978
Ind. Eng. Chem. Res. 1988,27,978-982
Phase Inversion Behavior of Water-Kerosene Dispersions Terry R. Guilinger,* Arne K. Grislingas, and Olav Erga Department of Chemical Engineering, Norwegian Institute of Technology, N - 7034 Trondheim, Norway
We conducted experiments to determine the physical processes involved a t the inversion point of water-kerosene dispersions. In the course of these experiments, we noted a viscosity maximum at the inversion point. This led to the development of an indirect method for determining the viscosity of concentrated liquid dispersions. Our data were found to be best fit by the dispersion viscosity equation (eq 6). Dispersion viscosity expressed as a function of dispersed-phase volume fraction gives some insight into the structure of the dispersed phase near the inversion point. Liquid-liquid dispersions are used to promote heat and mass transfer in mixer-settler units. The phase inversion behavior of these dispersions is important since the drop size of the dispersed phase and the settling time of the dispersion depend on which of the phases is continuous. Further, the rheological characteristics of liquid-liquid dispersions must be known to predict power consumption during agitation and pressure drop during flow in pipelines. A dispersion can be distinguished from an emulsion by the necessity to provide mechanical energy to a dispersion to retain macroscopic homogeneity. Phase inversion can occur as a result of changing the power input to the dispersion. The inversion point is defined as the volume fraction of dispersed phase above which this phase will become the continuous phase. In general, the inversion point will change with power input to the system and is not predictable from the physical properties of each of the phases present. The viscosity of liquid-liquid dispersions has received little attention in the past. Most work has focused on adapting existing models of the viscosity of solid suspensions to the viscosity of dispersions. The viscosity of solid suspensions has been studied extensively both experimentally and theoretically. The purpose of this study was to examine the phase inversion behavior of water-kerosene dispersions to determine the effects of operating parameters on the inversion point. During the course of this study, an indirect method for determining the dispersion viscosity at high volume fractions of the dispersed phase was developed.
Background and Objectives Phase inversion in liquid-liquid dispersions has been commonly studied by introducing known volumes of each phase into a beaker, starting agitation, and determining the continuous phase by its settling characteristics or by monitoring the conductivity of the dispersion. Early studies of this type by Quinn and Sigloh (1963) and Selker and Sleicher (1965) showed that the lower inversion point decreased with increasing impeller speed and often reached a limiting value above a sufficiently high speed. The lower inversion point was defined as the volume fraction of a phase below which that phase cannot be continuous. This behavior was also noted by Luhning and Sawistowski (1971),McClarey and Mansoori (19781, and Arashmid and Jeffreys (1980). These experiments further revealed that inversion does not occur at a volume fraction of dispersed phase of 50% as would be predicted by interfacial energy considerations for liquid dispersions in the absence of surface active agents. Also, dispersions can be produced with volume fractions of dispersed phase greater than the *To whom correspondence should be addressed. Present address: Sandia National Laboratories, Albuquerque, NM 87185.
74% which would be predicted from close packing of spheres of the same size. This observation may indicate that the dispersed-phase droplets have a wide range of diameters, which allows closer packing. It may also indicate that dilatency of the dispersion or deformation of the droplets occurs when the dispersed-phase volume fraction is high. The phase inversion experiments performed in previous investigations focused on attempting to predict the phase inversion point from the physical properties of the two phases present and also to discover the controlling mechanisms of phase inversion. Selker and Sleicher (1965) defined an ambivalence range as the range of volume fractions of a phase above which that phase is always continuous and below which that phase is always dispersed. They showed that the ambivalence range is widest at a ratio of kinematic viscosities of organic phase to polar liquid phase of 2. They also noted that, as the viscosity of a phase increased, its tendency to disperse increased. Yeh et al. (1964) also examined the effects of viscosity of the liquid phases on the inversion point, and from theoretical considerations they developed an equation for predicting the phase inversion point from the viscosities of the pure liquids and the interfacial viscosity, py,
where $C is the volume fraction of dispersed phase. Experimental results agreed well with this equation, although their method of developing the dispersion consisted of shaking the two phases in a flask rather than using mechanical agitation. Droplet size in a dispersion is determined by the competing phenomena of droplet breakup, droplet collison, and droplet coalescence. Arashmid and Jeffreys (1980) assumed that at the inversion point the frequency of droplet coalescence should equal the collision frequency. That is, every collision results in coalescence. Using expressions for collision frequency from Misek (1964) and coalescence frequency from Miller et al. (1963) and Howarth (1967)) they developed an equation with one adjustable parameter for predicting the change in the inversion point with stirrer speed. Experimental results agreed well with this equation, although incorrect forms of the collision frequency from Misek and the droplet size equation from Thornton and Buoyatiotes (1967) were used. The importance of viscosity on phase inversion prompted a survey of the literature on dispersion viscosity. A significant body of literature has been assembled concerning the viscosity of solid-liquid suspensions, and the thrust of most investigators in liquid-liquid dispersions was to modify the equations for suspension viscosity to include dispersion viscosity. Studies of this type include
