TRANSPORT CHARACTERISTICS OF POROUS CELLULOSE ACETATE MEMBRANES FOR T H E REVERSE OSMOSIS SEPARATION OF SUCROSE IN AQUEOUS SOLUTIONS SHOJl
K I M U R A ’ A N D S. SOURIRAJAN
Division of Applied Chemistry, National Research Council, Ot:awa, Canada
Analysis of the reverse osmosis separation data for the system sucrose-water using a number of LoebSourirajan type porous cellulose acetate membranes shows that the solute transport parameter, D A M / K 8 , for sucrose decreases with increase in its boundary concentration, XA2. The plot of log DA,/K6 vs. X A 2 is a straight line, and this relationship is independent of the combination of feed concentration and flow rate used, The slope of the above straight line is a function of the operating pressure, and a t a given operating pressure is essentially the same for all the membranes tested. For every film, a unique relationship exists between D A M / K 6 for sodium chloride and the extrapolated value of D A M / K 6 for sucrose a t XAz = 0, giving rise to a new method of expressing membrane selectivity on a relative scale. The predictability of membrane performance for the reverse osmosis separation of sucrose in aqueous solution and the effect of membrane compaction on solute separation, from the initial specifications of the film given in terms of the pure water permeability constant and D A M / K 6 for sodium chloride, are illustrated and discussed.
HE analysis of the reverse osmosis separation data for the T s y s t e m s glycerol-water, sodium chloride-water, and several others involving inorganic salts in aqueous solution using the Loeb-Sourirajan type of porous cellulose acetate membranes has been reported (Kimura and Sourirajan, 1967 ; Sourirajan and Kimura, 1967). These systems are characterized by the fact that the solute transport parameter, DA,w/K8, is independent of the concentration of the boundary solution a t any given operating pressure for a wide range of feed molalities and feed flow rates. The system sucrose-water is an example of one for which DAM/K6 is dependent on the boundary concentration. This paper discussses the results of the analysis of the reverse osmosis separation data for the system sucrose-water, using the above type of porous cellulose acetate membranes.
Experimental Details
Reagent grade sucrose and porous cellulose acetate membranes (designated here as CA-NRC-18 type films), made in the laboratory, were used. These films were cast at -10’ C. in accordance with the general method described earlier (Loeb and Sourirajan, 1963, 1964; Sourirajan and Govindan, 1967), using the following composition (weight per cent) for the film casting solution: acetone 68.0, cellulose acetate (acetyl content 39.870) 17.0, water 13.5, and magnesium perchlorate 1.5. The film details, apparatus, and experimental procedure have been reported (Sourirajan, 1964, 1967; Sourirajan and Govindan, 1965). Membranes shrunk a t different temperatures were used to give different levels of solute separation a t a given set of operating conditions. The aqueous sucrose solution (feed) was pumped under pressure past the surface of the membrane held in a stainless steel pressure chamber provided with two separate outlet openings, one for the flow of the membrane-permeated solution, and the other for the concentrated effluent. A porous stainless steel plate, specified to have pores of average size equal to 5 microns, was mounted between the 1 Present address, Department of Chemical Engineering, University of Tokyo, Tokyo, Japan.
