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Rates of extraction of cobalt from an aqueous solution to D2EHPA in a growing drop cell
Hydrometallurgy, 13 (1985) 249--264
249
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
RATES OF EXTRACTION OF COBALT FROM AN AQUEOUS SOLUTION TO D2EHPA IN A GROWING DROP CELL
M.A. HUGHES
Schools of Chemical Engineering, Bradford University, Bradford (Great Britain) and T. ZHU
Institute of Chemical Metallurgy, Academy of Science of China, Beijing (China) (Received November 11, 1983; accepted in revised form July 24, 1984)
ABSTRACT Hughes, M.A. and Zhu, T., 1985. Rates of extraction o f cobalt from an aqueous solution to D2EHPA in a growing drop cell. Hydrometallurgy, 13: 249--264. A technique has been developed to study the rate of extraction o f cobalt from an aqueous phase into a growing drop of heptane containing di(2-ethylhexyl) phosphoric acid (D2EHPA). The hydrodynamics of the growing drop are accounted for. Experiments have been carried out at the single temperature of 25 -+ 0.1°C where the pH, aqueous cobalt concentration and the organic D2EHPA concentration have been varied. A mathematical model is given which is based upon the control of rate by mass transfer with chemical reaction. The model fits the experimental data well considering the experimental errors and the complexity of the transfer of solute where fresh surfaces are continually produced by the growing drop.
1. INTRODUCTION
In some industrial liquid--liquid extraction contacting equipment used for metals extraction, the mass transfer will take place between the dispersed drops and the continuous phase. Although the mass transfer parameters for the real commercial equipment cannot be inferred from the ones obtained in experiments involving individual drops, the study of single drops can be significant in the isolation of the most important mass transfer characteristics of the liquid--liquid extraction system. Thus one may be able to distinguish between chemical or diffusion control or control b y contributions from both of these. This is w h y mass transfer to and from single drops has been investigated widely in a number of systems involving not only metal solutes but also organic ones [1]. Three stages will be involved in the total life time o f a drop in a contactor, that is, formation, travel and coalescence. Every stage is important for the mass transfer study, however much of the total transfer takes place during
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© 1985 Elsevier Science Publishers B.V.
250 the drop formation period. The methods previously used for the experimental determination of the transfer during the formation stage are reviewed by Walia and Vir [2]. The early models which were developed in order to describe mass transfer to the growing drop immersed in a continuous phase, are almost all based on the penetration theory and involve molecular diffusion. These models are summarised by Popovieh et al. [3] and t h e y can be represented b y the equation o f general form: J =~
(cl - c2)
where J is the mass transfer flux at time t, D is the diffusivity o f transferring species and (cl - c2) is its concentration difference within the diffusion film; is a constant dependent u p o n the behaviour o f the growing boundary layer and differs from one model to another. Some models developed later [4] can also be adapted so that t h e y accord to the above equation. The models are only valid for the case where no extra mass transfer occurs due to liquid flow, i.e., the drop is growing at a moderate speed and the interface is stable. In other words strong local eddy diffusion near the interface is not taken into account. It has been noticed before that when the drop is grown rapidly, the jet action [5] and internal circulation [6, 8] will enhance the mass transfer markedly, but when the rate of growth is very slow the free convection inside the drop will be the major factor affecting the rate of mass transfer. Walia and Vir [2] designed a model which t o o k the convective flow of fluid around the drop, the curvature of the boundary layer and the concentration change in both continuous and dispersed phase into account. The model fitted data better than other models but was applied only to mass transfer of organic solutes without chemical reaction. Skelland and Minhas [9], in their empirical model, considered all of those parameters which could influence mass transfer such as velocity of liquid through the nozzle, drop diameter, the inside diameter of the nozzle, diffusivity of the transferring solute, density, viscosity of the dispersed phase and interracial tension. The model then fitted extensive experimental results quite well. Zimmermann, Halwachs and Schfgerl [7] recently determined the mass transfer during the growth of a drop, and came to a conclusion that as the resistance located in the continuous phase increases, the drop formation rate has less influence on the mass transfer rate. Until now only a few research workers have seriously studied the mass transfer with chemical reactions during drop formation for metal solvent extraction systems. The advantages of the growing drop cell are several. Mass transfer at a known area accommodating known convective transport can be analysed. Fresh surfaces are generated and impurities cannot accumulate at the interface and it bears relevance to certain contactors since drop formation is that part of the hquid--liquid contacting process where a majority of solute transfer takes place.
251 Nakashio et al. [10] investigated the UO2(NO3)2--tri-cresyl phosphate and HC1--Amberlite LA-2 system during drop growth and drop travel. In their model, a pseudo first order reaction at the interface as a boundary condition for unsteady state diffusion was assumed and the t h e o r y o f life time distribution of drop surface elements was used to describe extraction to the growing drop. Bauer [11] studied the transfer in the Cu--KELEX 100 system in a growing drop cell and derived an empirical model based on the overall chemical eaction equation with a correcting factor for interfacial turbulence. Despite the fact that di(2-ethylhexyl) phosphoric acid (D2EHPA) has been established as an important commercial reagent for the solvent extraction of cobalt and uranium, comparatively few papers have been devoted to the kinetics and mechanisms involving this extractant. Brisk and McManamey [12] have studied the equilibrium and mass transfer respectively by means of an "equilibrium extraction technique". They observed an interfacial resistance to mass transfer and explained it in terms of chemical kinetics of the extraction reaction. These workers used a crude constant interface cell which must have operated with significant diffusion problems at the interface. Golding and his co-workers [13, 14] measured the mass transfer coefficients in the D2EHPA--cobalt and D2EHPA--nickel systems using both a pulsed sieve plate column and a modified Lewis cell. They reported that there was a resistance to mass transfer in both organic and aqueous phase and the mass transfer rate was diffusion controlled. A recent paper by Ajawin et al. [15] describes the extraction of zinc by D2EHPA using a constant interface cell. Despite postulating a mechanism involving interfacial species, the analysis does not use the concentration of such species but only the bulk phase values. Furthermore these workers have analysed rate data for aqueous solutions with ionic strengths of up to 1.0 kmol m -3. Their use of the simple Debye-Hfickel equation is unsound since it only applies to low ionic strengths of less than about 0.1 kmol m -3. Surfaces will be saturated at the concentrations of extractants used in these studies. Some account must be taken of the partitioning of the D2EHPA into the aqueous reaction film. The kinetics of extraction of cobalt and nickel by phosphorus-based extractants are therefore only little understood. In this work a technique for research into mass transfer during single drop formation was developed. The system studied was D2EHPA in heptane with cobalt in an aqueous sulphate media; concentrations of importance to industry were employed. 2. A MODEL FOR MASS TRANSFER WITH CHEMICAL REACTION IN AN AQUEOUS DROP GROWING AT A NEEDLE TIP The model which is described in this paper is one based on that developed by V. Rod [16] for the extraction of metals with organic acids in liquid-liquid extraction systems. However, this last worker's model was originally
252
used to explain the results from a fixed area transfer cell. The present work involves an experimental system which is quite different, e.g., where organic drops grow at a needle tip immersed in an aqueous phase. The model has to be adapted for this new experimental approach.
