formation and characteristics of dynamic membrane for ultrafiltration of protein in binary protein...

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journal of

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ELSEVIER Journal of Membrane Science 92 ( 1994) 107-l 15

Formation and characteristics of dynamic membrane ultrafiltration of protein in binary protein system

Hideto Matsuyama*, Takahide Shimomura, Masaaki Teramoto

for

Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606. Japan

(Received January 12, 1993; accepted in revised form January 24, 1994)

Abstract

A self-rejecting type dynamic membrane was formed by filtering a protein solution through a porous ceramic tube. In the dynamic membrane formed by a single protein (ovalbumin) solution, the effects of the linear velocity along the membrane, the bulk protein concentration, the pressure and pH in the feed solution on both membrane formation and ultrafiltration performance were studied in detail. The apparent protein rejection reached more than 0.8 in all cases. The volume fluxes at steady state increased with increasing linear velocity and with decreasing bulk concentration, but the pressure hardly influenced the flux. At the isoelectric pH, the flux in the early stages was the largest and that in the steady state of membrane formation was smallest. This behaviour is characteristic of a partially permeable dynamic membrane. The formation of a dynamic membrane was further attempted by using a binary mixture of proteins (ovalbumin and y-globulin) in solution. It is suggested that the formation of deposits occurred independently for the two proteins. The flux at steady state in the binary protein system agreed with the smaller flux in the corresponding single protein system.

Keywords: Dynamic membrane; Ultrafiltration; Concentration polarization equation; Gel polarization model; Binary mixture of proteins

1. Introduction

Dynamic membranes (dynamically formed membranes) are produced by filtering feed solutions containing membrane-forming materials such as inorganic hydrous oxides and macromolecular materials through porous supports. A fouling phenomenon accompanied by the formation of a gel layer, which is usually a disad- vantage in membrane operation, is actively ex- ploited in the formation of these membranes. Dynamic membranes are classified into two

types, a self-rejecting type and a pre-coated type [ 11. In the self-rejecting type the membrane- forming materials are the same as those to be separated, whereas they are different in the pre- coated type. The advantages of a dynamic membrane are high permeability, ease of regeneration and removal of the membrane, and the possibil- ity of membrane formation by various materials.

Research on dynamic membranes was ‘first carried out by Marcinkowsky’ et al. in 1966 [ 2 1. Then, these membranes were mainly applied for the rejection of salts in the reverse osmosis process [ 3-6 1. Igawa [ 7 ] reviewed in detail the per-

‘Corresponding author.

0376-7388/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved .S.SDI 0376-7388 (94)00038-Z

formance of the dynamic membrane for reverse osmosis.

There have been few studies on these membranes for the purpose of ultrafiltration [ 8- 111. Ohtani et al. [ 12 ] and Imanara et al. [ 131 reported the separation and concentration of proteins by these ultrafiltration membranes. How- ever, they used a feed solution containing only a single protein, although in practice the solutions to be treated contain protein mixtures.

In this work, we studied the effects of various experimental conditions on the ultrafiltration performance of the self-rejecting type of dynamic membrane formed by proteins. Investi- gation on membrane formation by feed solutions containing binary mixtures of proteins was a further objective of this work.

2. Experimental

The schematic layout of the system is shown in Fig. 1. The feed solutions containing protein were supplied from the feed tank, controlled at 298 K, to the membrane module by a pump (Iwaki Co., Ltd., LK-B52) equipped with an air chamber to prevent pulsed Bow. The membrane module consisted of an alumina ceramic tube (TDK Co., Ltd., DC-0005@, mean pore size 0.05 pm, length 45 cm, effective membrane area 65 cm*, outer diameter 4.6 mm, inner diameter: 1 mm) and an outer cylindrical stainless steel ves- sel (inner diameter 7.3 mm). The feed solution was passed along the ceramic tube in a cross-flow

Membrane module I

Pump

L I Feed tank

Fig. I. Schematic layout of the experimental system.

pattern. The flow rates were changed in the range of laminar flow. Permeate through the ceramic tube was returned to the feed tank.

