independent. In the non-linear viscoelastic range (as here), the viscosity values are not expected to be stress-independent.


50% deformolion

! I

2 7 12 17 22 27 32 37 42 52 62

Time (I) sec Figure 8. Effect of varying initial stress on compliance for petrolatum as calculated with Equation 8. Key: (O) 23.5 X 103; (]--]) 29.3 X 103; (/•) 35.1 X 103; (O) 38.0 >( 103 dynes cm -2. Average values, n = 3.

i i i i i I i i

2 7 12 17 22 27 32 37 42 52 62

Time (t) sec

Figure 9. Effect of varying initial sample plug height on compliance for petrolatum as calculated with Equation 8. Key: (I) 0.4; (O) 0.5; (A) 0.7; ([]) 0.9; (O) 1. ! cm. Average values, n -- 3.

MEASURING VISCOSITY OF SEMISOLIDS 2 5 3

0.6

0.5

0.4

0.25

0.2

O.I

i i i

2 7 12 17 22 27 32 37 42 52 62

Time (t) sec

Figure 10. Effect of initial sample plug height on plug height deformation, h (cm) for petrolatum. Key: (I) 0.4; (0) 0.5' (A) 0.7; ([•) 0.9; (O) 1.1 cm. Average values +_ S.D., n = 3.

is required to initiate and maintain the flow. These observations lead us to conclude that testing with the device should be restricted to small sample deformations (see 50% deformation line in Figure 8) via low stress levels which produce linearity in the terminal phase of the compliance curve. Since in these cases the viscosity was found independent of test time in the linear region of the curves, this indicates a dynamic equilibrium state in the material. With high-shear methods (11), such an equilibrium is difficult to establish prior to complete structural breakdown. Similar observations were obtained with PEG 1500 measurements.

EFFECT OF VARYING SAMPLE PLUG HEIGHT

Figure 9 shows the compliance curves for different plug heights between 0.4-1.1 cm for petrolatum. This is equivalent to changing the cup size in the rotoviscometer while retaining the same bob size. It may be noted that by converting the raw data to compliance values with the use of Equation 8, the curves in Figure 9 collapse to a narrow band in contrast to the original chart recording (Figure 10), indicating similar slopes and, hence, similar viscosities. Qualitatively, the 1.1-cm plug curve (Figure 9) shows an upward trend suggesting a somewhat faster flow, aided possibly by the collapse of a tall sample. This situation may be viewed as analogous to the plug flow effect in rotoviscometers where instead of each hypothetical layer participating in the flow process, only a few layers participate, while the remaining mass flows as a whole plug. Such a situation obviously offers less resistance to flow, causing faster flow and lower viscosity values. The 0.4-cm plug curve, conversely, shows a slower motion due to very little


kl.I

Z

0 5 IO 15 25 35 45 55 65 7 5 95

o Time (t) sec Figure 11. Effect of varying initial sample plug diameter on compliance for petrolatum as calculated with Equation 8. Key: (/•) 1.26; ([•) 1.57; (O) 2.03 cm. Average values, n = 3.

8

? I

I I I

i

i i

i i

/ i

i I •"

2 7 •2 17 22 27 •2 •7 •2 52 62 67

TIME (t) SEC

Figure 12. Comparison of compliance curves obtained using Equation 8 (A)and the plastometer Equation 9 (O). The experimental data used are from the original chart recordings for the 0.7-cm high sample (Figure 10).

MEASURING VISCOSITY OF SEMISOLIDS 2 5 5

Table I

Effect of Stress Level on Viscosity of Petrolatum and PEG 1500 at Ambient Temperature

Petrolatum (21.2- 21.5 øC)

F (dynes cm -2) x 10 -4 qq x 10 -6 (poise)

PEG 1500 (22.2-23.2øC)

F (dynes cm -2) X 10 -4 'q X 10 -6 (poise)

2.35 (81.31 g) 3.65 6.69 (231.31 g) 56.1 2.93 (101.31 g) 1.83 7.42 (256.31 g) 27.3 3.51 (121.31 g) 1.25 8.14 (281.31 g) 14.2 3.80 (131.31 g) 0.80 8.86 (306.31 g) 6.0

Sample diameter = 1.2 cm. Sample height = 0.7 cm.

room for flow, thus indicating that the ideal sample plug height for our apparatus is between 0.5 and 0.9 cm. However, no significant interactions (or = 0.05) were dem- onstrated by the ANOVA test, indicating that the measured viscosities were independent of the initial sample plug height. A similar optimal range of plug heights for the viscosity determinations was also observed for PEG 1500 (Table II).

