Ind. Eng. Chem. Fundam. 1083, 22, 167-172
Simulation of Phenol Removal from Wastewater by Liquid Membrane Emulsion Kyo-Seon Klm, SangJune Chol, and Son-KI Ihm” Depafiment of Chemical Engineering, The Korea Advanced Institute of Science and Technology, P.O. Box 150, Chongyangni, Seoul, Korea
been proposed for the removal of phenol from wastewater by use of a liquid membrane during the initial stage when the emulsions do not show any breakage, and a computer simulation of the model’s equations has been performed by estimating the appropriate values of the parameters. The model is based on the assumptions that the aqueous NaOH solution is confined within the radius, R,, of a water-indl emulsion with a constant volume fraction and that the core radius shrinks as phenol diffuses in. The computed results are found to be in good correlation with the experimental data. It has been shown that the mass transfer resistance for phenol removal exists mainly in the outer liquid membrane layer and that the value of R , obtained from the model fitting is almost the same as that determined by geometrical consideratlon. A model has
Introduction Li (1971a,b) proposed a novel separation technique based on the selectivity of a liquid membrane. Since then, the liquid membrane technique has been introduced to various separation processes. A mixture of hydrocarbons can be separated by using the difference in their solubilities in a liquid membrane (Li, 1971a,b; Shah and Owens, 1972), and phenol or ammonia in the wastewater can be treated by the acid-base reaction in the liquid membrane emulsion (Li and Shrier, 1972; and Cahn and Li, 1974; Matulevicius and Li, 1975). In addition, a few heavy metals, rare metals, or inorganic solutes can be concentrated by using the liquid membrane, inside which they are selectivelycombined with pertinent carriers (Matulevicius and Li, 1975; Cussler and Evans, 1974). In order to form a liquid membrane for removing phenol from wastewater (Li and Shrier, 1972; Cahn and Li, 1974; Matulevicius and Li, 1975), the water-in-oil (W/O) emulsion is prepared by rigorously mixing the aqueous NaOH solution with the organic phase containing the hydrophobic surfactant. The resulting W/O emulsion is then mixed with the aqueous phenol solution and the W/O/ W emulsion type liquid membrane is formed. Phenol in the outer aqueous phase diffuses through the liquid membrane of the surfactant-containing organic phase and reacts with NaOH upon reaching the inner aqueous phase. The acid-base reaction involved is C6H,0H + NaOH C6H50Na+ H 2 0 Phenol is a weak acid and can pass through the organic membrane phase in its undissociated form. Sodium phenolate which is formed in the inner aqueous phase is a strong electrolyte and remains as its respective ions, c6H50- and Na+. These ions are not soluble in the organic phase and are confined to the inner aqueous phase. Accordingly, phenol can continuously diffuse into the liquid membrane because it disappears due to the reaction in the inner aqueous phase. Several studies have been made on the liquid membrane model. Boyadzhiev et al. (1977) developed equations on the assumptions that the concentrations of the solvent, the intermediate phase, and the interior phase are constant and independent of its radius and that the emulsion breakage is proportional to the emulsion volume. Alessi et al. (1978) considered the liquid membrane as a particle in the separation of the hydrocarbon mixture and assumed the volume fraction of the hydrocarbon mixture to be
-
0196-43 1318311022-0 167$07.50/0
constant up to the surface of the liquid membrane and the feed and the aqueous solution to have attained equilibrium during the primary stirring. Casamatta et al. (1978) have suggested a model for hydrocarbon separation with the assumption that the volume fraction of hydrocarbon mixture is constant for 0 I r I R- and showed that the aqueous liquid membrane for R- I r I R provides the controlling mass transfer resistance. Matulevicius and Li (1975) presented a model for phenol removal from wastewater and assumed that the aqueous NaOH solution is filled within the radius, Ri, that there is no shrinkage of Ri during phenol diffusion, and that the rate-controlling step for phenol removal is the diffusion through the liquid membrane within Ri I r I Ro. In this work, the model equations are proposed with the assumptions that the initial radius of the unreacted inner core is Ri where the volume fraction of the aqueous NaOH solution is &, and that the radius of the unreacted inner core shrinks with the formation of sodium phenolate. It is also assumed that the aqueous phase containing sodium phenolate in the reacted inner core provides the diffusion path for the phenol. Computer simulations of the model’s equations are performed when the value of Ri obtained by fitting the computed results to the experimental data can be applied. The value of Ri used for the correlation is found to be almost the same as that obtained directly from gedmetrical considerations. Mathematical Model A model is developed as shown in Figure 1 according to the following assumptions. (1)The W/O emulsion drop is a rigid sphere with radius Ro. The inner core of