Ovalbumin (MW 45 000, isoelectric point 4.6 ) purchased from Nacalai Tesque Co., Ltd. and/ or bovine Cohn fraction II y-globulin (MW N 160 000, isoelectric point 5.5-7.5) purchased from Organon Teknika N.V. were used as the membrane forming proteins. Electrophoresis experiments on the y-globulin revealed five main bands at pH values of 5.5, 6.4, 6.7, 7.1 and 7.5. The pH values of the feed solutions were ad- justed by 0.01 mol/dm3 KH2P04-Na2HP04 buffer (pH 5.5-8.0) and 0.01 mol/dm3 Na2P0, - citric acid buffer (pH 3.0-5.0). Ionic strength was maintained at 0.1 mol/dm3 by the addition of NaCl. The concentrations of the proteins were measured by a spectrophotometer (Hitachi UV3200, measurement at 280 nm) for the single protein system and by gel permeation chromatography (Shimadzu Co., Ltd., pump LC- 6A, detector SPD-6A, column Shim-pack Diol- 300) for the binary protein system.

3. Results and discussion

3.1. Dynamic membrane in single protein (ovalbumin) system

Effect of linear velocity, protein concentration and pressure

Fig. 2 shows the effect of the linear velocity along the membrane surface on the time dependence of apparent rejection Robs given by Eq. ( 1) and volume flux through the membrane Jv.

R ch= (G-G>/G (1)

Here, C, and C, are bulk and permeate concentrations of protein, respectively. JV decreased with time and approached a constant value after 180 min. The constant values of Jv were fairly small compared with the water flux (7.02 x 1 Ow4 m/s at dP= 10 atm). The values of Robs were higher than 0.9, which indicates that a self-rejecting type of dynamic membrane for the ultrafiltration of protein had been formed. The constant volume flux after 180 min JV,con depended

H. Matsuyama et al. /Journal oj’hiembrane Science 92 (1994) 107- I15 109

OO- 50 100 150 200 Time Lminl

Fig. 2. Effect of linear velocity on time dependence of Roba and Jv. pH 6.0, C&O. 1 wt%, AP= 10 atm. Protein: ovalbumin.

0- _ 1001

2 80’ - 0 60 ;:p cb=;.g

-0 ‘;: 7'

40

li?_.-A \ z 0:06 wt.7 ‘e\,\ 0 0.10 WtX

20 ~&+--*- -- E

00 50 100 150 200 Time Imlnl

Fig. 3. Effect of C, on time dependence of R,, and Jv. pH 6.0, u=O.55 m/s, AP= 10 atm., Protein: ovalbumin.

on the linear velocity because this velocity, which contributes greatly to the mass transfer coefficient in the boundary layer, influences the protein concentration at the membrane surface, as described below. Robs was almost independent of the linear velocity.

The effect of C,, is shown in Fig. 3. The higher the value of C,, the lower Jv became. This is because the formation of the deposit layer occurs more easily with an increase of C,. Robs increased with increase in C,,. However, the real rejection (C, - C,) /C,, where C, is the concen-

tration at the membrane surface estimated by Eq. (2) as described below, was 0.999 at C,=O.Ol wt% and that at C,= 0.1 wt% was 0.998. This suggested that the real rejection was hardly affected by C,.

Fig. 4 shows the effect of the pressure difference AP. JV,con was hardly affected by the pressure. This means that the resistance to permeation became larger with the increase in pressure. Because Robs increased with the increase of pressure, an increase in density of the deposit layer, which corresponds to an increase in specific resistance of the layer, might be brought about at high pressure.

Protein concentration at membrane surface In order to discuss the effects of experimental

conditions on JV,con, we need to estimate the protein concentration at the membrane surface C,. The value of C,,, is obtained from the following concentration polarization equation [ 141:

(C,-C,)/(C,-C,)=exp(J,,~,,lk) (2) Here, k is the mass transfer coefftcient in the boundary layer, and is given by the Leveque equation under the laminar flow condition [ 12 J :

Sh= 1.62(Re-Sc-d/l)‘13 (3)

That is, k- 1 (j2u’/3D2/3d-1/3[--1/3 - . (4)

0- 0 50 100 150 20b

Time lmlnl

Fig. 4. Effect of AP on time dependence of Rob and Jv. pH 6.0, C,,=O. 1 wt%, u=O.55 m/s. Protein: ovalbumin.

110 H. Matsuyama et al. /Journal of Membrane Science 92 (1994) 107-l 15

We used the value of 7.5~ lo-” m*/s [ 151 as the diffusivity of ovalbumin.

Fig. 5 (a), (b) and (c) shows the calculated C,,, values with Jv,con. The values of C, were nearly constant under all experimental conditions. As can be found from Eq. (2)) both an increase in k brought about by increase in the linear velocity, and a decrease in C, lower C,. Therefore, JV,con tended to increase with increasing linear velocity and also with decreasing C,, as can be seen in Fig. 5 (a) and (b ), to keep C, constant. Because the pressure does not influence the value of k, JVscon was nearly constant at any pressure.

