THE VISCOSITY OF OIL-WATER EMULSIONS' GEOFFREY BROUGHTON
AND
LOMBARD SQUIRES
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts Received May 88, 19SY INTRODUCTION
Although the viscosity of concentrated emulsions is of considerable interest, it has received inadequate industrial and theoretical study. This may be traced to the complexity of the subject, many variables undoubtedly being of importance. Of these, the outstanding appear to be (1) volume concentration of the disperse phase, (.2) rate of shear, or shearing force, (3) viscosity of the continuous phase, (+$)viscosity of the disperse phase, (5) the stabilizer or emulsifying agent used, and (6) the particle size of the emulsion. Most investigators have considered the effects of the first and second variables, paying but little attention to the others involved. As will be seen, the nature of the disperse phase and the emulsifying agent cannot be neglected. For dilute suspensions, in which the small spherical particles can be considered to be rigid and substantially independent of each other, the viscosity is dependent only upon the volume concentration of the disperse phase. Einstein (3, 4) theoretically obtained the relation2 p = po(1
+ 0.025V)
(1) For dilute emulsions and suspensions this holds with a fair degree of accuracy (9). Besides mutual interference, deformation of the dispersed particles may occur, and Taylor (13) has shown theoretically that to correct for this Einstein's equation may be written
However, small drops behave substantially as solid bodies if their radius does not exceed a certain critical radius (I), ?-
= Z/T/(Pi--P)S
1 This article is based on the work of the late Kenneth R. Moll (Thesis, Massachusetts Institute of Technology, 1933). * For nomenclature see table 1. 253
254
GEOFFREY BROUGHTON AND LOMBARD SQUIRES
For most ordinary stable emulsions the drop size lies below this critical radius, making any experimental test of Taylor’s expression difficult. Hatschek ( 5 ) derived an expression for concentrated emulsions 1
=
&7]
(3)
which he was able to show held for an emulsion of paraffi oil in 0.75 per cent soap solution. With concentrated emulsions the rate of shear used in the viscosity determination becomes of importance, a point emphasized by Hatschek. As it is increased the apparent viscosity decreases, becomTABLE 1 Table of nomenclature IC= IC0
=
pi
=
p’ = p: =
Ti=
T = Pi =
P =
h= k =
K
=
viscosity of emulsion viscosity of solvent or continuous phase viscosity of internal or disperse phase limiting viscosity of emulsion limiting relative viscosity,of emulsion limiting relative viscosity of emulsion a t which yield point appears volume concentration, per cent surface tension of disperse phase density of disperse phase density of continuous phase volume concentration correction factor (Sibree) calibration constant in R . P . M . centipoises per degree MacMichael deflection in degrees MacMichael
R = R.P.M. M , = yield point a , b, e = constants
ing almost constant at high shear. Most investigators have, therefore, attempted to correlate the viscosities at infinite shear. Sibree (10) atltempted to verify the Hatschek equation, using paraffin-water emulsions to which 1 per cent of sodium oleate had been added as an emulsifier. The paraffin phase was weighted with bromoform, so that both phases possessed the same density.s By insertion of a correction factor h, so that equation 3 becomes
substantial agreement with experiment was obtained. Sibree was of the opinion that this correction factor, about 1.3, was an expression of the 9 It will be noted that this prevents creaming and tends t o make the drops deformable when the emulsion is under shear,
VISCOSITY O F OIL-WATER
EMULSIONS
255
increased volume of the drops due to a hydrated film of the emulsifier around their surface. Although he stated that the value of the volume factor might be specific for a given emulsion, no attempt was made to use different emulsifying agents and disperse phases beyond comparing the viscosities of emulsions made with limpid and viscous paraffins. These were found to have substantially the same viscosity at equal volume concentrations (11). Air entrainment leads to greatly increased viscosity (7), which apparently accounts for the observation of Sibree that coarse emulsions had much lower viscosities than fine ones. When all air was carefully removed, both coarse and fine emulsions had substantially the same viscosity.’ More recently Richardson has deduced on theoretical grounds the equation
d m
=
ecv
(5)
