L in which
T h e shado\v effect. introduced theoretically and contained in , proved to be essential in the corrected weight fractions. . x * ~ is the prediction of the pre'ssure drop across multicomponent glass fiber filters. I t has a tendency to increase the pressure drop. T h e experimental results give evidence of the existence of a structure effect. decreasing the pressure d r o p and overruling in magnitude the shado\v effect. Looking upon the effective composition factor as a statistical mean, the unusual way of averaging is striking. 'This must be the consequence of the phl-sical meaning of the effective composition factor, allowing for the structure effect. Nomenclature
Bo
= width of volume of air around fiber C = Cunningham slip correction factor (2 = arithmetic mean fiber diameter (12 = mean square fiber diameter E = subscript to a parameter. indicating that this parapeter stands for a property of a mixed multicomponent filter as a \\.hole ,q = acceleration d u e to gravity H = shadoiv effect k = resistance coefficient k-' = permeability coefficient 1 = mean fiber length
= thickness of glass fiber filter Ap = pressure drop across filter P = probability that two fibers within a given volume d o not "cut" each other S = surface fraction of a fiber screened from passing air flow by another fiber V = superficial velocity x = weight fraction x * = weight fraction corrected for shadow effect 01 = angle under Xvhich two fibers "cut" each other e = porosity of,filter 7 = viscosity of air K = composition factor Y = number fraction p = density of water
Acknowledgment
\Ye are grateful to the board of the National Research Defence Organization T N O for permission to publish this study. \\le thank L. C. van Schie, who carried out the experimental Lvork. \Ye are very much indebted to J. Kramei of Profiltra N.V for suppling the glass fibers. literature Cited
(1) Chen, C. Y.. Chem. Revs. 5 5 , 595 (1955). (2) Dabies, C. N., Proc. Inst. Mech. Engrs. (London) B 1 , 185 (1952). ( 3 ) LVerner, R. M . , Clarenburg, L. A,, IND.ENG.CHEM.PROCESS DESEXDEVELOP. 4, 288 (1965). (4) Lt'heat. J . A., Can. J . Chem. Eng. 41, 67 (1963).
RECEIVED for review May 14, 1964 ACCEPTED April 23, 1965 Second in a series of articles on aerosol filters.
COUNTERCURRENT EXTRACTION IN SALT-MEITAL SYSTEMS INVOLVING OX IDA T I O N R ED UCT ION R EACT IONS
-
PREMO C H l O T T l Institute for Atomic Research and Department of Metallurgy, Iowa State University, Ames, Iowa
The separation of solutes b y countercurrent techniques in a two-phase system wherein the transfer of solutes between the two phases depends on an oxidation-reduction reaction of fixed stoichiometry i s shown to b e analogous to the separation of components in a distillation column. A flow diogram for separating two solutes, such as uranium and thorium, in a KCI-LiCl/zinc system i s presented. Mathematical relations and graphical methods for determining the number of equilibrium stages required to effect a given separation are developed. The number of precipitate phases in the solvent streams must b e limited for the countercurrent system to b e operative.
XIDATION-reduction reactions in fused salt-liquid
metal
0 systems appear to hold promise as a method for separating fission products from reactor fuels (7-4). I n a KC1-LiC1 (44.4 weight 70LiC1)-zinc system some components such as uranium can be transferred from the zinc solvent to the salt by the addition of ZnCl?, which serves as a chlorinating or oxidizing agent. Similarly, uranium can be transferred from the salt to the zinc phase by the addition of a reducing agent such a s magnesium. Simple equilibration techniques followed by separation of the salt- and zinc-rich phases can be used to separate many metals from uranium. T h e zinc solvent can be removed by distillation a n d the
uranium recovered in the metallic state. Some metals, such as thorium, closely follow uranium in either the oxidation or reduction steps and cannot be effectively separated in a single batch process. T h e relative distribution of these components between the salt and metal phases will depend on competing reactions of the type U(in Zn soln.)