_C
T
I
HR
M-
CH
I
1
I
I I
I
I - -
I i
l
-CMR2
CMR2H2R~_~ .... : :
I
CHR
,NTE~FACE I
ORGANIC
i
AQUEOUS
Fig. 1. Concentration profiles in the diffusional films.
When the extractant D2EHPA (HR) in the organic phase is brought into contact with the cobaltous ion in the aqueous solution, the following steps, which consist of partition and chemical reaction, will occur, with superscript bar representing those species in the organic phase:
Ks H2R2
~
2 HR
(1)
P~R HR
(2)
HR KA H+ + R-
(3)
R- + Co 2+ kf CoR +
(4)
CoR + + R- ~- CoR2
(5)
CoR2 PMR~ CoR2
(6)
Ko CoR2 + H2R2 -~ CoR2 • H2R2
(7)
253 In this model the extractant is taken to exist in the organic phase in b o t h the dimer and m o n o m e r form, an equilibrium exists between them as expressed in eqn. (1). The overall reaction can be described b y the equation:
Kex
2 H 2 R 2 + C o 2+ ~
CoR2" H 2 R ~ + 2 H ÷
(8)
In these equations kf is the forward reaction rate constant for reaction (4), Ka is the acidic dissociation constant of D2EHPA in the aqueous reaction zone, P~R is the partition constant of D2EHPA and PMR2 is the partition constant of the metal complex. In the present analysis we assume reaction (4) to be the rate determining step and the other reactions are so fast that they are in effect at equilibrium. (In other analyses, reaction (5) might be taken as the rate determining step.) In the aqueous film an overall reaction involving m o n o m e r is assumed, i.e. 2 HR + Co 2+ K eq CoR2 + 2 H +
(9)
The flux o f the extractant H R at the interface, JHRi, is given b y [16] :
JHRi
r kfgaDHRCMi L
2 CHiP~R
(
~MR2iCHiKo 1
-
)
KexK2C~RiCMi
1/2 (C~Ri-- C ~ R ) ]
(10)
We note that: Keq -
Kex Ks P~I~ Ko PMR2
(11)
Equation (10) is similar to that of R o d [16], and only differs because the extractant is considered to be present as a dimer in equilibrium with the m o n o m e r in the organic phase but it is the m o n o m e r which is distributed to the reaction zone and which undergoes the reaction. A second difference is because the product is further complexed b y a dimer as in eqn. (7). Now we must take into account the nature of the changing surface area during the drop formation. In the case of a growing drop, not only is the interfacial area changing with time, b u t the mass transfer coefficient is changing as well. During the drop formation, see Fig. 2, the instantaneous mass balance of the transferred species in the drop can be considered as: I
d(VC) _ JA + FCo dt
(12)
V and A are the volume and area of the drop respectively. J is the mass transfer flux and F is the rate of the flow of the organic phase from the needle tip. C0 is the initial concentration of the transferring species in this phase and is the instantaneous concentration o f the transferring species in the drop. Then:
254
= dt
+.
(13)
dF
7
Here dF is the final diameter of the drop and tF is the total formation time for a drop, i.e., the drop life time; this is the time which is varied in these experiments.
I
F
Fig. 2. Scheme of the growing drop. In the case of the organic phase forming a drop at the needle tip the main resistance to the mass transfer with chemical reaction is in the film on the aqueous side of the drop. On the inside of the organic drop the mass transfer is based on penetration theory [1] and so eqn. (15) can be used to describe this part of the resistance to the overall transfer process. The complete model therefore includes the following equations for the changes in the species HR: d~HR = j 6 dt
( ~ ) 1/3
dF
+
~HR0 __ ~H R
(14)
kHR = 13, .I 2:-" V nt
(15)
where kHR is the overall mass transfer coefficient o f HR. DHR is the diffusivity of HR in the organic drop and ~3, is some constant.
JHRi= _I. OMi L2 CHi
KOOMZ iO 'i l
[1 -- K ~ M i I
(C&Ri-- CHR)
(16)
where 0 , = k f K a D H R / P ~ R .
CHR =
+
CMR2i + O2 CHRi }
(17)
255 where =
DHRPMR2Ko
(18)
DMR2PI-IRK2
CHai= CHa
--JHai
(19)
kHR CMa2i = CMR: + 0.5 ----JHRi
(20)
~MR: CMi = CM
JHRi kM
JHRi
CHi = CH + 0.5 - kH
(21) (22)
Equations (19)--(22) are the ones for the concentration of the species at the interface based u p o n the flux of the extractant. It is now assumed that for the individual film mass transfer coefficients the following identities hold:
~MR~ -~ ~HR kM = ~2 ~HR k H = kM where ~2 = (DHR//)HR) ln, and diffusivities can be estimated b y the Wilke and Chang method [18]. We have to use bulk phase diffusivities because diffusivities in the film are not available. It is assumed that the concentrations of cobalt and the proton ion do not change during these experiments, because the system is buffered and there is a large excess of cobalt, s_o CM and CH are constant. The organic concentration of cobalt complex, CMR2, in the drop at different drop formation times can be calculated from the above model. The parameters in the model were evaluated b y the Marquardt method. The sum of the weighted squared root deviations of the values of the CMR2 concentrations calculated b y this p r o c e dure, compared with the experimental ones, was minimised. The differential equation, eqn. (14), was integrated numerically by the Runge--Kutta--Merson method in conjunction with the differential material balances of the reactions expressed in eqns. (17)--(22).
3. EXPERIMENTAL
3.1. Apparatus A diagram of the growing drop cell is shown in Fig. 3. The internal volume of this thermostatted cell is about 150 ml. The drops grow at the needle tip
256
and travel ab o u t 15 mm before reaching a narrow neck, N, which is of length 15 mm and o f I.D. 3 mm. A narrow bore plastic tube, usually Teflon of I.D. 1 mm, is placed in this narrow neck and is c o n n e c t e d via a vacuum to the sample tube. The h y p o d e r m i c needle used in this work was 33 gauge but any gauge may be used to p r o d u c e drops o f varying size.
BURETTE SAMPLING / TUBE
N _
VACuuM
IN TERFACE i
I
NEEDLE
AQUEOUS
,,...
ORGAN IC Fig. 3. Schematic diagram of the growing drop apparatus.
