GREEKLETTERS
Nomenclature
1 to surface of mercury Dz,D 3 = coefficients in Eauation 11 = radial distribution function of a random packing of spheres = average number of spheres per unit radius interval = average number of spheres in contact with a given sphere = pressure = radius of spheres = dimensionless separation between spheres = maximum separation above which mercury is not excluded from between a pair of spheres = total excluded volume in an aggregate of spheres (dimensionless) = dimensionless excluded volume between a pair of spheres = volume of a spherical segment divided by ?r = excluded volume between a pair of spheres = volume of a hyperboloid of revolution divided by 2 T = abscissa = abscissa a t point of contact of mercury surface with a sphere = ordinate = ordinate a t pclint of contact of mercury surface with a sphere = root of Equation 11 a, b,
G
= constants to be determined in fitting Equation
*x 4 P
p1, p2 U
z
d
= 180’ minus the contact angle of mercury
= sum of 0 and 9 = = = = = =
X/Y
dimensionless mean radius of curvature principal radii of curvature of surface of mercury separation between surfaces of neighboring spheres surface tension of mercury angle measured from center of sphere to point of contact of mercury surface with a sphere
literature Cited
(1) Bernal, J. D., Nature 183, 141 (1959). (2) Bernal, J. D., Mason, J.. Ibid., 188, 910 (1960). ( 3 ) Fowkes, F. M., J . Phys. Chem. 66, 382 (1962). (4) Frank, F. C., Kaspar, 3. S., Acta Cryst. 11,184 (1958). ( 5 ) Kruyer, S., Trans. Faraday Sot. 54, 1758 (1958). (6) Lyon, R. N., “Liquid Metals Handbook,” NAVEXOS P733 (rev.), p. 43, U. S. Government Printing Office, Washington, D. C., 1952. (7) Mason, G., Clark, IV., Nu‘ature 207, 512 (1965). (8) Meijering, J. L., Phillzps Res. Rep. 8, 270 (1953). (9) Scott, G. D., iVuture 188, 908 (1960). (10) Zbid., 194, 956 (1962). RECEIVED for review December 27, 1965 ACCEPTED June 13, 1966
EFFECT OF D.C. ELECTRIC F I E L D S ON LIQUID-LIQUID SETTLING GLEN L. SJOBLOM AND SIMON L. GOREN Department of Chemical Engineering, University of California, Berkeley, Calif. The results of crn experimental study on the effectiveness of electric fields in separating water in oil dispersions are reported. The dispersions are made by flowing the liquids through mixing tubes and the average drop diameter i s correlated with the mixing velocity using transmitted light measurements. The variables studied are thle degree of mixing-i.e., drop size-dispersed phase volume fraction, residence time in the settler, depth of the oil layer, and strength of the imposed electric field. Electric fields are effective in reducing the water carry over by a factor of 3 to 200, depending on the mixing conditions and residence time. The contamination i s correlated as a function of two variables, (dA2ApgO/l8 p H ) and (sro,!?/ApgdA). The behavior of the drops in the electric field i s described. HE problem of rapidly and thoroughly separating the two Tliquids in a liquid-liquid dispersion is important and widespread in industry. This paper is concerned with the use of electric fields to separate water-in-oil dispersions. The problem was motivated by a newly proposed process for saline water conversion in which brine is to be heated by bringing it into direct contact with a hot immiscible liquid (in the ratio of about 1 to 7 , brine to oil) in highly turbulent pipe flow (78). After the heat has been exchanged it is necessary to separate the brine from the cooled oil so that the oil may be heated and recirculated. The large oil inventory required could be a serious economic drawback if srparation is to be by gravity settling alone. Of the methods in use for augmenting separation ( 3 ) , “electrical dehydration” or “deoiling” used as a n adjunct to gravity settling appears i o be the most promising for a saline watrr conversion process because of the low operating and equipment costs and the easy adaptability to large throughputs. Although electrical dehydration was introduced over 50