+ ThClS(in salt)
-+
+
UCla(in salt) T h ( i n Zn soln.) I n the absence of other oxidizing or reducing agents the transfer of uranium to the salt requires an equivalent transfer of thorium to the zinc-rich phase and similarly the transfer of thorium from the zinc to the salt requires an equivalent transfer VOL. 4
NO. 3
JULY
1965
299
9 MOLES K C l
- LlCl SALT
4 S MOLES LnC12 CLEIN SALT
top of a distillation column with most of the distillate returned as reflux. The parallel of this process with distillation may be further emphasized by considering the exchange reaction occurring in the separation of ethanol from water. H20(in vapor)
+ C2HSOH(insoln.)
-+
HpO(in s o h )
Figure 1, Flow diagram for countercurrent separation of two solutes, A and B, in KCI-LiCl/zinc system
of uranium to the zinc. T h e total equivalents of the two solutes in each phase will remain constant. I n principle at least it is possible to employ countercurrent techniques, possibly of the mixer-settler type, to separate components involved in an oxidation-reduction reaction of this type. Mathematical relations and graphical methods for determining the stages required to effect a given separation of two components are given below. However, the general features of a countercurrent salt-metal system will be considered first. A flow diagram for the separation of two trivalent solutes, A and B, in a KCl-LiCl/zinc system is shown in Figure 1. This separation is analogous to the separation of two components in a distillation column and the nomenclature employed for the present process along with corresponding quantities for a distillation process is summarized in Table I . Components A and B in Figure 1 may be considered to represent thorium and uranium, respectively. Then the competing reaction given above applies and at 700" C. the equilibrium mole fraction ratio, K.v, has been shown to have a value of about 10. The number of stages indicated is based on a value of 10 for K N . The feed corresponds to a thorium-rich alloy (1.13 weight 7' uranium) dissolved in liquid zinc which is introduced into the metal stream entering stage 8 at the steady-state rate of 9 moles of thorium and 0.1 mole of uranium per some unit of time. T h e zinc serves merely as a solvent or carrier for the solutes and the amount is determined primarily by the solubility of the solutes. The salt plays a similar role for the solute chlorides. Thorium or the A component tends to concentrate in the zinc, while the uranium or the B component tends to concentrate in the salt. The salt and metal streams will both contain primarily one component at each end of the countercurrent system. I n Figure 1 the zinc solvent at the A-rich end contains 12 moles of solute (qm), of which only a small fraction, xo = 1 x 10-5. is uranium or component B. Of the 12 moles of solute 9 are removed as product (up) and 3 are oxidized with ZnCl2 and transferred to the salt stream. These 3 moles are analogous to 3 moles of residue converted into vapor in a fractionating column. AS indicated in the diagram, 4 . 5 moles of zinc are produced as by-product. The zinc solvent is recovered by vaporization in a retort and 9.0 moles of metal sponge are obtained as a final product. .4t the B-rich end the salt is stripped clean of its 3 moles of solute with a reducing agent consisting of potassium and lithium dissolved in zinc. These two alkali metals are used in the proper proportion to maintain the composition of the salt solvent constant, and 9 moles of eutectic salt by-product are produced. Of the 3 moles of solute removed from the salt, 2.9 moles are returned in the zinc solvent stream as reflux. This step corresponds to the condensation of vapor from the 300
l & E C PROCESS D E S I G N A N D DEVELOPMENT
+ C2HjOH(in vapor)
The transfer of components between the liquid and vapor phases is usually assumed to occur on a mole per mole basis. This is true only if the two heats of transfer are equal. In such a column the temperature varies in the range 100' to 78' C. In a salt-metal system the temperature at each stage need not be constant but is assumed to be constant in the development which follows. Development of Mathematical Relations
In the treatment that follows it is not necessary that both solutes have the same valence. Possible reactions may be represented by the equations, AC13 AC13
+
A'Clr
+B B'
+A B'Cl, + A 2B"C12 + A '
+ BC18 +
+ 2B"
-+
These reactions can be generalized by the relation AClb
+ (b,'a)B
+
(b/a)BCl,
+A
(11