0888-5885/88/2627-09~8~0~.50~0 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 979 Table I. Dimensions of the Mixer Units overflow construction diameter, height, H, mixer materials DT, cm cm 45.6 33.9 1 stainless steel 10.0 2 stainless steel 11.3 10.0 3 Plexiglas 11.3
volume fractions. Vermuelen et al. (1955) proposed the equation volume, VT, L
41.0 0.95 0.95
Furuse (1972), who proposed the following equation for dispersion viscosity, pm,
while Laity and Treybal (1957) used two equations for water plus organic phase dispersions Pm
4W
Pw
+ Po
for water more than 40% by volume and and Bedeaux (1983), who proposed that the dispersion viscosity be given by
Pm
40
Pw
+ Po
for water less than 40% by volume where w denotes water phase and o denotes organic phase. where p, and Pd are the viscosities of the continuous and dispersed phases, respectively. Because of the difficulty in performing experiments to measure dispersion viscosity, few investigations have attempted these measurements. Barnea and Mizrahi (1976) measured dispersion viscosities below dispersed-phase volume fractions of 0.33 by taking advantage of the slow settling rates of dispersions relative to the rate at which the dispersion stops movement after stirring. In this technique, mechanical agitation is applied to produce a homogeneous dispersion. The agitation is stopped and, after 15 s, a viscometer reading is taken by using a rotating cylinder attached to a dynamometer. Fifteen seconds was found to be sufficient time to eliminate the effects of mechanical agitation on the viscosity measurement. On the basis of theoretical considerations and their experimental data, they proposed that the dispersion viscosity be represented by
where &* is an adjustable parameter representing the "effective" viscosity of the dispersed phase. It is the sum of the dispersed-phase viscosity and the effective surface viscosity at the interface. This equation is an altered form of the viscosity equation (Barnea and Mizrahi, 1976): Oq4 +
Pd/PC(4+ 4 6 / 3 + 411/3)
+Pd/k
1
(5)
Other investigations have dealt indirectly with the viscosity of dispersions and suspensions. Empirical correlations exist between power number and impeller Reynolds number for single-phase liquids. For two-phase liquid mixtures, the Reynolds number must be calculated using an effective mixture viscosity. In liquid-liquid dispersions, the most commonly used equations for calculating the dispersion viscosity are those due to Vermeulen et al. (1955) and Laity and Treybal (1957). Both of these equations are modifications of earlier theoretical equations based on dispersed liquids at low Table 11. Dimensions of the Turbine Impellers impeller no. no. of blades construction materials stainless steel 1 4 stainless steel 2 6 3 6 Plexiglas stainless steel 4 6 stainless steel 5 a
Experimental Section The experimental apparatus consisted of three mixers of different sizes or materials of construction. The pertinent dimensions of each unit are listed in Table I. The mixers were square in cross section, so the equivalent cylindrical mixer diameter shown in Table I is derived from the dimensions of the square mixer having the same volume. Four baffles, each with a height equal to the mixer height and a width equal to 10% of the mixer diameter, were equally spaced around the inside wall of the mixing chambers. Several impellers were used to provide mechanical agitation in the mixers. All of the impellers were of the turbine design with four to eight blades. The dimensions of each impeller are listed in Table 11. The remainder of the apparatus consisted of a variable-speed stirring motor to provide mechanical agitation in the smaller tanks and a Hottinger Baldwin Messtechnik Model DA 3418 dynamometer for agitation and power input measurements for the larger mixer. The stirrer speeds were measured with a tachometer. The liquids were introduced into the mixing tanks from feed vessels and were returned to the feed vessels after settling. Calibrated rotameters were used to determine the flow rates of each of the phases. Experiments were performed at room temperature, 20 f 2 O C . The liquids used in each experiment were Shellsol T, a commercial kerosene solvent, and 0.1 M KC1 in water. The liquids were mutually saturated to prevent mass transfer during the phase inversion experiments. Table I11 shows the physical properties of the mutually saturated liquids. Viscosities of the separate phases were measured with a Haake Model VT-181 viscometer, using a concentric cylinder arrangement. Interfacial and surface tensions were measured with a Kruss Model 12734 ring tensiometer. The mixer was filled with the desired initial continuous phase, stirring was initiated, and a desired feed mixture of dispersed and continuous phases was introduced. In the large mixer, power input to the tank was measured and recorded continuously. The inversion point was determined both by monitoring the electrical resistance of the diameter, DI, cm 4.4 6 6 12 16.5
length blade, L,cm 1.5 2 2 3 4
height blade, W , cm 1
3 3
2.5 3
980 Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 Table 111. Physical Properties of the Mutually Saturated Liauids liquid p , g/cm3 LC, CP u, dynlcm 7 , dynlcm 0.1 M KC1-water 0.998 1.04 36.3 10.6 0.746 1.31 30.0 10.6
d
I?
