Solute Preferential Sorption in Reverse Osmosis - ACS Publications

18 Solute Preferential Sorption in Reverse Osmosis J. M . D I C K S O N

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and D O U G L A S R.

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LLOYD

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: May 27, 1981 | doi: 10.1021/bk-1981-0154.ch018

Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

Since the e a r l y days of research in reverse osmosis (RO), it has been recognized t h a t , in comparison to the s e p a r a t i o n of salt s o l u t i o n s , c e r t a i n s o l u t e s e x h i b i t anomalous performance behavior. A typical example is the negative s e p a r a t i o n observed f o r aqueous phenol s o l u t i o n s when u s i n g c e l l u l o s e acetate membranes; i . e . , the permeate stream is more concentrated in phenol than is the feed stream. This anomalous behavior can be accounted f o r by p o s t u l a t i n g that s o l u t e s such as phenol are preferentially a t t r a c t e d t o or preferentially sorbed by the c e l l u l o s e acetate membrane m a t e r i a l . I t is t o t h i s t o p i c of s o l u t e preferential s o r p t i o n in reverse osmosis that t h i s paper is dedicated. Specifically, this discussion will i n v o l v e a d e s c r i p t i o n of s o l u t e preferential s o r p t i o n , an overview of the literature i n the area, and finally a p r e s e n t a t i o n of some recent work on the removal of aromatic hydrocarbons from water. The s i g n i f i c a n c e of t h i s work is a t l e a s t two-fold. From a practical p o i n t of view the c l a s s e s of s o l u t e s which demonstrate preferential attraction to the membrane m a t e r i a l tend to be organic compounds and the removal and recovery of these s o l u t e s from water is environmentally and economically important. From a t h e o r e t i c a l p o i n t of view an understanding of the phenomena i n v o l v e d is e s s e n t i a l t o the achievement of a fundamental d e s c r i p t i o n of the RO process. Although t h i s paper deals s o l e l y w i t h aqueous s o l u t i o n s and c e l l u l o s e acetate membranes, it is important t o recognize that the concepts discussed can be extended to i n c l u d e other membrane m a t e r i a l s and non-aqueous systems. Solute P r e f e r e n t i a l S o r p t i o n At t h i s p o i n t , i t i s important t o d e s c r i b e e x a c t l y what i s meant by s o l u t e p r e f e r e n t i a l s o r p t i o n and the consequences that r e s u l t from t h i s s i t u a t i o n . Consider f i r s t the c l a s s i c a l case of the s e p a r a t i o n of aqueous NaCl s o l u t i o n s by c e l l u l o s e acetate membranes. I n t h i s instance the membrane m a t e r i a l has a stronger a f f i n i t y f o r the s o l v e n t than i t has f o r the s o l u t e . The r e s u l t 1

TX

Current address: Department of Chemical Engineering, University of Texas, Austin, 78712. 0097-6156/81/0154-0293$05.50/0 © 1981 American Chemical Society

In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.


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i s the e x i s t e n c e of e s s e n t i a l l y pure water on the surface of and w i t h i n the membrane. This water i s subsequently transported through the membrane i n the RO process. While t h i s d e s c r i p t i o n holds t r u e f o r a number of s o l u t e s ( i n p a r t i c u l a r i o n i z e d s o l u t e s ) , there are c e r t a i n s o l u t e s which e x h i b i t anomalous behavior. I n such cases the membrane m a t e r i a l has a stronger a f f i n i t y f o r the s o l u t e than f o r the s o l v e n t . The r e s u l t may be p i c t u r e d as the establishment of a sorbed l a y e r of s o l u t e which may subsequently be transported through the membrane. The consequence of the s o l u t e being p r e f e r e n t i a l l y sorbed i s that the observed performance behavior i s d i f f e r e n t than i n the case of water p r e f e r e n t i a l s o r p t i o n . The main d i f f e r e n c e s i n performance can be summarized as f o l l o w s : For the case of water p r e f e r e n t i a l s o r p t i o n i ) i n c r e a s i n g the operating pressure u s u a l l y increases separation i i ) the decrease i n permeate f l u x w i t h i n c r e a s i n g c o n c e n t r a t i o n i s due to the osmotic pressure of the s o l u t i o n i i i ) s e p a r a t i o n i s always p o s i t i v e i v ) s e p a r a t i o n increases w i t h decreasing pore s i z e on the membrane s u r f a c e . However, f o r the case of s o l u t e p r e f e r e n t i a l s o r p t i o n i ) i n c r e a s i n g the operating pressure u s u a l l y decreases separation i i ) the permeate f l u x i s l e s s than the pure water f l u x , even when the osmotic pressure e f f e c t s are n e g l i g i b l e i i i ) s e p a r a t i o n may be p o s i t i v e , zero, or negative depending on the s o l u t e and the s p e c i f i c operating c o n d i t i o n s i v ) s e p a r a t i o n may e x h i b i t a maximum, a minimum, or both w i t h decreasing pore s i z e on the membrane s u r f a c e . The l i s t of s o l u t e s that are known to be p r e f e r e n t i a l l y sorbed by c e l l u l o s e acetate membranes i n c l u d e s many a l c o h o l s , phenols, un-ionized c a r b o x y l i c a c i d s and hydrocarbons ( 1 ) . Although s o l u t e p r e f e r e n t i a l s o r p t i o n i s a common occurrence w i t h a number of important aqueous organic systems l i t t l e experimental or q u a n t i t a t i v e work has appeared i n the l i t e r a t u r e . The purpose of the current work i s to r e c t i f y t h i s s i t u a t i o n . L i t e r a t u r e Review A number of models have been developed over the years to d e s c r i b e reverse osmosis. These models i n c l u d e the s o l u t i o n d i f f u s i o n model, the f i n e l y porous model, and the p r e f e r e n t i a l s o r p t i o n - c a p i l l a r y flow model. I n each case, the model was o r i g i n a l l y developed based on the s e p a r a t i o n of aqueous,salt s o l u t i o n s . The a p p l i c a t i o n of each of these models to systems which e x h i b i t anomalous behavior w i l l be discussed i n t h i s s e c t i o n . S o l u t i o n - D i f f u s i o n Model (2). I n t h i s model, the s o l u t e and solvent are transported through the membrane by f i r s t d i s s o l v i n g