548
I & E C PROCESS D E S I G N A N D DEVELOPMENT
pump and the cell to act as a filter for dust particles which might otherwise clog the pores on the membrane surface. Unless otherwise stated, the experiments were of the shortrun type, each lasting for about 2 hours, and were carried out a t the laboratory temperature. A few experiments were carried out for periods extending continuously up to 7 days. The reported product rates are those corrected to 25’ C., using the relative viscosity and density data for pure water. The feed rates used ranged from 120 to 560 cc. per minute, and the feed concentrations ranged from 0.1 to 2.OM. I n each experiment, the solute separation, j , defined as
-
f =
molality of feed ( m l ) molality of product (ma) molality of feed ( m l )
the product rate, [PR], and the pure water permeability, [PWP],in grams per hour per 7.6 sq. cm. of effective film area were determined at the preset operating conditions. I n all cases, the terms “product” and “product rate” refer to the membrane-permeated solutions. The concentrations of the solute in the feed and product solutions were determined by refractive index measurements, using a precision Bausch and Lomb refractometer. The accuracy of the separation data is within ly0,and that of [PR]and [PWP]data is within 3% in all cases. Aqueous sodium chloride (0.5M) feed solutions were used to obtain transport data for membrane specifications. Results and Discussion
Osmotic Pressure, Molar Density, Kinematic Viscosity, and Diffusivity Date. These data, given in Table I for the system sucrose-water a t 25’ C., were computed from the water activity, density, viscosity, and diffusivity data given in the literature (Hook and Russell, 1945; Robinson and Stokes, 1959; Timmermans, 1960). Similar data for the system sodium chloride-water have been reported (Kimura and Sourirajan, 1968a). Basic Transport Equations and Correlations. T h e Kimura-Sourirajan analysis gives rise to the following basic
Table 1.
Molality
Osmotic Pressure, Molar Density, Kinematic Viscosity, and Diffusivity for System Sucrose-Water at 25' C.
Concentration of Sucrose Mole fraction X 703 0
0
1.798 3.590 5.375 7.154 8.927 10.693 12.453 14.207 15.955 17.696 21.160 24.600 28.016 31.408 34.777 43.096 51.273 59.312 67.216
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .o 1.2 1.4 1.6 1.8 2.0 2.5 3 .O 3.5 4.0
Weight,
%
0
3.31 6.41 9.31 12.04 14.61 17.04 19.33 21.50 23.55 25.50 29.12 32.40 35.39 38.12 40.64 46.11 50.66 54.51 57.79
A =
x
36 73 110 148 186 225 265 305 345 387 470 557 645 734 826 1069 1324 1592 1866
[PWPI M , X 7.6 X 3600 X P
(3)
(4) From the [ P W P ] , [PR],and f data, the values of A, DAM/K8, and k can be calculated for every experiment. Both A and D,,/Kg are dependent on the porous structure of the membrane surface, and hence they are different for different membranes; both are functions of operating pressure, and, in addition, DA,/K8 is dependent on the chemical nature of the solute. While Equations 1 to 4 are general for the reverse osmosis process, the correlations of the transport parameters can be different for different type of membranes for a given solution system. For the type of membranes used in this work, a t a given remain essentially operating pressure, the values of DA,/'K6 constant for a wide range of feed concentrations and feed flow rates for systems such as sodium chloride-water or glycerolwater (Kimura and Sourirajan, 1967; Sourirajan and Kimura, 1967). Further, the mass transfer coefficient, k , is essentially a function of feed flow rate and feed concentration, and the values of k for the above systems have been well correlated by a gen~ N8h/Ns2.3a. O n the basis of the eralized log-log plot of N R us. above correlations, a single set of experimental [PWP],[ P R ] , and f data obtained with a system such as sodium chloridewater a t any given operating pressure specifies a film in terms of A and DAM/K8 at that pressure. Membrane Specifications. Table I1 gives the specifications of all the membranes used in this work in terms of A and DAM/K8for sodium chloride a t the specified operating pressure. These specifications are based on the data obtained from shortrun experiments and represent the initial characteristics of the film. For information, the table also includes the temperatures a t which the membranes were shrunk prior to use in the experi-
x
102
Dz@usivity, Cm ./See. X 706 0.523 0.509 0.499 0.490 0.483 0.477 0.472 0.467 0.463 0.459 0.455 0.448 0.441 0.434 0.428 0.421 0.404 0.387 0.370
102
0.8963 0.9615 1 ,0352 1.1151 1 ,2053 1 ,3033 1.4124 1.5330 1.6639 1.8083 1.9658 2.3270 2.7580 3.2701 3.8772 4,6023 7.0584 10.8171 16.5067 25,0529
5.535 5.431 5.330 5.233 5.140 5.050 4.965 4.881 4.802 4.723 4.649 4,506 4.373 4.248 4.131 4.021 3.771 3.553 3.362 3.193
0
equations relating the pure water permeability constant, A , the transport of the solvent water, N B , the solute transport parameter, DA,/K6, and the mass transfer coefficient, k :
Kinematic Viscosity, Cm./Sec .