years ago and there are numerous patents, there is very little information in the open literature concerning the quantitative effects of electric fields on improving the separation process. Studies ( 7 , 2) with individual drops a t a flat interface have shown that ordinary coalescence is a statistical phenomenon in which a drop will sit a t the interface for a random time (the average depends on drop size and fluid properties) and then coalesce in stages-Le., the drop will only partially coalesce, leaving behind a smaller daughter droplet. Moreover, collision of droplets in the continuous phase rarely results in coalescence which would permit growth of the drops followed by more rapid settling (72). However, electric fields reduce the average .‘sitting” time before coalescence, eliminate the daughter droplets, and promote coalescence upon collision in the continuous phase. One reason frequently given for the effectiveness of the electric field is that polarization of the drops results in strong local attractions between neighboring drops or the drops and the bulk fluid. This mechanism is used to explain the obVOL. 5
NO. 4
NOVEMBER 1 9 6 6
519
servations of Pearce (7 7) that water droplets in oil in an alternating electric field first align themselves into chains parallel to the field and then coalesce to form larger, faster settling drops. Another mechanism proposed to account for the improved separation is electrophoresis. Klinkenberg (8) has shown that water droplets falling through a petroleum distillate even in the absence of a n externally imposed electric field may acquire a net charge. Eberz and Waterman (4) studied the motion of single drops in d.c. fields and found the velocity of the drops proportional to the square of the imposed electric field and roughly proportional to the drop diameter. This indicates that the drops become charged in the electric field by preferential gain or loss of ions in a manner somewhat similar to the dust in a Cottrell dust collector (70). Sartor (72) conjectured that in a n electric field the interaction of drops which do not coalesce may produce a selective separation of charge between them. Experimental Methods
The liquids used were tap water to which 419 p.p,m. by weight of K2Cr04 had been added for purposes of analysis, and a light hydrocarbon oil, Standard Oil Solvent No. 99 (viscosity, p = 1.8 cp.; density, p = 0.80 gram per cc.; interfacial tension, u = 39 dynes per cm. at 23.5’ (2.). Both liquids flowed through separate rotameters and 5-micron Cuno filters before entering a mixing section. The mixing section consisted of a 1-inch brass tee where the two liquids met and four brass “mixing” tubes ‘/4 inch in i.d. by 9 inches long, through which the two liquids flowed together. Metal plugs were used to block off one, two, or three of these tubes, so that different mixing velocities could be obtained for a given volumetric flow rate through the settler. The mixing tubes fed into a 1-inch diameter pipe 9 inches in length where the dispersions produced in each tube were mixed and transmitted light measurements were made. The settler was a rectangular box constructed of ‘/*-inch thick Plexiglas, 4 inches in height, 6 inches in width, and 5 feet in length. The mixing pipe was screwed into the center of one end of the settler and outlet pipes for the oil and water were provided on the top and bottom 2 inches from the opposite end of the settler. A pair of Alumel screens and a semicircular baffle located ‘/a inch from the entrance appeared to distribute the flow evenly over the width of the settler. Two electrodes made from ‘/,-inch thick copper sheet were fastened to the top and bottom of the settler. T h e lower electrode, which was immersed in the aqueous phase, was 6 inches wide and 3’/2 feet long. The upper electrode, which was immersed in the oil phase, was 5‘/2 inches wide and 3 feet long, its leading edge being 13 inches from the upstream end of the settler so that the dispersion entered the settler in a region uninfluenced by the electric field. The potential applied to the upper electrode was generated from a 0- to 30-kv. d.c. power source manufactured by Plastic Capacitors, Inc. The supply and receiving tanks, the mixing tee, and the lower electrode were grounded. T o get a measure of the drop size of the dispersion, relative light transmittance measurements were made for each flow condition. Light from a GE 222 bulb operated a t 1 volt passed through a red glass filter and into the dispersion of immiscible liquids flowing through the pipe which followed the four mixing tubes. Light which was not absorbed or scattered passed through a second filter and into an RCA 1P41 phototube. A galvanometer was used to measure the output current from the phototube. T o relate the light scattering data to drop size, photographs of several dispersions were taken near the entrance of the settler and the drop size was determined from the negatives using a Vanguard motion analyzer. T o begin a series of runs the flow rates of the two liquids were set a t the desired values. The interface level was maintained constant by adjusting the oil and water outlet valves a t the exit of the settler until the outlet oil rotameter indicated the same flow rate as the inlet oil rotameter. The power supply was turned on and adjusted to the desired voltage. The settling process was then allowed to proceed for two or three 520