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i n the homogeneous s k i n l a y e r and then d i f f u s i n g through i t . Thus, p e r m e a b i l i t y i s the product of the s o l u b i l i t y and the d i f f u s i v i t y of the compound i n the membrane m a t e r i a l . The o r i g i n a l attempts to apply t h i s model to the phenol-water system were made by Lonsdale et a l . ( 3 ) . Phenol was found t o be r e a d i l y s o l u b l e i n the c e l l u l o s e a c e t a t e membrane and the d i f f u s i v i t y of phenol i n c e l l u l o s e a c e t a t e was approximately the same as that of water. The r e s u l t was negative s e p a r a t i o n i n RO a p p l i c a t i o n . The s o l u t i o n - d i f f u s i o n model i n i t s e x i s t i n g form proved to be i n s u f f i c i e n t to q u a n t i t a t i v e l y d e s c r i b e the negative s e p a r a t i o n . Therefore, the authors suggested the development of a coupled f l o w model ( i . e . the s o l u t e f l u x i s coupled to the water f l u x ) . Subsequent attempts to develop such a model met w i t h o n l y moderate success (*\_). Anderson e t a l . (5) conducted s t u d i e s that p a r a l l e l e d the work of Lonsdale. The emphasis was placed on s e p a r a t e l y measuring e q u i l i b r i u m s o r p t i o n and d i f f u s i o n c o e f f i c i e n t s f o r the s o l u t e i n the membrane m a t e r i a l . They a t t r i b u t e d the negative s e p a r a t i o n to the s t r o n g i n t e r a c t i o n between the phenol and the c e l l u l o s e a c e t a t e membrane m a t e r i a l . Pusch e t a l . (6) a l s o studied the s e p a r a t i o n of phenol and water. D i a l y s i s and s o r p t i o n experiments were performed, and the r e s u l t s were c o n s i s t e n t w i t h the n e g a t i v e s e p a r a t i o n observed i n RO. The decrease i n water f l u x i n the presence of phenol was a t t r i b u t e d to the decrease i n membrane water content under these c o n d i t i o n s . F i n e l y Porous Model. I n t h i s model, s o l u t e and s o l v e n t permeate the membrane v i a pores which connect the h i g h pressure and low pressure faces of the membrane. The f i n e l y porous model, which combines a v i s c o u s f l o w model and a f r i c t i o n model (7,8), has been developed i n d e t a i l and a p p l i e d to RO data by Jonsson (9-12). The most recent work of Jonsson (12) t r e a t e d s e v e r a l organic s o l u t e s i n c l u d i n g phenol and o c t a n o l , both of which e x h i b i t s o l u t e p r e f e r e n t i a l s o r p t i o n . I n h i s paper, Jonsson compared s e v e r a l models i n c l u d i n g that developed by S p i e g l e r and Kedem (13) (which i s e s s e n t i a l l y an i r r e v e r s i b l e thermodynamics treatment), the f i n e l y porous model, the s o l u t i o n - d i f f u s i o n i m p e r f e c t i o n model (14), and a model developed by Pusch (15). Jonsson i l l u s t r a t e d that the f i n e l y porous model i s s i m i l a r i n form to the Spiegler-Kedem r e l a t i o n s h i p . Both models f i t the data e q u a l l y w e l l , although not w i t h t o t a l accuracy. The Pusch model has a s i m i l a r form and proves to be l e s s a c c u r a t e , w h i l e the s o l u t i o n - d i f f u s i o n i m p e r f e c t i o n model i s even l e s s a c c u r a t e . In a l l models, the l a r g e s t discrepancy between the p r e d i c t e d performance and the experimental data occurred when negative s e p a r a t i o n was observed. Jonsson concluded that the f i n e l y porous model i s p r e f e r r e d over the a l t e r n a t i v e s , although the Pusch r e l a t i o n s h i p i s e a s i e r to use and y i e l d s reasonable r e s u l t s i n most cases. P r e f e r e n t i a l S o r p t i o n - C a p i l l a r y Flow Model. An a l t e r n a t i v e approach to those mentioned above has been presented by



