Ind. Eng. Chem. Res. 1994,33,744-747
744
CORRESPONDENCE Comments on Hold-Up (Volume Fraction) Measurements in Liquid/Liquid Dispersions Using an Ultrasonic Technique Rajinder Pal Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Sir: I have read with interest the papers recently published by Tavlarides and co-workers (Tsouris and Tavlarides, 1990, 1993; Yi and Tavlarides, 1990) on measurement of dispersed-phase holdup (volumefraction) in liquidlliquid dispersions. I would like to offer some comments. In the cited papers, the authors discuss the following two models for the prediction of dispersed-phase concentration (4) in emulsions using ultrasonic techniques:
t*-t,
model 1:
$=-
td-tc
model 2: where t* is the travel time of an ultrasonic wave in the emulsion, t, and td are travel times of an ultrasonic wave in the continuous phase and the dispersed phase, and g d and g, are factors given as follows:
or
[ (
1- 1--;2)3/2] 5r3 ?y2[ 5 1- (1 - $)5/2] - 1-
gc=1+--y2
[
+
$I3’’
for
y I1
(6)
where ultrasonic velocity in the dispersed phase = ultrasonic velocity in the continuous phase
The above two models, eqs 1and 2, could be rewritten in terms of ultrasonic velocities by substituting t* = L/ V*, t , = L/V,, and td = L/vd, where L is the distance between the ultrasonic transducers and V*, V,, and v d are ultrasonic velocities in the emulsion, continuous phase, and dispersed phase, respectively: model 1:
(7)
model 2: In the cited papers of Tavlarides and co-workers, the authors suggest that model 2 (eqs 2 and 8) is superior to model 1 (eqs 1 and 7). However, I find that this is not generally true. As an example, let us consider the ultrasonic velocity data published by Bonnet and Tavlarides (1987)for xylene/ water emulsions. The data are tabulated in Table 1 for convenience. The emulsions are xylene-in-watertype (i.e., xylene is the dispersed phase) for xylene concentrations less than 57% by volume. For xylene concentrations greater than or equal to 57 % by volume, the emulsions are water-in-oil type (i.e., water is the dispersed phase). The values of y, g,, and gd for xylene-in-water and water-inxylene emulsions are summarized in Table 2. Figure 1 shows the plot of ultrasonic velocity data of Table 1. Model 1 (eq 7) and model 2 (eq 8) have been plotted for comparison purposes. While model 1gives a single curve over the full range of xylene volume fraction (independent of whether the emulsion is xylene-in-water or water-in-xylene), model 2 gives two separate curves (one for xylene-in-water emulsions and the other for waterin-xylene emulsions). From the plots, it is clear that model 2 is not superior to model 1 even when the ultrasonic velocity in the continuous phase is higher than that in the dispersed phase i.e., y < 1. While both models underpredict the ultrasonic velocities in emulsions, model 1 is far better than model 2. The differences between the prediction capacities of the two models can be seen more clearly in Figure 2, where we have plotted the ratio of predicted volume fraction of xylene (from models) to true volume fraction of xylene. Obviously, model 1 gives relatively much more accurate predictions. Furthermore, it should be made clear that the prediction of phase-inversion point from model 2 (i.e., intersection of two curves), as suggested by Yi and Tavlarides (19901, is without any basis. The intersection of two curves predicted from model 2 (see Figure 1) cannot be used to estimate the phase-inversion point. Table VI of Yi and Tavlarides (1990)indicates that phase inversion predicted from the intersection of two curves (model 2) is in good agreement with experimental observation. In our view, this agreement is fortuitous. The phase-inversion point in emulsions can be shifted quite significantly by the addition of a minute quantity of an appropriate surfactant to the system whereas the intersection of the two curves predicted from model 2 would not be affected to any significant extent. Also, phase-inversion phenomenon generally exhibits a hysteresis effect. For example, Figure 3 shows the plots of viscosity as a function of water volume fraction for mineral oil/water emulsions studied by the present author. In 0 1994 American Chemical Society
Table 1. Measured Velocities of Ultrasound in Dispersion of Xylene and Water at 25 f 0.1 OC (Bonnet and Tavlarides, 1987) ultrasonic ultrasonic vol fraction vol fraction of xylene vel (m/s) of xylene vel (m/s) 1498 0.53 1397 0 1486 0.57 1391 0.0625 1478 0.67 1376 0.1176 0.166 1466 0.77 1359 1451 0.89 1340 0.25 1437 1.0 1304 0.311 1428 0.38
1.2
--
0 Model 2
W
.