l&EC FUNDAMENTALS
residence times (this was all that was needed to achieve steady state) and a sample of effluent oil was taken. Samples were taken at eight voltages from 0 to 17,000 volts for each flow condition, for an eightfold range of residence time, three volume fractions of water, three oil depths, and one, two, or four mixing tubes open. For each flow condition the relative light transmittance was measured. The water not removed from the oil was determined as follows: A 200-ml. sample of the oil phase was taken and added to 100 ml. of distilled water. This mixture was stirred for about 2 minutes at a moderate speed with a magnetic stirrer. The unsettled water drops containing K2Cr04 were mixed with the distilled water in this way. The water phase was separated from the oil and analyzed for chromium using a colorimetric reagent and a spectrophotometer. Experimentation showed that the stirring used forced all but a trace of the water from the oil without making oil in water dispersions that slowly settled. At low levels of entrainment the analysis was somewhat poor because of small readings on the spectrophotometer. At water weight per cents above 0.002 hetanalysis was accurate to approximately 5%. Observations. At low flow rates through the tubes the oil-water interface in the settler was smooth and free from a layer which others (5, 6, 75) have called an emulsion layer or interface layer-that is, the water drops coalesced into the bulk water as fast as they settled to the interface. At higher flow rates and mixing velocities the drops formed were more numerous and smaller and an interface layer was formed. Increasing the volume fraction of water for a constant mixing velocity increased the interface layer also. At the most severe mixing conditions of 838 cm. per second and a water volume fraction of the emulsion layer nearly filled the settler. A number of curious and rather spectacular phenomena took place in the settler in the presence of the electric field. At low potential gradients (5 cm. per second) upward to the electrode, where they reversed direction and traveled rapidly back to the interface, where again they rebounded. Single drops made many such traverses before coalescing into the water phase. A rather large drop was observed to fall to the interface and partially coalesce, leaving a smaller “daughter droplet.” This droplet, apparently having exchanged charge a t the interface, rose to the electrode, exchanged charge, rebounded, and traveled back to the interface. I t too coalesced partially, and the smaller droplet left made the upward and downward travel. The maximum number of daughter droplets formed in the above manner which could be followed visually was four. The pulling of drops from the interface and the phenomenon of rebounding occurred a t lower voltages when the emulsion
layer was present a t the interface. However, the phenomenon could be observed even a t zero flow rates and from a clear interface by applying upward of 26,000 volts across a 2-inch oil layer. Near this voltage, the interface became distorted and rippled throughout the length of the settler. The distortions took the form of dimples and peaks which moved rapidly and randomly about. The sharper peaks, approximately '/4 inch and greater in height, began streaming droplets, which rebounded as described above. IVhen the voltage was raised still higher, sparks could be seen and heard traveling along a stream of drops between the electrode and interface. Discharging through the oil layer also took place occasionally a t lower voltages with high mixing velocities. At the leading edge of the interface layer, a shiny transparent film formed which war stripped from the interface by high voltage gradients. I t rose to a vertical position and a t times current traveled along it, then broke u p and bounced up and down as the drops did. Another experiment was performed by injecting the water through eight rows of 24 hypodermic needles into the flowing oil a t the upstream end of the settler. At low injection velocities, the water streamed out of the needles in the form of jets which then broke up into drops of nearly uniform size approximately 1 m m . in diameter; these drops, a t relatively large distances apart, moved with the oil down the length of the settler. When the electric field was switched on with the upper electrode charged positively, all the drops rapidly fell to the interface and coalesced. When the field was reversed, all the drops rose toward the electrode. When the injection velocities from the needles were increased to approximately