the W/O emulsion drop for 0 5 r I Ri is composed of the aqueous and the organic phases, while the outer liquid membrane for Ri I r IRo is composed of the organic phase only. The volume fraction of the aqueous phase in the inner core is constant and equal to 41. (2) The radius of an emulsified aqueous droplet, R,, is so small that the surface area of the emulsified aqueous phase is very large in comparison. Due to the large contact area, the organic phase and the inner aqueous phase are at equilibrium at any given location of the inner core. The values of R, and Ro were observed to be about 2.6 pm and 0.0264 cm, respectively. According to Casamatta et al. (1978), if A J A = @(Ro/R,),with the experimental value of 4 = 0.5, A P I Awould become 51. In addition, phenol 0 1983 American Chemlcal Society
168
Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1983
#
c
-
Figure 1. Model of a liquid membrane for phenol removal
diffuses through the emulsified aqueous phase at a faster rate than it does through the continuous organic phase in the W/O emulsion drop. Therefore, it is believed that phenol is in equilibrium with the emulsified aqueous phase and the organic phase at any given location of the inner core. (3) As phenol diffuses through the outer organic liquid membrane, the aqueous solution, initially containing NaOH only, is neutralized into a C8H50Nasolution and the radius of the unreacted inner core, c, shrinks. Phenol disappears by the acid-base reaction at the surface of the unreacted inner core, i.e., r = ri, and the concentration of phenol is zero at this surface. In the reacted inner core for ri 5 r 5 Ri, phenol diffuses through the aqueous phase as well as through the organic phase, and the two phases are in equilibrium at the same location. (4) The diffusivities of phenol in the organic and the aqueous phases are constant and independent of the concentrations of phenol and C6H50Nasince their concentrations in the W/O emulsion drop are very low. (i) Mass Balance of Phenol in the Outer Aqueous Phase
3Ve/R0is the total surface area of the W/O emulsion drops and k ( C , / n ~ l ~-=Co) ~ is the mass flux of phenol at the surface of the \sl/O emulsion drop. (ii) Mass Balance of Phenol in the Outer Liquid Membrane of Organic Phase for Ri < r < Ro. The liquid membrane is composed of the organic phase only and the mass balance can be written
(iii) Mass Balance of Phenol in the Reacted Inner Core for ri < r < Ri(CI1). For the reacted inner core, the volume fraction of the aqueous phase is q!J1 and that of the organic phase is 1- c$~.The mass balance can be written
(
l-q!J1+a): - =
(iv) Shrinkage Rate of the Unreacted Inner Core Radius (Ti)
-$( d
4W%Wt4 3MN
)=
The left side of the above equation represents the change of the equivalent of the NaOH solution in the unreacted inner core, and the right side is the transfer rate of the phenol which diffuses in at the radius, r = ri. The above equation can be rewritten
The initial conditions for Co, CI, CII, and ri and the boundary conditions at r = Ro,Ri, and ri can be expressed as follows t = 0: Co(0) = Coi, CI(O, r ) = 0 CII(O, r ) = 0 , ri(0) = Ri
C I ( ~Ri) , = C I I ( ~Ri) , r = ri CII(t, Ti) = 0 Equations 1to 4, together with their initial and boundary conditions, can be transformed into dimensionless equations through the following dimensionless variables. W = Co/Coi; x = r/Ro; xi = ri/Ro
VI = rCI/RoCoi; VI, = rCII/RoCoi
Through VI and VI, can the diffusion equations of the spherical coordinate be transformed into those of the rectangular one. Computer simulation can be performed by the Crank-Nicolson implicit method (Carnahan et al., 1969; Crank, 1975). Experimental Section The authors (Ihm et al., 1981) have made experimental investigations of phenol removal from wastewater by the liquid membrane technique employing pilot-scale operations. New beaker-scale experiments, however, have been carried out in the present study to corroborate the proposed model and to examine the effects on the removal rate of the NaOH concentration, initial phenol concentration, and volume ratio of W/O emulsion and phenol wastewater. The equipment used consisted of two beakers (400 and 2000 mL), two stirrers, and sampling beakers (10 mL). A marine-type mixing impeller was used in the mixer for thorough axial mixing and a four-paddle impeller was used in the emulsifier. In the emulsifier (400-mL beaker), the W/O emulsion was prepared by adding the aqueous NaOH solution to the surfactant solution while mixing at a velocity of 1300 rpm for 10 min. The surfactant solution used was mineral oil (paraffin oil with carbon number of 12 to 18) containing the hydrophobic surfactant known as Span 80 (HLB = 4.3). The W/O emulsion was then mixed with the aqueous phenol solution in the mixer (2OOO-mL, beaker) at a velocity of 200 rpm to make the W/O/W emulsion. The range of experimental variables was chosen such that good emulsion stability could be maintained. After the stirrer was started, samples were taken at desired time
Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1933 169
intervals by means of the sampling beakers. The concentration of phenol in the aqueous phase was analyzed by a UV spectrophotometer.