Shen and Probstein [ 161 suggested that the concentration dependence of diffusivity through the boundary layer had to be considered in order to estimate C,. The usual concentrations of proteins at the membrane surface were reported to be lo-30 wt% [ 171. However, in this system, the bulk concentration was low and the concentration at the membrane surface was also as low as

o’o i -2.0 -1.5 -1.0 -0.5

Fig.S.Effectof(a)u,(b)C,and(c)dPonC,andJv. (a) pH 6.0, C,=O.l wt%,dP= IOatm; (b) pH 6.0, u=O.55 m/s, dP= 10atm; (c) pH 6.0, C,=O.l wtl, 24~0.55 m/s. Protein: ovalbumin.

2.3 wt%, so that the effect of the concentration in the boundary layer on the parameters is considered not to be significant.

The experimental finding that C,,, was constant in various conditions means that deposition is stopped once C, becomes lower than a certain critical value (2.3 wt% for ovalbumin) and the formation of the deposit layer depends only on C,. Of course, the value of C, is depen- dent on the degree of concentration polarization, the adsorptiveness of the protein and so on. A constant value of C, is predicted by the gel polarization model [ 17- 19 1.

Effect of pH

Fig. 6 shows the effect of pH on Robs and Jv.

The volume flux at steady state JV,con was smallest at pH 4.6, which is the isoelectric point pI of ovalbumin. This is because, at p1, the electrical repulsion is weak and the deposit layer forms easily. Such a phenomenon was earlier reported with respect to the fouling of ultrafiltration membranes [ 201. The protein concentrations at the membrane surface in the steady state, estimated from Jv,con, are listed in Table 1. The concentration at pI is the lowest, as expected. The values of C, were calculated by using the constant diffusivity. Although the diffusivity may vary with pH and the values of C, may thus con-

Tlme lminl

Fig. 6. Effect of pH on time dependence of R,,, and Jv. C,=O. I wt%, ~~0.55 m/s, LIP= 10 atm. Protein: ovalbumin.

H. Matsuyama et al. /Journal ofMembrane Science 92 (1994) 107-I I5 111

Table 1 Protein concentration at membrane surface in steady state

PH Concentration at membrane surface (wt%)

3.0 4.8 4.6 0.97 6.0 2.3

tain errors, the generalization that C, is lowest at p1 is considered to be valid.

In the early stage of membrane formation, the protein rejection Robs at p1 is the lowest. This is probably due to the small electrical repulsion and the compact conformation of the protein. When the rejection is low, the protein concentration near the membrane pores does not become high because the protein can pass through the pores. Therefore the initial plugging of pores is not likely to occur at p1 although it may be rapid in gen- eral. This is why Jv in the early stages is largest at p1, contrary to the tendency of Jv,con as can be seen in Fig. 6. This phenomenon is characteristic of a dynamic membrane, through which the solute can permeate in the early stage.

3.2. Dynamic membrane in binary protein system

As far as we know, there has been no investi- gation on the dynamic membrane formed by solutions of protein mixtures. Even with respect to the fouling phenomena of an ultrafiltration membrane studies using protein mixtures have seldom been reported [ 18,2 11.

Fig. 7 shows the experimental results using a protein mixture (ovalbumin and y-globulin) solution and each single protein solution at pH 3.0. In the early stage, Jv was smaller and the deposit layer formed more easily in the binary protein system than with each single protein. However, J V,COll in the binary protein system agreed with the smaller JV,con in the single protein system, that is, the Jv,con of ovalbumin. The value of Robs of y-globulin in the binary protein system was much larger than that in the single protein system, whereas Robs of ovalbumin in the binary protein system was only a little larger. In the binary pro-

8

0 **' I I I I

osingle avalbumln system *single globulin system - fJblnory protein system

4

0 60 120 180 Time Imlnl

Fig. 7. Time dependence ofR, and Jv in binary protein system and each single protein system. pH 3.0, u=O.55 m/s, AP= 10 atm. Single protein system: C,, (ovalbumin) =O.Ol wt%, C,, (y-globulin) = 0.03 wt%, binary protein system: C,,=O.O4 wt% (ovalbumin 0.01 wt%+y-globulin 0.03 wt%).