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S o u r i r a j a n (16) and i s i l l u s t r a t e d s c h e m a t i c a l l y i n Figure 1. I n t h i s approach the c e l l u l o s e acetate membranes are considered t o be porous. Separation i s j o i n t l y governed by the p r e f e r e n t i a l s o r p t i o n of one of the c o n s t i t u e n t s of the s o l u t i o n a t the membrane-solution i n t e r f a c e , and the number, s i z e , and s i z e d i s t r i b u t i o n of the pores on the membrane s u r f a c e . I n the case of s a l t s o l u t i o n s , water i s p r e f e r e n t i a l l y sorbed. This means that a sharp c o n c e n t r a t i o n gradient e x i s t s i n the v i c i n i t y of the membrane m a t e r i a l , l e a d i n g to a l a y e r of almost pure water on the surface of the membrane. Applying pressure allows t h i s pure water to be c o n t i n u o u s l y withdrawn through the membrane pores. Smaller pore s i z e leads t o higher s e p a r a t i o n . This s i t u a t i o n of water p r e f e r e n t i a l s o r p t i o n i s a p p l i c a b l e t o most s a l t s o l u t i o n s and many organic s o l u t e s . The t r a n s p o r t of these s o l u t i o n s i s q u a n t i t a t i v e l y described by the Kimura-Sourirajan a n a l y s i s (16,17). With t h i s model, i t i s p o s s i b l e to p r e d i c t s o l u t e s e p a r a t i o n and f l u x f o r many systems which e x h i b i t water p r e f e r e n t i a l s o r p t i o n (17,18). However, some s o l u t e s e x h i b i t a strong a t t r a c t i o n t o the membrane m a t e r i a l and are t h e r e f o r e p r e f e r e n t i a l l y sorbed compared to the s o l v e n t water. This can lead t o p o s i t i v e , zero, or negative s e p a r a t i o n depending on both the magnitude of the a t t r a c t i v e f o r c e s and the m o b i l i t y of the s o l u t e a t the solution-membrane i n t e r f a c e ( r e l a t i v e to the m o b i l i t y of water i n t h i s r e g i o n ) . Both the p o l a r and nonpolar character of the s o l u t e may be important i n the s e p a r a t i o n process. Consider the case of a p o l a r s o l u t e . Since the c e l l u l o s e acetate membrane m a t e r i a l has a net proton acceptor nature ( 1 ) , any p o l a r compound i s a t t r a c t e d t o the membrane s u r f a c e . The more p o l a r the compound the stronger the a t t r a c t i o n . When the s o l u t e i s more p o l a r than the s o l v e n t , as i s the case i n phenol-water systems, the s o l u t e i s p r e f e r e n t i a l l y sorbed by the membrane. [Note: the p o l a r nature of a compound can be c o n v e n i e n t l y and q u a n t i t a t i v e l y expressed by the T a f t number (1,19).] Since the s o l u t e and the s o l v e n t are both p o l a r , a strong i n t e r a c t i o n e x i s t s between the two s o l u t i o n components. This i n t e r a c t i o n allows the s o l u t e t o be r e l a t i v e l y mobile i n the v i c i n i t y of the pore, and thus i t can be c a r r i e d through the pore w i t h the water, r e s u l t i n g i n negative s e p a r a t i o n . On the other hand, f o r a hydrocarbon s o l u t e such as benzene, the nonpolar f o r c e s predominate. The c e l l u l o s e acetate membrane m a t e r i a l has a nonpolar character due t o i t s carbon backbone. This nonpolar character r e s u l t s i n the a t t r a c t i o n of nonpolar s o l u t e s . Since the s o l u t e has l i t t l e p o l a r c h a r a c t e r , i t i s more s t r o n g l y immobilized on the membrane s u r f a c e than i s water. Thus, the s o l v e n t passes through the membrane r e l a t i v e l y f a s t and p o s i t i v e s e p a r a t i o n i s observed. The s t r e n g t h of t h i s nonpolar a t t r a c t i o n , q u a n t i t a t i v e l y represented by the modified Small's number CI,20), w i l l , i n p a r t , determine the extent of s e p a r a t i o n . The presence of p r e f e r e n t i a l l y sorbed s o l u t e on the membrane surface w i l l block or impede the flow of the s o l v e n t water. This



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pore b l o c k i n g e f f e c t r e s u l t s i n the permeate f l u x f o r feed s o l u t i o n s , even d i l u t e s o l u t i o n s of n e g l i g i b l e osmotic p r e s s u r e , being l e s s than the f l u x observed f o r a pure water feed under s i m i l a r o p e r a t i n g c o n d i t i o n s ; i . e . , permeate f l u x (PF) i s l e s s than pure water f l u x (PWF) . The advantage of the p r e f e r e n t i a l s o r p t i o n - c a p i l l a r y flow approach to r e v e r s e osmosis l i e s i n i t s emphasis on the mechanism of s e p a r a t i o n at a molecular l e v e l . This knowledge i s u s e f u l when i t becomes necessary to p r e d i c t membrane performance f o r unknown systems. A l s o , the approach i s not r e s t r i c t e d to the s o - c a l l e d " p e r f e c t " , d e f e c t - f r e e membranes, but encompasses the whole range of membrane pore s i z e . U n t i l r e c e n t l y , the a p p l i c a t i o n of a q u a n t i t a t i v e model to the case of s o l u t e p r e f e r e n t i a l s o r p t i o n has been m i s s i n g . Attempts to change t h i s s i t u a t i o n have been made by Matsuura and S o u r i r a j a n (21) by using a m o d i f i e d f i n e l y porous model. In a d d i t i o n to the u s u a l f e a t u r e s of t h i s model (9-12), a Lennard-Jones type of p o t e n t i a l f u n c t i o n i s i n c o r p o r a t e d to d e s c r i b e the membrane-solute i n t e r a c t i o n . This model i s discussed elsewhere i n t h i s book. Separation of Aromatic Hydrocarbons In t h i s paper, the removal of two aromatic hydrocarbons, benzene and toluene, from water i s i n v e s t i g a t e d . Toluene can be shown to be more nonpolar than benzene by comparing the m o d i f i e d Small's numbers (1,), which are 549 and 425 ( c a l cm )^/mol for toluene and benzene, r e s p e c t i v e l y . The greater nonpolar character of toluene ( i n d i c a t e d by the l a r g e r m o d i f i e d Small's number) suggests t h a t , i n comparison to benzene, toluene w i l l be more s t r o n g l y a t t r a c t e d to the membrane, and t h e r e f o r e w i l l e x h i b i t lower m o b i l i t y . The r e s u l t i s that under i d e n t i c a l o p e r a t i n g c o n d i t i o n s the s e p a r a t i o n of toluene from water should be greater than the s e p a r a t i o n of benzene from water. The v a l i d i t y of t h i s assumption i s checked i n the present study. I n a p r e v i o u s study of these s o l u t e s , data was reported f o r a s i n g l e feed c o n c e n t r a t i o n (22). The e f f e c t of feed c o n c e n t r a t i o n on membrane performance i s examined i n t h i s work. The q u a n t i t a t i v e treatment of the data generated i n the present study w i l l i n i t i a l l y be based on a set of equations r e c e n t l y reported (23). These equations, which have proven to be adequate for d i l u t e p-chlorophenol-water systems, are as f o l l o w s : (1)

PWF N

X

A

A2

= K

=

X

X

2

A3

+

P

A 2

X

< A1

_

(2)

X

A3>

e x

pF

k

P ( / P>

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ref

AB

AB,ref

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(4)