Molar Density, Moles/Cc .
Osmotic Pressure, P.S.I.
Specifications of Porous Cellulose Acetate Membranes Used A X 706 Film Operating Mole H2O Shrinkage Pressure, Sq. Cm. Temp., ' C. P.S.I.G. Sec. Atm.
Toble It.
Film No. 29 29 29 30 30 30 34 34 34 111 111 111 113 113 113 114 114 114 115 116 116 116
86 86 86 84 84 84 80 80 80 86 86 86 79.5 79.5 79.5 78 78 78 78 76.5 76.5 76.5
500 1000 1500 500 1000 1500 500 1000 1500 500 1000
1500 500 1000 1500 500 1000 1500 500 500 1000 1500
2.365 2.066 1.838 3.011 2.679 2.377 3.700 3.311 2.841 1.574 1.475 1.393 4.216 3.750 3.385 3.486 3.150 2.878 5.685 7.045 6.100 5.286
52.0 42.9 40.0 109.0 91.1 80.7 720.1 483.1 350.0 2.14 2.13 2.12 148.6 110.0 94.2 47.7 39.5 35.4 524.1 1183.0 770.0 604.5
men ts ; these temperatures have no precise significance from the point of view of membrane specification. Experiments with Aqueous Sucrose Solutions. These experiments were carried out with the membranes specified in Table I1 and using feed solutions in the concentration range 0.1 to 2.OM, and feed flow rates in the range 120 to 560 cc. per minute at the operating pressures of 500, 1000, and 1500 p.s.i.g. Generally, for a given feed solution and feed molality, increase of operating pressure increases both f and [ P R ] ; for a given operating pressure and feed molality, both f and [PR]increase with increase in feed rate; and, for a given operating pressure and feed rate, [PR] decreases and f increases a t first and then passes through a slight maximum, with increase in feed molality. Some of these results have been reported (Sourirajan, 1967). Variation of Solute Transport Parameter DA,/K6 for Sucrose with Boundary Concentration X A 2 . The values of DA,/K6 and X,, calculated from the experimental [PWP], [PR],and f data for the system sucrose-water using Equations 1, VOL. 7
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2, and 3 are plotted in Figure 1 for operating pressures of 500, 1000, and 1500 p.s.i.g. for four different films involving solute separations in the range 54 to 99%. These data show that DAM/K6 for sucrose decreases with increase in X A z ; the plot of log ( D A M / K 6 )us. X A zis a straight line and this relationship is independent of the particular combination of the feed concentration and feed flow rate used. The slope of the above straight line is a function of the operating press= the higher the operating pressure, the higher is the slope, and a t a given operating pressure the slope is essentially the same for all the films tested. Consequently, the relationship between the solute transport parameter and the boundary concentration for the system sucrose-water can be expressed as
where (DAM/K6) is the extrapolated value of (DAM/K6)suorose a t X A 2 = 0, X A 2is the mole fraction of sucrose a t the concentrated boundary layer calculated from Equations 1 and 2, and E is a constant which is a function of the operating pressure. Figure 2 gives the plot of the average value of E us. operating pressure for the data presented in Figure 1. The E values given in Figure 2 are applicable for the type of membranes used in this work for XAz x lo3 values a t least up to 30, 50, and 70, respectively, a t the operating pressures of 500, 1000, and 1500 p.s.i.g. Relative Scale of Membrane Selectivity. Figure 3 relates the values of (DA,w/K6)NaC1 with those of (DA,w/K6)*suorose as a function of operating pressure for several membranes of different surface porosities. Such a relationship illustrates a new method of expressing membrane selectivity on a relative scale, and is a useful way of characterizing different types of membranes. For the type of membranes used in this work, Figure 3 shows that the log-log plot of ( D A . ~ / K S ) N ~US.C (DA,w/K6) I *suorose is essentially a straight line whose slope depends on the operating pressure. Figures 2 and 3 are useful; they define Equation 5 for any particular membrane whose (DA.M/K6)NaClis known. 1
I
'
I I ' I I
FILM TYPE: CA-NRC-18
OPERATING PRESSURE A
L
A
0 0 ' 0
30 A 34 FILM TYPE
CA-NRC-I8 SYSTEM : SUCROSE-WATER FEED MOLALITY : 0.1 t o 2.OM FEED RATE : 120 t o 560
114 0
t -
,114 3x
cc/minute
OPERATING PRESSURE 0 500 p.r.i.g. A 1000 p 3,i.g. 0 I500 p . 3 . i . g .
