- Email: [email protected]
A method for characterization of ultrafiltration membranes
Desalination, 58 (1986) 187--198 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
A METHOD FOR CHARACTERIZATION MEMBRANES
187
OF ULTRAFILTRATION
G. TR.~G~RDH and K. (~LUND Division o f Food Engineering, Lund University, P.O. Box 124, S-221 O0 Lund (Sweden) Tel. 46-107000; Telex 33533 L UNIVERS
(Received October 15, 1985)
ABSTRACT Several m e m b r a n e s h a v e b e e n t e s t e d in a t e s t l o o p especially b u i l t in o r d e r t o achieve w e l l - d e f i n e d f l o w c o n d i t i o n s at the m e m b r a n e surface. A t e s t s o l u t i o n o f d e x t r a n was u l t r a f i l t r a t e d at 0.5 MPa a n d 2 5 ° C at five c i r c u l a t i o n velocities f r o m 5 m / s to 1 m / s . This c o r r e s p o n d s to R e y n o l d s n u m b e r s o f 2 0 0 0 0 - - 4 0 0 0 at a c h a n n e l h e i g h t o f 2 m m . F o r t h e e v a l u a t i o n o f t h e results, the film-theory model, the three-parameter model of Kedem and Katchalsky a n d t h e o s m o t i c pressure m o d e l w e r e applied. T h e r e l a t i o n s h i p s b e t w e e n o b s e r v e d r e t e n t i o n a n d c i r c u l a t i o n v e l o c i t y as well as o b s e r v e d r e t e n t i o n versus m o l e c u l a r w e i g h t w e r e also c o n s i d e r e d .
SYMBOLS C C b
Cm Cp D Dh Js Jv h Lp Mn Mw P AP
- - c o n c e n t r a t i o n ( k m o l / m 3) -( C m - - Cp)/ln ( C m / C p ) - - s o l u t e c o n c e n t r a t i o n in t h e b u l k ( k m o l / m 3 ) - - s o l u t e c o n c e n t r a t i o n a t t h e m e m b r a n e surface ( k m o l / m 3 ) - - solute c o n c e n t r a t i o n in t h e p e r m e a t e ( k m o l / m 3) - - d i f f u s i o n c o e f f i c i e n t (m2/s) -- hydraulic diameter (m) - - solute f l u x ( k m o l / m 2" s) - - v o l u m e f l u x ( m 3 / m 2" s) -- mass transfer coefficient (m/s) - - p u r e w a t e r p e r m e a b i l i t y ( m 3 / m 2" S" MPa) - - n u m b e r average m o l e w e i g h t - - w e i g h t average m o l e w e i g h t - - solute p e r m e a b i l i t y (m/s) - - pressure ( M e a )
0011-9164/86/$03.50
© 1986 Elsevier Science Publishers B.V.
188 R RH Rob s Rtrue
Re Sc Sh T U ~? um
a
- - gas c o n s t a n t ( k J / k m o l " K) - - h y d r o d y n a m i c radius (A) - - o b s e r v e d r e t e n t i o n 1 - - Cp/Cb - - t r u e r e t e n t i o n 1 - - Cp/Cm -- Reynolds number -- Schmidt number -- Sherwood number - - t e m p e r a t u r e (K) - - circulation v e l o c i t y (m/s) - - viscosity ( k g / m . s) - - o s m o t i c pressure at t h e m e m b r a n e (MPa) -- reflection coefficient
INTRODUCTION T o d a y it is very difficult t o c o m p a r e m e m b r a n e s f r o m d i f f e r e n t m a n u facturers since t h e s e p a r a t i o n characteristics given are o f t e n based o n e x p e r i m e n t s using d i f f e r e n t test m o l e c u l e s u n d e r d i f f e r e n t o p e r a t i n g c o n d i t i o n s . T h e aim o f t h e w o r k p r e s e n t e d here is t o t a k e o n e step t o w a r d s a s t a n d a r d m e t h o d o f c h a r a c t e r i z i n g U F m e m b r a n e s . I n this p a p e r t h e test results f o r eight m e m b r a n e s r e p r e s e n t i n g five d i f f e r e n t p o l y m e r s are given. T h e t e s t e d m e m b r a n e s are listed in Table I. T h e test s o l u t i o n used was a 0.5% d e x t r a n s o l u t i o n ( P h a r m a c i a Fine Chemicals) w i t h an average m o l e w e i g h t o f 1 0 0 0 0 daltons. T o p r e v e n t self-interactions o f t h e d e x t r a n a 0.05 M NaC1 s o l u t i o n was used as a solvent. Moreover, in practice, salts are generally p r e s e n t w h e n ultrafiltrating m a c r o m o l e c u l e s . T h e r e f o r e , it is possible t o test t h e U F - - m e m b r a n e s in t h e p r e s e n c e o f a salt.
TABLE I THE MEMBRANES TESTED IN THIS WORK Manufacturer
Type
Membrane material
Cut-off (daltons)
DDS
GR 61 PP 600
polysulphone cellulose acetate
20000 20000
NITTO
NTU 2120
polyolefine
20000
ABCOR
HFM 100 HFM 180
confidential confidential
10000 18000
DAICEL
DUY HH DUY H DUY M
polyacrylonitrile polyacrylonitrile polyacrylonitrile
5000 10000 20000
189 EXPERIMENTAL DETAILS T h e m e m b r a n e tests T h e test l o o p used f o r t h e c h a r a c t e r i z a t i o n e x p e r i m e n t s c o n t a i n s a magnetic drive seal-less gear p u m p , a t h e r m o c o u p l e f o r t e m p e r a t u r e registration, a m e m b r a n e m o d u l e , a pressure gauge, a flow m e t e r and a heat exchanger. T h e m e m b r a n e m o d u l e is s h o w n in detail in Fig. 1. T h e inlet and t h e o u t l e t o f t h e m o d u l e have been c h a m f e r e d in o r d e r t o avoid sharp edges w h i c h w o u l d disturb the flow profile at the m e m b r a n e surface. F o r the same reason t h e g e o m e t r y o f t h e inlet is identical to t h a t o f t h e m e m b r a n e flow channel f o r a distance o f at least 40 hydraulic diameters. T h e m e m b r a n e area is 2 0 x 100 m m 2. Five d i f f e r e n t channel heights can be c h o s e n b e t w e e n 1--5 m m b y inserting P T F E rods o f v e r y e x a c t heights. T h e P T F E rods r u n all the way t h r o u g h t h e inlet c h a n n e l and t h e m o d u l e .
Fig. 1. Photograph showing the membrane module used in the experiments.