obtaining good agreement with benzene in water emulsions stabilized with sodium oleate (8). Richardson again investigated but one dispersed phase and one emulsifying agent. Sibree’s data, when plotted in the form log g / p 0 against V , give straight lines which do not pass through the origin, although data of some other workers (8) conform to the Richardson formula. In view of the fact that most of the investigators to date have studied but one emulsion or one variable, it was felt that investigation of several emulsions at varying rates of shear using different stabilizing agents would be of value. EXPERIMENTAL
The preparation of emulsions Seven types of emulsions were prepared, using aqueous solutions of sodium oleate, saponin, and triethanolamine oleate (1, 2, and 3 per cent by weight, respectively) as continuous phases, and Nujol, benzene, and olive oil as the disperse phases. The materials used were of C.P. grade 01 its equivalent. To prevent creaming or separation of the disperse phase on standing, all the oils were weighted with a-bromonaphthalene to a specific gravity of 1.00, so that on standing for several days the most dilute emulsions showed no tendency to cream. Emulsification was performed by adding appropriate quantities of the weighted oil to the solution of the emulsifier, and thoroughly stirring the mixture in a high-speed electric stirrer. Intermittent stirring was found to be most effective, and a definite schedule of 1 min. of stirring followed by 1 min. of rest was selected. For some of the emulsions, particularly those stabilized by triethanolamine oleate, little or no stirring was necessary, emulsification being almost spontaneous.
256
GEOFFREY BROUGHTON AND LOMBARD SQUIRES
The emulsions prepared in this way were sometimes coarse and always contained an appreciable amount of air. For removal of this a vacuum homogenizer, such as recommended by Briggs (2), was found satisfactory. All emulsions were given four or more passes through the homogenizer and showed no change in viscosity on standing for several weeks.
Viscosity determinations The MacMichael viscosimeter was used in this investigation. It consists of an inner disc, suspended by a torsion wire inside an outer cup, which can be rotated a t any constant speed desired. I n all the experiments the viscosimeter was allowed to run a t the indicated speed until the deflection of the wire became constant, four or more points in all being taken on the R2.M.-deflection curves. The temperature is maintained constant (25" i 1°C.) by means of the water bath surrounding the cup. TABLE 2
Viscosity of liquid phases
at 96T.
1
PEABE
VISCOSITY
centipoise8
Benzene, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nujol., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . Olive oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 per cent sodium oleate solution., . . . . . . . . . . . . . . . . . . . . . . . . . . . "'I 3 per cent sodium oleate solution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I 2 per cent saponin solution., . . . . . . . . . . . . . . . . . . . . . . . . . . ........... 3 oer cent triethanolamine oleate solution. . . . . . . .
"""""'I
0.82 33.2 121.0 0.983 1,138 1.001 4,730
Three torsion wires were required to cover the range of viscosities encountered in this investigation. The viscosity was calculated from the R.P.M.and deflection by the relation p =
IC.- M R
the calibration constants, k , of the wires being obtained by measurements a t 25°C. against a 60 per cent sugar solution. The value of the viscosity of this solution was taken as 44 centipoises (6). The viscosities of the phases, listed in table 2, were determined in an Ostwald viscosimeter, except that of the weighted olive oil, which was measured in the MacMichael viscosimeter. RESULTS
When the viscosities of the various emulsions are calculated it is found, in agreement with the results of other investigators, that this quantity is
VISCOSITY O F OIL-WATER
257
EMULSIONS
not a constant for any given emulsion, but varies with the rate of shear. All the emulsions behave as non-Newtonian liquids, e&, figure 1shows the variatior, for an emulsion containing 50 volume per cent of weighted Nujol in 3 per cent aqueous triethanolamine oleate solution. Thus the asymptote of the viscosity rate of shear curve (the limiting viscosity) or viscosity a t infinite shear will be chosen as the quantity for consideration in the following discussion. The experimental data for all the emulsions were plotted as R.P.M.deflection curves, representative straight lines being drawn through the
y
IS
cn
E
8
I6
i
t
14 5 Y
f g 2
12
10 0
20
40 BO 80 RATE OF SHEAR. R P U
100
I20 RAT[: OF
SHEAR R . P M .