Table 1. 'p
0.091
0.200
0.333
0.200
umix, H, 9: Inches Mzn. Cm ./Sec 615 2 1 .o 307 1. o 154 1. o 307 2.0 154 2.0 307 0.5 410 1.5 0.75 410 1.5 103 2 1. o 700 350 1 .o 1. o 175 2.0 350 2.0 175 2.0 88 175 4.0 350 0.5 465 1.5 465 0.75 116 1.5 2 1.5 560 1.5 140 419 1. o 1 .o 210 2.0 419 2.0 210 105 2.0 210 4.0 3 0.75 465 1 465 0.75 350 3 1. o 1 350 1. o 232 3 1.5 2 232 1.5 1 232 1.5
300 cm. per second or greater, the flow formed a dispersion of smaller nonuniform drops a t the upstream end of the settler. As this dispersion flowed through the electric field, there was some clearing but no general motion to either the electrode or the interface. Rather, the motion of the drops seemed as described, with the water and oil mixing in tubes. Some of the droplets rose to the electrode and some fell to the interface. I t is believed that, in the case of low injection velocity when the drops do not interact once they are formed, their charge is of one sign, positive. At high injection velocities the drops may interact after they are formed and achieve some randomness in sign and magnitude of charge. Results and Discussion
Table I gives the results for the separation of the water and the petroleum distillate in the presence of a n electric field. Also included are the transmitted light measurements. Drop Size. The drop size is of great importance in determining the performance of the settler. The method of mixing the two fluids used does not produce monodisperse drops, but rather drops having a wide size distribution. Kolmogoroff ( 9 ) and Hinze (7) have derived a theoretical relationship for in a homogeneous isothe maximum stable drop size, d,,, tropic turbulent field. The result is d,,,(pc/a)
3 1 W 5
= constant
(1)
where pc is the continuous phase density, u is the interfacial tension, and e is the rate of energy dissipation per unit mass of fluid. For pipe flow (which is not homogeneous and isotropic) the dissipation rate is related to the friction factor, f,by
Experimental Data for Contamination and Light Transmittance Contamination, Wt. 70at E = ( ) Kv./Cm. 6 VI dD, 0.000 0.454 0.908 1.306 1.910 2.390 2.870 Cm .
lo--l 0.044 0.182 0.468 0.154 0.335 0.191 0.096 0.104 0.294 0.044 0.133 0.266 0.119 0.349 0.577 0.467 0.148 0.090 0.097 0.358 0.072 0.381 0.105 0.198 0.116 0.247 0.563 0.299
... ... ... ...
... ... ...
0.0028 0.0065 0.0197 0.0065 0.0197 0.0065 0.0046 0,0046 0.0225 0.0024 0.0056 0.0125 0.0056 0.0125 0.0285 0.0125 0.0056 0.0040 0.0040 0.0206 0,0032 0.0074 0,0045 0.0103 0.0045 0.0103 0.0225 0.0103 0.0040 0.0040 0.0056 0.0056 0.0092 0.0092 0.0092
0.831 0.042 0.005 0.030, 0.001 0.245 0.158 0.280 0.002 1.010 0.087 0.017 0.091 0.006 0.004 0.004 0.393 0.251 0.532 0.002 0.152 0.003 0.110 0.023 0.082 0.010 0.003 0.008
0.610 0.249 0.210 0.068 0.030 0.014 0.012
0.268 0.044 0.008
0.031 0.003 0.133 0.081 0.152 0.002 0.281 0.064 0.018 0.054 0.010 0.003 0.006 0.206 0.110 0.217 0.002 0.111 0.004 0,074 0.026 0.068 0.009 0.003 0.011 0.243 0.140 0.143 0.062 0.042 0.021 0.013
0.143 0.029 0.007 0.020 0.002 0.104 0.052 0.135 0.001 0.166 0.055 0.014 0.031 0.007 0,002 0.005 0.103 0,077 0.110 0.001 0.067 0.004 0.054 0.017 0.034 0.009 0.002 0.004 0.137 0.080 0.080
0.045 0.027 0.014 0.012
0.053 0.020 0.005 0.015 0.001 0.069 0.023 0.065 0.001 0.108 0.038 0.012 0.018 0.003 0.002 0.004 0.062 0.045 0.059 0.001 0.032 0.002 0.026 0.011 0.012 0.003 0.002 0.003 0.094 0,032 0.050 0.021 0.014 0.006 0.003
3.345
0.022 0.012 0.004 0.007
0.008 0.004 0.002 0.002
0.003 0.001 0.005 0.002
0.000
0.000
0.000
0.024 0.003 0.014 0.001 0.012 0.010 0,002 0.004 0.000 0.002 0.002 0.036 0.002 0.018 0,001 0.026 0,001 0.009 0.008 0.010
0.000
0.015 0.005 0,010
0.012 0.036 0.011 0.001 0.005
0.040 0.010 0,034 0.001 0.036 0.028 0.007 0.005 0.000 0,002 0.004 0.044 0.014 0.054 0,001
0.012 0,001 0.026 0.006 0.006 0.000 0.002 0.003 0.060 0.013 0.028 0.008
0.011 0.002 0.003
VOL. 5
NO. 4
0,001
0.004 0.004 0.001 0.003 0.000 0.002 0.002 0,025 0.004 0,010 0.001 0.030 0,001 0.008 0:023
0.000
0.000
0.002 0.002 0.031 0.006 0.014 0.005 0.006 0.001 0.002
0.002 0.002 0.016 0.004 0.009 0.003 0.004 0.000 0.001
0.003 0.000 0: 003
...