EFFECT OF VARYING SAMPLE PLUG DIAMETER

Figure 11 presents the compliance curves with varying plug diameters for petrolatum and again shows parallel slopes in the terminal linear regions, thus indicating similar viscosities. Varying plug diameters here is equivalent to varying the bob size while maintaining the same cup size in the rotoviscometer. The applied stress in this set of experiments was such that with increasing diameters the applied weight was increased so as to maintain a constant stress. Table III lists the obtained viscosities for both the

petrolatum USP and the PEG 1500. No significant differences in the viscosity values (ix = 0.05) were seen within the range of diameters studied, excepting the largest PEG 1500 plug diameter (1.57 cm). One possible explanation for such deviation in the case of a large diameter of PEG 1500 could be the difference in the degree of anisotropy of this material as compared to petrolatum. The petrolatum matrix being more uniform due to its smaller crystals blended homogeneously with the non-crystalline surrounding (Figure 4), possibly behaved more ideally than the PEG 1500. Such behavior, it appears, was more evident with a larger diameter sample because of the large mass in- volved.

Table II

Effect of Sample Plug Height on Viscosity of Petrolatum and PEG 1500 at Ambient Temperature

Petrolatum (22.7 - 23.2øC)

Plug height (cm) qq X 10 -6 (poise)

PEG 1500 (21.4-21.8øC)

Plug height (cm) qq X 10 -6 (poise)

O.5 O.97 O.5 --

0.7 1.06 0.7 14.1 0.9 0.87 0.9 12.6 1.1 1.1 10.6

Diameter = 1.2 cm.

Applied stress levels: Petrolatum, 2.35 X 10 4 dynes cm-2; PEG 1500, 11.03 X 10 4 dynes cm -2.


Table III

Effect of Sample Plug Diameter on Viscosity of Petrolatum and PEG 1500 at Ambient Temperature

Petrolatum (21.9-22.2øC)

Plug diameter (cm) qq X 10 -6 (poise)

PEG 1500 (23.2-23.7øC)

Plug diameter (cm) 10-6 (poise)

1.26 4.87 0.87 15.7 1.57 4.46 1.08 13.3 2.03 4.88 1.20 18.8

1.35 18.1 1.57 67.4

Sample height/diameter ratio: Petrolatum, 0.55; PEG 1500, 0.7. Applied stress levels: Petrolatum, 2.32 • 10 4 dynes cm-2; PEG 1500, 9.58 • 10 4 dynes cm -2.

COMPARISON OF EQUATION 8 WITH THE PLASTOMETER EQUATION

Figure 12 shows a comparison of compliance data calculated with the use of our Equa- tion 8 as well as with the equation referred in the literature for plastometer (12,13). The plastometer equation is shown as

= (9) where h and ho are equivalent to H and H o of our Equation 8.

While solid lines represent the converted experimental data from the 0.7-cm high sample curve (Figure 10), the dotted lines represent extrapolated values for an extended time period.

From both of these equations, the viscosity is represented by the reciprocal of the slopes. While our plot shows a linear terminal slope and, hence, a constant viscosity, the plastometer plot shows increasing slope and, hence, a dropping viscosity. In a very short duration of 67 seconds, the latter model suggests infinite slope and, hence, zero viscosity, which is highly unlikely. Looking at the original chart recording also (Figure 10), we notice a steady flow suggesting a steady viscosity value which should not drop suddenly to zero as suggested by the plastometer curve.

Furthermore, after a longer period, due to considerable reduction in the "effective" stress value, the original flow and the compliance curve should show a gradual cessation of the flow, or a downward curve. This would imply a phenomenal increase in the viscosity values, contrary to the zero value from the plastometer curve. Thus, our Equa- tion 8 appears to be a better model to provide a more realistic interpretation of our experimental data than the plastometer Equation 9.

CONCLUSIONS

For low levels of applied stress and strain measurement, viscosity values independent of time (absence of thixotropy) are obtainable with the proposed simple device. Addi- tional advantages over existing viscosity measuring devices and methods are summa- rized below:


1. The method provides viscosity in absolute units unlike those obtained with the penetrometer, tube extrusion, and others (18). Although the Brookfield RVT viscometer with T-bar and helipath provides single viscosity values in absolute units (maximum range of 104 poise) (19), the mathematically undefined geometry of the T-bar renders it an empirical device.

2. Within limits, varying sample size does not affect the results with this device. The selection of sample height and diameter is equivalent to changing the cup and bob size of rotoviscometers, respectively, which in turn requires the application of different instrument constants.