The system for obtaining a constant drop f o r m a t i o n t i m e consisted o f a b u rette attached to a stand with a fine height adjustment device. In this way a constant pressure head can be ke pt t h r o u g h o u t an experimental run. It is this constant head which can be varied f r o m one e x p e r i m e n t to anot her t o give different f or m at i on times for the drops. It should be n o t e d t hat the volu me o f a drop is d e p e n d e n t mainly on the needle tip diameter and the physical parameters o f the system, e.g., interfacial tension. The shortest practical drop f or m at i on times are around one second, while for long forma-
257 tion times of the drop (longer than t w e n t y seconds to form) the experiment becomes too extended in time.
3.2. Reagents D2EHPA was from BDH Ltd., Laboratory Grade reagent, and was used with further purification to give a product o f 99.8% in D2EHPA. Other reagents were from BDH Ltd. and were of AR grade. The aqueous solutions were buffered by additions of 0.5 mol dm -3 a m m o n i u m di(hydrogen phosphate}. The organic phase was various concentrations of D2EHPA made up in heptane without the addition of any modifier.
3.3. Technique for operation of the cell The drop formation cell was first filled with the aqueous solution under test and allowed to reach the temperature of the experiment. The burette was filled with the organic solution and that part of the solution in the tube leading to the needle was at the same temperature as the aqueous phase. The organic flow was then started and drops were seen to grow at the needle tip. After reaching a m a x i m u m size the drop broke from the tip, travelled the very short distance, before rising into the neck of the cell to be sucked away into the sample tube. The coalescence is considered to be absent because the drop is immediately sucked away and the effects of coalescence are ignored in subsequent analysis of the mass transfer. The drops appeared to be spherical. Although these would not be true spheres according to the theory of the drop growing at a needle tip, it is assumed that the error introduced through this assumption is negligible. The average formation time of a single drop is measured by counting ten drops and timing the total forming time for all these drops. The formation time, so measured, is considered to have an average deviation of about +5%. The average volume of the drop is obtained from the initial and final burette readings and the total drop number. For any one point on the experimental data plots shown in section 4, about one to two hundred drops are required. After any one run the aqueous pH changed by only 0.01 unit and the total cobalt in the aqueous phase changed by less than 2%. After the number of drops from a run had been collected in the sample tube, the total collecting system was rinsed with heptane and the final volume sample made up to 2 ml. In this way, any evaporation which occurred during the sampling was accounted for. The cobalt in the organic sample collected above was then analysed by a colorimetric method using the blue colour of the Co2÷--SCN - complex in acetone. A Pye Unicam SP8-100 spectrophotometer was used and concentrations were determined from calibration graphs. The analysis error was less than + 2%.
258 4. R E S U L T S A N D D I S C U S S I O N
The experimental results have been set d o w n in Figs. 4--8. The biggest discrepancy in the results compared with theory are at small formation times. W e believe this is due to turbulence in the droplet during this initial period and note that the same p h e n o m e n o n is observed in classical polarography leading to a maximum in the current voltage curve. In these experiments the main error was caused b y the complicated and changing hydrodynamic conditions around the forming drop. For example, if the needle tip had been previously wetted by the aqueous solution (even slightly) it affected the force balance of the forming drop on the needle tip and probably altered the mass transfer during formation. Comparing the duplicate experiments, it was estimated that the average error in the cobalt concentration in the organic phase was about 12%. 3O
'E o o
E E20 Q_ O rr r~ Z
~1o cn 0
"
5
10
is
o
3.403
•
3,625
+
2.849
2b
DROP FORMATION TIMEs Fig. 4. I n f l u e n c e of the aqueous solution pH o n the cobalt transfer in the growing drop cell. D 2 E H P A 0.286 m o l din -3, cobalt 0.0938 tool dm -3.
Some slight alteration in drop volume occurs when the formation time is made larger. This p h e n o m e n o n was also observed by Heertjes and DeNie [19]. Figures 4--8 show the experimentally found dependences of cobalt concentration in the total forming time of a drop. The calculated curves are based upon the model. It is obvious that all those data at very short formation times are much higher than those predicted b y the model: this is because there is enhancement of the mass transfer caused by high flow rate of organic phase in the initial stage. So far this aspect has not been taken
259
10
"?E 8 "E3
pH D2EHPA motd~ 0.286 2.849
O
0,429
2.984
O
E E
6
{2O rY [:3
z
4
H.J <~ r~
o
2
CD
i
s
i0
2'0
1~
DROP FORMATION TIME.s Fig. 5. C o b a l t t r a n s f e r in t h e growing d r o p cell for l o w e r pH c o n d i t i o n s . C o b a l t 0 . 0 9 3 8 m o l dm -3.
301
/
.Y
Oq
'E
q~
/
/
o 20
E E
Y
[2_ O
f •
pH 3.625
o
3.367
Zl0 cn oQ)
5
10
15
20
DROP FORMATION TIME s Fig. 6. I n f l u e n c e o f t h e a q u e o u s s o l u t i o n p H o n t h e c o b a l t t r a n s f e r in t h e growing d r o p cell. D 2 E H P A 0 . 5 7 2 tool dm-% c o b a l t 0 . 0 9 3 8 m o l d m -3.
260
30 I
E
Rz)
f
-6 E 20 E CL O OC d3
-ZlO
COBALTmo,
m o c)
5
10
o
o.o188
+
0.047
•
0,0938
15 20 DROP FORMATION TIME. s
Fig. 7. Influence o f the cobalt concentration on the cobalt transfer in the growing drop cell. D 2 E H P A 0.572 tool dm 3, pH 3.626.
30 C'3
IE o
E E 20 CL O OC C3
D2EHPA moi drE 3 •
"
o
0.286
•
Q572
Z
©
s
lb
1'5
~0
DROP FORMATION TIME. s Fig. 8. Influence of D 2 E H P A concentration on the cobalt transfer in the growing drop cell. Cobalt 0 . 0 9 3 8 tool dm -3, pH 3.403.