B e f o r e starting an u l t r a f i l t r a t i o n e x p e r i m e n t , distilled and m e m b r a n e filtered w a t e r is circulated in t h e test l o o p until s t e a d y state is reached. This is d o n e at the same o p e r a t i n g c o n d i t i o n s as used with t h e test solution afterwards. T h e circulation v e l o c i t y is regulated b y t h e p u m p , and n i t r o g e n gas is used to adjust t h e pressure i n d e p e n d e n t l y o f circulation velocities. The p e r m e a t e which is lost f r o m t h e test l o o p during an e x p e r i m e n t is i m m e d i a t e l y replaced b y p e r m e a t e f r o m a pressure vessel c o n n e c t e d to t h e circuit. When
190 steady state is reached, a test solution of dextran is ultrafiltered at five circulation velocities from 5 m/s to 1 m/s. This corresponds to Reynolds numbers of 20000--4000 at a channel height of 2 mm. Permeate is collected at each circulation velocity at constant permeate flux. Analysis
of samples
The samples collected during ultrafiltration are fractioned according to size by gel permeation chromatography, GPC, using a column packed with Sephacryl S-200 (Pharmacia Fine Chemicals) and detected by a differential refractometer (Optilab multiref 902 B). In this way the molecular weight distribution can be f o u n d and the observed retention o f different molecular weights can be estimated from relative concentration values. The samples are analysed by polarimetry for absolute concentration measurements. To find the correlation between molecular weight and particle size for dextran, five calibration fractions of known average molecular weights supplied by Pharmacia Fine Chemicals, were measured by light scattering. In this work the light source was a Spectra Physics 164-06, 2 W argon ion laser. The spectrometer and the compact autocorrelator/microcomputer unit used belong to the Malvern system 4600, and include software for the system. EVALUATION It is a fact that the concentration at the membrane surface is higher than that in the bulk because of concentration polarization. One way of estimating Cm, the concentration at the membrane surface, is to apply the film theory model, [1] Cm -- Cp
-- exp ( J v / h )
Cb -- Cp
(I)
To find Co the mass transfer coefficient k must be known. This is f o u n d for different circulation velocities from the Chilton and Colburn correlation Sh
-
k "Dh
0 . 0 2 3 - R e ° ' s " S c °'33
-
(2)
D
When Cm is known the true retention is easily calculated from C~
Rtrue -
-
Cm
Cp
(3)
The true retention versus circulation velocity f o u n d in this way does n o t take into account any molecular weights. To determine the true retention for different molecular weights the film theory model (1) and the relation k ~ U °'s
(4)
191 are used to g eth er in the f or m
n(1 "=I Robs
=el+con=
]
Rtrue
/
U0.---~
(5)
F r o m this relation and the observed retentions f o u n d from GPC the true r e t e n t i o n f o r d i f f e r ent molecular weights can be det erm i ned indirectly by e x tr ap o latio n to infinite circulation velocity. A n o t h e r approach f or estimating concentrations at the m e m b r a n e surface is the osmotic pressure model. Jv = L p ( A P - -
~m)
(6)
The difference in permeate flux o f water c om pared with the flux obtained when ultrafiltrating a test solution is assumed to be caused only by the osmotic pressure at the m e m b r a n e surface [ 2 ] . When the osmotic pressure is k n o w n the c o n c e n t r a t i o n can be f o u n d f r o m ref. [ 3 ] . lr -
RTC
/~---~- +
RT1.3~?C 2
/~v
(7)
A n o t h e r mo de l is the three-parameter model of Kedem and Katchalsky
[4]. J~ = L p ( A P - - oATr)
(8)
Js = P ( C m - - Cp) + (1 -- O ) J v C
(9)
In this mo d el the three parameters characterizing a m e m b r a n e are Lp, P and o. F o r an ideal m e m b r a n e where only solvent passes through the m e m b r a n e a = 1. If o = 0 no separation takes place. RESULTS AND DISCUSSION F o r each t y p e of m e m b r a n e at least three different pieces were tested and the results given are an average o f two or more. In Fig. 2 observed r e t e n t i o n calculated f r o m c o n c e n t r a t i o n measurements by polarimetry vs. circulation velocity are shown. F o u r o f the membranes had a r e p o r t e d cut-off value equal to 20000 daltons. These are all made of different materials. Going f r o m th e m e m b r a n e with the highest observed r e t e n t i o n to t hat with the lowest observed r e t e n t i o n the materials are: cellulose acetate, polysulphone, polyolefine and polyacrylonitrile. Although t h e y have the same r e p o r t e d cut-off, the mem br anes behaved very differently with the dextran, especially one o f the polyacrylonitrile membranes which had Robs----0. The A bcor m e m b r a n e called HFM 100, with a cut-off o f 10000 daltons, had a lower r e t e n t i o n than the A bc or m e m b r a n e called HFM 180 with a cut-off of 18000. In Figs. 3, 4 and 5 the observed r e t e nt i on vs. molecular weight and hydro-
192
dynamic radius is shown for circulation velocities o f 3 m/s and 5 m/s. At a higher circulation velocity the retention is higher, except in some cases such as DDS GR 61 PP and NITTO NTU 2 1 2 0 where there was n o difference between observed retention at 4m/s and at 5 m/s. In our previous work
I 0{1
Robs
S0
¢
DIIS 6 0 0
•
I)I)S (;R 61 PP
x
ABCOR IIFM 1 8 0
+
N[TTO NTIJ 2 1 2 0
o
DAICEL I)UY tltl
&
ABCOR ttFM
100
DAICEL DUY tt •
DAICEI+ DUY },1
0
i
,
1
i
3
4
5
Circulation
velocity
[m/s)
Fig. 2. Observed r e t e n t i o n versus circulation velocity.
1 O0
¢
Robs
I)DS 6 0 0
•
DBS (;R 61
+
NITTO NTU 2 1 2 0
PP
SO
/ ],X"
/¢,
[
3 m/s S m/s
115
25 i
I
10 0 0 0
35 i
45
I
20 0 0 0
i
30
RH(A)
I
000
P4W ( d a l t o n s )
Fig. 3. Observed r e t e n t i o n versus molecular w e i g h t and h y d r o d y n a m i c radius at circulation velocities o f 3 and 5 m/s.
193
[5] the observed retention for a cellulose acetate membrane was compared with that of a p o l y s u l p h o n e membrane with t h e same cut-off and the results were presented for five circulation velocities. The differences in molecular weight distribution in permeates were also investigated. It was f o u n d that at 100
Robs x
ABCOR HFM 18(/ ABCOR ItEM 1 0 0
50
5 m/s 5 m/s
5 0
35
25
I
i
l0
I
i
000
20
45
I
i
000
30
RH ['%)
I
000
H',~~ ( d a l t o n s )
Fig. 4. Observed r e t e n t i o n versus molecular w e i g h t and h y d r o d y n a m i c radius at circulation velocities o f 3 and 5 m/s.
100
Robs
(%)
50
J
DtJY 1111
o
I)AICEI,
"
DAICEI, I)UY It
•
DA1CI'21, D[JY M
3 m/s S m/s
T T
T
1~ 0
~
T
251
T
35j
I
!