8 0

. g]obulln>si"gie system

," $$f$,"> binary system

I

60

-I o stngle ovalbumln system l single globulln system o binary protein system

0

i

I OO

I I I 60 120 180

TlllE Imlnl

Fig. 8. Time dependence of RObg and .lv in binary protein system and each single protein system. pH 5.3, 24=0.55 m/s, AP= 10 atm. Single protein system: C, (ovalbumin) =O.Ol wt%, C, (y-globulin)=0.05 wt%, binary protein system: C,=O.O6 wt% (ovalbumin 0.01 wt%+pglobulin 0.05 wt%).

tein systemRob, of y-globulin was larger than that of ovalbumin because of the higher molecular weight. In the data for single protein systems, y-

112 H. Malsuyarna cl al. /Journal of Membrane Science 92 (I 994) 107- 115

globulin had a lower initial rejection than ovalbumin, although it is the larger protein. How- ever, this is not surprising because the initial rejection depends not only on the size of the protein but also on the ease of deposit formation as influenced by the affinity of the protein and the support membrane, the interaction between proteins and so on.

the slope of a plot of 1 /Jv versus t. The relationships between 1 /Jv and t, obtained from the data in Figs. 7 and 8, are shown in Fig. 9(a) and (b). In each case, linear relationships were obtained initially and gradually deviated from linearity because the formation of the deposit layer stopped.

The results at pH 5.3 are also shown in Fig. 8. J V,COll in the binary protein system agreed with that of y-globulin in single protein system, which was smaller than that of ovalbumin. Thus, JVzcon in the binary system was confirmed as agreeing with the smaller Jv,con in the single protein system regardless of the kind of protein. With respect to Robs, the same tendency as at pH 3.0 was observed.

This means that the deposit formation rates were constant in each early stage, although whether plugging of the membrane pores or increase of the deposit layer thickness was the dominating phenomenon was not clear.

The slopes of the linear relationships are listed in Table 2. In the two cases, at different pH values, the slope in the binary system is almost in agreement with the sum of the two slopes in the single protein system. Therefore the above as-

The relationship between the volume flux and the formation rate of the deposit layers is needed when discussing JV,con in the binary protein system. The flux is expressed as follows.

Jv(t)=dP/@u[& +R(t) II (5)

Here, p is viscosity and R. and R(t) are the resistance of the support membrane and that of the deposit layer at time t, respectively. R(t) is given

by

R(t)=aM(t) (6)

where CY is the specific resistance per unit mass and M(t) is the mass of the deposit layer at t. From Eqs. (5 ) and (6), the following equation is derived:

(a)

I I I I I _ 0 20 40 60

Time IminI

d(llJv)ldt=(Y(~uldP)(dMldt) (7)

In the binary protein system, Eqs. ( 8 ) and (9 ) are obtained:

Jv(t) =dPlb[& +alMl (t>

+WK(t) II (8)

0 20 40 60 +a,(dM,ldt) 1 (9) Time [mini

Here it was assumed that the values of cy in the binary protein system were constant and equal to those in the single protein system. Thus the deposit formation rate dM/dt can be found from

Fig. 9. Relationship between 1 /Jv and time. (a) pH 3.0. 0, single ovalbumin system; 0, single y-globulin system; 0, binary protein system. (b) pH 5.3. 0, single ovalbumin system, 0, single y-globulin system; Cl, binary protein system.

H. Malsuyama et al. IJournalofMembraneScience 92 (1994) 107-115 113

Table 2 Initial slope of 1 /Jv for various cases [ 1 /m]

PI-I Single ovalbumin Single y-globulin Binary protein system system system

3.0 40.0 15.0 56.6 5.3 38.3 46.1 91.7

sumption that the values of (Y in the binary system were equal to those in the single protein system was confirmed as being valid, at least in these experimental conditions. It is also suggested that the deposit formation rate in the binary protein system was equal to the sum of each rate in the single protein systems, and that deposit formation in the binary system occurred for each protein independently of the other.

The fact that cy values in the binary system were equal to those in the single protein systems indicated that the packing densities of proteins in the binary system were similar to those in the single protein systems. When two different proteins are used as solutes, it is usually considered that the difference in the size and charge of the proteins influences the packing densities. How- ever, if each protein forms a deposit layer alone more easily than formation occurs with the mixture of two types of protein, there are domains formed from each protein alone in the deposit layer. In this case, the effects of the size and charge of the different proteins are much weaker than those when the deposit layer is formed ir- regularly from two proteins. Our case may cor- respond with the former situation. In order to confirm this, more experiments are necessary.