0: 002 0.002
0:002 0.028 0.005 0.009
0.001 0.039 0.001 0.026
...
o:001 0:001 0.010 0.003 0.016 0.001 0.002 0.000
0.001
NOVEMBER 1 9 6 6
521
v3
v 3
D
D
~ = 2 - f ~ 2 - X 0 . 0 4 4
(2)
where Vis the average velocity in the mixing pipe of diameter
D. An approximate equation correlating the friction factor
1.0
f
---
dm*x
D
constant
(T)
-0.6
peVD
(->
= 1 f
kA
(5)
\
I
I
I
doq
1
crn
0.21
A \
0.008
A'
c
%
0.006
0.I
"L
0.06
0.002
0.04100
150 I 200 I
300 I 403
6CC 800 IC03
MIXING V E L O C I T Y ,
crnlsec
0
rp = 0.091
0 A
p = 0.200 p = 0.333
(7)
I n Equation 3, the drop size is predicted to be proportional to V-1.28. Thus, for a single pair of liquids,
k and k' are determined experimentally by photographing the dispersion formed a t a few typical velocities. The relative light transmittance measurements are plotted in Figure 1 . The left-hand ordinate is 6 pl/(Z0 - I ) and the abscissa is the velocity in the mixing tubes. The plot is independent of the water phase volume fraction and the slope can be taken to be -1.28 as suggested by Equation 8. Drop size distributions were measured photographically for several mixing conditions: QW = 0.091, V = 154 cm. per second; pW = 0.200, V = 175 cm. per second; pw = 0.333, V = 210 cm. per second. From the drop size distribution three drop sizes were determined such that 1 0 , 50, and 90% of the dispersed phase volume was contained in drops of diameter less than dlo, dA, and dgo, respectively. When these diameters were plotted against the mixing velocity, lines of slope -1.28 could be drawn through the points for each diameter. This enabled constants k and k' in Equation 8 or, alternatively, the constant in Equation 3, to be determined. The results for the dimensionless constant in Equation 3 for the three representative drop diameters are: 0.66 1.6 2.2
These are in good agreement with the value 1.9 suggested by Hinze for the maximum drop diameter and indicate that any representative drop size can be correlated by Equation 3 with different values for the constant-Le., the major portion of the drop size distribution depends on a single parameter, as dA. l&EC FUNDAMENTALS
I
0.02
0 0
Combining Equations 4 and 5, we get
522
I
Figure 1. Correlation of light intensity measurements (open symbols) and average drop diameter (solid symbols) with mixing velocity
where d is the average diameter of the drops defined by
- I)
I
0.0I
(4)
QW/A
d = k 6 ppZ/'(Io
1
(3)
Volumetric considerations on the dispersed phase of volume fraction, pw, give d = 6
I
-0.08
Hinze (7) estimated the constant to be 1.9. Van de Hulst (76) has shown that the scattering of plane parallel light by spherical particles is determined by the relative refractive indices of the two phases and by cross-sectional area of the spheres. Vermeulen, Langlois, and Gullberg (77) adapted this to the measurement of interfacial area in liquid-liquid agitated vessels. They found that