This equation shows that the transfer of 1 mole of A from the salt to the metal phase results in the transfer of (&!a) moles of B from the metal to the salt. B may be considered as the more active component which tends to concentrate in the salt. In the following development it is assumed that both the salt solution and the metal solution are sufficiently dilute so that the activity coefficient ratio, K,, for Reaction 1 may be considered constant. The mole fraction ratio K- may then be considered constant and is given by the relation K.v =
(A' BCl,)"' .VAm (sAClb) (.VB~)~/'
where S BC1, and N ACIb are the mole fractions of the solute chlorides in the salt and and .VBmare the mole fractions of the solutes in the metal solvent. The two solvents serve primarily as carriers for the solutes. The total moles of solutes. or the total equivalents in terms of oxidizing or reducing capacity if the valences of their chlorides are not the same, must remain constant in each solvent. Therefore, the transfer of solutes between the two phases in passing from stage to stage is best described in terms of the relative amounts of the two solutes in each solvent rather than in terms of mole fractions or concentrations. The problem of determining the number of equilibrium stages to effect a separation of B and -4then becomes analogous to separation of tivo components in a distillation or fractionating column. In terms of the number of moles of each component the above equation becomes (nBm)b/a
(nAm)
(z)
( b : , ) -1
Ks
=
(nBs)b!a nAs
~
(2)
In this relation ns and nm represent the total number of moles of salt and metal solution, respectively. n B s and nAs the moles of B and A in the salt. respectively, and nBm and nAm the corresponding moles of components in the metal phase. The total number of moles of salt solution and the total number of moles of metal solution are considered to be constant. If the valences
of the t\vo solutes are not the same, there will be a n unequal exchange of moles of solute components between the salt and metal phases during the extraction process. I n the case of dilute solutions this unequal transfer \vi11 not appreciably alter the total moles of salt and metal present. I n oxidizing or reducing power 1 mole of A is equivalent to (b!a) moles of B. T h e number of equivalents. in this sense, in the salt or metal phase will remain constant from one equilibrium stage to the next. T h e numh'er of equivalents in the salt, q s , and the corresponding quantity. qm. for the metal phase are defined as
+ nBs ( b / ' a ) n A m + nBm
ys = ( b , ' a ) n A s
qm
and
=
I n the case where 6 ,'a is unity, both components have the same valence. and the number of equivalents and the number of moles become identic ial. Let? = nB.r,'q, and x = nBm,'qm be the equivalent fraction of B in the salr and metal: respectively. Subscripts i and o are used to indicate these fractions for the incoming and outgoing streams. respectively. for any particular stage. .4 material
balance on component B entering and leaving a particular stage gives
+ qmXt
=
~syt
qsyo
Salt-'Metal System .v = mole fraction = moles of €I in solution in liquid nBm metal = moles of .4 in solution in liquid nAm metal n Rs = moles of I) in solution in salt as chloride nAs = moles of A in solution in salt as chloride ns = total moles of salt solution nm = total moles of metal solution q: = (b/a)nAs nBs = total equivalents of A and B in salt Qr. = (b/a)nAm nBm = total equivalents o f A and B in metal gs and gm = analogous quantities for streams on B-rich side of feed plate nBs equivalent fraction of B Q" in salt nBm -~ = equivalent fraction of B X
-+ +
Distillation
Moles B in liquid Moles A in liquid Moles B in vaDor Moles A in vapor
Vn, V n ' + ' I L n , L - 1
+
Vm, Vm 1 and L m , Lm - 1
Y X
Qrn
in metal nBm = equivalent fraction of B
XP
--
Y'
=
X'
=
XP
-
qP
in product 1 - y = ( b / a ) n A s / q , = equivalent fraction of .A in salt 1 - x = ( b / a ) n A m / q , = equivalent fr.action of A in metal (b/a)nAm - equivalent fraction QP
1 1 - x
1 -
xg
of A in product F number of equivalents of A and B in feed = fraction of total equivalents in J feed introduced into salt stream entering feed stage qP = equivalents of A and B in A-rich W product 0, = equivalents of A and B in B-rich D _. product = total equivalents of B in comQB bined salt and metal phases Subscripts i and o employed with x and y indicate, respectively, streams passing into or Bout of a particular equilibrium stage.