FIG.1 FIQ.2 FIG.1. Effect of rate of shear on viscosity for emulsion 10 FIG. 2. Torque-rate of shear diagram. Wire X ; temperature = 26" ==! 1°C. See table 3 for key to figures
points. Typical curves are shown in figure 2. It is obvious that the slopes of the straight-line portions are inversely proportional to the limiting viscosities. These slopes were determined, and the limiting viscosities are listed in column 4 of table 3. At very high rates of shear the points begin to deviate from this straight line, becoming concave t o the deflection axis4 If the R.P.M.-deflection curves are extrapolated to low rates of shear it is found, in most cases, that they do not pass through the origin but Taylor (12) has shown that this condition occurs when the flow ceases to be lamiaar and becomes vertical or turbulent.
258
GEOFFREY BROUGHTON AND LOMBARD SQUIRES
intersect the torque axis at a definite positive value. This point of intersection has been termed the yield point, and represents the theoretical distorting force necessary to initiate flow. While there is doubt as to TABLE 3 Summary of calcuEated data RELATIVE LIMITINQ VISCOSITY
LIMITINQ VIBCOBITY
EMUMION
centipoiaea
1.94 5.0 84.0 178.5
8 14 29 37
94 75 9 5
1
1
,
9 15 30 38
09 0 4 15
I
0.54 5.0 440 838 2.9 8.0 83.0 1320
15 16 26 Benzene-sodium oleate 20 21 22 Olive oil-triethanolamine oleate 17
60 70 75
27.5
50 60 70
0.97 4.0 36.0
50
24
50 0.32 8.0
10.97 36.3 78.5 143,s 10 97 18 85 32 45
8.02 12.07 32.10 66.5 ;:1 ::
25.2 22.95 60.30 8.90
10.97 36.3 78.5 143.8
1 '
1 1
1
,1
2 31 3.98 6 87
1.70 2.55 6.78 14.05 7.95 12.42 22.1 4.85 12.72 7.82 20.9
whether this extrapolated value is a definite physical entity, nevertheless it is obvious that, knowing the value of the yield point and the limiting viscosity, the flow characteristics of the emulsion can be calculated over the range where the R.P.M.-deflection relation is linear. I n such cases,
VISCOSITY O F OIL-WATER EMULSIONS
259
over wide ranges the two quantities,-the extrapolated yield point and the limiting viscosity,-define the viscous behavior of the emulsion. In column 3 of table 3 are listed the yield points determined by extrapolating the R.P.M.-deflection curves and expressed in terms of the equivalent deflection that would have been produced had one common wire been used for all the emulsions.