10 0 0 0
20 0 0 0
45 !
30
!
000
RII (A) ,qW ( d a l t o n s )
Fig. 5. Observed r e t e n t i o n versus molecular w e i g h t and h y d r o d y n a m i c radius at circulation velocities o f 3 and 5 m/s.
194 a circulation velocity of 5 m/s, the permeate from a CA membrane had a more restricted molecular weight distribution than the permeate from a PS membrane. This effect was lost at low circulation velocities. In order to estimate the concentrations at the membrane surface, the mass transfer coefficients were calculated from eq. (2), see Table II. TABLE II MASS T R A N S F E R COEFFICIENTS AT D I F F E R E N T CIRCULATION VELOCITIES Circulation velocity, U m/s
Mass transfer coefficient k • l 0 s m/s
1 2 3 4 5
0.680 1.184 1.638 2.062 2.465
In Tables III and IV the concentrations at the membrane surface calculated u s i n g t h e f i l m t h e o r y m o d e l ( 1 ) w i t h t h e m a s s t r a n s f e r c o e f f i c i e n t s in T a b l e II are compared with concentrations calculated using the osmotic pressure m o d e l ( 6 ) . T h e l a t t e r o f t e n g i v e s h i g h e r Cm v a l u e s b u t f o r s o m e m e m b r a n e s t h e m o d e l s a r e in a g r e e m e n t . T h i s is t h e c a s e f o r t h e c e l l u l o s e a c e t a t e membrane with a cut-off of 20000 daltons and the polyacrylonitrile membrane with a cut, off of 5000 daltons. The osmotic pressure model does not take i n t o c o n s i d e r a t i o n o t h e r p a r a m e t e r s s u c h as e l e c t r o s t a t i c f o r c e s b e t w e e n t h e membrane and the fluid or clogging of the membrane pores which also affect t h e f l u x . Cm v a l u e s f o u n d a t a c i r c u l a t i o n v e l o c i t y o f 1 m / s w e r e s o m e t i m e s very high and these unrealistic values are not reported. T h e t r u e r e t e n t i o n f o u n d u s i n g t h e c a l c u l a t e d Cm v a l u e s s h o w n in T a b l e s
TABLE III Cm (%) CALCULATED USING THE FILM THEORY MODEL Membrane
Circulation velocity (m/s) 2
DDS GR 61 PP DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH
2.61 10.41 4.11 13.48 11.94 7.92
3 + 0.18 +- 1.78 + 0.16 + 4.13 + 5.77 +- 1.22
1.74 5.09 3.06 7.53 6.07 4.81
4 +- 0.15 +- 0.31 + 0.26 + 2.27 + 0.39 + 0.08
1.45 3.72 3.45 4.91 4.29 3.66
+ 0.07 + 0.24 +- 1.17 + 1.22 + 0.26 + 0.55
1.34 3.23 2.38 3.52 4.35 2.96
+- 0.01 +- 0.55 + 0.30 + 0.07 + 0.45 + 0.48
195 TABLE IV C m (%) C A L C U L A T E D
USING THE OSMOTIC PRESSURE
Membrane
Circulation velocity (m/s) 2
D D S G R 61 P P DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH DAICEL DUY H DAICEL DUY M
18.70 11.40 16.57 16.71 17.53 7.43 21.73 19.91
3 + 2.33 + 1.23 -+ 2 . 7 5 + 3.83 -+ 1 . 7 3 -+ 0 . 3 2 + 1.38 +- 2 . 1 1
MODEL
4
17.71 8.11 14.72 14.66 17.77 4.73 20.4 19.23
+ 2.85 + 1.84 +- 1 . 6 2 +- 4 . 7 5 + 1.65 + 3.00 + 1.06 + 18.7
5
16.63 5.18 8.18 12.41 17.05 3.5 19.20 16.64
-+ 2 . 7 0 +- 1 . 6 2 + 6.54 -+ 5 . 9 5 + 2.70 + 1.06 + 3.23
14.10 1.55 8.58 9.50 16.14 0.6 15.70 11.58
+ 3.00 + 1.20 +- 5 . 9 8 + 4.52 + 1.97 + 0.42 + 1.24
TABLE V T H E T R U E R E T E N T I O N (%) A T D I F F E R E N T C I R C U L A T I O N LATED USING Cm FROM THE FILM THEORY MODEL Membrane
CALCU-
Circulation velocity (m/s) 2
D D S G R 61 P P DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH
VELOCITIES
92.6 98.0 94.4 97.6 96.7 96.7
3 + 0.3 + 0.6 +- 2 . 1 + 0.8 + 1.9 -+ 0 . 1
90.5 97.2 92.2 96.0 95.3 95.1
4 + + + + + +
0.6 0.5 0.4 1.8 0.2 0.1
89.7 97.2 92.7 95.2 94.6 94.3
5 + 0.7 +- 0 . 3 +- 3 . 5 +- 0 . 8 + 0.7 + 0.1
89.1 97.7 91.3 95.0 94.4 92.9
+ 0.8 + 0.4 +- 1 . 8 + 1.8 +- 0 . 5 + 0.7
TABLE VI T H E T R U E R E T E N T I O N (%) A T D I F F E R E N T C I R C U L A T I O N LATED USING Cm FROM THE OSMOTIC PRESSURE MODEL Membrane
CALCU-
Circulation velocity (m/s) 2
D D S G R 61 P P DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH DAICEL DUY H
VELOCITIES
98.9 98.2 98.7 98.2 98.1 96.4 98.2
3 + 0.2 +- 0 . 5 + 0.2 + 0.6 + 0.1 + 0.7 + 0.3
99.3 98.2 98.4 97.9 98.4 93.7 98.2
4 + + + + + + +
0.5 0.6 0 0.8 0.2 4 0.2
99.1 97.9 96.1 98.0 98.7 93.3 92.3
5 + 0.1 + 0.5 + 2.7 -+ 0 . 7 + 0.3 +- 0 . 0 -+ 0 . 0
98.9 92.9 97.0 97.4 98.5
+ + + + +
0.3 6.1 1.9 0.8 0.2
9 9 . 0 +- 1 . 3
196 I I I a n d I V t u r n e d o u t t o b e v e r y h i g h f o r all c i r c u l a t i o n v e l o c i t i e s , a n d t h e r e was not much difference between the membranes. These true retention v a l u e s d i d n o t give m u c h i n f o r m a t i o n a b o u t t h e s e p a r a t i o n q u a l i t i e s o f t h e m e m b r a n e s , s e e T a b l e s V a n d VI. In Table VII the relationship between the true retention and molecular w e i g h t s is g i v e n . T h e d i f f e r e n c e i n t r u e r e t e n t i o n a t d i f f e r e n t m o l e c u l a r w e i g h t s is n o t t h e s a m e f o r all t h e m e m b r a n e s . T h i s i n d i c a t e s t h a t t h e i r p o r e s i z e d i s t r i b u t i o n s d i f f e r . T h e s a m e c o n c l u s i o n is d r a w n w h e n c o m p a r i n g t h e observed retentions in Figs. 3--5. TABLE VII THE TRUE RETENTION AT D I F F E R E N T MOLE WEIGHTS Membrane