261
into account in the model. When the formation time was less than three seconds, the linear velocity inside the needle is higher than 50 mm s -1 and the Reynolds number is as high as 10 to 30. The observed enhancement was also described b y other workers [6, 8], where drops are grown for short periods. The equilibrium distribution of cobalt between the organic and aqueous phase for the system has been measured in separate experiments and the extraction equilibrium constant Kex = 10 -s's has been evaluated. The resulting values of the parameters of the model from the optimization are listed in Table 1. The last column of the table contains the mean relative deviation between the measured and calculated values o f the concentration o f cobalt in drop. TABLE 1 P a r a m e t e r values a n d m e a n square error P a r a m e t e r values 1
Mean s q u a r e error %
~2
Log®l
®2
LogKex
U n s m o o t h e d data
2.64
1
-13.4
0.145
-5.48
±11.8
Smoothed data
2.64
1
--13.4
0.124
--5.50
±9.9
The adequacy of the model is supported not only by the agreement existing between the experimental and calculated values, but also by the values of some constants deduced from the model parameters. The value of 2.64 for ~1 is higher than that in the literature [2]. It shows that there is enhanced mass transfer into the drop. ~2 is the parameter which, if altered, has the least effect on the rate and it means that the ratio of diffusivities in both phases is relatively unimportant in determining the overall rate o f mass transfer. It has been calculated from the value of O1 in the model that the rate constant k f of reaction (4) is equal to 104.3 s -1. For this calculation values of KA, />Ha were taken from Kolarik [17] and the value Of DHR was estimated b y the Wilke--Chan_g method. Eigen [20] divided the metal ions according to their reaction behaviour in aqueous phases into three categories. The hydrated cobalt(II) species, Co(H20)~ ÷, belongs to that group in which the rate of ligand exchange, or in other words the complex formation rate, is independent of the entering ligand. The rate constant for water replacement in the species, Co(H20)~ ÷, ranges between 104 and 10 s'7 s -1. The value 1 0 4.3 for kf found here (and taking reaction (4) as the rate determining step) is therefore reasonable. Considering the parameter ® 2, if DHR and DMR~ are assumed to be of the same magnitude a n d PMR2 is tWO orders of magnitude bigger than PHR then
262 Ko is about three orders of magnitude smaller than K2 and it has a value between 10 and 102. It has been assumed in the model that the reaction occurs in the aqueous film. According to the model proposed here, and under the experimental conditions adopted, the rate of extraction is described in terms of diffusion with chemical reaction. Brisk and McManamey [12] observed that the chemical reaction was the main resistance for cobalt transfer from aqueous solution to a D2EHPA organic phase. Because of interfacial resistance the authors assumed the reaction was taking place at the interface, but t h e y admitted that it was only a conjectured reaction mechanism. They also said that the reaction could be in the aqueous phase. Some other authors emphasise that for those metal extraction reactions in which the solubility of the extractant in aqueous solution is small, the reaction can only take place at the interface. These authors do not take into consideration that the extractant molecules at the interface are well structured so that a higher activation energy would be needed for reaction than if the extraction occurred in the aqueous film. Therefore, although the formal concentration of extractant at the interface may be higher than that in the aqueous reaction film, the contribution of these interface molecules to the reaction is not necessarily higher than those at lower concentration in the aqueous reaction film. Finally, Golding and his co-workers [13, 14] concluded that there was resistance to mass transfer in both phases and the transfer process was diffusion controlled. This is probably because these last authors were working in the higher pH range (3.8--4.0); consequently, the overall reaction rate was higher than that observed by Brisk and McManamey and the present authors. CONCLUSION
The growing drop technique for the study of the rate of mass transfer in a liquid--liquid extraction system is useful on two counts. First, the hydrodynamics are understood and, second, a majority of mass transfer in the droplet lifetime occurs during the growth period. In the case of the extraction o f cobalt by D2EHPA the rate appears to fit a model based on diffusion coupled with chemical kinetics. The site of the reaction may involve a true surface reaction at a monolayer of D2EHPA but it is more likely that a reaction zone, extending a short distance (a few micrometers) into the aqueous phase, is involved. The chemical rate step is in accordance with ligand replacement of the co-ordinated water by the extractant. LIST O F S Y M B O L S
K2 KA
dimerization constant of D2EHPA, 104.47 acidic dissociation constant of D2EHPA, 10-*'72
263 go Kex Keq
kf P D k J F d A V c t
O1 Q: ~2
equilibrium constant for eqn. (7) extraction constant complex formation constant forward reaction constant of eqn. (4), s -1 partition constant diffusivity, m 2/s mass-transfer coefficient, m/s flux
flow rate, ma/s diameter of drop, cm area of drop, cm 2 volume of drop, cm 3 concentration, mol/dm 3 time, s model parameter, m2/s 2 model parameter, m2/s: model parameter, m2/s: model parameter, m2/s:
Subscripts HR
H2R2 M H MR2 i
0 F
D2EHPA (D2EHPA)2 Co 2+
H+ Co(D2EHPA)2 at interface initial concentration for drop at end of formation time
REFERENCES
1 Heertjes, P.M. and DeNie, L.H., in: Hanson, C. (Ed.), Recent Advances in Liquid-Liquid Extraction, Pergamon Press, New York, 1971, p. 367. 2 Walia, D.S. and Vir, D., Chem. Eng. J., 12 (1976) 133. 3 Popovich, A.T., Jervis, R.E. and Tross, O., Chem. Eng. Sci., 19 (1964) 357. 4 Angelo, J.B., Lightfoot, E.N. and Howard, D.W., AIChE J., 12 (4) (1966) 751. 5 Groothuis, H. and Kramers, H., Chem. Eng. Sci., 4 (1955) 17. 6 Heertjes, P.M., Holve, W.A. and Talsma, H., Chem. Eng. Sci., 3 (1954) 122. 7 Zimmermann, V., Halwachs, W. and Schiigerl, K., Proc. Int. Conf. Solvent Extraction ISEC '80,University of Li6ge, Belgium, 1980, paper 80--18. 8 Marsh, B.D. and Heideger, W.J., Ind. Eng. Chem. Fundam., 4 (1965) 129. 9 Skelland, A.H.P. and Minhas, S.S., AIChE J., 17 (1971) 1316. 10 Nakashio, F., Tsuneyuki, T., Inoue, K. and Sakai, W., Proc. Int. Conf. Solvent Extraction ISEC '71, Soc. Chem. Ind., London, 1971, paper 97. 11 Bauer, G.L., Ph.D. Thesis, University of Wisconsin, U.S.A., 1974. 12 Brisk, M.L. and McManamey, W.J., J. Appl. Chem., 19 (1969) 109.
264 13 Golding, J.A., Fonda, S.A. and Saleh, V.N., Proc. Int. Conf. Solvent Extraction ISEC '77, C.I.M., Canada, 1979, p. 227. 14 Golding, J.A. and Saleh, V.N., Proc. Int. Conf. Solvent Extraction ISEC '80, University of Liege, Belgium, 1980, paper 80--194. 15 Ajawin, L.A., P4rez de Ortiz, E.S. and Sawistowski, H., Chem. Eng. Res. Des., 61 (1983) 62. 16 Rod, V., Cheml Eng. J., 20 (1980) 131. 17 Kolarik, Z., in: Marcus, Y. (Ed.), Solvent Extraction Reviews, Part 1, Marcel Dekker, New York, 1971. 18 Wilke, C.R. and Chang, P., AIChE J., 1 (1955) 264. 19 Heertjes, P.M. and DeNie, L.H., Chem. Eng. Sci., 12 (1966) 755. 20 Eigen, M., Pure Appl. Chem., 6 (1963) 97.