The nomenclature i s d e f i n e d i n the Legend of Symbols s e c t i o n a t the c o n c l u s i o n of t h i s paper and i s i l l u s t r a t e d i n F i g u r e 1. Equation 1 i s an e m p i r i c a l r e l a t i o n which d e s c r i b e s the extent of pore b l o c k i n g , expressed by the pore b l o c k i n g f a c t o r 1-(PF/PWF). In the case of the RO s e p a r a t i o n of a d i l u t e s o l u t e - c o n t a i n i n g feed stream i n which there i s no pore b l o c k i n g by the s o l u t e , the f l u x of the permeating stream i s equal to the f l u x obtained f o r a s i m i l a r experiment i n which the feed stream i s pure water ( i . e . , permeate f l u x (PF) equals pure water f l u x (PWF)). In t h i s case, the f l u x r a t i o PF/PWF i s u n i t y and the pore b l o c k i n g f a c t o r 1-(PF/PWF) i s zero. Conversely, when the pores are completely blocked PF i s zero, and thus, the pore b l o c k i n g f a c t o r i s u n i t y . Equation 1 i n d i c a t e s t h a t the pore b l o c k i n g f a c t o r i s p r o p o r t i o n a l to the c o n c e n t r a t i o n of the boundary l a y e r (XA2) r a i s e d to a power of n^ This r e l a t i o n s h i p w i l l be d i s c u s s e d below. Equation 2 i s an e m p i r i c a l r e l a t i o n which r e l a t e s s o l u t e f l u x (NA) to both X^2 (again r a i s e d to a power of n j ) and the o p e r a t i n g pressure ( r a i s e d to a power of n2). The exponents rii and n2,as w e l l as the proportionality factors and K 2 , are f u n c t i o n s of pore s i z e and the nature of the s o l u t e . Equation 3, which a l l o w s the c a l c u l a t i o n of X ^ from experimental data, i s based on a simple " f i l m " theory f o r mass t r a n s f e r and i s d e r i v e d elsewhere (17,23). Equation 4 a l l o w s the mass t r a n s f e r c o e f f i c i e n t on the feed s i d e , k, to be c a l c u l a t e d f o r any s o l u t e based on the value obtained f o r a r e f e r e n c e s o l u t e ( u s u a l l y sodium c h l o r i d e ) i n the same t e s t c e l l . The p o s s i b i l i t y of u s i n g equations of t h i s form f o r aromatic hydrocarbon s o l u t i o n s w i l l be examined i n t h i s paper. Experimental The c e l l u l o s e a c e t a t e membranes used were batch 316(0/25) type membranes (24) made by the general Loeb-Sourirajan technique (25). The s i x f l a t c a s t membranes were shrunk at d i f f e r e n t temperatures (from 68 to 85°C) p r i o r to l o a d i n g the membranes i n t o the r e v e r s e osmosis t e s t c e l l s . This treatment a d j u s t s the average surface pore s i z e of each membrane so t h a t a range of p o r o s i t i e s could be s t u d i e d . A p r e p r e s s u r i z a t i o n at a pressure of 11 720 kPa f o r 2 hours was used to s t a b i l i z e the membranes f o r subsequent use a t pressures of 6900 kPa or lower. ( A l l pressures l i s t e d are gauge pressure.) The general experimental procedure was s i m i l a r to that r e p o r t e d i n the l i t e r a t u r e (25). The s i x flow type reverse osmosis c e l l s were connected i n s e r i e s and were c o n s t r u c t e d i n a design s i m i l a r to that r e p o r t e d by S o u r i r a j a n (25). The c e l l s were placed i n a constant temperature box and the system was c o n t r o l l e d to 25 ± 1°C. The feed f l o w r a t e was maintained constant at 400


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ml/min. For each experiment, the pure water f l u x (PWF) and the permeate f l u x (PF) were measured. I n a d d i t i o n , the s o l u t e c o n c e n t r a t i o n was determined i n the feed and permeate s o l u t i o n s and the s e p a r a t i o n , f , was c a l c u l a t e d as m

f =T " 3 (5) l where m^ and 1113 are the feed and permeate m o l a l i t i e s r e s p e c t i v e l y . For d i l u t e s o l u t i o n s t h i s can be approximated as m


m

^ _ ppml - ppm3 ppml

(6)

where ppml and ppm3 are the feed and permeate c o n c e n t r a t i o n s expressed i n p a r t s per m i l l i o n . The s o l u t e c o n c e n t r a t i o n s f o r benzene and toluene samples were analyzed u s i n g an Oceanography I n t e r n a t i o n a l C o r p o r a t i o n T o t a l Carbon A n a l y z e r . The sodium c h l o r i d e s o l u t i o n s were analyzed w i t h e i t h e r a Laboratory Data C o n t r o l D i f f e r e n t i a l Refractometer o r a YSI Model 31 C o n d u c t i v i t y Meter. The water used was d e i o n i z e d and d i s t i l l e d and a l l other chemicals were a n a l y t i c a l reagent grade. R e s u l t s and D i s c u s s i o n s Membrane C h a r a c t e r i z a t i o n . The s i x c e l l u l o s e a c e t a t e membranes were c h a r a c t e r i z e d according t o the sodium c h l o r i d e performance data. These data are presented i n Table I . A c t u a l experiments were repeated a t r e g u l a r i n t e r v a l s i n order t o monitor the membrane changeând the i l l u s t r a t e d data represent the average of nine t e s t s . Since the s o l u t e t r a n s p o r t parameter D^M/KS f o r sodium c h l o r i d e , and hence l n C*N Cl> remained e s s e n t i a l l y constant over the experimental time p e r i o d i t can be assumed that the membrane pore s i z e remained constant. The q u a n t i t y l n C* -^ i s r e p r e s e n t a t i v e of the average pore s i z e on the membrane s u r f a c e and i s independent of the s o l u t e under c o n s i d e r a t i o n (26). B r i e f l y , a decrease i n the v a l u e o f l n C*NaCl i n d i c a t e s a decrease i n the average pore s i z e . The v a l u e s of l n C * N c i f o r the membranes t e s t e d cover a wide range of s u r f a c e pore s i z e , thereby maximizing experimental design. The pure water p e r m e a b i l i t y constant A tended t o decrease over the p e r i o d of s e v e r a l experiments; t h i s decrease was a t t r i b u t e d to membrane compaction. This change i n A v a r i e d from a 10% decrease f o r the membranes of l a r g e s t pore s i z e t o a 5% decrease f o r the membranes of s m a l l e s t pore s i z e . The r a t e o f compaction f o r these hydrocarbon s t u d i e s was s l i g h t l y h i g h e r than would normally be observed f o r s a l t s o l u t i o n experiments. This a c c e l e r a t e d decrease i n A may be the r e s u l t of the d e t r i m e n t a l e f f e c t that h i g h i n t e r f a c i a l c o n c e n t r a t i o n of organics have on the c e l l u l o s e a c e t a t e . The average s e p a r a t i o n and the permeate f l u x f o r aqueous NaCl s o l u t i o n s measured under the i n d i c a t e d c o n d i t i o n s are a l s o l i s t e d i n Table I . a