Rtrue (%) at different tool wt 5 000
DDS GR 61 PP DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH
75.3 82.1 66.1 96.7 83.3 87.1
+ 4.7 +- 7.7 + 1.6 + 3.5 +- 8.3 +- 3.3
10 000
15 000
20 000
25 000
83.9 98.3 79.8 98.0 88.1 90.7
89.5 99.5 81.7 97.3 87.5 94.9
92.5 99.8 87.4 98.1
94.2 +- 1.1 99.5 + 0.7 96.1 + 0.6
+ 1.9 + 1.1 + 9.5 + 2.3 +- 3.3 + 0.9
+ 0.9 +- 0.5 + 5.8 +- 3.5 +- 3.4 + 1.1
+- 0.0 +- 0.3 +- 7.1 +- 2.3
96.5 -+ 0.4
95.8 + 1.0 97.3 + 0.4
I n T a b l e V I I I t h e r e s u l t s o f t h e t h r e e - p a r a m e t e r m o d e l a r e p r e s e n t e d in descending order from reflection coefficients. The coefficients o and P are f o u n d f r o m E q . ( 9 ) a n d Lp is f o u n d f r o m E q . (6). I t is i n t e r e s t i n g t o c o m p a r e t h e o v a l u e s w i t h t h e o b s e r v e d r e t e n t i o n s in F i g . 2. E x c e p t f o r t w o m e m b r a n e s , t h e D D S G R 6 1 P P a n d t h e A B C O R H F M 1 0 0 , t h e r e is a c o r r e l a t i o n between the two kinds of separation factors. The DAICEL DUY HH and NITTO NTU 2120 membranes have almost the same reflection coefficient. TABLE VIII RESULTS FROM THE THREE-PARAMETER MODEL Membrane
a
Lp" 104 (m3/m 2 • s" MPa)
P" 106 (m/s)
DDS 600 ABCOR HFM 180 ABCOR HFM 100 DAICEL DUY HH NITTO NTU 2120 DDS GR 61 PP DAICEL DUY H
0.74 0.70 0.68 0.63 0.60 0.54 0.48
1.04 1.97 1.82 1.25 1.32 0.86 5.07
1.85 3.14 3.71 3.99 3.44 2.26 16.88
197 T h e c o r r e l a t i o n is e v e n m o r e striking if t h e results f r o m t h e t h r e e p a r a m e t e r m o d e l are p r e s e n t e d in increasing o r d e r o f solute p e r m e a b i l i t y , see T a b l e IX. In this case o n l y o n e m e m b r a n e deviates. TABLE IX SOLUTE PERMEABILITY CALCULATED FROM THE THREE-PARAMETER MODEL Membrane
P" 106 (m/s)
DDS 600 DDS GR 61 PP ABCOR HFM 180 NITTO NTU 2120 ABCOR HFM 100 DAICEL DUY HH DAICEL DUY H
1.85 2.26 3.14 3.44 3.71 3.99 16.88
CONCLUSIONS
I t was f o u n d t h a t t h e m e m b r a n e s h a d v e r y d i f f e r e n t o b s e r v e d r e t e n t i o n s a l t h o u g h t h e r e p o r t e d cut, o f f values given b y t h e m a n u f a c t u r e r s w e r e , in s o m e cases, t h e same. T h e curves f o r o b s e r v e d r e t e n t i o n s h a d d i f f e r e n t f o r m s f o r d i f f e r e n t m e m b r a n e m a t e r i a l s . This indicates t h a t it is possible t o see t h a t t h e p o r e size d i s t r i b u t i o n differs f o r d i f f e r e n t m a t e r i a l s w i t h o u t giving a n y a b s o l u t e figures a b o u t t h e p o r e size d i s t r i b u t i o n o f t h e m e m b r a n e s . I t w a s also f o u n d t h a t t h e t r u e r e t e n t i o n values c a l c u l a t e d in this w a y w e r e n o t p a r t i c u l a r l y useful in describing t h e s e p a r a t i o n qualities o f U F m e m b r a n e s . T h e film t h e o r y m o d e l has b e e n criticized b e c a u s e it m a k e s use o f a m a s s t r a n s f e r c o r r e l a t i o n w h i c h is valid f o r n o n - p o r o u s d u c t s a n d w h i c h d o e s n o t c o n s i d e r t h e change o f p h y s i c a l p r o p e r t i e s , like viscosity a n d d i f f u s i o n coefficient, due to the concentration polarization phenomenon [6]. In o u r d e p a r t m e n t we are n o w f u r t h e r investigating t h e m a s s t r a n s f e r p h e n o m e n o n in o r d e r t o find a c o r r e l a t i o n w h i c h h o p e f u l l y e l i m i n a t e s these disadvantages. T h e o s m o t i c pressure m o d e l was u s e d t o c a l c u l a t e Cm values a n d h e r e t h e q u e s t i o n is w h e t h e r t h e Cm values f o u n d are t r u e . T h e t h r e e - p a r a m e t e r m o d e l o f K e d e m a n d K a t c h a l s k y gave p r o m i s i n g results w h e n c o m p a r e d w i t h o b s e r v e d r e t e n t i o n s a n d will b e i n v e s t i g a t e d f u r t h e r f o r o t h e r U F membranes. T h e m e t h o d d e s c r i b e d in this p a p e r is o n l y o n e o f t h e useful m e t h o d s f o r describing U F m e m b r a n e s . T h e r e is a great n e e d f o r a s t a n d a r d m e t h o d o f t e s t i n g s e p a r a t i o n qualities o f U F m e m b r a n e s , t h e r e f o r e w o r k in d e v e l o p i n g this m e t h o d will c o n t i n u e .
198
ACKNOWLEDGEMENTS
The authors wish to thank the membrane manufacturers for kindly supplying us with samples of their membranes and the Swedish Foundation for Membrane Technology for financial support.
REFERENCES 1 2 3 4 5
S. Nakao and S. Kimura, J. Chem. Eng. Jpn., 14 (1981) 32--37. G. Jonsson, Desalination, 51 (1984) 61--77. K. Granath, J. Colloid. Sci., 13 (1958) 308--328. O. Kedem and A. Katchalsky, Biochim. Biophys. Acta, 27 (1958) 229--246. G. Tr~gfirdh and K. ()lund, Separation characterization of ultrafiltration membranes, paper presented at the Europe--Japan Congress on Membranes and Membrane Processes, Stresa, Italy, June 18--22 (1984). 6 A.G. Fane, in R.J. Wakeman (Ed.), Progress in Filtration and Separation, Vol. 4, Elsevier, Amsterdam, 1986.