249
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
RATES OF EXTRACTION OF COBALT FROM AN AQUEOUS SOLUTION TO D2EHPA IN A GROWING DROP CELL
M.A. HUGHES
Schools of Chemical Engineering, Bradford University, Bradford (Great Britain) and T. ZHU
Institute of Chemical Metallurgy, Academy of Science of China, Beijing (China) (Received November 11, 1983; accepted in revised form July 24, 1984)
ABSTRACT Hughes, M.A. and Zhu, T., 1985. Rates of extraction o f cobalt from an aqueous solution to D2EHPA in a growing drop cell. Hydrometallurgy, 13: 249--264. A technique has been developed to study the rate of extraction o f cobalt from an aqueous phase into a growing drop of heptane containing di(2-ethylhexyl) phosphoric acid (D2EHPA). The hydrodynamics of the growing drop are accounted for. Experiments have been carried out at the single temperature of 25 -+ 0.1°C where the pH, aqueous cobalt concentration and the organic D2EHPA concentration have been varied. A mathematical model is given which is based upon the control of rate by mass transfer with chemical reaction. The model fits the experimental data well considering the experimental errors and the complexity of the transfer of solute where fresh surfaces are continually produced by the growing drop.
1. INTRODUCTION
In some industrial liquid--liquid extraction contacting equipment used for metals extraction, the mass transfer will take place between the dispersed drops and the continuous phase. Although the mass transfer parameters for the real commercial equipment cannot be inferred from the ones obtained in experiments involving individual drops, the study of single drops can be significant in the isolation of the most important mass transfer characteristics of the liquid--liquid extraction system. Thus one may be able to distinguish between chemical or diffusion control or control b y contributions from both of these. This is w h y mass transfer to and from single drops has been investigated widely in a number of systems involving not only metal solutes but also organic ones [1]. Three stages will be involved in the total life time o f a drop in a contactor, that is, formation, travel and coalescence. Every stage is important for the mass transfer study, however much of the total transfer takes place during
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© 1985 Elsevier Science Publishers B.V.
250 the drop formation period. The methods previously used for the experimental determination of the transfer during the formation stage are reviewed by Walia and Vir [2]. The early models which were developed in order to describe mass transfer to the growing drop immersed in a continuous phase, are almost all based on the penetration theory and involve molecular diffusion. These models are summarised by Popovieh et al. [3] and t h e y can be represented b y the equation o f general form: J =~
(cl - c2)
where J is the mass transfer flux at time t, D is the diffusivity o f transferring species and (cl - c2) is its concentration difference within the diffusion film; is a constant dependent u p o n the behaviour o f the growing boundary layer and differs from one model to another. Some models developed later [4] can also be adapted so that t h e y accord to the above equation. The models are only valid for the case where no extra mass transfer occurs due to liquid flow, i.e., the drop is growing at a moderate speed and the interface is stable. In other words strong local eddy diffusion near the interface is not taken into account. It has been noticed before that when the drop is grown rapidly, the jet action [5] and internal circulation [6, 8] will enhance the mass transfer markedly, but when the rate of growth is very slow the free convection inside the drop will be the major factor affecting the rate of mass transfer. Walia and Vir [2] designed a model which t o o k the convective flow of fluid around the drop, the curvature of the boundary layer and the concentration change in both continuous and dispersed phase into account. The model fitted data better than other models but was applied only to mass transfer of organic solutes without chemical reaction. Skelland and Minhas [9], in their empirical model, considered all of those parameters which could influence mass transfer such as velocity of liquid through the nozzle, drop diameter, the inside diameter of the nozzle, diffusivity of the transferring solute, density, viscosity of the dispersed phase and interracial tension. The model then fitted extensive experimental results quite well. Zimmermann, Halwachs and Schfgerl [7] recently determined the mass transfer during the growth of a drop, and came to a conclusion that as the resistance located in the continuous phase increases, the drop formation rate has less influence on the mass transfer rate. Until now only a few research workers have seriously studied the mass transfer with chemical reactions during drop formation for metal solvent extraction systems. The advantages of the growing drop cell are several. Mass transfer at a known area accommodating known convective transport can be analysed. Fresh surfaces are generated and impurities cannot accumulate at the interface and it bears relevance to certain contactors since drop formation is that part of the hquid--liquid contacting process where a majority of solute transfer takes place.
251 Nakashio et al. [10] investigated the UO2(NO3)2--tri-cresyl phosphate and HC1--Amberlite LA-2 system during drop growth and drop travel. In their model, a pseudo first order reaction at the interface as a boundary condition for unsteady state diffusion was assumed and the t h e o r y o f life time distribution of drop surface elements was used to describe extraction to the growing drop. Bauer [11] studied the transfer in the Cu--KELEX 100 system in a growing drop cell and derived an empirical model based on the overall chemical eaction equation with a correcting factor for interfacial turbulence. Despite the fact that di(2-ethylhexyl) phosphoric acid (D2EHPA) has been established as an important commercial reagent for the solvent extraction of cobalt and uranium, comparatively few papers have been devoted to the kinetics and mechanisms involving this extractant. Brisk and McManamey [12] have studied the equilibrium and mass transfer respectively by means of an "equilibrium extraction technique". They observed an interfacial resistance to mass transfer and explained it in terms of chemical kinetics of the extraction reaction. These workers used a crude constant interface cell which must have operated with significant diffusion problems at the interface. Golding and his co-workers [13, 14] measured the mass transfer coefficients in the D2EHPA--cobalt and D2EHPA--nickel systems using both a pulsed sieve plate column and a modified Lewis cell. They reported that there was a resistance to mass transfer in both organic and aqueous phase and the mass transfer rate was diffusion controlled. A recent paper by Ajawin et al. [15] describes the extraction of zinc by D2EHPA using a constant interface cell. Despite postulating a mechanism involving interfacial species, the analysis does not use the concentration of such species but only the bulk phase values. Furthermore these workers have analysed rate data for aqueous solutions with ionic strengths of up to 1.0 kmol m -3. Their use of the simple Debye-Hfickel equation is unsound since it only applies to low ionic strengths of less than about 0.1 kmol m -3. Surfaces will be saturated at the concentrations of extractants used in these studies. Some account must be taken of the partitioning of the D2EHPA into the aqueous reaction film. The kinetics of extraction of cobalt and nickel by phosphorus-based extractants are therefore only little understood. In this work a technique for research into mass transfer during single drop formation was developed. The system studied was D2EHPA in heptane with cobalt in an aqueous sulphate media; concentrations of importance to industry were employed. 2. A MODEL FOR MASS TRANSFER WITH CHEMICAL REACTION IN AN AQUEOUS DROP GROWING AT A NEEDLE TIP The model which is described in this paper is one based on that developed by V. Rod [16] for the extraction of metals with organic acids in liquid-liquid extraction systems. However, this last worker's model was originally
252
used to explain the results from a fixed area transfer cell. The present work involves an experimental system which is quite different, e.g., where organic drops grow at a needle tip immersed in an aqueous phase. The model has to be adapted for this new experimental approach.