NaC

a



2

?

k,

1.342 -12.59

0.6914 -13.25

3

2

— ^ — , 2 m s

xlO

3

13.27

97.0

61.7 25.80

82.8 24.41

93.5 19.38

-8.69

66.15

2.487

6

29.3

-9.49

29.69

2.331

5

47.0

44.0

-10.73

-11.84

38.5

8.653

1.868

4

2.846

1.268

3

a) F i l m area, 1.443 x l O m ; o p e r a t i n g pressure 6900 kPa; feed c o n c e n t r a t i o n 10 000 ppm NaCl; temperature 25°C; feed f l o w r a t e 400 ml/min.

Permeate f l u x ,

9.05

0

7.43

l

98.1

X

98.8

>

Solute Separation, %

m / s

0.8547

38.2

6

>NaCl>

*NaCl

/K6

0.7051

28.3

C

AM

4

2

Mass t r a n s f e r c o e f f i c i e n t , m/s, x l O

l n

(D

S o l u t e t r a n s p o r t parameter,

2

Pure water p e r m e a b i l i t y constant, A, (mol H 0)/(m s k P a ) , x l O

1

a

F i l m Number

C h a r a c t e r i z a t i o n and Performance of the C e l l u l o s e Acetate Membranes

TABLE I


18.

DICKSON

AND LLOYD


Benzene - Water Reverse Osmosis Data. The e x p e r i m e n t a l l y determined performance f o r the s e p a r a t i o n of benzene and water a t four d i f f e r e n t pressures i s i l l u s t r a t e d i n Figures 2 through 5. The s e p a r a t i o n and pore b l o c k i n g f a c t o r observed f o r s e v e r a l d i f f e r e n t feed concentrations are p l o t t e d as a f u n c t i o n of the membrane pore s i z e , l n C * N c i . Although there i s s c a t t e r i n the data, i t i s p o s s i b l e t o observe trends that apply c o n s i s t e n t l y i n Figures 2 through 5. As the pore s i z e decreases the s e p a r a t i o n i n c r e a s e s . As the feed c o n c e n t r a t i o n i n c r e a s e s , the s e p a r a t i o n i n c r e a s e s . The extent of t h i s c o n c e n t r a t i o n e f f e c t i s s m a l l f o r the membranes of l a r g e pore s i z e , and increases w i t h decreasing pore s i z e u n t i l the greatest i n f l u e n c e i s observed f o r the membrane of s m a l l e s t pore s i z e . I n a l l cases, the extent of pore b l o c k i n g increases l i n e a r l y w i t h decreasing pore s i z e . I n a d d i t i o n , i n c r e a s i n g the feed c o n c e n t r a t i o n increases the extent of pore blocking. The e f f e c t of s o l u t e c o n c e n t r a t i o n on s e p a r a t i o n i s i l l u s t r a t e d by e x t r a c t i n g the data f o r any given membrane from the curves i n Figures 2 through 5, and r e p l o t t i n g the data i n the form of s e p a r a t i o n as a f u n c t i o n of s o l u t e c o n c e n t r a t i o n i n the feed stream. T y p i c a l r e s u l t s are shown i n Figure 6. This r e l a t i o n s h i p c l e a r l y i l l u s t r a t e s that s e p a r a t i o n increases w i t h i n c r e a s i n g c o n c e n t r a t i o n , e v e n t u a l l y l e v e l i n g o f f a t a constant v a l u e . This p l o t a l s o a l l o w s the comparison of s e p a r a t i o n a t d i f f e r e n t pressures. For the range of pressures 690 to 3450 kPa, the s e p a r a t i o n increases w i t h decreasing pressure, which i s c o n s i s t e n t w i t h the general behavior of p r e f e r e n t i a l l y sorbed s o l u t e systems as discussed above and w i t h the data p r e v i o u s l y obtained (1). However, the data f o r 6900 kPa does not f o l l o w t h i s trend and i n d i c a t e s that s e p a r a t i o n passes through a minimum w i t h i n c r e a s i n g pressure. This behavior w i l l be i n v e s t i g a t e d i n more d e t a i l i n the f u t u r e . The trends i n Figures 2 to 6 a r e c o n s i s t e n t w i t h the q u a l i t a t i v e f e a t u r e s of s o l u t e p r e f e r e n t i a l s o r p t i o n discussed e a r l i e r i n t h i s paper. The permeate f l u x i s lower than the pure water f l u x due to pore b l o c k i n g . This e f f e c t i s enhanced by e i t h e r decreasing the pore s i z e or i n c r e a s i n g the feed c o n c e n t r a t i o n . Both of these f a c t o r s l e a d to a r e l a t i v e increase i n the s o l u t e content of the pore and thus, to r e s t r i c t e d water t r a n s p o r t through the pore. Since the s o l u t e i s r e l a t i v e l y immobile a t the membrane s u r f a c e , p o s i t i v e s e p a r a t i o n i s observed. Both i n c r e a s i n g the feed c o n c e n t r a t i o n and decreasing the pore s i z e l e a d to higher s e p a r a t i o n . The a d d i t i o n a l s o l u t e r e t a i n e d on the h i g h pressure s i d e must a l s o be r e l a t i v e l y immobile. I t i s hypothesized that benzene can be sorbed i n m u l t i p l e l a y e r s which are bound to the membrane. The l a y e r s i n the immediate v i c i n i t y of the membrane m a t e r i a l / p o r e w a l l are s t r o n g l y bound to the membrane. The s t r e n g t h of the a t t r a c t i o n f o r c e decreases as the d i s t a n c e between each subsequent l a y e r and the membrane surface i n c r e a s e s . a