F
=
~
m
~
o
Rearranging terms gives QmXt
- QsYo
4mXo
- 401
As is apparent from a consideration of a stage on the right side of Figure 1. x, and y i for stage 2 are the same as x i and yo, respectively, for stage 1. T h e above equation requires that the difference in equivalents of B in the salt and metal streams on either side of a particular stage be equal. If qmxi - qAyo = c, then qmx, - qsyi = c and the same constant c applies to all stages u p to the feed stage. Therefore, the relation yi =
Qm
-x,
-
57s
C 4s
(3)
along with a relation for the equilibrium values for x , and yo suffices to calculate the compositions of the streams entering and leaving successive stages. Equation 2 may be expressed in terms of the equilibrium values, x and y . T h e substitution of the relations
y q s = nBs, (b/a)nAs Table I. Nomenclature Describing Countercurrent Separation of Two Compontents in a Salt-Metal System and Analogous Quantities Usually Employed in Describing a Distillation Column
+
xqm
=
=
(1 - j ) q s
n B m , ( b / a ) n A r n = (1
-
x)qm
into Equation 2 yields ns
p i a
qm
(bia)-l Ksxbla
1=(&J l--x (4) Within the limitations imposed by the assumptions outlined above, this equation may be employed to calculate values of x and y (x, and y o ) for the exit streams of an equilibrium stage. This equation shows that except for the case in which b / a is unity the equilibrium values of x and y depend on the relative concentration of solutes, qs/ns in the salt and q,/nrn in the metal. For stages on either side of the feed stage these latter two quantities may be made constant. Values for both x and y must be in the range 0 to 1, and a s x - 1 , y 1 and a s x - 0, y 6 0. To obtain a high degree of separation of the two solutes the two streams at either end of the countercurrent system must contain predominantly one component. Similar conditions are necessary in the separation of two components by distillation in a fractionating column. T h e graphical procedure for determining the number of equilibrium stages is also similar, as shown below. Equation 4 may be solved graphically. When the coefficient on the right-hand side is unity, the equation is symmetrical in the two variables, y and x . A plot of x us. x b i Q / ( l x ) must be coincident with a plot ofy us.yb"/'(l - y ) . T h e coefficient K ' = K s ( n s qm/nmqs)'b'a)-' simply shifts the curve along the horizontal axis, as shown in Figure 2. I n this plot b j a is and the procedure for obtaining y , for an arbitrary equilibrium value of x : when K' = 10. is sho\vn on the graph, For values of x and y approaching 1.0 a similar plot of . Y ' = 1 - x and y ' = 1 - j, the equivalent fractions for the A component, is more suitable. I n terms of the equivalent fractions of A, Equation 4 becomes
-
e
' bla ns (b'a)-l K (1 - y ' ) b ' a .1-(1-z 1 = (Eqs) ~-X ' (5) Y' When b j a is unity. Equations 4 and 5 simplify to the following expressions : y =
K,,
1
+ (K,v - 1 ) ~
VOL. 4
NO. 3
JULY 1965
301
-
-
-
-
le3.