Estimation of Parameters for Computer Simulation (1) Radius of the Inner Aqueous Solution Droplets in the W/O Emulsion (R,,). The W/O emulsion prepared in the emulsifier was photomicrographed with a small amount of water soluble dye, Neutralrot (Merck Co.), added to the aqueous NaOH solution for better contrast. From the photomicrographs, the radius of the aqueous NaOH solution droplets was observed to range from 0.5 to 5 pm. It was found that the smaller the aqueous droplets, the more stable the W/O emulsion (Becher, 1966). The W/O emulsion was prepared by intensive mixing to make the aqueous droplets as small as possible. The average radius was about 2.6 pm. The size distribution of the aqueous droplets did not vary considerably within the experimental range of the NaOH concentration (0.25-1 wt
0 r=R
Rua r=R -R
o
2Rua
r-R - 2 R
ua
0
Y
lia
Figure 2. Frequency of the center of the inner aqueous solution droplets per volume of W/O emulsion as a function of the distance from the W/O emulsion surface.
%).
(2) Radius of the W / O Emulsion Drop in Mixer (Ro). The W/O emulsion was fed to the aqueous phenol solution in the mixer at a velocity of 200 rpm and the resulting W/O/W emulsion was photographed. A strip of 1 mm width was attached to the inside wall of a 2000mL beaker and was compared with the size of the W/O emulsion drop. To see the W/O emulsion drop clearly, Neutralrot was again added to the aqueous phenol solution. The average drop radius Ro of 0.0264 cm was determined after counting more than one thousand drops. Ro was observed to be independent of the NaOH concentration, phenol concentration, and small changes in the value of Vel vw. (3) Measurement of the Distribution Coefficient ( m )of Phenol between the Organic and the Aqueous Phases. The aqueous phenol solution was added to the oil phase with sufficient mixing. After the phenol had reached equilibrium with the aqueous phase and the mineral oil, the stirrer was removed. The aqueous phase and the mineral oil were separated by their different densities and the concentration of phenol in the aqueous phase was analyzed. The concentration of phenol in the mineral oil was determined by mass balance. The value of m was calculated to be about 0.13, obeying Henry's law as the concentrations of phenol in the experiment were small. It was found that the presence of Span 80 up to 1 wt % had little effect on the value of m. (4) Estimation of Diffusivities of Phenol in the Organic and the Aqueous Phases (Doand D,). Do and D, can be predicted by the Wilke-Chang equation (Reid et al., 1977),which is available for dilute solutions. The association parameters for the solvents were taken as 2.6 for water and unity for unassociated oil. The molar volume of phenol at its normal boiling point is 100. The viscosity of mineral oil is measured to be 42 CPand its average molecular weight is chosen to be 212. Do and D, are estimated to be 4.527 X lo-' cm2/s and 9.3588 X lo* cm2/s, respectively, at 293 K. (5) Estimation of the Mass Transfer Coefficient (k).The mass transfer coefficient k at the surface of the W/O emulsion drop is expressed as D,/6. The boundary layer thickness of the concentration, 6 , can be assumed to be very small as the stirring at 200 rpm appeared to be quite intensive. Since the ratio D,/Do is 20.7 by the Wilke-Chang equation, D, is much larger than Do and the diffusion in the outer aqueous phase is much faster than the diffusion in the organic liquid membrane. Thus, the mass transfer resistance at the surface of the W / O
'b
0,
I
I
r-R
r=Ro-2RNb
r=R - 2 R 0
ua
r=Ro-2R
LIC
Figure 3. The cumulative profile of 6 as a function of the distance from the w/o emulsion surface; bal = 0.267, &Jbl = 0.133, and = 0.100.