a
IS0
350
450
150
STIRRER RPM, N
Figure 2. Effect of tank materials on the inversion point.
0
3
1
tie
Figure 1. CSTR model of mixer 1.
dispersion through a digital multimeter and, after experience, by visual means. A resistance probe similar to that used by Selker and Sleicher (1965) was used in conjunction with the multimeter. At the inversion point, the feed was stopped, the phases were allowed to separate, and the volume fractions of each phase present in the mixer were measured. The time to inversion from the initiation of the feed dispersion also was measured to determine if the mixers were adequately modeled by a continuous stirred tank reactor (CSTR) model. The CSTR model is given by 4~ = dJ~[1- exp(-t/6)1 (8) where 6 is the residence time in the mixer and dJT and dJF denote volume fractions in the mixing tank and feed, respectively.
Results and Discussion Since the power input to the large mixer-settler was measured versus time and it was desired to measure the power input versus the volume fraction of dispersed phase in the mixer, preliminary experiments were performed to determine how well the CSTR model fit the large mixer unit. Results of these experiments are shown in Figure 1. These results were obtained using both the water and the kerosene phase as the continuous phase with varying feed compositions and mixer residence times. The CSTR model fit the data satisfactorily under all conditions. Phase Inversion Results. Numerous inversion experiments were performed in all three of the mixers, with the variables being the impeller used, the impeller clearance above the bottom of the mixer, the stirrer speed, the mixer residence time, and the composition of the feed dispersion. In the small mixer-settlers, each experiment was performed 4 times so that the results reported here are the average of each of these four experiments. The reproducibility of the inversion point from these repetitions was found to be, in the worst case, 4.5%. The average reproducibility was f1.6%. In the large mixer unit each experiment was performed at least twice, yielding a worst case reproducibility of 1.2% and an average reproducibility of *0.8%. We investigated impeller clearance above the mixer bottom by varying the clearance from 0.7 to 1.5 impeller
diameters. In the range of impeller clearances studied, no effect of the height of the turbine above the tank bottom was found. However, it should be noted that, when phase inversion experiments are performed in a batch mode, the location of the impeller may be critical in determining the continuous phase. Numerous investigators, for example, Rodger et al. (1956), Quinn and Sigloh (1963), and Selker and Sleicher (1965), have observed that, when operated in a batch mode, the phase in which the impeller starts generally becomes the continuous phase. This area points out one of the differences between continuous and batch operation. In a continuous mode, as long as the impeller is situated so that sufficient turbulence is generated to prevent settling of the denser phase and rising of the lighter phase, the location of the impeller does not affect the phase inversion point. Since coalescence is one of the phenomena which must control the phase inversion point, it was thought that the materials present in the tank may affect the inversion point through preferential wetting by one of the phases. For this reason, we assembled identically shaped mixers, using stainless steel for one and Plexiglas for the other. Figure 2 shows comparisons between the effect of stirrer rate on the inversion point using the two different tanks when the organic phase was initially continuous and the feed was pure water phase. A t low rpm, the effect of the tank material is pronounced but becomes less with higher power input. Since the organic phase preferentially wets the Plexiglas, it tends to be the continuous phase over higher volume fractions of the water phase than when compared to the same experiments in a stainless steel mixer. Further, inversions from water-phase continuous to organic-phase continuous could not be produced in the small steel mixer. However, as will be discussed later, this type of inversion could be made to occur in the large steel mixer. It is conceivable that, as the mixer size increases, the effect of the materials of construction diminishes. Figure 3 shows the inversion point as a function of stirrer speed for kerosene-in-water dispersions when the feed to the mixer was only the initially dispersed phase. The dispersed phase volume fraction at inversion decreases with increasing power input in agreement with previous investigators. Thus, the effect of stirring rate is qualitatively the same whether operating in a batch or continuous mode. Two areas in which operating continuously differs from batch operation are residence time in the mixer and dispersed-phase volume fraction in the mixer feed. We found that longer residence times favor the initially continuous phase as did increasing the feed fraction of dispersed
Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 981 200
I -2
Q c
20 W +
150
IY' W
0.9
2 za 100 % B
ow >w/o 8 = 3 mln. +JF = 1.0
n
I
0.8
I
I
501 0
STIRRING RATE, N (rpm)
'
I ' l ~ l ~ 1 1 1 1 1 1
'
'
'
0.1
0.2
0.3
0.4
1
1
I
I
1
I
0.5
0.6
0.7
0.8
0.9
1.0
DISPERSED PHASE VOLUME FRACTION
Figure 3. Effect of stirring rate on the inversion point. 1 ' 1 ' 1 ' 1 1 1 1 1 1
5
EXPERMENTAL
c'
MIXER 1 IMPELLER 4
P W
,
Figure 5. Prediction of power input by various viscosity equations.