I
IIIIII
I I
10-2
Id'
1.0
K, x3/2
I -x
101
102
Figure 2. Graphical method for obtaining equilibrium y values for arbitrary x values from equilibrium Equation 4
"
and
X'
+ Kv(l - x')
x'
I n this case the equilibrium curve in terms of (x,J ) or ( x ' , j ' ) is obtained readily from these relations and the graphical method offers no particular advantage. A plot of these two equations for K v = 10 is shown in Figure 3. The calculation of the equilibrium values of 2 and j for a single batch equilibration when the input salt and metal phases contain arbitrary amounts of A and B requires the solution of a quadratic equation when b,a = 1 and a higher degree equation \+hen b a > 1. I n any case a material balance on the B component gives qS)i
and
f
=
qmxl
+
qSJG
QB
lo=-Qs
where q p is the number of equivalents (moles in this case) of solute A and B in the A-rich product and x p is the equivalent fraction of B in this product. T h e product q p x p is equal to c in Equation 3. T h e operating line for the B-rich section is Pm J
o
=
:
4s
PPRP X
i
f
Y
('b)
4s
am
where and qs are the equivalents of solute in the metal and salt. respectively, for the B-rich section, Q, is the number of equivalents of .4 and B in the B-rich prucluct. and R, is the equivalent fraction of B in the product. T h e t\vo operating lines with slopes qm ' q s and intersect the 2 = x line at y P
Pm
4mxG = Q B
qm
- xo Qs
ivhere Q B is the total equivalents of B in the combined salt and metal phases. Substitution of Equation 6 in 4 leads to a quadratic or higher degree equation. T h e equilibrium values of x and J may be obtained graphically by plotting Equations 6 and 4 . T h e point of intersection of 6 with 4 yields the equilibrium values of xG and yo. Equation 6 applies for a single batch equilibration. I n passing from stage to stage in a countercurrent process Q B varies. Graphical Determination of Number of Equilibrium Stages
T h e graphical procedure for determining the number of equilibrium stages to effect a given separation of A and B is analogous to the McCabe-Thiele (5) method for determining the equilibrium stages for a fractionating column. A typical graph for the case b ' a = 1 and K.,- = 10 is shown in Figure 4 . T h e operating lines for the B-rich and A-rich sections have the form of Equation 3. T h e B-rich and .4-rich sections are analogous to the rectifying and stripping sections. respectively. of a fractionating column. For the A-rich section the operating line may be written as 4m Ji = - X G QS
302
-
4pxP 4s
(74
l&EC PROCESS DESIGN A N D DEVELOPMENT
kt / 10'
10-4
10"
lo'
IO0
Figure 3. Log-log plot for determining number of equilibrium stages
I
I
"-
/
I
Lvhere f is the fraction of solutes in the feed introduced into the salt stream. Substituting these two relations in the above equation gives
I
/
/
I1 I
jFy
II
=
-(I
- /)Fx + F
x ~
I
II
I
This equation is identical with the feed line equation given by McCabe and Smith (5). T h e parallel between the feed line for all possible feed conditions to a fractionating column and the feed line for an oxidation-reduction reaction in a saltmetal system is shown in Table 11.
I-
I I
I-
V
I I
General Considerations and Discussion
Previous work ( 7 ) on the reaction between uranium and thorium in a KCI-LiCl/zinc system indicates that both uranium and thorium in the salt have a valence of 3 and at 700' C. the value of K \ is approximately 10 for the reaction
U Figure 4. McCabe-Tbiiele diagram for determining number of equilibrium stages
and gD.respectively. 'The limiting values o f j are given by the points of intersection of the operating lines with the equilibrium curve. T h e simultaneous solution of the equation for an operating line and Equation 4 will also yield the limiting value for y . When b ' a is not unity, the same equilibrium y us. x curve may or may not apply for stages on both sides of the feed stage. As is evident from Equation 4 and Figure 2, a single equilibrium curve applies only if the concentration of solutes q,,'nrn and qs, ns in the metal and salt streams, respectively, is maintained the same on both sides of the feed stage. This condition can be met if necessary by adjusting the total amount of each solvent employed in the two sections. In Figures 1. 3, and 4 the system considered is one in which the feed is all introduced into the metal stream at the feed plate. T h e effect of adding part of the feed to the salt stream is analogous to the effect of a vapor plus liquid feed in a fractionating column. Treatment of the latter problem may be found in the text of McCabe and Smith (5) as well as other texts. T h e so-called feed line for the present problem can be obtained from the relatlon for an over-all material balance on component B and the relations for the two operating lines and the condition that these lines intersect at a common point. An over-all balance on B fivps