emulsion drop is negligible since Iz is large enough. Equilibrium between the outer aqueous phase and the surface of the W/O emulsion drop may be assumed. It was found from numerical computation that an equilibrium can be justified if the value of k is larger than 0.01 cm/s. In the present study, 0.02 cm/s was used for the numerical computations. (6) Estimation of the Initial Radius of the Unreacted Inner Core ( R J . In the present mathematical model, the volume fraction of the inner aqueous phase is @1 for 0 Ir IRi and 0 for Ri < r 5 Ro. As the W/O emulsion in the experiment was made by intensive mixing in the emulsifier, it can be seen that the inner aqueous droplets' center with radius R, will be seen at a frequency offal for 0 Ir IRo - R,, and 0 for Ro - R,, < r IRo. In Figure 2, fa is shown as a function of the distance y from the surface of the W/O emulsion drop. Thus, the volume fraction @,, of the inner aqueous phase by the droplets with radius R,, will be constant at @al for 0 Ir 5 Ro - 2R,,, as shown in Figure 3. I t decreases with the radius at Ro 2R,, Ir IRo and becomes zero at r = Ro. As the ratio of Ro/R, was observed to be about 100, the thin shell for Ro - 2R,, Ir IRo can be considered as a flat slab. In Figure 4, an aqueous solution droplet with radius R,, in the vicinity of the W/O emulsion surface is described. @a for 0 5 y I2R, (i.e., Ro - 2R, 5 r IR,) can be expressed as
170
Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1983
Since 4, = 4al at y = 2R,, one can obtain
Equation 5 describes the profile of 4, as a function of y for 0 I y I 2R,,: The aqueous droplets show the size spectrum to be wthin the range of R, = 0.5 to 5 pm. The cumulative profile of 4 is ascertained by adding the contributions from this size distribution (Le,, $ = & &, + &). Figure 3 shows one example where the values of R,,, Rub,R, are 2.6, 1.5, and 3.7 pm, respectively, and also when #al, 4b1, &l are taken as 0.263, 0.133, and 0.100 to make 41equal to 0.5. Thus the value of Ri is determined by the distribution of R, and Ro. Accordingly, Ri is independent of the initial phenol concentration, NaOH concentration, or small changes in VelV , as R , and Ro are not affected by the concentrations and changes. By eq 5 and Figure 3, it can be seen that Ri = Ro - R, and Ri becomes 0.99Ro with the average size of R, (recall that Ro/R, N 100). Ri is obtained by adjusting the computer simulation to the experimental results with the following conditions: NaOH concentration = 1 wt %, initial phenol concentration = 1000 ppm and V,/V, = ll3. When Ri = 0.9906R0,the computed results agree very closely with the experimental data as will be seen in the next section. One can see that Ri obtained in this manner is nearly consistent with the geometrically estimated value of Ri (i.e., 0.99Ro).