Ia/I
I
1
0.6 O.
with the Reynolds number has been introduced. Combining these two equations, Sleicher (74) obtains upon rearrangement
peV2D
1
The value of dA obtained as a function of the mixing velocity was used in correlating the settling data. The ordinate on the right-hand side of Figure 1 gives dA, and shown in the figure are the three points used in establishing the value of the constant for this drop size. Settling with Zero Applied Electric Field. A straightforward computation (73) of the removal of droplets in the settler gives the following expression for the volume fraction of water in the oil effluent from the settler : (9)
where F is a dimensionless factor depending on the initial size distribution given by so(i8 r H / A P e e ) i ' *
n ( d )d5dd
F = - 4n d 2
lm
(10)
n(d)cPdd
This expression is based on the assumption that the terminal velocity is given by Stokes' law, that there is no interaction between the drops-Le., no coalescence or hindered settlingthat the oil phase is in plug flow, and that initially the water drops are distributed uniformly in the oil. If the distribution of drop sizes is given by a single parameter-e.g., dA-aS is indicated in the measurements of dlo, dA, and d N , the contamination would be a function of dAzAp@/18 pHalone. The exact functionality would depend on the initial size distribution. The dimensionless group dA2ApgB/18 pH represents the ratio of the time available to the time required for a drop of diameter dA to settle a distance H by gravity settling alone. Experiments were carried out where the degree of mixing, the residence time, the depth of the oil layer, and the volume fraction of water were varied independently. It was found
that the amount of water carried over in the oil phase was
a strong function of the correlated average drop diameter. Large increases in contamination were noted when the mixing velocity was increased above the value for which the average drop diameter was about '/2(18 pH/ApgO)'Iz. According to Stokes' law the settling velocity is proportional to the square of the drop diameter. From this one would expect that decreasing the drop size would increase the contamination. The effect is compounded by the nature of the drop size distributions. As the mixing velocity is increased, not only is the average drop size reduced, but also a larger fraction of the water is in drops smaller than an assigned diameter-e.g., li2(18p H / ApgO)1'2. Similar trends were found for the effect of the residence time and oil depth. T h e contamination was independent of the water volume fraction. This somewhat surprising result is contrary to Equation 9, which indicates that the contamination should be proportional to the inlet water volume fraction. The explanation of this lack of dependence is probably to be found in the coalescence of drops. ,4t larger volume fractions of the dispersed phase, coagulation occurs to a greater extent and so settling should be more rapid. This would lead one to expect a dependence on the volume fraction less than the first power. The fact that the dependence is observed to be zero is probably fortuitous. The combined effects of average drop size, residence time, and oil depth may be seen by plotting the contamination against the dimensionless group dAzApgO/18 pH. This is shown in Figure 2. The plot superimposes all the data taken with zero applied electric field. Also shown in the figure are some data taken by Sweeney (75) for the system Aroclor (p = 5.1 cp.; p = 1.43 grams per cc.; u = 39 dynes per cm. a t 190' F.) and water usin? a mixing device identical to the one in this study and a n oil depth of 6 inches and settler length of 4 feet. Since he did not calibrate the light transmittance device for his liquids, it was necessary to choose a value of the constant k in Equation 8. The value 0.07 cm. (compared with 0.065 for the fluids studied here) was found to superimpose his data onto ours. Settling in Presence 'of an Electric Field. Figure 3 shows the contamination as a function of the strength of the applied electric field for three typical flow conditions. R u n 37 illustrates a flow with intense mixing conditions and small residence times for which the electric field is most useful in reducing the carryover. The Contamination can be reduced 200-fold by application of the electric field. An example for less severe mixing conditions is run 47, which shows only a factor of 10 decrease in contamination. For mild mixing conditions as exemplified by run 22, separation by gravity settling alone is rapid and the electric field offers no improvement. O n the contrary, there is an initial increase in contamination with increasing field strength. This can be explained by assuming that the drops become ch.arged and some of them are attracted to the upper electrode. Therefore some of the drops may be balanced by the field and carried out of the settler, whereas a t higher fields they would be forced upward or downward. All of the runs showNed a n increase in contamination a t sufficiently high voltage. This was correlated with the phenomenon of interface breakup and bouncing. Although its onset was somewhat dependent on the extent of the emulsion layer present, the minimum in the contamination us. field strength curves occurred between 2.5 and 3.0 kv. per cm. for most cases. As in the case of zero applied field, the contamination increased as the average drop diameter or the residence time
a
z
I' 0.01
0
0
0.001 0.0001
Figure 2.