XF.F =
g p f p
+ qpxp
qmX
q,l
qs = qs
+ f17 and qm
f = 1
=
Condition of Feed to Fractionating Column Superheated vapor
gppap
Considering t h e balance on total solutes entering and leaving the feed stage i n the salt and metal streams gives
qm
+ (I
UC13
+ Th
Table II. Feed Conditions for Fractionating Column Compared to Analogous Feed Conditions to a Salt-Metal System in Which Separation Is Based on Oxidation-Reduction Reaction
Value off
Subtracting ?a f r o m 7b gives
+
If the alloy is a thorium blanket material, the concentration of would probably be less than 1.13 weight yo uranium, but whatever the concentration might be, it would be desirable to strip the thorium as free from uranium as practicable. One of the end products might be a T h - U alloy suitable for a reactor furl material. I n this case the number of stages on the uranium-rich side of the feed stage would be small. Examination of Figure 3 indicates that two or three stages would be sufficient. For the separation indicated in Figure 1, eight stages would be required on the A-rich side of the feed stage to give a product in which the mole fraction of B has been reduced to 3.0 x 10-6 and seven stages on the B-rich side to obtain a B-rich product in which the mole fraction of A is 1 x 10-5. Each 9.1 moles of feed processed result in the production of 9 moles of KCI-LiC1 salt and 4 . 5 moles of zinc. The excess salt results from the use of a K-Li-Zn alloy to scrub the salt free of solutes at the B-rich end of the process. The use of potassium and lithium, in the proper proportion, as reductant is necessary in order to maintain the composition of the salt solvent constant. At the A-rich end ZnCle is used to oxidize and transfer part of the solutes from the exit metal stream to the salt stream for reflux. Each 3 moles of solute oxidized consume 4 . 5 moles of ZnCI:! and produce 4 . 5 moles of zinc. Both of the by-products.
Equations 7a and 7b maly be written as
q::y =
+ ThC13
0
>f >
f
=
f < O
0
Vapor at dew point 1 Vapor plus liquid
Liquid at bubble point Cold liquid
Condition of Feed to Salt-Metal Syslcm Salt solution containing solutes and oxidizing agent such as ZnCl:! Salt solution containing solutes only
Salt and metal solutions containing solutes Metal solution containing solutes
Metal solution containing solutes and reducing agent such as magnesium. o r potassium and lithium
-f)F VOL. 4
NO. 3
JULY
1965
303
salt and zinc, can be avoided by employing electrolytic cells to carry out the oxidation and reduction steps. Zinc is very corrosive to most construction materials at 700' C. .4system in \vhich KC1-LiC1 eutectic (melting point 354' C.) and zinc (melting point 419' C.) are used as solvents would probably be sufficiently fluid a t temperatures as low as 450' C. to permit countercurrent operation. Hoivever, many elements are only very sparingly soluble in zinc at this temperature, particularly solutes of interest in nuclear fuel reprocessing. At 500' C . the binary solubilities of uranium and thorium in zinc are 0.033 and 0.022 Lveight yo:respectively. T h e solubility in the ternary solution is not known but \vi11 vary with the relative amounts of thorium and uranium present and probably be less than 0.1 \veight 76. At 700' C. the combined solubility is probably Lvithin the range of 1 .O to 2.0 Lveight yo. Experimental results indicate the precipitate phase is a ternary solid with 8.5 or more zinc atoms per solute atom. T h e presence of a precipitate phase may not be too troublesome in a mixer-settler type of operation. T h e slo\\diffusion of solutes in the solid phase and the low concentration of solutes in the liquid phase would require maintaining the precipitate in a finely divided state and intimately dispersing or mixing the salt and metal phases to obtain equilibrium in a reasonable period of time. T h e presence of precipitate phases in the zinc solvent places certain restrictions on the exchange of solutes between the salt and metal solvents. If t\vo different precipitates exist in