3. While in this study the viscosity values were found to be stress-dependent due to stress application in the non-linear viscoelastic range, stress-independent viscosities using stress in the linear viscoelastic range are also obtainable (1). Thus viscosities approaching 108-10 •ø poise range, usually associated with undisturbed structure or "ground-state," demonstrable by the rheogoniometer and creep test apparatus (7,20,21), can be measured with this simple device (1). In essence, absolute viscosity values independent of such variables as applied stress, time, sample size, unique only to the material and unaffected by the method of measurement, are obtainable with the device.

4. The device shows a sensitivity to non-homogeneity in a sample via its shape of deformation.

ACXNOWLEDGMENTS

Abstracted in part from a dissertation submitted by Shivaji Purwar to the graduate School of West Virginia University, in partial fulfillment of the Doctor of Philosophy • .......... ; ...... • ...... •'='• partly •' .... •.•lo•;p grants c•,• •h,• qo,-i,•y •c •_ roetic Chemists to Mr. Purwar. The authors wish to thank Drs. William R. Powell and

J. Krall, formerly of the Department of Mechanical En•ineerin• and the School of Medicine at West Virginia University, respectively, for their valuable assistance.

REFERENCES

(1) S. Purwar, A. R. Padhye, and J. K. Lim, A new method for measuring the viscoelastic parameters of pharmaceutical and cosmetic semisolids, J. Soc. Cosmet. Chem., 35, 115-129 (1984).

(2) S.S. Davis, E. Shotton, and B. Warburton, Some limitations of continuous shear methods for the study of pharmaceutical semisolids, J. Pharm. Pharmac., 20, [Suppl.], 157S- 167S (1968).

(3) B. W. Barry and E. Shotton, Performance of the Ferranti-Shirley viscometer with automatic flow curve recorder unit, 1bid., 20, 167-168 (1968).

(4) G. B. Thurston and A. Martin, Rheology of pharmaceutical systems: Oscillatory and steady shear of non-Newtonian viscoelastic liquids, J. Pharm. Sci., 67, 1499-1506 (1978).

(5) J. C. Boylan, Rheological estimation of the spreading characteristics of pharmaceutical semisolids, 1bid., 56, 1164-1169 (1967).

(6) G. W. Radebaugh and A. P. SimoneIll, Phenomenological viscoelasticity of a heterogeneous pharmaceutical semisolid, 1bid., 72, 415-422 (1983).

(7) B. W. Barry, Advances in Pharmaceutical Sciences, Vol. 4 (Academic Press, New York, 1974), pp. 1-72.

(8) A. N. Martin, J. Swarbrick, A. Cammarata, and A. H. C. Chun, Physical Pharmacy (Lea & Febiger, Philadelphia, 1969), p. 500.

(9) L. H. Block and P. P. Lamy, The rheological evaluation of semisolids, J. Soc. Cosmet. Chem., 21, 645-660 (1970).


(lO) (11)

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(17) (18)

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H. Umstiitter, Kolloid-Z., 70, p. 174 (1935); through Ref #9. A. N. Martin, G. S. Banker, and A. H. C. Chun, Advances in Pharmaceutical Sciences, Vol. 1 (Aca- demic Press, New York, 1964), pp. 19-47. R. Houwink and Ph. N. Heinze, Plastometry of synthetic resins, Inds. Enggo Chemistry, 10, 680-683 (1938). S. Oka, "Principles of Rheometry," in Rheology, Vol. 3 (Academic Press, New York, 1960), pp. 73 -75.

C. O. Bennett and J. E. Myers, Momentum, Heat and Mass Transfer, 2nd ed. (McGraw-Hill, Inc., 1974), pp. 104-111.

J. D. Ferry, Viscoelastic Properties of Polymers, 2nd ed. (,John Wiley and Sons, Inc., New York, 1970), pp. 6, 27, 51, 188. D. H. Kaelble, Physical Chemistry of Adhesion (,John Wiley and Sons, Inc., New York, 1971), p. 221. A. N. Martin, Physical Pharmacy (Lea & Febiger, Philadelphia, 1960), p. 632. Brookfield Table of Viscosity Ranges for Brookfield Model RVT Viscometer With T-Bar Spindles (Brookfield Engineering Lab., Inc., Stoughton, MA). J. H. Wood, G. Catacalos, and S. V. Liberman, Adaptation of commercial viscometers for special applications in pharmaceutical rheology. I. The Brookfield Viscometer, J. Pharm. Sci., 52, 296-298 (1963). B. W. Barry and A. J. Grace, Grade variation in the rheology of white soft paraffin B.P., J. Pharm. Pharmac., 22 [Suppl.], 147S-156S (1970).

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Measuring viscosity of pharmaceutical and cosmetic semisolids