group
0.001
0.0 I
"* p g e
0.I
(m)
D IM E N S 10N L E S S
Contamination as a function of dimensionless
(dA2Apge le-)
with zero applied electric field
0
A 0
0
cp = 0 . 0 9 1 , H = 2 inches cp = 0 . 3 3 3 , H = 2 inches q = 0.200, H = 1 inch cp = 0.200, H = 2 inches p = 0.200, H = 3 inches
x = Sweeney's (75) data for Aroclor-water at 19OoF., p = 0.150,
H = 6 inches
/
/
,
l
,
I
I
I
i
/
,
,
r R U N 37
V,,,=615
crn/sec
3 0.1 RUN 4 7
0.001
'
I
I
1
I
I
'
I
I
I
I
I
decreased. However, the dependence of the contamination on these variables was not so strong below dA = l/2(18 pH/ApgB)1/2 as it had been in the absence of the electric field. Since many drops are charged, it is of interest to assess the role electrophoresis might play. For a small drop, say 0.005 cm. in diameter, in a voltage gradient of 1000 volts per cm. the ratio of the electrophoretic velocity to the gravity settling velocity is about 150 to 1, assuming the mobility relation given by Eberz and Waterman ( 4 ) . I t would seem reasonable on that basis to neglect gravity forces for all but the very lowest field strength, and a plot of contamination as a function of E2dA0 would be expected to give a good fit to the VOL. 5
NO. 4
NOVEMBER 1 9 6 6
523
1 0%
A 0
0
A 0
A 0 OAo
A
0.0011
1
!
I
1
I
I
I /
a3
E2d 8 x
a
0 3
b
I
&8 IA
0.I
0.01
0.00I
Ao
A
In
I I 1
1.0
v o l t s 2 - s e c /cm
Figure
Figure 4. Attempted correlation of contamination as a function of electric field based on mechanism of charging and electrophoresis 0
p = 0.091 p=oo.200
A
p = 0.333
0
data for fixed oil depth. However, as is shown on Figure 4, the fit is not adequate to represent the data. I t does show general trends, but the points for the low gradients scatter considerably. I n spite of the apparent magnitude of the ratio of electrical to gravity forces, it appears that gravity cannot be neglected. The drops may not all be of the same sign; some may not be charged a t all. Also the expression used for the electrophoretic velocity may not be valid for diqpersions, as it was derived from data on electrophoresis of single drops. Eberz and Waterman (4) state " . . .although individual drops exhibit active electrophoresis, petroleum distillate emulsions in general show few signs of it." The results with no applied electric field have been correlated by plotting the contamination as a function of dA2ApgO/ 18 pH, the dimensionless ratio of the time available for settling to the time necessary. I n Figure 5 we present a similar plot for data with a n applied electric field using as a parameter a dimensionless group which represents the ratio of the electric to the gravity forces, eeoE2/Apgd.+ The points for Figure 5 were obtained from curves such as shown in Figure 3 by picking off the contamination a t the value of E which made the group eeoE2/ApgdA a specified constant. Again the contamination seems to be independent of dispersed phase volume fraction. This method of plotting yields straight lines of constant slope on log-log plots which intersect the line for zero applied field. The intersection represents the point where gravity settling is already so rapid that it cannot be improved with a n electric field of the given field strength. Although the group eeoE2/ApgdA was arrived a t on the basis of electrophoresis of drops which become charged in the electric field, the same group (including the term eeo) arises in considering the force between two electrically neutral droplets due to the induced dipole, which force might be important in promoting the rate of drop coalescence. The results of the present study are not capable of distinguishing bemeen the two mechanisms. The continuous phase viscosity, the density difference, and especially the electrical properties of the two 524
l & E C FUNDAMENTALS
5.
Final correlation of contamination as a
fllnr-
D , m , o p = 0.091
o,.,a
$0 = 0.200 A , A , p P = 0.333
liquids were not varied in the present experiments; their use in the correlation made the numbers dimensionless. Further work is needed to establish the dependence on these variables. Conclusions
The relative light transmittance technique with photographic calibration was an effective method of determining drop sizes in turbulent flow in tubes. Electric fields improved gravity settling considerably ; the improvement was greatest a t high extents of mixing and high flow rates. At the lowest rates investigated, the reduction in contamination was approximately threefold compared to no electric field. At the highest rate, the reduction was 200-fold. The carryover was correlated as a function of two dimensionless groups: the ratio of the residence time to the time required for a drop of diameter d~ to settle a distance H and the ratio of the electrostatic force to the gravity force. The magnitude of the electric field which can be used is limited by the phenomenon of bouncing and electrical breakup of drops which leads to increases in contamination. Nomenclature
dlo
= interfacial area per unit volume of dispersion = drop diameter = drop diameter such that 10% of volume is contained
dA
= drop diameter such that
A d
dgo =
D E F
= = =
g
=
H Z Io
= = = k , k' =
Qa
=
in drops of diameter less than dlo 50% of volume is contained in drops of diameter less than d~ drop diameter such that 90% of volume is contained in drops of diameter less than dw diameter of mixing tubes electric field strength dimensionless factor acceleration of gravity oil depth in settler transmitted light intensity for dispersion transmitted light intensity for.continuous phase constants volumetric flow rate of oil
co
= dielectric constant of oil = permitivity of free space
E
residence time in settler
6
=
p p u
= viscosity = density = surface tension
p
= volume fraction of water
Literature Cited
(1) Charles, G. E., Mason, S. G., J . ColloidSci. 15,105 (1960). ( 2 ) Zbid., p. 236. ( 3 ) Clayton, LV., “The Theory of Emulsions and Their Technical Treatinent.” DD. 582-90. Blakiston. New York, 1954. (4) Eberz, W.’6., LYatel’man, L. C., A.1.Ch.E. Preprint 31d, 56th Annual Meeting, Ilecember 1-5, 1963. (5) Epstein, A. D., University of California, Berkeley, UCRL Rept. 10625 (1963). (6) Graham, R. J., Zbtd., 110048 (1962). ( 7 ) Hinze, J . O., A.Z.Ch.E. J . 1, 284 (1955). ( 8 ) Klinkenberg. Adcan. Petrol. Chem. Rejnzng 8 , 98-118 (1964).