( D A M / K ~ ) ~ , , , - c~m . / s e c .
I
I
I
I
I
I
IO
20
30
40
50
60
xA2x io3
Figure 3. Relative scale of membrane selectivity for systems sodium chloride-water and sucrose-water
Figure 1 . Variation of solute transport parameter for sucrose with its boundary concentration 40 r
rn
I13 0
:
-
150
100
I
80 60
NS h 0.33 NSC
50
-
F I L M T Y P E : C A - N R C - I8 SYSTEM: SUCROSE-WATER F E E D M O L A L I T Y : 0.1 to 2.0 M
-
30 40
20
-
I5t IO
20
I 30
I
I
I l l 1 1
40 5060
80
100
I
I
150 200
l
l
I 1 1
300 400
600
NR, Figure 4. Experimental mass transfer coefficient data for system sucrose-water 550
I & E C PROCESS D E S I G N A N D DEVELOPMENT
Mass Transfer Coefficient Correlation. T h e values of k obtained from the experimental [PWP],[ P R ] ,a n d f data using Equations 1, 2, and 4 are plotted in Figure 4 in the form N R e us. NBh/NE,O.aa on the log-log scale as before (Kimura and Sourirajan, 1967; Sourirajan and Kimura, 1967). The experimental data involved four different films, and a wide range of solute separations, feed flow rates, and feed concentrations, and operating pressures of 500, 1000, and 1500 p.s.i.g. Most of the data plotted in Figure 4 are considerably lower than those obtained by the diffusion current method reported earlier; but
the important feature of this figure is that the mass transfer coefficient correlation thus given seems independent of the membrane used. I t hence seemed reasonable to draw a mean representing straight line for the correlation NRe us. Nsh/Ns,0.33 the experimental data. Based on the above straight-line correlation, the values of k were calculated and plotted in Figure 5, as a function of the feed flow rate, Q, and feed molality. Figure 5 shows that for a given feed concentration
k
E Q0.865
(6)
for the system sucrose-water under the experimental conditions
.
u
2 \
used in this work. Predictability of Membrane Performance. If the applicable values of A , DA,/K6, and k are given, the values of X,,, X,,,and NB (and, hence, f and [ P R ] )can be calculated as a function of operating pressure, feed molality, and feed rate, using Equations 2, 3, and 4, by the procedure illustrated earlier (Sourirajan and Kimura, 1967).
40-
-
30-
E
u 20P
2
15-
X
F I L M NO. 10-
A;1‘4
-
I .c
5 L
3J
Z 0.6
1.0
1.5
2
3
4
5
7
15
10
30 40
20
FEED RATE cc./sec.