301


302

SYNTHETIC

MEMBRANES:

HF

AND

UF

USES

BULK FEED SOLUTION UNDER "OPERATING GAUGE PRESSURE P -CONCENTRATED

Â2

BOUNDARY

-PREFERENTIALLY -DENSE

SOLUTION

SORBED INTERFACIAL

LESS DENSE MICROPOROUS "MEMBRANE LAYER


FLUID

MICROPOROUS MEMBRANE SURFACE

-SPONGY

POROUS

TRANSITION

MEMBRANE

P R O D U C T S O L U T I O N AT ATMOSPHERIC PRESSURE

Â3

NRCC Publications

Figure 1.

Schematic of RO transport under steady-state conditions (16)

0.4 —

J

I

I

I

I

-13

-12

I -II

l n

C

-L

I

-10

L_

-9

NaCI

Figure 2. Effect of feed concentration on the RO performance for the benzenewater system. Operating conditions: membrane material = CA; membrane area = 1.443 X IO' m , In C* obtained at 6900 kPa; feedflowrate = 400 mL/min; T = 25°C; operating pressure = 690 kPa. Curve a (O) 20.6 ppm; Curve b (%) 31.7 ppm; Curve c O 54.0 ppm; Curve d (^) 96.0 ppm. 3

2

Nam



DICKSON

AND

LLOYD


303

Figure 3. Effect of feed concentration on the RO performance for the benzenewater system. The operating conditions are identical to those of Figure 2 except that the operating pressure = 1725 kPa. Curve a (O) 18.0 ppm; Curve b (%) 29.8 ppm; Curve c O 49.0 ppm; Curve d (U) 98.8 ppm.



304

SYNTHETIC

MEMBRANES:

HF

AND

UF

USES

Figure 4. Effect of feed concentration on the RO performance for the benzenewater system. The operating conditions are identical to those of Figure 2 except that the operating pressure = 3450 kPa. Curve a (O) 20.9 ppm; Curve b (%) 31.0 ppm; Curve c (Q) 44.8 ppm; Curve d (^) 54.5 ppm; Curve e (A) 92.6 ppm.


A N D LLOYD



DICKSON


305


306

SYNTHETIC

80

MEMBRANES: HF

AND

UF

USES

-

0

20

40

60

80

FEED CONCENTRATION (ppm BENZENE)

Figure 6. Effect of feed concentration and operating pressure on separation for the benzene-water system. Data illustrated for the CA membrane with In C* i = -13.25. Curve a (O) 690 kPa; Curve b (%) 1725 kPa; Curve c O 3450 kPa; Curve d ( | ) 6900 kPa. NaC



18.

DICKSON

A N D LLOYD


307

The r e s u l t s observed f o r the benzene-water system can be compared to those observed f o r the p-chlorophenol-water system. I n the l a t t e r case, higher feed concentrations and s m a l l e r pore s i z e l e a d to lower s e p a r a t i o n ( 2 3 ) . As discussed e a r l i e r i n t h i s r e p o r t , t h i s d i f f e r e n c e i n behavior i s c o n s i s t e n t w i t h the d i f f e r e n c e s i n m o b i l i t y of the two s o l u t e s . With both benzene and p-chlorophenol, i n c r e a s i n g the c o n c e n t r a t i o n i n c r e a s e s the amount of s o l u t e bound t o the membrane pore w a l l . Since the p-chlorophenol i s more h i g h l y hydrated i t can move through the pore w i t h the water, which decreases the s e p a r a t i o n . For benzene, the s o l u t e i s r e l a t i v e l y immobilized, and w i t h i n c r e a s i n g c o n c e n t r a t i o n more and more of the pore i s occupied w i t h immobilized s o l u t e . The r e s u l t i s higher s e p a r a t i o n . Thus, i t appears that the s e p a r a t i o n and pore b l o c k i n g f a c t o r a r e both c o n t r o l l e d by the r e l a t i v e amount of immobilized s o l u t e i n the pore. This r e l a t i v e q u a n t i t y of s o l u t e can be increased by i n c r e a s i n g the feed c o n c e n t r a t i o n a t a f i x e d pore s i z e o r by decreasing the pore s i z e a t a f i x e d feed c o n c e n t r a t i o n . As c o n c e n t r a t i o n i s i n c r e a s e d , the a d d i t i o n a l s o l u t e assumes a p o s i t i o n i n sorbed l a y e r s which are i n c r e a s i n g l y f a r from the membrane s u r f a c e . Thus, the a t t r a c t i o n f o r c e s exerted by the membrane m a t e r i a l on the s o l u t e are p r o g r e s s i v e l y l e s s , and the a d d i t i o n a l s o l u t e i s not so t i g h t l y bound. The r e s u l t i s the permeation of a p o r t i o n of the concentrated boundary l a y e r . Therefore, there i s a l e v e l i n g o f f i n s e p a r a t i o n w i t h i n c r e a s i n g concentration. C o r r e l a t i o n of X A 2 w i t h Pore B l o c k i n g f o r Benzene-Water Data. The b l o c k i n g of the pores on the membrane surface by the p r e f e r e n t i a l l y sorbed s o l u t e , which was discussed q u a l i t a t i v e l y i n the preceding s e c t i o n , i s now t r e a t e d more q u a n t i t a t i v e l y . Equation 4 was used to estimate the a p p r o p r i a t e k value f o r each c e l l . The d i f f u s i v i t y of the s o l u t e i n water was estimated by the method of Wilke and Chang ( 2 7 ) , and the d i f f u s i v i t y of sodium c h l o r i d e i n water used was 1 . 6 0 x 10~" cm /s ( 2 6 ) . Then X A 2 was c a l c u l a t e d f o r each run from Equation 3 . F i g u r e 7 i l l u s t r a t e s the r e l a t i o n s h i p between 1 -(PF/PWF) and X A 2 - W i t h i n the s c a t t e r of t h i s data, i t i s reasonable to use a s t r a i g h t l i n e through the o r i g i n f o r a l l s i x membranes. This data corresponds to an n i value of 1 . 0 i n Equation 1 . The K j v a l u e s , obtained by l e a s t squares a n a l y s i s of the data i n F i g u r e 7 , a r e p l o t t e d i n Figure 8 as a f u n c t i o n of l n C * N C l * This r e l a t i o n s h i p can be described by the equation 5