+
Experimental Correlation With the value of Ri obtained from the aforementioned conditions, the computer simulation has been performed by changing other variables and compared with the corresponding experimental results. ( 1 ) Effect of NaOH Concentration. With Ri = 0.9906R0 obtained at 1 wt % NaOH concentration, computer simulation is performed at 0.25 wt % NaOH concentration and compared with the experimental results. Figure 5 shows a strong agreement between the computed results and the experimental data. When the NaOH concentration is decreased from 1wt % to 0.25 wt 9%,the radius of the unreacted inner core, ri, shrinks more rapidly and the mass transfer resistance to phenol removal would increase. Thus, at a lower NaOH concentration, phenol is removed more slowly. As can be seen in Figure 5, there is a great difference in ri between 1wt % and 0.25 wt % NaOH concentrations, but the difference in the rate of change of Co is not that significant. The mass transfer resistance in the organic liquid membrane for Ri < r 5 Ro seems to be far larger than that in the reacted inner core for ri 5 r 5 Ri. (2) Effect of Initial Phenol Concentration. Computer simulation is performed at an initial phenol concentration of 3000 ppm with Ri obtained at the initial phenol concentration of lo00 ppm. The computed and the experimental results are shown in Figure 6. With higher initial phenol concentration, ri shrinks more rapidly and the mass transfer resistance for phenol removal becomes larger. The value of Co/Coidecreases more slowly when the initial phenol concentration increases from lo00 ppm to 3000 ppm. (3) Effect of the Amount of W/O Emulsion Solution. With Ri obtained at VelV , = ll3,a computer solution of the model equations is obtained at VelV , = ll4. Figure 7 shows that as the ratio of VelV , decreases from to 1/4, phenol is removed more slowly. As the ratio of VelV , is decreased, the surface area for phenol removal, 3Ve/Ro,is decreased and ri is decreased more rapidly.
Figure 4. The view of the inner aqueous solution droplet with radius R, in the vicinity of the W/O emulsion surface. 1000
1.0
900
0.9 TEMPERATURE:
ZO0C
M I X I N G I N T E N S I T Y : 200 r p m I N i T I A L PHENOL CONC.: 1000 ppm
800
Iwt
SURFACTANT CONC.:
-5
o,B
%
- 0.7
700 NaOH conc. 0.25wt Z NaOH conc.
lwt
X
?o
I
z
0
600
4 c
z *
g
::
500
d w
5 400
300
- 0.3
200
-
0.2
100
1
2
3
4
5
6
7
8
9
1
0
MINUTE
Figure 5. Effect of NaOH concentration on phenol removal as a function of time; computed and experimental results.
Discussion (1) Mass Transfer Resistance. In the present system of phenol removal, the main resistance to mass transfer exists not in the reacted inner core but in the external organic phase layer. This is proven by the phenol removal rate, which is much less sensitive than the shrinking rate of the unreacted inner core as shown in Figures 5,6, and 7 to experimental variables such as the NaOH concentration, initial phenol concentration, and volume ratio of Ve/V,. This phenomenon can also be explained by the sensitivity of the phenol removal rate to small differences in the thickness of the outer oil layer. Figure 8 shows that for a given value of Ro the removal rate increases abruptly with small increases of Ri/R,. Reasons for this include the fact that the ratio of D,/Do is very large (20.7) and that the distribution coefficient is relatively small (rn = 0.13). The merit of the shrinking core model proposed in this paper could well be established if the removal rate were directly related to the shrinking rate. Even if the effect of shrinkage does not appear to be very large, it is obvious that the shrinking core model can explain the effects of
Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1983 171 1.0
1.0
1.0 NaOH SOL./SURFACTANT
SOL.
= 1
I N I T I A L PHENOL CONC. = 1 0 0 0 ppm
0.9
0.9
0.9
I N I T I A L NaOH CONC. = 1 w t % Ve/Vw = 1 : 3 Ro = 0 . 0 2 6 4 c m
0.8
0.8
0.7
0.7
MIXING INTENSITY: 2 0 0 r p m lwt % I N l T I A L NaOH CONC.:
0.6
SURFACTANT CONC. :
0.8
k = 0.02 c m l s e c m = 0.13
0.7
0.6
0,
=
4 . 5 2 7 E-07 cm2/sec
0
=
9.3588 E-06 cm'lsec
0.6
lwt %
NaOH SOL./SURFACTANT SOL. = 1
y00.5
ve/vw
u
= 1 : 3
0.5
, u
Computed r e s u l t X
"
3000 ppm i n i t i a l p h e n o l
0.4
0.4
.