The formation of the deposit layer in the binary protein system is considered as follows. Here, the proteins are designated as A and B, and Jv of Protein A in the single protein system (Jv ) is assumed to be larger than that of protein B (J+ ). When Jv in the binary protein system is larger than .&v, the deposit layer is probably formed by both proteins A and B. However, when Jv in the binary system becomes lower than Jv , the concentration of protein A at the membrane surface becomes lower than its critical value for deposit formation (for example, 2.3 wt% for

ovalbumin) and therefore the deposition of protein A is stopped insofar as the deposition in the binary system is due to the independent deposi- tions of both proteins. Thus, only the deposition of protein B continues and the deposition layer is formed by protein B alone. Once Jv becomes lower than .E$, the C,,, of protein B becomes lower than its critical value and the deposition of protein B also stops. Therefore, Jv in the binary protein system finally becomes the constant value equal to JG, which is the smaller Jv in the single protein system. This result with regard to Jv was confirmed experimentally as mentioned above. Moreover, in order to confirm the proposed theory, analysis of the protein composition on the membrane surface at various times of deposition was carried out. The experimental condition was the same as that described in Fig. 7. The deposit layers were mechanically stripped from the membrane surface and were dissolved in weak alkaline solutions. Then the protein concentrations in the solutions were measured by gel permeation chromatography. The results obtained are listed in Table 3. Obviously, the amount of ovalbumin in the deposit layer increased with the deposition time. According to our theory, in the condition described in Fig. 7, the deposit layer is formed by both ovalbumin and y-globulin in the early stage of deposition and, later, the deposition of y-globulin is stopped and only the deposition of ovalbumin continues. Therefore it is expected by our theory that the amount of ovalbumin in the deposit layer will increase with the deposition time. The obtained result agreed with this expectation, and our theory was thus also confirmed to be valid from the analysis of protein composition.

Both proteins are positively charged at pH 3.0,

Table 3 Time dependence of composition of deposit layer. Experi- mental condition was the same as in Fig. 7

Deposition time (min)

5 10 30 180

Ratio of amount of ovalbumin 0.28 0.34 0.43 0.62 to that of y-globulin

114 H. Matsuyama et al. /Journal ofMembrane Science 92 (1994) 107-l 15

while at pH 5.3 ovalbumin is charged negatively and y-globulin is charged positively. Because the deposit formation occurred independently even in the two cases with different states of the proteins, interaction between molecules of the same kind of protein is considered to contribute to the deposit formation more effectively than interaction between the different types of protein.

4. Conclusions

1. In respect of dynamic membrane formation by a single protein solution, the effects of linear velocity, bulk protein concentration, pressure and pH in the feed solution were studied in detail. The volume fluxes at the steady state increased with an increase in the linear velocity and with a decrease in the protein concentration, whereas the pressure hardly influenced the flux. The protein concentrations at the membrane surface were found to be constant under any conditions.

2. A dynamic membrane was formed by using a solution of a binary mixture of proteins. De- posit formation was as suggested as taking place with each protein independently. The flux in the binary protein system was first smaller than that in each single protein system, but finally agreed with the lower flux in the corresponding single protein systems.

5. List of symbols

c concentration of solute (wt% ) D diffusivity ( m2/s) d equivalent hydraulic diameter (m )

J” volume flux through membrane (m3/ m2s)

J” larger Jv in single protein system ( m3/ m2s)

J; smaller Jv in single protein system (m3/m2 s)

J V,COll volume flux at steady state ( m3/m2 s) k mass transfer coefficient in boundary

layer (m/s) 1 channel length ( m ) M(l) mass of deposit layer (kg)

AP

R(t) Re R obs

RO SC Sh U

cy

P

pressure difference (Pa) resistance of deposit layer (m - ’ ) Reynolds number apparent rejection resistance of support membrane (m- ’ ) Schmidt number Sherwood number linear velocity along membrane surface (m/s) specific resistance per unit mass (m- ’

kg-‘) viscosity (Pa s)

5. I. Subscripts

b value at bulk phase of feed solution m value at membrane surface

P value in permeate

Acknowledgements

We express our thanks to Dr. S. Furuyoshi with respect to the electrophoretic measurements. We also thank TDK Co., Ltd., Japan for supplying the ceramic tubes.

References

[ 1 ] T. Ohtani, A. Watanabe and S. Kimura, The characteristics and applications of dynamic and inorganic membranes, Maku, 13 (1988) 321.