, ( ~ 1 ' 1 1 l l ,
-
8 -
-
-0
P
-
83 ;g 2g
7 -
6
u
EE
F
EQUATION NO. I N TEXT 11. 10 71, 7b
c
0":
ia
LINE NO.
0 0
LAITY 6 TREYBAL 11957)
Five dispersion viscosity equations were tested. Four of these equations have been discussed previously as eq 4,5, 6, 7a, and 7b. The other equation was (Laity and Treybal, 1957)
2
Since the Barnea and Mizrahi (1976) equation (eq 4) includes an adjustable parameter, &*, which is unknown for Shellsol T-water dispersions, two limiting cases were examined for this equation: c
01 10'
'
' 1 / 1 ' 1 / 1 ' 1 '
2
3 4 5 678910'
'
* ' , " ' 1 1 1 1 1
2
3 4 5 678910'
'
1
2
, 13 ~415' 1678910' 1lIll
IMPELLER REYNOLDS NUMBER, ND: p l p
Figure 4. Power number-Reynolds number correlation (from Laity and Treybal (1957)).
phase. However, neither of these variables exhibited a strong effect on the inversion point. Their effect may be tied to nonequilibrium phenomena not present when operating in a batch mode. Dispersion Viscosity Results. As the dispersed-phase volume fraction in the tank increases to near the inversion point, the dispersion becomes less efficiently agitated. Precisely after inversion occurs, a high degree of turbulence resumes, indicating more efficient agitation. These effects are due to the change in the viscosity of the dispersion with increasing volume fraction of the dispersed phase. Falco et al. (1974) reported a viscosity maximum at the inversion point when working with stable liquid emulsions. They proposed that this maximum is associated with a change in structure of the dispersed phase from spheres to cylinders to lamellae to continuous phase. Viscosity may not be so much a controlling mechanism in the inversion as a secondary effect produced by the change in structure of the dispersed phase as its volume fraction increases. An indirect method for measuring dispersion viscosity can be developed by monitoring the power input to a dispersion as a function of dispersed-phase volume fraction. From these power input curves, a power number versus Reynolds number curve can be developed using various forms of the dispersion viscosity equation in the calculation of the impeller Reynolds number. Alternatively, a Reynolds number may be calculated, using a specific dispersion viscosity equation, and a power number, and hence, power of agitation may be calculated from the Reynolds number through a curve (Figure 4) such as that developed by Laity and Treybal(l957). The second approach was the one used in this study. For dispersion density, a volume-weighted average of the two phases present was used. That is, P m = 4Pd
+ (1 - #')Pc
(9)
Figure 5 shows the experimental power input data versus calculated volume fraction of dispersed phase in the mixer. Dispersed-phase volume fraction was calculated from the CSTR model of eq 8. Also shown in Figure 5 are the predicted power versus dispersed-phase volume fraction using the five tested dispersion viscosity equations. The viscosity equations are very similar up to a dispersed-phase volume fraction of about 0.3. Beyond this point, the equations begin to diverge in their predictions of power input. The experimental data show an increase in power input as the dispersed-phase volume fraction initially increases. This is to be expected since, although the Reynolds number does not change significantly, so that the power number is approximately constant, the dispersion density increases with increasing amounts of the water phase. At higher volume fractions of water, the power input levels as the competition between increasing the power input, due to increasing dispersion density, and decreasing the power input, due to decreased power number at lower Reynolds number, becomes significant. At the inversion point, a step in power input is observed as the Reynolds number jumps in response to the change in viscosity at the inversion point. Qualitatively and quantitatively, the dispersion viscosity equation from Vermeulen et al. (1955) (eq 6) fits the experimental data better than the other proposed equations. Figure 6 shows the predicted power input versus dispersed-phase volume fraction for experiments at different stirrer rpm and different feed volume fraction of dispersed phase. Again, the Vermeulen et al. (1955) equation fits the experimental data satisfactorily.