VOLUUE CONCENTRATION
W W L COKENTRATIW
FIG.4 FIG.3 F I ~3.. Relative viscosity versus volume concentration FIG.4. Sibree correction factor h versus volume concentration of disperse phase. See figure 3 for key to figures DISCUSSION OF RESULTS
The effect of volumetric concentration Inspection of the values of the limiting viscosity given in column 4 of table 3 shows that this quantity varies with the concentration over a wide range of values. It is therefore more convenient to plot not the limiting viscosity itself but its logarithm. Furthemore, t o place the various emulsions on a comparative basis it is preferable to plot the logarithm of the limiting relative viscosity, defined as the ratio of the limiting viscosity to the viscosity of the continuous phase. Examination of figure 3 shows that the logarithm of the limiting relative viscosity is linear in the volumetric concentration for the majority of the emulsions studied and hence may be represented by the equation Log fi: = a
+ b~
(7)
260
GEOFFREY BROUGHTON AND LOMBARD SQUIRES
This relationship is somewhat analogous to that of Richardson (equation 5). Since the present data when extrapolated to V = 0 do not show relative limiting viscosity of unity, equation 5 does not hold. Curve 7 of figure 3, showing the viscosity for the benaene-triethanolamine oleate emulsion, cannot be represented by a straight line and is an exception to the generalization given above. This may be related to the fact that this emulsion shows no yield point up to 70 per cent concentration. The Hatschek equation, as modified by Sibree, may be expressed as h = t$>’/V
Figure 4 shows the value of h calculated according to this equation plotted against the volumetric concentration for the data of table 3. If the data followed equation 2, h would lie uniformly on the line h = 1. If it followed equation 3 a series of straight lines parallel to the concentration axis, but having a different value for each emulsion, would be obtained. I t is evident that no such behavior was found; in some cases h decreased with increasing concentration and for the Nujol-saponin emulsion even exhibited a maximum. If h were a measure of the percentage increase in volume of the disperse phase due to the layer of hydrated stabilizer around each particle, as suggested by Sibree, it would necessarily always be greater than unity. However, curves 6 and 7 of figure 4 show values of h far belovi unity a t the loIver volumetric concentrations, excluding such an interpretation. Hence, it can be seen that the Hatschek equation or its modification is not of general applicability. It is interesting to note that h is most nearly constant for emulsions of hydrocarbons stabilized by sodium oleate (curves 3 and 4), which are the type Sibree prepared. While the slopes of the lines in figure 4 are smallest for these types, even in them considerable variation in h occurs. In fact, Sibree’s own data show a yariation in h from 1.45 at a volume concentration of 0 5 t o 1.28 at 0.75 volume concentration for the viscous paraffin emulsion. Furthermore, for his data h always decreased with increasing volumetric concentration, although in many cases the decrease was not so marked as in the example quoted above. Considering figure 4, this change in h is significant and corroborates the present data, although Sibree concluded from his experiments that h was constant. The results as shown in figures 3 and 4 indicate that the volumetric roncentration of the emulsion is not the only important variable influencing the limiting relative viscosity.
VISCOSITY O F OIL-WATER
261
EMULSIONS
Variation of the yield point Inspection of column 3 of table 3 shows that the yield point as defined above varies even more widely with concentration than does the limiting viscosity. It is well known that relatively dilute emulsions behave like true liquids, showing no yield point and hence no variation in viscosity with rate of shear. Above a fairly definite concentration, however, the viscosity becomes a function of the rate of shear and a yield point develop^.^ All the emulsions studied were in a concentration range well above this limit, with the exception of the benzene-triethanolamine oleate emulsion (curve 7 , figure 3). This emulsion showed no yield point up t o a volume concentration of 0.70. In table 4 are listed the estimated concentrations at which a yidd point appeared, obtained by linear extrapolation of the TABLE 4 Volume concentvation and viscosity at initial yield point EMULBION
i
APPEAR0
centzpoisea
Nujol-sodium oleate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sujol-saponin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.437 0.489
5 5 11 0 1 65 8 7 6 0 1 8 G O
yield point-concentration curve. The third column of table 4 also shows the limiting relative viscosity of the emulsion at this concentration. If the logarithm of the yield point is plotted against the logarithm of the difference between the limiting relative viscosities a t the corresponding concentration and a t the concentration at which the yield point appears, the curves shown in figure 5 are obtained. While it is to be admitted that these calculations are based on somewhat questionable extrapolations, the plot indicates an interesting though approximate correlation, the points seriously off the curve lying a t low volume concentrations where accurate estimation of the yield point is difficult. It will be observed that the logarithm of the yield point is linear with the logarithm of the viscosity difference and that the curves have the same slope. This would indicate that the yield point is a function of the type of stabilizer and limiting visI n certain emulsions the behavior may be more complex, the fluid showing anomalous viscosity before development of a yield point.