w w
Table 2. Values bf y , go and g d Based on Bonnet and Tavlarides (1987) Data for Xylene and Water Dispersions emulsion type xylene-in-water water-in-xylene 1500e
--
8
Y
gd
gc
0.8705 1.149
1.1623 0.7578
1.149 0.7512
i
8
cn
E'
I
*
*
1460
U
J
-
> 1420
5
0.4 0.0
~ ~ . . I ~ . ~ ~ I
Experimental data - - model 1 model 2
W
*
-I
Xy I e ne/w at e r emulsions
n
\
8
v
0
-
0.2
0.4
0.6
0.8
1.0
Xylene
@True
Figure2. Ratio of predicted volume fraction of xylene to true volume fraction of xylene.
-
\
.->\ 0 4-J
0 -
8
1340
1300 0.0
Phase
0.2
0.4
0.6
0.8
1.0
Xylene volume fraction Figure 1. Ultrasonic velocity data for xylene/water emulsions (data given in Table 1).
Figure 3a, the starting phase is oil to which water is added to produce water-in-oil (W/O) emulsions; in this case, inversion of water-in-oil to oil-in-water (O/W) emulsion occurs at a water concentration of 41.7% by volume. (Notice that a sudden change in viscosity occurs upon phase inversion; a sudden change in electrical conductance of emulsions also occurs upon phase inversion.) In Figure 3b, the starting phase is water to which oil is added to produce oil-in-water emulsion; in this case, phase inversion of oil-in-water emulsion to water-in-oil emulsion occurs at a much lower water concentration of 22.47% by volume. I t should also be pointed out that model 2 has an additional limitation from a practical point of view. It requires the knowledge of the type of emulsion (Le., oilin-water or water-in-oil)before it can be applied to calculate the volume fraction of the dispersed phase. Model 1on the other hand is simple to use, and it does not depend on whether the emulsion is oil-in-water or water-in-oil. In fact, the more general way of writing model 1is to use oil volume fraction (or water volume fraction) rather than dispersed-phase concentration:
_1 ----+40 1-40 v* vo v, or
t* - t , 4o = to - tw
(10)
where 4ois oil volume fraction, Voand V , are ultrasonic velocities in pure oil and water phases, and to and tw are travel times of ultrasonic wave in pure oil and water phases. One can calculate the oil volume fraction from the above equation for both oil-in-water and water-in-oil emulsions. In Figure 4, I have replotted the experimental data of Bonnet and Tavlarides (1987) given in Table 1. The data are plotted as true xylene volume fraction versus volume fraction of xylene predicted from model 1. The lines shown in the figure are obtained from model 2. Several figures of Yi and Tavlarides (1990) are plotted in a manner similar to that shown in Figure 4; as an example, Figure 5 shown here is their figure (Figure 9 of Yi and Tavlarides) for the watedtoluene system. Upon comparison of Figures 4 and 5, one finds that the behavior of the waterlxylene system is very different from that of the water/toluene system. I am curious to learn why there exists such a drastic difference between the two systems even though the physical (and sonic) properties of both systems are very similar. It should also be noted that the y = 1line in the Yi and Tavlarides figure (Figure 5 in this correspondence) is very confusing. When y = 1, i.e., the ultrasonic velocities in
746 Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994 1.0 l
1
l
*
Xylene/w a t er System
0/ Experimental data
t
W
-
Y
0.6
> d C
-
-
3 v,
Lc
0 >r .c,
' t i
t
0
1380
1
.-
0
Phase 0.0
0.2
0.4
0.6
1.0
0.6
Xylan. %cdel
0.0
0,4
0.6
0.0
1.0
Xylene volume fraction Figure 6. Comparison of ultrasonic velocity data for xylene/water emulsions with the new proposed model.