Figure 5. Variation of mass transfer coefficient with feed flow rate for system sucrose-water
0
c a u 0.8
2W v)
W
3
6
m
FEED RATE : 3 9 0 C c l m i n u t e 0 0A 0 @ 0 EXPERIMENTAL DATA
-
CALCULATED DATA
0.7
c
FILM TYPE:CA-NRC-IB S Y S T E M : SUCROSE-WATER F E E D M O L A L I T Y : 0.5 M
I
0.9
0.5
I
.
0.6
200
r
-4-
F I L M TYPE: CA-NRC-18 SYSTEM:SUCROSE-WATER FEED RATE: 390 c c . / m i n u t e OPERATING PRESSURE: 1500 p,%l,g. 0 0 A 0 e 0 EXPERIMENTAL DATA C A L C U L A T E D DATA
I60
-
W v)
W
I40 I
c 0.7 3
. \
L
I
0
cn
\
cj
120
W
I
I
I
2c
100
I-
I
o
2
\’
80
0 [L
cl.
60 40 20
0
500
1000
OPERATING PRESSURE
1500
p.s.i.g.
Figure 6. Effect of operating pressure on solute separation and product rate for system sucrose-water
I
0
I
I
I
0.5
1.0
1.5
1 2.0
FEED M O L A L I T Y Figure 7. Effect of feed concentration on solute separation and product rate for system sucrose-water VOL 7
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NO,
/FILM
1.0 Y-
-g
0.9
2
0.8
sP
W
TYPE : C A - N R C - 1 8 S Y S T E M L SUCROSE-WATER FEED MOLALITY: 0 . 5 M OPERATING PRESSURE: I 5 0 0 p.s.1.g. Q O A rn 0 (BO E X P E R I M E N T A L DATA C A L C U L A T E D DATA
Ill6 K o ' l F l L M
v)
W
2
0.7
J
0 U J
0.6
-
'
0.5 100
0
I
'
'
I
'
I
'
'
I
100
200
400
300
'
/ 116 I NO.
FILM
r
500
The mass transfer coefficient, k, is a function of feed concentration, feed flow rate, and the geometry of the apparatus used; for any given experimental conditions, the applicable mass transfer correlation has to be determined either theoretically as illustrated earlier (Kimura and Sourirajan, 1968b) or experimentally as illustrated in Figure 5. For the purpose of this work, Figure 5 is used to obtain k for the system sucrose-water. Since (DAM/K6)suoroae is not a constant, Equation 5 should also be solved simultaneously to obtain X A , and N,. Equation 5 can be defined for this purpose from the experimental values of (DAM/K8)eucrase a t two different values of XA, a t any given operating pressure. Consequently, the separation and permeability characteristics of a membrane for the system sucrose-water a t a given operating pressure can be predicted as a function of feed molality and feed flow rate from two experimental values of [PR]and f (corresponding to two different values of XA2)along with the [PWP]data, and the simultaneous solution of Equations 2, 3, 4, and 5. When the transport characteristics of a particular type of membrane for the system sucrose-water are given in the form of Figures 2 and 3, the performance of any particular membrane with the system sucrose-water can be predicted just from its specifications in terms of A and ( D A M / K 8 ) N s c ~as given in Table 11. This is illustrated in Figures 6, 7, and 8, which give the
600
F E E D RATE C C . / m i n U t e
Figure 8. Effect of feed flow rate on solute separation and product rate for system sucrosewater
rc
z 0
1.0
FILM T Y P E : C A - N R C - 1 8 SYSTEM : SUCROSE -WATER FEED RATE : 390 c c l m i n u t e OPERATING PRESSURE : 1500 p.s.i.g. C ) 0 0 EXPERIMENTAL DATA -CALCULATE0 DATA YO-C) Ill
113
I-
2 2W
f
0.9
pI F FILM TYPE:CA-NRC-18 S Y S T E M : SUCROSE-WATER FEED MOLALITY: 0.5 M F E E D RATE : 1 2 0 - 5 6 0 c c / m i n u t e OPERATING PRESSURE 1500 p.s.i.9.