..-. 0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
1
2
4
3
5
6
7
a
9
:0
0
10
MINUTE
Figure 6. Effect of initial phenol concentration on phenol removal as a function of time; computed and experimental results. 1000
900
aoo TEMPERATURE:
20°C
200 rpm 1000 ppm SURFACTANT CONC.: I w t 4, I N I T I A L NaOH CONC.: l w t 'i NaOH SOL./SURFACTANT SOL. = 1
MIXINC, INTENSITY:
I N I T I A L PHENOL CONC.:
700
-H
5 600 z
CI-c cv,
0
O0 T
c
B
0.5
500
z
J 2 x=
FS
::
-n
2
0x0 z 1
400 &
300
200
100
0
1
2
3
4
5
6
7
8
g
0.3
10
WINLTE
Figure 7. Effect of V J V , on phenol removal as a function of time; computed and experimental results.
the differences in concentration of NaOH and phenol on the removal rate while a model without shrinkage or with a uniform core cannot.
1
2
3
4 5 MINbTE
6
7
8
9
10
Figure 8. Computed results of phenol removal as a function of Ri/Roand time.
(2) Effects of Other Parameters, R o and m. Even though computed results on the effect of Roand m are not given here, they comply well with physical phenomena. In spite of the change of Ro,the difference, Ro- Ri, will not vary unless R, changes. According to the model solutions with a constant value of Ro- Ri, phenol is removed more rapidly as Rois decreased because the surface area for mass transfer 3 VelRois increased. The value of Rowill become smaller as the mixing intensity in the mixer becomes more intense. On the other hand, phenol is removed more rapidly as m becomes larger because phenol is more soluble in the organic phase. The value of m changes when CH,COOH or H2S in wastewater is removed or when organic materials other than mineral oil are used.
Conclusions A model for the removal of phenol from wastewater by using a liquid membrane is proposed for the initial stage, and computed results are discussed. Study of the proposed model reveals the following essential points. (1)Riis determined to be 0.9906Roby adjusting the computer solution to the experimental results with conditions of 1wt % NaOH concentration, 1000 ppm initial phenol concentration, and VelV, = After Rihas been obtained, computer simulation is performed and compared with the experimental results for different values of these variables. The results agree fairly well with the experimental data. (2)Geometrically, Riis estimated to be 0.99Ro,a value very close to the value of 0.9906R0obtained from the numerical solution. This seems to be evidence of the validity of the geometrical estimation of Ri. (3) The proposed model can aid in predicting the kinetics of wastewater treatment by liquid membrane and in better understanding the mechanism in various separation techniques by liquid membranes.
Ind. Eng. Chem. Fundam. 1983, 22, 172-176
172
Nomenclature A = surface area of a W/O emulsion droplet, cm2 A , = surface mea of all emulsified aqueous droplets in a W/O emulsion drop, cm2 C, = concentration of phenol in the outer aqueous phase, g/cm3. Coi = initial concentration of phenol in the outer aqueous phase, g/cm3 CI = concentration of phenol in the organic liquid membrane phase for Ri < r 5 Ro, g/cm3 CII = concentration of phenol in the organic phase of the reacted inner core for ri 5 r 5 Ri, g/cm3 Do = diffusivity of phenol in the organic phase, cm2/s D , = diffusivity of phenol in the aqueous phase, cmz/s fa = frequency of the center of the aqueous droplets with radius, R,,, per unit volume of the W/O emulsion fal = frequency of the center of the aqueous droplets with radius, R,,, per unit volume of the W / O emulsion for 0 5 r 5 Ro - R,, HLB = hydrophile-lipophile balance k = mass transfer coefficient between the outer aqueous phase and the organic liquid membrane phase, cm/s m = distribution coefficient of phenol between the aqueous and the organic phases MN = molecular weight of NaOH M , = molecular weight of phenol R = radius of an emulsion drop, cm r = radius, cm Ri = initial radius of the unreacted inner core, cm ri = radius of the unreacted inner core, cm R, = radius of the W/O emulsion drop, cm R, = radius of the emulsified aqueous droplet, cm R,,, Rrb, R,, = radius of the emulsified aqueous droplets, respectively, cm R- = radius of the inner core of an emulsion drop, cm t = time, s V , = total volume of the W / O emulsion, cm3 V , = total volume of the aqueous phenol solution, cm3 VI = dimensionless concentration of phenol, rCI/RoCoi VI, = dimensionless concentration of phenol, rCII/RoCoi W = dimensionless concentration of phenol, Co/Coi W , = concentration of NaOH in the inner aqueous phase, g/cm3
W/O = water-in-oil W/O/W = water-in-oil-in-water x = dimensionless radius, r / R o xi = dimensionless radius of the unreacted inner core, r i / R o y, y' = distances from the surface of W/O emulsion drop, cm Greek Letters 6 = boundary layer thickness of the concentration at the surface of W/O emulsion drop, cm 4 = volume fraction of the aqueous phase in the W / O emulsion drop &, $b, & = volume fractions of the aqueous phase by droplets of radius, R,,, Reb,and R,,, respectively 4al = volume fraction of the aqueous phase by droplets of radius, R,,, for 0 5 r 5 Ro - 2R,, 41= volume fraction of the aqueous phase in a W/O emulsion drop for 0 < r < Ri T , = dimensionless time, Dnt/Rn2
Registry No. NaOH, 1310-73-2; C6H,0H, 108-95-2.