A METHOD FOR CHARACTERIZATION MEMBRANES
187
OF ULTRAFILTRATION
G. TR.~G~RDH and K. (~LUND Division o f Food Engineering, Lund University, P.O. Box 124, S-221 O0 Lund (Sweden) Tel. 46-107000; Telex 33533 L UNIVERS
(Received October 15, 1985)
ABSTRACT Several m e m b r a n e s h a v e b e e n t e s t e d in a t e s t l o o p especially b u i l t in o r d e r t o achieve w e l l - d e f i n e d f l o w c o n d i t i o n s at the m e m b r a n e surface. A t e s t s o l u t i o n o f d e x t r a n was u l t r a f i l t r a t e d at 0.5 MPa a n d 2 5 ° C at five c i r c u l a t i o n velocities f r o m 5 m / s to 1 m / s . This c o r r e s p o n d s to R e y n o l d s n u m b e r s o f 2 0 0 0 0 - - 4 0 0 0 at a c h a n n e l h e i g h t o f 2 m m . F o r t h e e v a l u a t i o n o f t h e results, the film-theory model, the three-parameter model of Kedem and Katchalsky a n d t h e o s m o t i c pressure m o d e l w e r e applied. T h e r e l a t i o n s h i p s b e t w e e n o b s e r v e d r e t e n t i o n a n d c i r c u l a t i o n v e l o c i t y as well as o b s e r v e d r e t e n t i o n versus m o l e c u l a r w e i g h t w e r e also c o n s i d e r e d .
SYMBOLS C C b
Cm Cp D Dh Js Jv h Lp Mn Mw P AP
- - c o n c e n t r a t i o n ( k m o l / m 3) -( C m - - Cp)/ln ( C m / C p ) - - s o l u t e c o n c e n t r a t i o n in t h e b u l k ( k m o l / m 3 ) - - s o l u t e c o n c e n t r a t i o n a t t h e m e m b r a n e surface ( k m o l / m 3 ) - - solute c o n c e n t r a t i o n in t h e p e r m e a t e ( k m o l / m 3) - - d i f f u s i o n c o e f f i c i e n t (m2/s) -- hydraulic diameter (m) - - solute f l u x ( k m o l / m 2" s) - - v o l u m e f l u x ( m 3 / m 2" s) -- mass transfer coefficient (m/s) - - p u r e w a t e r p e r m e a b i l i t y ( m 3 / m 2" S" MPa) - - n u m b e r average m o l e w e i g h t - - w e i g h t average m o l e w e i g h t - - solute p e r m e a b i l i t y (m/s) - - pressure ( M e a )
0011-9164/86/$03.50
© 1986 Elsevier Science Publishers B.V.
188 R RH Rob s Rtrue
Re Sc Sh T U ~? um
a
- - gas c o n s t a n t ( k J / k m o l " K) - - h y d r o d y n a m i c radius (A) - - o b s e r v e d r e t e n t i o n 1 - - Cp/Cb - - t r u e r e t e n t i o n 1 - - Cp/Cm -- Reynolds number -- Schmidt number -- Sherwood number - - t e m p e r a t u r e (K) - - circulation v e l o c i t y (m/s) - - viscosity ( k g / m . s) - - o s m o t i c pressure at t h e m e m b r a n e (MPa) -- reflection coefficient
INTRODUCTION T o d a y it is very difficult t o c o m p a r e m e m b r a n e s f r o m d i f f e r e n t m a n u facturers since t h e s e p a r a t i o n characteristics given are o f t e n based o n e x p e r i m e n t s using d i f f e r e n t test m o l e c u l e s u n d e r d i f f e r e n t o p e r a t i n g c o n d i t i o n s . T h e aim o f t h e w o r k p r e s e n t e d here is t o t a k e o n e step t o w a r d s a s t a n d a r d m e t h o d o f c h a r a c t e r i z i n g U F m e m b r a n e s . I n this p a p e r t h e test results f o r eight m e m b r a n e s r e p r e s e n t i n g five d i f f e r e n t p o l y m e r s are given. T h e t e s t e d m e m b r a n e s are listed in Table I. T h e test s o l u t i o n used was a 0.5% d e x t r a n s o l u t i o n ( P h a r m a c i a Fine Chemicals) w i t h an average m o l e w e i g h t o f 1 0 0 0 0 daltons. T o p r e v e n t self-interactions o f t h e d e x t r a n a 0.05 M NaC1 s o l u t i o n was used as a solvent. Moreover, in practice, salts are generally p r e s e n t w h e n ultrafiltrating m a c r o m o l e c u l e s . T h e r e f o r e , it is possible t o test t h e U F - - m e m b r a n e s in t h e p r e s e n c e o f a salt.
TABLE I THE MEMBRANES TESTED IN THIS WORK Manufacturer
Type
Membrane material
Cut-off (daltons)
DDS
GR 61 PP 600
polysulphone cellulose acetate
20000 20000
NITTO
NTU 2120
polyolefine
20000
ABCOR
HFM 100 HFM 180
confidential confidential
10000 18000
DAICEL
DUY HH DUY H DUY M
polyacrylonitrile polyacrylonitrile polyacrylonitrile
5000 10000 20000
189 EXPERIMENTAL DETAILS T h e m e m b r a n e tests T h e test l o o p used f o r t h e c h a r a c t e r i z a t i o n e x p e r i m e n t s c o n t a i n s a magnetic drive seal-less gear p u m p , a t h e r m o c o u p l e f o r t e m p e r a t u r e registration, a m e m b r a n e m o d u l e , a pressure gauge, a flow m e t e r and a heat exchanger. T h e m e m b r a n e m o d u l e is s h o w n in detail in Fig. 1. T h e inlet and t h e o u t l e t o f t h e m o d u l e have been c h a m f e r e d in o r d e r t o avoid sharp edges w h i c h w o u l d disturb the flow profile at the m e m b r a n e surface. F o r the same reason t h e g e o m e t r y o f t h e inlet is identical to t h a t o f t h e m e m b r a n e flow channel f o r a distance o f at least 40 hydraulic diameters. T h e m e m b r a n e area is 2 0 x 100 m m 2. Five d i f f e r e n t channel heights can be c h o s e n b e t w e e n 1--5 m m b y inserting P T F E rods o f v e r y e x a c t heights. T h e P T F E rods r u n all the way t h r o u g h t h e inlet c h a n n e l and t h e m o d u l e .
Fig. 1. Photograph showing the membrane module used in the experiments.