FILM NO.
v)
w 0.8
116
I3 J
0
0.7
t
loo L:
r
80
I
>
(3
W
2 e
60
I-
%
40
0
0
a
n
I 30
I
40
XA2
I
I
50
60
X I 03
Figure 9. Effect of membrane compaction on log (DAM/K8)suorose vs. XA2 relationship 552
I & E C PROCESS D E S I G N A N D DEVELOPMENT
20
0 1.0
0.8
0.6
0.4
0.2
A FACTOR Figure 10. Effect of membrane compaction on solute separation for system sucrose-water
correspond to A-factors in the range 1.0 to 0.97. Figure 9 shows that for a given value of X,,, the D A M / K 6 values obtained a t lower A-factors are the same as the ones obtained a t A-factor = 1.0. I n other words, membrane compaction does not affect the D A M / K 6us. X A Zrelationship expressed by Equation 5 for the system sucrose-water. Variations of Solute Separation during Membrane Compaction. O n the basis of the observation that Equation 5 is valid for all A-factors-Le., (DA,/K6) *8u0109e and E values are unaffected by membrane compaction-one can calculate product rate and solute separation as a function of A-factor for the system sucrose-water from the initial specifications of the membrane given in Table I1 using Figures 2, 3, and 5, and Equations 2 to 5. Such calculations are illustrated for three different membranes in Figure 10, which shows the variations in solute separation as the product rate decreases because of membrane compaction. Some of the experimental results obtained are also plotted in Figure 10. The excellent agreement between the experimental and the calculated results shows that the decrease in solute separation obtained with the decrease in product rate is a consequence of the effect of membrane compaction on the transport characteristics of the membrane, and is not due to membrane deterioration caused by chemical interaction of any kind. These results, which are similar to those reported earlier (Kimura and Sourirajan, 1968a), again confirm the validity of the analysis employed. Consequently it is clear that variations in solute separation with decrease in product rate due to membrane compaction must be expected, and can be calculated and allowed for in the design of practical reverse osmosis units for the system sucrose-water; this aspect is of particular interest in process design of the reverse osmosis concentration units for natural maple sap and other industrial sugar solutions.
effect of pressure, feed molality, and feed flow rate on solute separation and product rate for the system sucrose-water calculated for some arbitrarily chosen experimental conditions for several membranes from their specifications given in Table I1 ; some available experimental data are also plotted in Figures 6, 7, and 8 for comparison. The excellent agreement between the experimental and the calculated results shows that the mass transfer coefficient correlation in Figure 5 (based on the mean straight-line correlation given in Figure 4) is sufficiently good for practical purposes. Membrane Compaction and Relationship between (DAM/K6).uorose and XA2. During extended continuous operation of the reverse osmosis process under pressure, the flux through the membrane decreases because of membrane compaction. T h e A-factor, defined as the ratio of the pure water permeability constant, A, a t any instance to its initial value, may be considered as a relative measure of membrane compaction. The effect of A-factor on DAM/K6, and hence on [PR]and f, for such systems as sodium chloride-water and glycerol-water has been discussed (Kimura and Sourirajan, 1968a). T o find the effect of A-factor on the DAM/K6 us. X,, relationship given in Figure 1, continuous test runs were conducted with three different films a t 1500 p.s.i.g. using a 0.5M sucrosewater feed solution for periods extending up to 7 days. From the experimental [PR]and f data obtained a t different time intervals during the extended test runs, and the mass transfer correlations given in Figure 5, the corresponding values of A, DAM/K6,and X A 2were calculated using Equations 2, 3, and 4; from the initial specifications of the films, the corresponding Afactors were also calculated. Some of the results are plotted in Figure 9. T h e solid lines are those given in Figure 1, and they