2

a

Ki =

-2189

l n C*

N a C 1

-

12840

(7)

For the membranes used i n t h i s study, ¥L\ v a r i e d from 6 x 1 0 t o 1 6 x 1 0 . I t should be noted that F i g u r e s 7 and 8 i n c l u d e d data from a l l pressures t e s t e d and t h e r e f o r e Equation 7 w i l l p r e d i c t K i f o r a l l pressures and c o n c e n t r a t i o n s w i t h i n the range s t u d i e d . The i n v e r s e dependence of on l n C*NaCl r e f l e c t s the increased 3

3




o

LO 00

18.

DICKSON

A N D LLOYD


309


importance of s o l u t e pore b l o c k i n g f o r the membranes of s m a l l e r pore s i z e , E q u a t i o n 7, t h e r e f o r e , can be used to estimate the extent of pore b l o c k i n g that w i l l be caused by p r e f e r e n t i a l l y sorbed benzene. This e s t i m a t i o n can be performed by simply conducting experiments w i t h NaCl-water systems to determine the l n C*NaCl value f o r the membrane i n use. The a p p l i c a t i o n of Equation 7 to aqueous systems c o n t a i n i n g benzene p l u s a s o l u t e such as NaCl w i l l be explored i n f u t u r e s t u d i e s . Toluene-Water Reverse Osmosis Data. Data f o r the reverse osmosis s e p a r a t i o n of aqueous toluene s o l u t i o n s a t 3450 kPa and three d i f f e r e n t c o n c e n t r a t i o n s , u s i n g the same s i x membranes as above, a r e i l l u s t r a t e d i n Figure 9. These r e s u l t s are q u a l i t a t i v e l y s i m i l a r t o those f o r the benzene s t u d i e s . That i s , s e p a r a t i o n and extent of pore b l o c k i n g i n c r e a s e w i t h both i n c r e a s i n g c o n c e n t r a t i o n and decreasing pore s i z e . Further s t u d i e s t o i n v e s t i g a t e the e f f e c t s of pressure are c u r r e n t l y underway. C o r r e l a t i o n of XA2 w i t h Pore B l o c k i n g f o r Toluene-Water Data. An a n a l y s i s s i m i l a r t o that used f o r the benzene data was a p p l i e d to the toluene data to i n v e s t i g a t e pore b l o c k i n g as a f u n c t i o n of c o n c e n t r a t i o n . Figure 10 i l l u s t r a t e s t h i s r e l a t i o n s h i p f o r a l l s i x membranes. The data f o r membranes 5 and 6 can be approximated by a s t r a i g h t l i n e ; t h e r e f o r e , n\ was s e t to 1.0 i n Equation 1. For the other f i l m s , a l e a s t squares parameter e s t i m a t i o n was a p p l i e d and the n\ and K j values generated. The r e s u l t s are i l l u s t r a t e d i n F i g u r e 11, where K j ( p l o t t e d as l n K^ f o r convenience) and ni are shown as f u n c t i o n s of l n C*NaCl» r e g i o n of l n C * N d l e s s than -10.5 both n^ and K^ i n c r e a s e w i t h l n C*NaCl« Above t h i s value n i and K j l e v e l o f f a t 1.0 and 40 x 1 0 ( i . e . , l n K i = 10.6), r e s p e c t i v e l y . This r e s u l t i s s i m i l a r to that obtained p r e v i o u s l y i n p-chlorophenol s t u d i e s (23) , where n i was found to l e v e l o f f a t l n C*^ n^ values greater than -12.0. In general, the s e p a r a t i o n and pore b l o c k i n g data f o r the toluene-water system are c o n s i s t e n t w i t h those obtained f o r the benzene-water system. P o s i t i v e s e p a r a t i o n occurs, and the general trends of i n c r e a s i n g s e p a r a t i o n and pore b l o c k i n g w i t h i n c r e a s i n g c o n c e n t r a t i o n and decreasing pore s i z e are observed. This i s not s u r p r i s i n g s i n c e toluene and benzene are s i m i l a r i n s t r u c t u r e . However, based on the modified Small's number f o r these s o l u t e s , as discussed e a r l i e r i n t h i s paper, i t would be expected that toluene would be more s t r o n g l y sorbed by the membrane than i s the benzene. I f t h i s i s t r u e , then a t otherwise i d e n t i c a l c o n d i t i o n s toluene should demonstrate greater pore b l o c k i n g and higher s e p a r a t i o n than benzene. Curve c_ i n Figure 9 f o r toluene and curve a i n Figure 4 f o r benzene a r e a t the same pressure and approximately the same molar c o n c e n t r a t i o n . I n a l l cases, the expected r e s u l t i s found. For example, f o r membrane 2, the separations are 41% and 9% and the pore b l o c k i n g f a c t o r s are 0.30 and 0.08 f o r toluene and benzene, r e s p e c t i v e l y . Thus, the modified Small's F

o

r t

n

e

a

3

a(


310

SYNTHETIC

MEMBRANES:

HF AND U F

USES


K.xlO"

Figure 8. Correlation ofK of Equation 1 with membrane pore size (In C* ci) for separation of the benzene-water system t

Na

6

In C .