[2]A.E. Marcinkowsky, K.A. Kraus, H.O. Philips, J.S. Johnson, Jr. and A.J. Shor, Hypertiltration studies. IV. Salt rejection by dynamically formed hydrous oxide membranes, J. Am. Chem. Sot., 88 (1966) 5744.

[3]A.J. Shor, K.A. Kraus, W.T. Smith, Jr. and J.S. John- son, Jr., Hyperfiltration studies. XI. Salt-rejection prop- erties of dynamically formed hydrous zirconium (IV ) oxide membranes, J. Phys. Chem., 72 ( 1968) 2200.

[ 41 D.G. Thomas and J.S. Watson, Hypertiltration studies. XII. Reduction of concentration polarization of dynamically formed hypertiltration membranes by detached turbulence promoters. Ind. Eng. Chem. Process Des. Dev., 7 (1968) 397.

[ 5 ] J.S. Johnson, Jr., R.E. Mintum and P.H. Wadia, Hyper- filtration. XXI. Dynamically formed hydrous zirconium(N) oxide-polyacrylate membranes, J. Elec- troanal. Chem., 37 (1972) 267.

H. Matsuyama et al. /Journal of Membrane Science 92 (I 994) 107-I 15 115

[ 6]G. Tanny and 0. Kedem, The hyperliltration streaming potential as a tool in the characterization of polyelectro- lyte membrane, J. Colloid Interface Sci., 5 1 ( 1975) 177.

[ 7]M. Igawa, Reverse osmosis by dynamic membrane, Ni- hon Kaisui Gakkaishi, 3 1 ( 1977) 52.

[8]A.K. Turkson, J.A. Mikhlin and M.E. Weber, Dynamic membranes for ultrafiltration, J. Colloid Interface Sci., 101 (1984) 583.

[ 9 ] S. Nakao, T. Nomura, S. Kimura and A. Watanabe, For- mation and characteristics of inorganic membranes for ultrafiltration, J. Chem. Eng. Jpn., 19 ( 1986) 22 1.

[ lO]A. Watanabe, N. Nakajima, T. Ohtani, T. Ohi, N. Na- betani and S. Kimura, Formation of Zr(IV) and Fe(II1) dynamic membranes for ultrafiltration, Maku, 12 (1987) 168.

[ 11 IS. Kishihara, H. Tamaki, S. Fujii and M. Komoto, Clar- ification of technical sugar solutions through a dynamic membrane formed on a porous ceramic tube, J. Mem- brane Sci., 41 (1989) 103.

[ 12]T. Ohtani, A. Watanabe, C. Hoshino and S. Kimura, Application of dynamic membrane to ultrafiltration, Kagaku Kogaku Ronbunshu, 11 ( 1985 ) 140.

[ 13]T. Imanara, N. Shishido, T. Kikkawa, Y. Yahiro and M. Tachi, Concentration of gelatin solutions by dynamic ultrafiltration membranes, Kagaku Kogaku Ronbun- shu, 16 (1990) 1.

[ 141 S. Kimura and S. Sourirajan, Analysis of data in reverse osmosis with porous cellulose acetate membranes used, AIChE J., 13 ( 1967) 497.

[ 15 ] M. Nystrom, Fouling of unmodified and modified po- lysulfone ultrafiltration membranes by ovalbumin, J. Membrane Sci., 44 ( 1989) 183.

[ 16lT.S. Shen and R.F. Probstein, On production of limiting flux in laminar ultrafiltration of macromolecular solutions. Ind. Eng. Chem. Fundam., 16 (1977) 459.

[ 17 ] W.F. Blatt, in J.E. Flinn (Ed. ) , Membrane Science and Technology, Plenum Press, New York, 1970, p. 55.

[ 18 ] R.W. Baker and H. Strathmann, Ultrafiltration of macromolecular solutions with high-flux membranes, J. Appl. Polym. Sci., 14 (1970) 1197.

[ 191 MC. Porter, Concentration polarization with membrane ultrafiltration., Ind. Eng. Chem. Process Des. Dev., 11 (1972) 234.

[ 20lA.G. Fane, C.J.D. Fell and A. Suki, The effect of pH and ionic environment on the ultrafiltration of protein solutions with retentive membranes, J. Membrane Sci., 16 (1983) 195.

[ 2 1 ]G.B. van den Berg and C.A. Smolders, Concentration polarization phenomena during dead-end ultraliltra- tion of protein mixtures. The influence of solute-solute interactions., J. Membrane Sci., 47 (1989) 1.

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