_C
T
I
HR
M-
CH
I
1
I
I I
I
I - -
I i
l
-CMR2
CMR2H2R~_~ .... : :
I
CHR
,NTE~FACE I
ORGANIC
i
AQUEOUS
Fig. 1. Concentration profiles in the diffusional films.
When the extractant D2EHPA (HR) in the organic phase is brought into contact with the cobaltous ion in the aqueous solution, the following steps, which consist of partition and chemical reaction, will occur, with superscript bar representing those species in the organic phase:
Ks H2R2
~
2 HR
(1)
P~R HR
(2)
HR KA H+ + R-
(3)
R- + Co 2+ kf CoR +
(4)
CoR + + R- ~- CoR2
(5)
CoR2 PMR~ CoR2
(6)
Ko CoR2 + H2R2 -~ CoR2 • H2R2
(7)
253 In this model the extractant is taken to exist in the organic phase in b o t h the dimer and m o n o m e r form, an equilibrium exists between them as expressed in eqn. (1). The overall reaction can be described b y the equation:
Kex
2 H 2 R 2 + C o 2+ ~
CoR2" H 2 R ~ + 2 H ÷
(8)
In these equations kf is the forward reaction rate constant for reaction (4), Ka is the acidic dissociation constant of D2EHPA in the aqueous reaction zone, P~R is the partition constant of D2EHPA and PMR2 is the partition constant of the metal complex. In the present analysis we assume reaction (4) to be the rate determining step and the other reactions are so fast that they are in effect at equilibrium. (In other analyses, reaction (5) might be taken as the rate determining step.) In the aqueous film an overall reaction involving m o n o m e r is assumed, i.e. 2 HR + Co 2+ K eq CoR2 + 2 H +
(9)
The flux o f the extractant H R at the interface, JHRi, is given b y [16] :
JHRi
r kfgaDHRCMi L
2 CHiP~R
(
~MR2iCHiKo 1
-
)
KexK2C~RiCMi
1/2 (C~Ri-- C ~ R ) ]
(10)
We note that: Keq -
Kex Ks P~I~ Ko PMR2
(11)
Equation (10) is similar to that of R o d [16], and only differs because the extractant is considered to be present as a dimer in equilibrium with the m o n o m e r in the organic phase but it is the m o n o m e r which is distributed to the reaction zone and which undergoes the reaction. A second difference is because the product is further complexed b y a dimer as in eqn. (7). Now we must take into account the nature of the changing surface area during the drop formation. In the case of a growing drop, not only is the interfacial area changing with time, b u t the mass transfer coefficient is changing as well. During the drop formation, see Fig. 2, the instantaneous mass balance of the transferred species in the drop can be considered as: I
d(VC) _ JA + FCo dt
(12)
V and A are the volume and area of the drop respectively. J is the mass transfer flux and F is the rate of the flow of the organic phase from the needle tip. C0 is the initial concentration of the transferring species in this phase and is the instantaneous concentration o f the transferring species in the drop. Then:
254
= dt
+.
(13)
dF
7
Here dF is the final diameter of the drop and tF is the total formation time for a drop, i.e., the drop life time; this is the time which is varied in these experiments.
I
F
Fig. 2. Scheme of the growing drop. In the case of the organic phase forming a drop at the needle tip the main resistance to the mass transfer with chemical reaction is in the film on the aqueous side of the drop. On the inside of the organic drop the mass transfer is based on penetration theory [1] and so eqn. (15) can be used to describe this part of the resistance to the overall transfer process. The complete model therefore includes the following equations for the changes in the species HR: d~HR = j 6 dt
( ~ ) 1/3
dF
+
~HR0 __ ~H R
(14)
kHR = 13, .I 2:-" V nt
(15)
where kHR is the overall mass transfer coefficient o f HR. DHR is the diffusivity of HR in the organic drop and ~3, is some constant.
JHRi= _I. OMi L2 CHi
KOOMZ iO 'i l
[1 -- K ~ M i I
(C&Ri-- CHR)
(16)
where 0 , = k f K a D H R / P ~ R .
CHR =
+
CMR2i + O2 CHRi }
(17)
255 where =
DHRPMR2Ko
(18)
DMR2PI-IRK2
CHai= CHa
--JHai
(19)
kHR CMa2i = CMR: + 0.5 ----JHRi
(20)
~MR: CMi = CM
JHRi kM
JHRi
CHi = CH + 0.5 - kH
(21) (22)
Equations (19)--(22) are the ones for the concentration of the species at the interface based u p o n the flux of the extractant. It is now assumed that for the individual film mass transfer coefficients the following identities hold:
~MR~ -~ ~HR kM = ~2 ~HR k H = kM where ~2 = (DHR//)HR) ln, and diffusivities can be estimated b y the Wilke and Chang method [18]. We have to use bulk phase diffusivities because diffusivities in the film are not available. It is assumed that the concentrations of cobalt and the proton ion do not change during these experiments, because the system is buffered and there is a large excess of cobalt, s_o CM and CH are constant. The organic concentration of cobalt complex, CMR2, in the drop at different drop formation times can be calculated from the above model. The parameters in the model were evaluated b y the Marquardt method. The sum of the weighted squared root deviations of the values of the CMR2 concentrations calculated b y this p r o c e dure, compared with the experimental ones, was minimised. The differential equation, eqn. (14), was integrated numerically by the Runge--Kutta--Merson method in conjunction with the differential material balances of the reactions expressed in eqns. (17)--(22).
3. EXPERIMENTAL
3.1. Apparatus A diagram of the growing drop cell is shown in Fig. 3. The internal volume of this thermostatted cell is about 150 ml. The drops grow at the needle tip
256
and travel ab o u t 15 mm before reaching a narrow neck, N, which is of length 15 mm and o f I.D. 3 mm. A narrow bore plastic tube, usually Teflon of I.D. 1 mm, is placed in this narrow neck and is c o n n e c t e d via a vacuum to the sample tube. The h y p o d e r m i c needle used in this work was 33 gauge but any gauge may be used to p r o d u c e drops o f varying size.
BURETTE SAMPLING / TUBE
N _
VACuuM
IN TERFACE i
I
NEEDLE
AQUEOUS
,,...
ORGAN IC Fig. 3. Schematic diagram of the growing drop apparatus.