262
GEOFFREY BROUQHTON AND LOMBARD SQUIRES
cosity of the resulting emulsion. Hence it would appear that if, at one volumetric concentration, the yield point and limiting viscosity were known together with the viscous behavior over a wide range of concentrations could be quantitatively predicted by the relations shown in figures 3 and 5. No generalizations can be made as to the influence of the viscosity of the disperse phase on the resulting viscosity of the emulsion. Curves 5, 6, and 7 of figure 3 show that the viscosities of emulsions at the same volumetric concentration and for the same stabilizer are in the order of the viscosities of the disperse phases. However, this relation is reversed for the benzene and Nujol emulsions at 75 volume per cent. Again, comgar-
4,
LOG (9;-Pi)
FIG.5. Logarithm of the yield point plotted against the logarithm of the difference between the limiting relative viscosities a t the corresponding concentration and at the concentration a t which the yield point appears. See figure 3 for key to figures.
ing curves 1 and 4 for olive oil and benzene stabilized by sodium oleate, the viscosities of the more concentrated emulsions are in the order of the viscosities of the disperse phases, but at 50 volume per cent the viscosities of the two emulsions are identical. The e$ect of stabilizers
The effect of the type of stabilizer on the viscosity of a given phase pair may be observed by comparison of the appropriate curves of figure 3 (curves 2, 3, and 6 for Nujol-water, curves 4 and 7 for benzene-water, and curves 1 and 5 for olive oil-water). It d l be seen that for a given phase pair the limiting relative viscosity at a definite concentration vanes widely with the type of stabilizer employed. For curves 2, 3, and 6 the variation in viscosity at the same concentration is in the order of increasing ease of
VISCOSITY O F OIL-WATER
EMULSIONS
263
emulsification, the most efficient stabilizer producing the emulsion of lowest viscosity, Thus triethanolamine oleate emulsified Nujol practically spontaneously, but the saponin emulsion was quite difficult to prepare. The same order is shown in curves 4 and 7 for the benzene emulsions and in curves 1 and 5 for the olive oil emulsions. Without doubt, the effect of the stabilizer is exceedingly important. Thus, the relative viscosity a t 70 volume per cent of Nujol-water emulsions stabilized with saponin and triethanolamine oleate varied thirteenfold. It is true that difference in particle size may, in part, account for this variation but, in view of the work of Sibree already referred to, this appears unlikely. The influence of the stabilizer may, however, well account for some of the confusing results obtained in the past by different investigators. CONCLUSIONS
1. The viscosity of a concentrated emulsion is a function of the rate of shear, approaching an asymptote as the rate of shear is increased. Over wide ranges the relation between shearing stress and rate of shear is linear. For a given emulsion, Le., a given phase pair and stabilizer concentration (based on the dispersing medium), the limiting viscosity at infinite rate of shear increases with the volume concentration of the disperse phase. The quantitative relation between the concentration and the limiting viscosity is best' represented by a modified form of the Richardson equation. The Hatschek equation, as modified by Sibree, does not apply. 2. Other than volumetric concentration, the type of stabilizer employed seems to be the variable of most significance in determining themagnitude of the viscosity of any phase pair. Stabilizers producing the best eniulsification give emulsions of the lowest limiting relative viscosity. REFERENCES (1) BOND:Phil. Mag. 6, 794 (1928). (2) BRIGGS:J. Phys. Chem. 19, 223 (1915). (3) EINSTEIN:Ann. Physik 9, 289 (1906). (4) EINSTEIN:Ann. Physik 34, 591 (1911). (5) HATSCHEK: Kolloid-Z. 8, 34 (1911). (6) International Critical Tables, Vol. V, p. 23. 3lcGram-Hill Book Co., Kew York (1929). AND WATSON: J. Indian Inst. Sei. 17A, (vi), 75 (1934). (7) KARAYAKASWAMY (8) RICHARDSON: Kolloid-Z. 66, 32 (1933). AND TYLER:Proc. Phys. SOC. (London) 46, 142 (1933). (9) RICHARDSOX (10) SIBREE:Trans. Faraday SOC.26, 26 (1930). (11) SIBREE:Trans. Faraday SOC.27, 161 (1931). (12) TAYLOR:Trans. Roy. Soc. (London) A223, 289 (1923). (13) TAYLOR: Proc. Roy. SOC. (London) 138,41 (1932).