( 9 ) Kolmogoroff, A. N., Dokl. Akad. Nauk SSSR ( N S ) 66, No. 5, 825 (1949). (10) Pauthenier, M., Compt. Rend. 193, 1068 (1931). (11) Pearce, C. A. R., Brit. J . Appl. Phys. 5 , 136 (1954). (12) Sartor, D., J . Meteorol. 11, 91 (1954). (13) Sjoblom, G. L., “Effect of Electric Field on Liquid-Liquid Settling,” M.S. thesis, University of California, Berkeley, 1964. (14) Sleicher, C. A , , Jr., A.I.Ch.E. J . 8,471 (1962). (15) Sweeney, W. F., Wilke, C. R., University of California, Berkeley, UCRL Rept. 11182 (1964). (16) Van de Hulst, H. C., “Optics of Spherical Particles,” J. F. Duwaer and Sons, Amsterdam, 1946. (17) Vermeulen, T., Gullberg, J. E., Langlois, G. E., Rev. Sci. Znstr. 25, 360 (1954). (18) Flrilke, C. R., Cheng, C. T., Ledesma, U. L., Porter, J. W., Chem. Eng. Progr. 59, 69 (1963).
RECEIVED for review November 1, 1965 ACCEPTED June 20, 1966 Work carried out under the auspices of the Sea Water Conversion Laboratory, University of California at Berkeley, supported financially by the Water Resources Center of the State of California.
EFFECT OF IONIC MIGRATION ON LIMITING CURRENTS JOHN N E W M A N
Ino?ganic .Ma/erials Research Division, L,awrence Radiation Laboratory, and Department of Chemical Engineering, University of California, Berkeley, Calif.
The effect of migration on limiting currents is calculated for four hydrodynamic situations: the rotating disk, the growing mercury drop, the semi-infinite stagnant fluid, and the Nernst diffusion layer, and for several electrolytic systems.
HE
addition of supporting or indifferent electrolyte to a
Tsolution tends to change the value of the limiting current
for an electrode reaction. This mav be because the viscosity and diffusion coefficients, the activity coefficients and driving forces for diffusion, or the conductivity and the driving force for migration are changed. We are concerned here with the last of these effects. For sufficiently dilute solutions the first two can be ignored. If the ratio of the supporting electrolyte concentration to the concentration of the reactant is very large, the high conductivity wppresses the electric field, and the resulting limiting current, In, is due solely to diffusion. If the supporting electrolyte concentration is reduced, the electric field becomes larger and may enhance or depress the limiting current, depending upon the sign of the charge of the limiting reactant and the direction of the current. The ratio IL,’Zn of the limiting current to the limiting diffusion current is a convenient measure of the effect of migration. T h e mechanism of this effect has been discussed qualitatively by Heyrovsk?
(4).
PVr have ralciilated this effect of migration for four geometries of the diffusion layer. T h e results are presented in the form of IL/ID as a functicln of the ratio of the concentration of the supporting ion to that of the counter ion. Mathematical Formulation
I n dilute electrolytic solutions, transport processes can be described by the following four equations:
.Ir