Conclusions We investigated phase inversion phenomena in continuously operated mixers. We found that continuous op-
982 Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 200,
f
I
,
I
, ,
I
I
Npo= power number, P/pN3Df NRe= impeller Reynolds number, ND?p/y O/ W = organic-in-water dispersion P = power input, W Q = volumetric flow rate, L/min t = time, s VT = mixer volume, L W = impeller blade height, cm W / O = water-in-organic dispersion
I
OSTIRRER rpm = 350, &I = 0.89 ASTIRRER rpm = 300, +F = 1.0
n
Q
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DISPERSED PHASE VOLUME FRACTION,@
Figure 6. Predicted vs experimental power input.
eration yields similar results to batch operation in terms of the effect of stirrer rpm on the inversion point. However, continuous operation precludes an effect of stirrer clearance above the tank bottom on the inversion point because the volume fraction of dispersed phase can be changed without stopping the stirrer. Operating in a continuous mode does, however, introduce two new variables into the phase inversion process, namely the residence time in the mixer and the feed fraction of dispersed phase. However, neither of these variables exhibited a strong effect on the phase inversion point. Finally, by changing the materials used in the mixers from water to organic wet, we found that the construction materials affect the inversion point by promoting the preferentially wetting phase to be the continuous phase. This effect was diminished in a larger mixer. Because of the apparent maximum in viscosity at the inversion point, we developed an indirect method for the determination of dispersion viscosity by monitoring the power of agitation to the mixer. The viscosity of these dispersions is a property which indicates the inversion point but is not the controlling factor.
Acknowledgment One of the authors (TRG) thanks Norges Teknisk Naturvitenskapelige Forskningsrad (NTNF) for a research fellowship and the permission to publish these results. Publication costs for this article were assisted by Sandia National Laboratories.
Nomenclature DI = impeller diameter, cm DT = tank diameter, cm H = overflow height of mixer, cm L = impeller blade length, cm N = stirrer rpm, mip-l
Greek Symbols y = interfacial tension, dyn/cm y = viscosity, CP yd* = “effective” viscosity of dispersed phase, CP y, = viscosity of dispersion, CP y., = viscosity of interfacial phase, CP
4 = volume fraction of dispersed phase p = density, g/cm3 p, = density of dispersion, g/cm3 u = surface tension, dyn/cm 8 = mixer residence time, VT/QF, min Subscripts
c = continuous phase d = dispersed phase F = feed o = organic phase T = tank w = water phase
Literature Cited Arashmid, M.; Jeffreys, G. V. AIChE J. 1980,26(1),51. Barnea, E.; Mizrahi, J. Ind. Eng. Chem. Fundam. 1976,15(2), 120. Bedeaux, D. Physica A l983,121A,345. Falco, J. W.; Walker, R. D.; Shah, D. 0. AZChE J . 1974,20(3),510. Furuse, H. Jpn. J. Appl. Phys. 1972,II(lO), 1537. Howarth, W. J. AZChE J. 1967,13, 1007. Laity, D. S.; Treybal, R. E. AIChE J . 1957,3(2),176. Luhning, R. W.; Sawistowski, H. Proceedings of the International Solvent Extraction Conference, The Hague, 1971, Paper 136,p 873. McClarey, M. J.; Mansoori, G. A. AZChE Symp. Ser. 1978,74(173), 134. Miller, R. S.; Ralph, J. L.; Curl, R. L.; Towell, G. D. AZChE J. 1963, 9,196. Misek, T. Collect. Czech. Chem. Commun. 1964,29,2086. Quinn, J. A.; Sigloh, D. B. Can. J. Chem. Eng. 1963,41, 15. Rodger, W.A.; Trice, V. G.; Rushton, J. H. Chem. Eng. Prog. 1956, 52(12),515. Selker, A. H.; Sleicher, C. A. Can. J . Chem. Eng. 1965, 43, 298. Thornton, J. D.; Buoyatiotes, B. A. Znst. Chem. E. Symp. Ser. 1967, 26,43. Vermeulen, T.; Williams, G. M.; Langlois, G. E. Chem. Eng. Prog. 1955,51(2),85. Yeh, G. C.; Haynie, F. H.; Moses, R. A. AZChE J. 1964,10(2),260.
Receiued for reuiew March 31, 1987 Accepted January 26, 1988