B e f o r e starting an u l t r a f i l t r a t i o n e x p e r i m e n t , distilled and m e m b r a n e filtered w a t e r is circulated in t h e test l o o p until s t e a d y state is reached. This is d o n e at the same o p e r a t i n g c o n d i t i o n s as used with t h e test solution afterwards. T h e circulation v e l o c i t y is regulated b y t h e p u m p , and n i t r o g e n gas is used to adjust t h e pressure i n d e p e n d e n t l y o f circulation velocities. The p e r m e a t e which is lost f r o m t h e test l o o p during an e x p e r i m e n t is i m m e d i a t e l y replaced b y p e r m e a t e f r o m a pressure vessel c o n n e c t e d to t h e circuit. When
190 steady state is reached, a test solution of dextran is ultrafiltered at five circulation velocities from 5 m/s to 1 m/s. This corresponds to Reynolds numbers of 20000--4000 at a channel height of 2 mm. Permeate is collected at each circulation velocity at constant permeate flux. Analysis
of samples
The samples collected during ultrafiltration are fractioned according to size by gel permeation chromatography, GPC, using a column packed with Sephacryl S-200 (Pharmacia Fine Chemicals) and detected by a differential refractometer (Optilab multiref 902 B). In this way the molecular weight distribution can be f o u n d and the observed retention o f different molecular weights can be estimated from relative concentration values. The samples are analysed by polarimetry for absolute concentration measurements. To find the correlation between molecular weight and particle size for dextran, five calibration fractions of known average molecular weights supplied by Pharmacia Fine Chemicals, were measured by light scattering. In this work the light source was a Spectra Physics 164-06, 2 W argon ion laser. The spectrometer and the compact autocorrelator/microcomputer unit used belong to the Malvern system 4600, and include software for the system. EVALUATION It is a fact that the concentration at the membrane surface is higher than that in the bulk because of concentration polarization. One way of estimating Cm, the concentration at the membrane surface, is to apply the film theory model, [1] Cm -- Cp
-- exp ( J v / h )
Cb -- Cp
(I)
To find Co the mass transfer coefficient k must be known. This is f o u n d for different circulation velocities from the Chilton and Colburn correlation Sh
-
k "Dh
0 . 0 2 3 - R e ° ' s " S c °'33
-
(2)
D
When Cm is known the true retention is easily calculated from C~
Rtrue -
-
Cm
Cp
(3)
The true retention versus circulation velocity f o u n d in this way does n o t take into account any molecular weights. To determine the true retention for different molecular weights the film theory model (1) and the relation k ~ U °'s
(4)
191 are used to g eth er in the f or m
n(1 "=I Robs
=el+con=
]
Rtrue
/
U0.---~
(5)
F r o m this relation and the observed retentions f o u n d from GPC the true r e t e n t i o n f o r d i f f e r ent molecular weights can be det erm i ned indirectly by e x tr ap o latio n to infinite circulation velocity. A n o t h e r approach f or estimating concentrations at the m e m b r a n e surface is the osmotic pressure model. Jv = L p ( A P - -
~m)
(6)
The difference in permeate flux o f water c om pared with the flux obtained when ultrafiltrating a test solution is assumed to be caused only by the osmotic pressure at the m e m b r a n e surface [ 2 ] . When the osmotic pressure is k n o w n the c o n c e n t r a t i o n can be f o u n d f r o m ref. [ 3 ] . lr -
RTC
/~---~- +
RT1.3~?C 2
/~v
(7)
A n o t h e r mo de l is the three-parameter model of Kedem and Katchalsky
[4]. J~ = L p ( A P - - oATr)
(8)
Js = P ( C m - - Cp) + (1 -- O ) J v C
(9)
In this mo d el the three parameters characterizing a m e m b r a n e are Lp, P and o. F o r an ideal m e m b r a n e where only solvent passes through the m e m b r a n e a = 1. If o = 0 no separation takes place. RESULTS AND DISCUSSION F o r each t y p e of m e m b r a n e at least three different pieces were tested and the results given are an average o f two or more. In Fig. 2 observed r e t e n t i o n calculated f r o m c o n c e n t r a t i o n measurements by polarimetry vs. circulation velocity are shown. F o u r o f the membranes had a r e p o r t e d cut-off value equal to 20000 daltons. These are all made of different materials. Going f r o m th e m e m b r a n e with the highest observed r e t e n t i o n to t hat with the lowest observed r e t e n t i o n the materials are: cellulose acetate, polysulphone, polyolefine and polyacrylonitrile. Although t h e y have the same r e p o r t e d cut-off, the mem br anes behaved very differently with the dextran, especially one o f the polyacrylonitrile membranes which had Robs----0. The A bcor m e m b r a n e called HFM 100, with a cut-off o f 10000 daltons, had a lower r e t e n t i o n than the A bc or m e m b r a n e called HFM 180 with a cut-off of 18000. In Figs. 3, 4 and 5 the observed r e t e nt i on vs. molecular weight and hydro-
192
dynamic radius is shown for circulation velocities o f 3 m/s and 5 m/s. At a higher circulation velocity the retention is higher, except in some cases such as DDS GR 61 PP and NITTO NTU 2 1 2 0 where there was n o difference between observed retention at 4m/s and at 5 m/s. In our previous work
I 0{1
Robs
S0
¢
DIIS 6 0 0
•
I)I)S (;R 61 PP
x
ABCOR IIFM 1 8 0
+
N[TTO NTIJ 2 1 2 0
o
DAICEL I)UY tltl
&
ABCOR ttFM
100
DAICEL DUY tt •
DAICEI+ DUY },1
0
i
,
1
i
3
4
5
Circulation
velocity
[m/s)
Fig. 2. Observed r e t e n t i o n versus circulation velocity.
1 O0
¢
Robs
I)DS 6 0 0
•
DBS (;R 61
+
NITTO NTU 2 1 2 0
PP
SO
/ ],X"
/¢,
[
3 m/s S m/s
115
25 i
I
10 0 0 0
35 i
45
I
20 0 0 0
i
30
RH(A)
I
000
P4W ( d a l t o n s )
Fig. 3. Observed r e t e n t i o n versus molecular w e i g h t and h y d r o d y n a m i c radius at circulation velocities o f 3 and 5 m/s.
193
[5] the observed retention for a cellulose acetate membrane was compared with that of a p o l y s u l p h o n e membrane with t h e same cut-off and the results were presented for five circulation velocities. The differences in molecular weight distribution in permeates were also investigated. It was f o u n d that at 100
Robs x
ABCOR HFM 18(/ ABCOR ItEM 1 0 0
50
5 m/s 5 m/s
5 0
35
25
I
i
l0
I
i
000
20
45
I
i
000
30
RH ['%)
I
000
H',~~ ( d a l t o n s )
Fig. 4. Observed r e t e n t i o n versus molecular w e i g h t and h y d r o d y n a m i c radius at circulation velocities o f 3 and 5 m/s.
100
Robs
(%)
50
J
DtJY 1111
o
I)AICEI,
"
DAICEI, I)UY It
•
DA1CI'21, D[JY M
3 m/s S m/s
T T
T
1~ 0
~
T
251
T
35j
I
!
10 0 0 0
20 0 0 0
45 !
30
!