the zinc and the temperature and pressure remain constant. the phase rule requires that the composition of each phase, the zinc-rich solution and the t\vo precipitates. remain constant. Only the relative amounts of the phases can change. Therefore, as long as three phases exist in the metal stream the composition of the salt attains its equilibrium value after the first contact and no further transfer occurs in passing from stage to stage. If only one precipitate phase of variable composition exists in the zinc solvent. the countercurrent process is still operative. I n case the solutes are uranium and thorium, the precipitate phase may have the approximate stoichiometry (U. Th)Zna,5. I n this case it is apparent that to obtain thorium essentially free of uranium. the precipitate
phase in the exit zinc stream must approach the stoichiometry ThZns,s \l'ith a precipitate phase present it is possible to describe the equilibrium constant for the competing reaction in terms of the activities of the t\vo solutes as chlorides in the salt and the activities of the tivo solutes in the precipitate or in the zinc liquid. I n either case the equilibrium constant must be the same. Similarly, there are t\vo possible representations for Ks. one based on the composition of the solid phase and one based on the composition of the liquid zinc solution. It is unlikely that both \vi11 have the same value. since this ivould require that the activity coefficient ratio for the t\vo solutes be the same in the solid and liquid solutions. Equation 4 could not be used to calculate an approximate equilibrium x - 3 curve and the equilibrium curve ivould have to be determined experimentally. As long as Y represents the equivalent fraction of solute B in the zinc alloy, based on the total solutes in liquid and precipitate phases, the general treatment outlined above for determining the equilibrium stages required is still valid. Similar arguments hold for the existance of precipitate phases in the salt. Literature Cited
(1) Chiotti. P., Parry, S. J. S..J . Less-Common . l . f f t ~ i4,~ 315-37 (1962). (2) Chiotti. P.. Voigt, A. F.. '.Pyrometallurgical Processing." in "Progress i n Nuclear Energy." Ser. 111. Vol. 3. p. 340. Pergainon Press, New York. 1961. (3) Chiotti, P.. \Voerner. P. F.. Parry. S.J. S.. "Pyroriietallurgical Reprocessing of Thorium-Uranium Fuel. I1 Cicolo Combustible U-Th," p. 405, Coniitato Nazionale Enerqia Nucleare. Rome, Italy. 1961. (4) Dwyer. 0. E.. Eshaya, .A. M.. Hill, F. B.. .'Continuous Removal of Fission Products from Uranium-Bismuth Fuels." Proceediiigs of Second United Nations Intcrnational Conference on Peaceful Uses of .itornic Energy. Vol. 17. p . 429. United Sations. Geneva, 1958. (5) McCabe. LV. L., Smith, J. C.. "Unit Operations of Chemical Engineering," p. 665. McGraw-Hill. N c l v York. 1956. for revimv July- 17. 1964 RECEIVED ACCEPTEDJanuary 7 , 1965
Division of Suclear Chemistry and Technology. 148th Meeting., ACS. Chicago, Ill.. September 1964. Contribution No. 1564. Research done i n the .imes Laboratory of the U. S. Atomic Energy Commission.
CONCENTRATION POLARIZATION O N ION EXCHANGE RESIN MEMBRANES
I N ELECT ROD IA LYT IC D E M I N ERA LIZAT IO N W .
G. E. M A N D E R S L O O T AND
R . E.
H I C K S
Counciljor SnentlJic and Industrial Resfarch, Pretorta, South .4frlca
HE transport number of the counterions in a highly selective T i o n exchange resin membrane is near to 1 and the difference in transport number of these ions in the membrane and in the adjacent solution gives rise to a n electrol>-te concentration gradient in a .'diffusion layer" on the membrane surface. and hence to concentration polarization (5. 2 s ) . Counterion transport to\vard the membrane is then parti)- electrical, partly by diffusion and. particularly if the soliltion is stirred or floiving. partly by convrction.
304
I & E C PROCESS D E S I G N A N D DEVELOPMENT
The degree of polarization increases Lvith the mass transfer rate (current densit)- as a result of applied electric potential gradient). Under limiting conditions the electrolyte concentration in the solution on the membrane surface is reduced virtually to zero. causing a ver!- high electric resistance. Only under limiting conditions is the mass transfer across the liquidmembrane interface controlled by diffusion in the liquid boundar)- la)-er. .it lo\ver mass transfer rates the process is controlled by the electric resistance of the sy-stem.