Literature Cited Alessi, P.; Kikic, I.; Canepa, B.; Costa, P Sep. Sci. Techno/. 1978, 13, 613. Becher, P. "Emulsions: Theory and Practice", 2nd ed.; Reinhold Publishing Co.: New York, 1966. Boyadzhiev, L.; Sapundzhiev, T.; Bozenshek, E. Sep. Sci. 1977, 12, 541. Cahn, R. P.; Li, N. N. Sep. Sci. 1974, 9 , 565. Carnahan, B.; Luther, H. A,; Wilkes, J. 0 . "Applied Numerical Methods"; Wiley: New York, 1969; pp 446, 451. Casamatta, G.; Chavarie, C.; Angelino, H. AIChE J . 1978, 2 4 , 945. Crank, J . "The Mathematics of Diffusion"; 2nd ed.; Clarendon Press: Oxford, 1975; pp 144, 286. Cussler, E. L.; Evans, D. F. Sep. Purif. Methods 1974, 3 , 339. Ihm, S.K.; Kim, K. S.; Choi, S. J. J . Korean Inst. Chem. Eng. 1981, 19, 217. Li, N. N. AIChE J . 1971a, 1 7 , 459. Li, N. N. Ind. Eng. Chem. Process Des. Dev. 1971b, 10, 215. Li, N. N.; Shrier, A. L. In "Recent Developments In Separation Science", Li. N. N., Ed.; Chemical Rubber Co.: Cleveland, 1972; Vol I, p 163. Matulevicius, E. S.;Li, N. N. Sep. fur;f. Methods 1975, 4 , 73. Reid, R. C.; Prausnitz, J. M.; Sherwood. T. K. "The Properties of Gases and Liquid"; McGraw-Hill: New York, 1977; p 567. Shah, N. D.; Owens, R. C. Ind. Eng. Chem, Prod. Res, Dev. 1972, 1 1 , 58.
Received f o r review November 30, 1981 Revised manuscript received December 21, 1982 Accepted January 19, 1983
Continuous Multicomponent Parametric Pumping Wu Xlang-Zhlt and Phillip C. Wankat' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 4 7907
A new parametric pumping method which will fractionate two noninteracting solutes is developed. Cyclic steady-state experimental results for separating pyrene from acenaphthylene in 2-propanol are reported. Results from a short column disagreed qualitatively with the local equilibrium theory. A reverse separation was observed. I n a longer column results were in qualitative agreement with the same theory. A staged equilibrium model was in good agreement with single-component separation data from both long and short columns. With two solutes present, however, agreement was only qualitative because the acenaphthylene is more strongly adsorbed when pyrene is also present.
Introduction Parametric pumping systems have been extensively studied Over t h e past dozen y e w s a n d has been reviewed t Department of Chemical Engineering, Beijing Institute of Chemical Technology, Beijing, China.
0196-4313/83/1022-0172$01.50/0
by Sweed (1971), Rice (1976), Chen (1979), a n d Wankat (1981). Most of the articles on Parametric Pumping have been concerned with either removing a single solute from a nonsorbed material or separating two ions by ion-exchange parametric pumping. Separation of noncompeting solutes a n d of competing solutes or ions is quite different. I n the former system the 0 1983 American Chemical Society