000
RII (A) ,qW ( d a l t o n s )
Fig. 5. Observed r e t e n t i o n versus molecular w e i g h t and h y d r o d y n a m i c radius at circulation velocities o f 3 and 5 m/s.
194 a circulation velocity of 5 m/s, the permeate from a CA membrane had a more restricted molecular weight distribution than the permeate from a PS membrane. This effect was lost at low circulation velocities. In order to estimate the concentrations at the membrane surface, the mass transfer coefficients were calculated from eq. (2), see Table II. TABLE II MASS T R A N S F E R COEFFICIENTS AT D I F F E R E N T CIRCULATION VELOCITIES Circulation velocity, U m/s
Mass transfer coefficient k • l 0 s m/s
1 2 3 4 5
0.680 1.184 1.638 2.062 2.465
In Tables III and IV the concentrations at the membrane surface calculated u s i n g t h e f i l m t h e o r y m o d e l ( 1 ) w i t h t h e m a s s t r a n s f e r c o e f f i c i e n t s in T a b l e II are compared with concentrations calculated using the osmotic pressure m o d e l ( 6 ) . T h e l a t t e r o f t e n g i v e s h i g h e r Cm v a l u e s b u t f o r s o m e m e m b r a n e s t h e m o d e l s a r e in a g r e e m e n t . T h i s is t h e c a s e f o r t h e c e l l u l o s e a c e t a t e membrane with a cut-off of 20000 daltons and the polyacrylonitrile membrane with a cut, off of 5000 daltons. The osmotic pressure model does not take i n t o c o n s i d e r a t i o n o t h e r p a r a m e t e r s s u c h as e l e c t r o s t a t i c f o r c e s b e t w e e n t h e membrane and the fluid or clogging of the membrane pores which also affect t h e f l u x . Cm v a l u e s f o u n d a t a c i r c u l a t i o n v e l o c i t y o f 1 m / s w e r e s o m e t i m e s very high and these unrealistic values are not reported. T h e t r u e r e t e n t i o n f o u n d u s i n g t h e c a l c u l a t e d Cm v a l u e s s h o w n in T a b l e s
TABLE III Cm (%) CALCULATED USING THE FILM THEORY MODEL Membrane
Circulation velocity (m/s) 2
DDS GR 61 PP DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH
2.61 10.41 4.11 13.48 11.94 7.92
3 + 0.18 +- 1.78 + 0.16 + 4.13 + 5.77 +- 1.22
1.74 5.09 3.06 7.53 6.07 4.81
4 +- 0.15 +- 0.31 + 0.26 + 2.27 + 0.39 + 0.08
1.45 3.72 3.45 4.91 4.29 3.66
+ 0.07 + 0.24 +- 1.17 + 1.22 + 0.26 + 0.55
1.34 3.23 2.38 3.52 4.35 2.96
+- 0.01 +- 0.55 + 0.30 + 0.07 + 0.45 + 0.48
195 TABLE IV C m (%) C A L C U L A T E D
USING THE OSMOTIC PRESSURE
Membrane
Circulation velocity (m/s) 2
D D S G R 61 P P DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH DAICEL DUY H DAICEL DUY M
18.70 11.40 16.57 16.71 17.53 7.43 21.73 19.91
3 + 2.33 + 1.23 -+ 2 . 7 5 + 3.83 -+ 1 . 7 3 -+ 0 . 3 2 + 1.38 +- 2 . 1 1
MODEL
4
17.71 8.11 14.72 14.66 17.77 4.73 20.4 19.23
+ 2.85 + 1.84 +- 1 . 6 2 +- 4 . 7 5 + 1.65 + 3.00 + 1.06 + 18.7
5
16.63 5.18 8.18 12.41 17.05 3.5 19.20 16.64
-+ 2 . 7 0 +- 1 . 6 2 + 6.54 -+ 5 . 9 5 + 2.70 + 1.06 + 3.23
14.10 1.55 8.58 9.50 16.14 0.6 15.70 11.58
+ 3.00 + 1.20 +- 5 . 9 8 + 4.52 + 1.97 + 0.42 + 1.24
TABLE V T H E T R U E R E T E N T I O N (%) A T D I F F E R E N T C I R C U L A T I O N LATED USING Cm FROM THE FILM THEORY MODEL Membrane
CALCU-
Circulation velocity (m/s) 2
D D S G R 61 P P DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH
VELOCITIES
92.6 98.0 94.4 97.6 96.7 96.7
3 + 0.3 + 0.6 +- 2 . 1 + 0.8 + 1.9 -+ 0 . 1
90.5 97.2 92.2 96.0 95.3 95.1
4 + + + + + +
0.6 0.5 0.4 1.8 0.2 0.1
89.7 97.2 92.7 95.2 94.6 94.3
5 + 0.7 +- 0 . 3 +- 3 . 5 +- 0 . 8 + 0.7 + 0.1
89.1 97.7 91.3 95.0 94.4 92.9
+ 0.8 + 0.4 +- 1 . 8 + 1.8 +- 0 . 5 + 0.7
TABLE VI T H E T R U E R E T E N T I O N (%) A T D I F F E R E N T C I R C U L A T I O N LATED USING Cm FROM THE OSMOTIC PRESSURE MODEL Membrane
CALCU-
Circulation velocity (m/s) 2
D D S G R 61 P P DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH DAICEL DUY H
VELOCITIES
98.9 98.2 98.7 98.2 98.1 96.4 98.2
3 + 0.2 +- 0 . 5 + 0.2 + 0.6 + 0.1 + 0.7 + 0.3
99.3 98.2 98.4 97.9 98.4 93.7 98.2
4 + + + + + + +
0.5 0.6 0 0.8 0.2 4 0.2
99.1 97.9 96.1 98.0 98.7 93.3 92.3
5 + 0.1 + 0.5 + 2.7 -+ 0 . 7 + 0.3 +- 0 . 0 -+ 0 . 0
98.9 92.9 97.0 97.4 98.5
+ + + + +
0.3 6.1 1.9 0.8 0.2
9 9 . 0 +- 1 . 3
196 I I I a n d I V t u r n e d o u t t o b e v e r y h i g h f o r all c i r c u l a t i o n v e l o c i t i e s , a n d t h e r e was not much difference between the membranes. These true retention v a l u e s d i d n o t give m u c h i n f o r m a t i o n a b o u t t h e s e p a r a t i o n q u a l i t i e s o f t h e m e m b r a n e s , s e e T a b l e s V a n d VI. In Table VII the relationship between the true retention and molecular w e i g h t s is g i v e n . T h e d i f f e r e n c e i n t r u e r e t e n t i o n a t d i f f e r e n t m o l e c u l a r w e i g h t s is n o t t h e s a m e f o r all t h e m e m b r a n e s . T h i s i n d i c a t e s t h a t t h e i r p o r e s i z e d i s t r i b u t i o n s d i f f e r . T h e s a m e c o n c l u s i o n is d r a w n w h e n c o m p a r i n g t h e observed retentions in Figs. 3--5. TABLE VII THE TRUE RETENTION AT D I F F E R E N T MOLE WEIGHTS Membrane