The system for obtaining a constant drop f o r m a t i o n t i m e consisted o f a b u rette attached to a stand with a fine height adjustment device. In this way a constant pressure head can be ke pt t h r o u g h o u t an experimental run. It is this constant head which can be varied f r o m one e x p e r i m e n t to anot her t o give different f or m at i on times for the drops. It should be n o t e d t hat the volu me o f a drop is d e p e n d e n t mainly on the needle tip diameter and the physical parameters o f the system, e.g., interfacial tension. The shortest practical drop f or m at i on times are around one second, while for long forma-
257 tion times of the drop (longer than t w e n t y seconds to form) the experiment becomes too extended in time.
3.2. Reagents D2EHPA was from BDH Ltd., Laboratory Grade reagent, and was used with further purification to give a product o f 99.8% in D2EHPA. Other reagents were from BDH Ltd. and were of AR grade. The aqueous solutions were buffered by additions of 0.5 mol dm -3 a m m o n i u m di(hydrogen phosphate}. The organic phase was various concentrations of D2EHPA made up in heptane without the addition of any modifier.
3.3. Technique for operation of the cell The drop formation cell was first filled with the aqueous solution under test and allowed to reach the temperature of the experiment. The burette was filled with the organic solution and that part of the solution in the tube leading to the needle was at the same temperature as the aqueous phase. The organic flow was then started and drops were seen to grow at the needle tip. After reaching a m a x i m u m size the drop broke from the tip, travelled the very short distance, before rising into the neck of the cell to be sucked away into the sample tube. The coalescence is considered to be absent because the drop is immediately sucked away and the effects of coalescence are ignored in subsequent analysis of the mass transfer. The drops appeared to be spherical. Although these would not be true spheres according to the theory of the drop growing at a needle tip, it is assumed that the error introduced through this assumption is negligible. The average formation time of a single drop is measured by counting ten drops and timing the total forming time for all these drops. The formation time, so measured, is considered to have an average deviation of about +5%. The average volume of the drop is obtained from the initial and final burette readings and the total drop number. For any one point on the experimental data plots shown in section 4, about one to two hundred drops are required. After any one run the aqueous pH changed by only 0.01 unit and the total cobalt in the aqueous phase changed by less than 2%. After the number of drops from a run had been collected in the sample tube, the total collecting system was rinsed with heptane and the final volume sample made up to 2 ml. In this way, any evaporation which occurred during the sampling was accounted for. The cobalt in the organic sample collected above was then analysed by a colorimetric method using the blue colour of the Co2÷--SCN - complex in acetone. A Pye Unicam SP8-100 spectrophotometer was used and concentrations were determined from calibration graphs. The analysis error was less than + 2%.
258 4. R E S U L T S A N D D I S C U S S I O N
The experimental results have been set d o w n in Figs. 4--8. The biggest discrepancy in the results compared with theory are at small formation times. W e believe this is due to turbulence in the droplet during this initial period and note that the same p h e n o m e n o n is observed in classical polarography leading to a maximum in the current voltage curve. In these experiments the main error was caused b y the complicated and changing hydrodynamic conditions around the forming drop. For example, if the needle tip had been previously wetted by the aqueous solution (even slightly) it affected the force balance of the forming drop on the needle tip and probably altered the mass transfer during formation. Comparing the duplicate experiments, it was estimated that the average error in the cobalt concentration in the organic phase was about 12%. 3O
'E o o
E E20 Q_ O rr r~ Z
~1o cn 0
"
5
10
is
o
3.403
•
3,625
+
2.849
2b
DROP FORMATION TIMEs Fig. 4. I n f l u e n c e of the aqueous solution pH o n the cobalt transfer in the growing drop cell. D 2 E H P A 0.286 m o l din -3, cobalt 0.0938 tool dm -3.
Some slight alteration in drop volume occurs when the formation time is made larger. This p h e n o m e n o n was also observed by Heertjes and DeNie [19]. Figures 4--8 show the experimentally found dependences of cobalt concentration in the total forming time of a drop. The calculated curves are based upon the model. It is obvious that all those data at very short formation times are much higher than those predicted b y the model: this is because there is enhancement of the mass transfer caused by high flow rate of organic phase in the initial stage. So far this aspect has not been taken
259
10
"?E 8 "E3
pH D2EHPA motd~ 0.286 2.849
O
0,429
2.984
O
E E
6
{2O rY [:3
z
4
H.J <~ r~
o
2
CD
i
s
i0
2'0
1~
DROP FORMATION TIME.s Fig. 5. C o b a l t t r a n s f e r in t h e growing d r o p cell for l o w e r pH c o n d i t i o n s . C o b a l t 0 . 0 9 3 8 m o l dm -3.
301
/
.Y
Oq
'E
q~
/
/
o 20
E E
Y
[2_ O
f •
pH 3.625
o
3.367
Zl0 cn oQ)
5
10
15
20
DROP FORMATION TIME s Fig. 6. I n f l u e n c e o f t h e a q u e o u s s o l u t i o n p H o n t h e c o b a l t t r a n s f e r in t h e growing d r o p cell. D 2 E H P A 0 . 5 7 2 tool dm-% c o b a l t 0 . 0 9 3 8 m o l d m -3.
260
30 I
E
Rz)
f
-6 E 20 E CL O OC d3
-ZlO
COBALTmo,
m o c)
5
10
o
o.o188
+
0.047
•
0,0938
15 20 DROP FORMATION TIME. s
Fig. 7. Influence o f the cobalt concentration on the cobalt transfer in the growing drop cell. D 2 E H P A 0.572 tool dm 3, pH 3.626.
30 C'3
IE o
E E 20 CL O OC C3
D2EHPA moi drE 3 •
"
o
0.286
•
Q572
Z
©
s
lb
1'5
~0
DROP FORMATION TIME. s Fig. 8. Influence of D 2 E H P A concentration on the cobalt transfer in the growing drop cell. Cobalt 0 . 0 9 3 8 tool dm -3, pH 3.403.