25
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Relationship between Mole Fraction of Solute in Concentrated Boundary Solution (XA2)a n d in Product Solutions (XA3) for System Sucrose-Water. I n the reverse osmosis separation process, there exists a relationship between the values of X A 2and X,, which is uniquely fixed for each particular membrane-solution system; this relationship depends on the over-all porous structure of the membrane and the chemical nature of the solute, but it is independent of feed concentration and feed flow rate (Kimura and Sourirajan, 1968a; Sourirajan and Kimura, 1967). T h e data obtained with the system sucrose-water also confirm the above observation (Figure 11). Conclusions
The fact that (DAM/K6)suorase is a unique function of X A 2 , irrespective of the particular combination of feed concentration and feed flow rate used, makes the cellulose acetate membrane-sucrose-water system different from those reported earlier (Kimura and Sourirajan, 1967; Sourirajan and Kimura, 1967). I t is possible that several similar systems exist. The analysis and correlations reported in this paper illustrate the methods applicable for the treatment of reverse osmosis performance data for such systems. Acknowledgment
The authors are grateful to A. G. Baxter and Lucien Pageau for their valuable assistance in the progress of these investigations, One of the authors (S.K.) thanks the National Research Council of Canada for the award of a postdoctoral fellowship. Nomenclature
A
=
c1, c2, 63
=
= d = D DAMIK~= E
f
h
554
= = =
pure water permeability constant, gram mole H2O sq. cm. sec. atm. molar density of feed solution, concentrated boundary solution, and product solution, respectively, gram mole per sec. effective diameter of membrane surface, cm. diffusivity of solute, sq. cm. per sec. solute transport parameter, cm. per sec. constant solute separation depth of cell, cm.
I&EC PROCESS DESIGN A N D DEVELOPMENT
r(XA,), .(X.43)
mass transfer coefficient, cm. per sec. solute molality in feed solution and product solution, respectively concentration of solution in molality unit molecular weight of water, grams per mole solvent water flux through membrane, gram mole per sq. cm. per sec. Reynolds number = Q / h v Schmidt number = v / D Sherwood number = kd/D operating pressure, atm. product rate, grams per hour per 7.6 sq. cm. of film area pure water permeability, grams per hour per 7.6 sq. cm. of film area feed flow rate, cc. per sec. mole fraction of solute in the feed solution, concentrated boundary solution and product solution, respectively effective membrane thickness, cm. kinematic viscosity of feed solution, sq. cm. per sec. = osmotic pressure of solution corresponding to XA, and XA3,respectively, atm.
literature Cited Hook, A. V., Russell, H. D. J . Am. Chem. SOC. 67, 370 (1945). Kimura, S., Sourirajan, S., A.2.Ch.E. J . 13, 497 (1967). Kimura, S., Sourirajan, S., IND. ENG. CHEM.PROCESS DESIGN DEVELOP. 7,197 (1968a). DESIGN Kimura, S., Sourirajan, S., IND. ENG. CHEM.PROCESS DEVELOP. 7, 539 (196813). Loeb S., Sourirajan, S., Advan. Chem. Ser., No. 38, 117 (1963). Loeb, S.,Sourirajan, S., U. S.Patent 3,133,132 (May 12, 1964). Robinson R. A., Stokes R. H., “Electrolyte Solutions,” 2nd ed., p. 478, Butterworths, London, 1959. Sourirajan, S., Ind. Eng. Chem. Fundamentals 3,206 (1964). Sourirajan, S., IND.ENG. CHEM.PROCESS DESIGNDEVELOP.6, 154 (1967). Sourirajan, S., Govindan, T. S., “Proceedings of First International Symposium on Water Desalination,” Vol. 1, p. 251, U. S. Department of the Interior, Washington, D. C., 1965. Sourirajan, S., Kimura, S., IND.ENG. CHEM.PROCESS DESIGN DEVELOP. 6, 504 (1967). Timmermans, J., “Physicochemical Constants of Binary Systems in Concentrated Solutions,” Vol. 4, p. 302, Interscience, New York, 1960.
RECEIVED for review October 30, 1967 ACCEPTED April 22, 1968 Issued as N.R.C. No. 10267.