, , , ,
ID.
Water/ Toluene Syst T = 24°C e Experiments
0 Proposed Model
-
b q 11)
1.2
(4CO,500ond600RPM)
true
0.2
1
Figure 4. Comparison of the true volume fraction of xylene with the volume fraction of xylene predicted from model 1. The lines are predicted from model 2.
+Org 0 5
1300
inversa,
-
0.6
1
0.4 0.0
0.2
0.4
0.6
0.8
1.0
Xylene
Figure 6. Comparison of the true volume fraction of the organic phase with the volume fraction of organicphase predicted from model 1 (also called TA model). The solid lines are predicted from model 2 (see Figure 9 of Yi and Tavlarides (1990)).
the dispersed phase and the continuous phase are the same, eqs 3-6 give g d = g, = 1and therefore model 2 reduces to model 1. However, for y = 1, V* = V, = v d at all concentrations of dispersed phase, and therefore, one cannot use the ultrasonic technique to measure the dispersed-phase concentration of emulsions. (&del 1 becomes indeterminate when y = 1 and t* = t, = td.1 Finally, I would like to propose a new and simple model for the prediction of ultrasonic velocities in emulsions. The model is based on a simple mixing rule and is given as follows:
where the quantities @o, V,, V,, and V* have been defined earlier. This model is independent of whether the emulsion is oil-in-water (O/W) or water-in-oil (W/O). Figure 6 compares the above model with the experimental data of Bonnet and Tavlarides (1987) for xylene/
+True
Figure 7. Ratio of predicted volume fraction of xylene (from proposed model) to true volume fraction of xylene.
water emulsions (given in Table 1). The model predicts the experimental data rather well. The ratio of xylene concentration predicted from the model to true xylene concentration is plotted in Figure 7. Upon comparison of this figure with Figure 2, it is clear that the model given in eq 11 is superior to models 1 and 2 discussed earlier. Equation 11can further be rewritten in terms of travel times of ultrasonic wave:
v* - v,
4o = -
=(;)(-)
(12)
where $I~,to,t,, and t* have been defined earlier. In terms of t , and t d (travel times in continuous and dispersed phases), the above equation reduces to (13)
Ind. Eng. Chem. Res., Vol. 33,No.3, 1994 747 For low values of dispersed-phase concentrations (6is small), eq 13 can be approximated to
Acknowledgment Financial support from Natural Sciences and Engineering Research Council (NSERC) of Canada is gratefully appreciated. Literature Cited
This equation is similar to the empirical model of Tsouris and Tavlarides (1993):
whereg is an empirical constant. Upon comparison of eqs 14 and 15, g is equal to (tdtd).
Bonnet, J. C.; Tavlarides, L. L. Ultrasonic technique for dispersedphase holdup measurements. Ind. Eng. Chem.Res. 1987,26,811815. Tsouris, C.; Tavlarides, L. L. Comments on model for holdup measurements in liquid dispersions using an ultrasonic technique. Ind. Eng. Chem. Res. 1990,29,2170-2172. Tsouris, C.;Tavlarides, L. L. Volume fraction measurements of water in oil by an ultrasonic technique. Ind. Eng. Chem. Res. 1993,32, 998-1002. Yi, J.; Tavlarides, L. L. Model for hold-up measurements in liquid dispersion using an ultrasonic technique. Ind. Eng. Chem. Res. 1990,29,475-492.