261
into account in the model. When the formation time was less than three seconds, the linear velocity inside the needle is higher than 50 mm s -1 and the Reynolds number is as high as 10 to 30. The observed enhancement was also described b y other workers [6, 8], where drops are grown for short periods. The equilibrium distribution of cobalt between the organic and aqueous phase for the system has been measured in separate experiments and the extraction equilibrium constant Kex = 10 -s's has been evaluated. The resulting values of the parameters of the model from the optimization are listed in Table 1. The last column of the table contains the mean relative deviation between the measured and calculated values o f the concentration o f cobalt in drop. TABLE 1 P a r a m e t e r values a n d m e a n square error P a r a m e t e r values 1
Mean s q u a r e error %
~2
Log®l
®2
LogKex
U n s m o o t h e d data
2.64
1
-13.4
0.145
-5.48
±11.8
Smoothed data
2.64
1
--13.4
0.124
--5.50
±9.9
The adequacy of the model is supported not only by the agreement existing between the experimental and calculated values, but also by the values of some constants deduced from the model parameters. The value of 2.64 for ~1 is higher than that in the literature [2]. It shows that there is enhanced mass transfer into the drop. ~2 is the parameter which, if altered, has the least effect on the rate and it means that the ratio of diffusivities in both phases is relatively unimportant in determining the overall rate o f mass transfer. It has been calculated from the value of O1 in the model that the rate constant k f of reaction (4) is equal to 104.3 s -1. For this calculation values of KA, />Ha were taken from Kolarik [17] and the value Of DHR was estimated b y the Wilke--Chan_g method. Eigen [20] divided the metal ions according to their reaction behaviour in aqueous phases into three categories. The hydrated cobalt(II) species, Co(H20)~ ÷, belongs to that group in which the rate of ligand exchange, or in other words the complex formation rate, is independent of the entering ligand. The rate constant for water replacement in the species, Co(H20)~ ÷, ranges between 104 and 10 s'7 s -1. The value 1 0 4.3 for kf found here (and taking reaction (4) as the rate determining step) is therefore reasonable. Considering the parameter ® 2, if DHR and DMR~ are assumed to be of the same magnitude a n d PMR2 is tWO orders of magnitude bigger than PHR then
262 Ko is about three orders of magnitude smaller than K2 and it has a value between 10 and 102. It has been assumed in the model that the reaction occurs in the aqueous film. According to the model proposed here, and under the experimental conditions adopted, the rate of extraction is described in terms of diffusion with chemical reaction. Brisk and McManamey [12] observed that the chemical reaction was the main resistance for cobalt transfer from aqueous solution to a D2EHPA organic phase. Because of interfacial resistance the authors assumed the reaction was taking place at the interface, but t h e y admitted that it was only a conjectured reaction mechanism. They also said that the reaction could be in the aqueous phase. Some other authors emphasise that for those metal extraction reactions in which the solubility of the extractant in aqueous solution is small, the reaction can only take place at the interface. These authors do not take into consideration that the extractant molecules at the interface are well structured so that a higher activation energy would be needed for reaction than if the extraction occurred in the aqueous film. Therefore, although the formal concentration of extractant at the interface may be higher than that in the aqueous reaction film, the contribution of these interface molecules to the reaction is not necessarily higher than those at lower concentration in the aqueous reaction film. Finally, Golding and his co-workers [13, 14] concluded that there was resistance to mass transfer in both phases and the transfer process was diffusion controlled. This is probably because these last authors were working in the higher pH range (3.8--4.0); consequently, the overall reaction rate was higher than that observed by Brisk and McManamey and the present authors. CONCLUSION
The growing drop technique for the study of the rate of mass transfer in a liquid--liquid extraction system is useful on two counts. First, the hydrodynamics are understood and, second, a majority of mass transfer in the droplet lifetime occurs during the growth period. In the case of the extraction o f cobalt by D2EHPA the rate appears to fit a model based on diffusion coupled with chemical kinetics. The site of the reaction may involve a true surface reaction at a monolayer of D2EHPA but it is more likely that a reaction zone, extending a short distance (a few micrometers) into the aqueous phase, is involved. The chemical rate step is in accordance with ligand replacement of the co-ordinated water by the extractant. LIST O F S Y M B O L S
K2 KA
dimerization constant of D2EHPA, 104.47 acidic dissociation constant of D2EHPA, 10-*'72
263 go Kex Keq
kf P D k J F d A V c t
O1 Q: ~2
equilibrium constant for eqn. (7) extraction constant complex formation constant forward reaction constant of eqn. (4), s -1 partition constant diffusivity, m 2/s mass-transfer coefficient, m/s flux
flow rate, ma/s diameter of drop, cm area of drop, cm 2 volume of drop, cm 3 concentration, mol/dm 3 time, s model parameter, m2/s 2 model parameter, m2/s: model parameter, m2/s: model parameter, m2/s:
Subscripts HR
H2R2 M H MR2 i
0 F
D2EHPA (D2EHPA)2 Co 2+
H+ Co(D2EHPA)2 at interface initial concentration for drop at end of formation time
REFERENCES
1 Heertjes, P.M. and DeNie, L.H., in: Hanson, C. (Ed.), Recent Advances in Liquid-Liquid Extraction, Pergamon Press, New York, 1971, p. 367. 2 Walia, D.S. and Vir, D., Chem. Eng. J., 12 (1976) 133. 3 Popovich, A.T., Jervis, R.E. and Tross, O., Chem. Eng. Sci., 19 (1964) 357. 4 Angelo, J.B., Lightfoot, E.N. and Howard, D.W., AIChE J., 12 (4) (1966) 751. 5 Groothuis, H. and Kramers, H., Chem. Eng. Sci., 4 (1955) 17. 6 Heertjes, P.M., Holve, W.A. and Talsma, H., Chem. Eng. Sci., 3 (1954) 122. 7 Zimmermann, V., Halwachs, W. and Schiigerl, K., Proc. Int. Conf. Solvent Extraction ISEC '80,University of Li6ge, Belgium, 1980, paper 80--18. 8 Marsh, B.D. and Heideger, W.J., Ind. Eng. Chem. Fundam., 4 (1965) 129. 9 Skelland, A.H.P. and Minhas, S.S., AIChE J., 17 (1971) 1316. 10 Nakashio, F., Tsuneyuki, T., Inoue, K. and Sakai, W., Proc. Int. Conf. Solvent Extraction ISEC '71, Soc. Chem. Ind., London, 1971, paper 97. 11 Bauer, G.L., Ph.D. Thesis, University of Wisconsin, U.S.A., 1974. 12 Brisk, M.L. and McManamey, W.J., J. Appl. Chem., 19 (1969) 109.
264 13 Golding, J.A., Fonda, S.A. and Saleh, V.N., Proc. Int. Conf. Solvent Extraction ISEC '77, C.I.M., Canada, 1979, p. 227. 14 Golding, J.A. and Saleh, V.N., Proc. Int. Conf. Solvent Extraction ISEC '80, University of Liege, Belgium, 1980, paper 80--194. 15 Ajawin, L.A., P4rez de Ortiz, E.S. and Sawistowski, H., Chem. Eng. Res. Des., 61 (1983) 62. 16 Rod, V., Cheml Eng. J., 20 (1980) 131. 17 Kolarik, Z., in: Marcus, Y. (Ed.), Solvent Extraction Reviews, Part 1, Marcel Dekker, New York, 1971. 18 Wilke, C.R. and Chang, P., AIChE J., 1 (1955) 264. 19 Heertjes, P.M. and DeNie, L.H., Chem. Eng. Sci., 12 (1966) 755. 20 Eigen, M., Pure Appl. Chem., 6 (1963) 97.