Rtrue (%) at different tool wt 5 000
DDS GR 61 PP DDS 600 NITTO NTU 2120 ABCOR HFM 100 ABCOR HFM 180 DAICEL DUY HH
75.3 82.1 66.1 96.7 83.3 87.1
+ 4.7 +- 7.7 + 1.6 + 3.5 +- 8.3 +- 3.3
10 000
15 000
20 000
25 000
83.9 98.3 79.8 98.0 88.1 90.7
89.5 99.5 81.7 97.3 87.5 94.9
92.5 99.8 87.4 98.1
94.2 +- 1.1 99.5 + 0.7 96.1 + 0.6
+ 1.9 + 1.1 + 9.5 + 2.3 +- 3.3 + 0.9
+ 0.9 +- 0.5 + 5.8 +- 3.5 +- 3.4 + 1.1
+- 0.0 +- 0.3 +- 7.1 +- 2.3
96.5 -+ 0.4
95.8 + 1.0 97.3 + 0.4
I n T a b l e V I I I t h e r e s u l t s o f t h e t h r e e - p a r a m e t e r m o d e l a r e p r e s e n t e d in descending order from reflection coefficients. The coefficients o and P are f o u n d f r o m E q . ( 9 ) a n d Lp is f o u n d f r o m E q . (6). I t is i n t e r e s t i n g t o c o m p a r e t h e o v a l u e s w i t h t h e o b s e r v e d r e t e n t i o n s in F i g . 2. E x c e p t f o r t w o m e m b r a n e s , t h e D D S G R 6 1 P P a n d t h e A B C O R H F M 1 0 0 , t h e r e is a c o r r e l a t i o n between the two kinds of separation factors. The DAICEL DUY HH and NITTO NTU 2120 membranes have almost the same reflection coefficient. TABLE VIII RESULTS FROM THE THREE-PARAMETER MODEL Membrane
a
Lp" 104 (m3/m 2 • s" MPa)
P" 106 (m/s)
DDS 600 ABCOR HFM 180 ABCOR HFM 100 DAICEL DUY HH NITTO NTU 2120 DDS GR 61 PP DAICEL DUY H
0.74 0.70 0.68 0.63 0.60 0.54 0.48
1.04 1.97 1.82 1.25 1.32 0.86 5.07
1.85 3.14 3.71 3.99 3.44 2.26 16.88
197 T h e c o r r e l a t i o n is e v e n m o r e striking if t h e results f r o m t h e t h r e e p a r a m e t e r m o d e l are p r e s e n t e d in increasing o r d e r o f solute p e r m e a b i l i t y , see T a b l e IX. In this case o n l y o n e m e m b r a n e deviates. TABLE IX SOLUTE PERMEABILITY CALCULATED FROM THE THREE-PARAMETER MODEL Membrane
P" 106 (m/s)
DDS 600 DDS GR 61 PP ABCOR HFM 180 NITTO NTU 2120 ABCOR HFM 100 DAICEL DUY HH DAICEL DUY H
1.85 2.26 3.14 3.44 3.71 3.99 16.88
CONCLUSIONS
I t was f o u n d t h a t t h e m e m b r a n e s h a d v e r y d i f f e r e n t o b s e r v e d r e t e n t i o n s a l t h o u g h t h e r e p o r t e d cut, o f f values given b y t h e m a n u f a c t u r e r s w e r e , in s o m e cases, t h e same. T h e curves f o r o b s e r v e d r e t e n t i o n s h a d d i f f e r e n t f o r m s f o r d i f f e r e n t m e m b r a n e m a t e r i a l s . This indicates t h a t it is possible t o see t h a t t h e p o r e size d i s t r i b u t i o n differs f o r d i f f e r e n t m a t e r i a l s w i t h o u t giving a n y a b s o l u t e figures a b o u t t h e p o r e size d i s t r i b u t i o n o f t h e m e m b r a n e s . I t w a s also f o u n d t h a t t h e t r u e r e t e n t i o n values c a l c u l a t e d in this w a y w e r e n o t p a r t i c u l a r l y useful in describing t h e s e p a r a t i o n qualities o f U F m e m b r a n e s . T h e film t h e o r y m o d e l has b e e n criticized b e c a u s e it m a k e s use o f a m a s s t r a n s f e r c o r r e l a t i o n w h i c h is valid f o r n o n - p o r o u s d u c t s a n d w h i c h d o e s n o t c o n s i d e r t h e change o f p h y s i c a l p r o p e r t i e s , like viscosity a n d d i f f u s i o n coefficient, due to the concentration polarization phenomenon [6]. In o u r d e p a r t m e n t we are n o w f u r t h e r investigating t h e m a s s t r a n s f e r p h e n o m e n o n in o r d e r t o find a c o r r e l a t i o n w h i c h h o p e f u l l y e l i m i n a t e s these disadvantages. T h e o s m o t i c pressure m o d e l was u s e d t o c a l c u l a t e Cm values a n d h e r e t h e q u e s t i o n is w h e t h e r t h e Cm values f o u n d are t r u e . T h e t h r e e - p a r a m e t e r m o d e l o f K e d e m a n d K a t c h a l s k y gave p r o m i s i n g results w h e n c o m p a r e d w i t h o b s e r v e d r e t e n t i o n s a n d will b e i n v e s t i g a t e d f u r t h e r f o r o t h e r U F membranes. T h e m e t h o d d e s c r i b e d in this p a p e r is o n l y o n e o f t h e useful m e t h o d s f o r describing U F m e m b r a n e s . T h e r e is a great n e e d f o r a s t a n d a r d m e t h o d o f t e s t i n g s e p a r a t i o n qualities o f U F m e m b r a n e s , t h e r e f o r e w o r k in d e v e l o p i n g this m e t h o d will c o n t i n u e .
198
ACKNOWLEDGEMENTS
The authors wish to thank the membrane manufacturers for kindly supplying us with samples of their membranes and the Swedish Foundation for Membrane Technology for financial support.
REFERENCES 1 2 3 4 5
S. Nakao and S. Kimura, J. Chem. Eng. Jpn., 14 (1981) 32--37. G. Jonsson, Desalination, 51 (1984) 61--77. K. Granath, J. Colloid. Sci., 13 (1958) 308--328. O. Kedem and A. Katchalsky, Biochim. Biophys. Acta, 27 (1958) 229--246. G. Tr~gfirdh and K. ()lund, Separation characterization of ultrafiltration membranes, paper presented at the Europe--Japan Congress on Membranes and Membrane Processes, Stresa, Italy, June 18--22 (1984). 6 A.G. Fane, in R.J. Wakeman (Ed.), Progress in Filtration and Separation, Vol. 4, Elsevier, Amsterdam, 1986.