8 0

i< OC 6 0

& W UJ Z W

40

1-

a

20

_J O 0 -12

-II l n

c

NaCI

Figure 9. Effect of feed concentration on the RO performance for the toluenewater system. The operating conditions are identical to those of Figure 2 except that the operating pressure = 3450 kPa. Curve a (O) 8.7 ppm; Curve b (%) 12.4 ppm; Curve c (Q) 20.8 ppm.



DICKSON A N D

LLOYD


311

Figure 10. Correlation of the pore-blocking factor, 1-(PF/PWF), and the boundary layer concentration of toluene, X . The operating conditions are the same as in Figure 9 with Membranes 1 (*), 2 (Q), 3 (A), 4 (A), 5 (O), and 6 (M) as designated in Table I. A2

Figure 11. Correlation of In K j and n of Equation 1 with membrane pore size (In C* ci) for separation of the toluenewater system t

Na

NaCl


312

SYNTHETIC

MEMBRANES:

HF

AND

UF

USES

number i s a u s e f u l t o o l f o r q u a l i t a t i v e l y p r e d i c t i n g d i f f e r e n c e s i n the reverse osmosis performance f o r toluene-water and benzene-water systems.


Conclusions In c o n c l u s i o n , s e v e r a l important p o i n t s of t h i s work should be r e i t e r a t e d . An understanding and q u a n t i t a t i v e d e s c r i p t i o n of s o l u t e p r e f e r e n t i a l s o r p t i o n i s imperative to the advancement of a fundamental knowledge of the s e p a r a t i o n mechanism and to the a p p l i c a t i o n of reverse osmosis. For the systems s t u d i e d , i n c r e a s i n g the feed c o n c e n t r a t i o n was found to i n c r e a s e s e p a r a t i o n and decrease permeate f l u x . This behavior can be contrasted to the case of water p r e f e r e n t i a l s o r p t i o n where both s e p a r a t i o n and permeate f l u x would remain constant f o r these d i l u t e c o n c e n t r a t i o n s . The r e s u l t s f o r the benzene s t u d i e s and the toluene s t u d i e s were s i m i l a r i n that s e p a r a t i o n increased and f l u x decreased w i t h i n c r e a s i n g feed c o n c e n t r a t i o n or decreasing pore s i z e . The benzene s t u d i e s showed a minimum i n s e p a r a t i o n w i t h i n c r e a s i n g pressure. At s i m i l a r experimental c o n d i t i o n s the toluene system showed higher s e p a r a t i o n and lower f l u x than the benzene system. This observation i s c o n s i s t e n t w i t h the d i f f e r e n c e i n the nonpolar character of the s o l u t e s as expressed by the Small's number. Further work i s needed i n order to improve the q u a n t i t a t i v e understanding of systems which e x h i b i t solute p r e f e r e n t i a l sorption. Legend of Symbols A

= pure water p e r m e a b i l i t y constant, mol (m s kPa)

H2O/

2

D^g D

= d i f f u s i v i t y of A i n B, K(

=

AM/ 5

2

m /s

s o l u t e t r a n s p o r t parameter,

f

= separation

k

= mass t r a n s f e r c o e f f i c i e n t ,

Ki,K

m/s

m/s

= p r o p o r t i o n a l i t y f a c t o r s defined i n Equations 1 and 2, r e s p e c t i v e l y

2

ln C*N d

= r e l a t i v e measure of the membrane pore s i z e

mi

= concentration, m o l a l i t y

a

ni,n

2

= exponents defined i n Equations respectively 2

NA

= s o l u t e f l u x , mol/(m

P

= operating pressure, kPa gauge

PF

= permeate f l u x , kg/(m s ) '

1 and

2,

s)

2


18.

DICKSON

A N D LLOYD


ppm

= c o n c e n t r a t i o n , p a r t s per m i l l i o n

PWF

= pure water f l u x , kg/(m s)

X

= c o n c e n t r a t i o n , mole f r a c t i o n

p

= s o l u t i o n d e n s i t y , kg/m

313

2

3


Subscripts 1

= feed s o l u t i o n

2

= boundary l a y e r s o l u t i o n

3

= permeate s o l u t i o n

M

= membrane phase

A

= solute

B

= solvent

ref

= reference s o l u t e

Acknowledgements The authors wish t o thank The Engineering Foundation f o r t h e i r support of t h i s research and the N a t u r a l Sciences and Engineering Research C o u n c i l of Canada f o r the s c h o l a r s h i p support of one of the authors (JMD). Literature Cited 1.

S o u r i r a j a n , S.; Matsuura, T. in "Reverse Osmosis and S y n t h e t i c Membranes"; S o u r i r a j a n , S., Ed.; N a t i o n a l Research C o u n c i l of Canada: Ottawa, 1977; Chapter 2.

2.

Lonsdale, H.K.; Merten, U.; R i l e y , R.L. J. Appl. Polymer Sci. 1965, 9, 1341-1362.

3.

Lonsdale, H.K.; Merten, U.; Tagami, M. J. Appl. Polymer Sci. 1967, 11, 1807-1820.

4.

Merten, U.; Lonsdale, H.K.; R i l e y , R.L.; Tagami, M. presented at NATO Advanced Study Institute on S y n t h e t i c Polymer Membranes, R a v e l l o , Sept. 1966.

5.

Anderson, J.E.; Hoffman, S.J.; P e t e r s , C.R. J. Phys. Chem. 1972, 76, 4006-4011.

6.

Pusch, W.; Burghoff, H.G.; Staude, E. 5 t h I n t e r n . Symp. on Fresh Water from the Sea 1976, 4, 143-156.

7.

Merten, U., Ed. " D e s a l i n a t i o n by Reverse Osmosis"; M.I.T. Press: Cambridge, Mass., 1966; p. 15-54.

8.

S p i e g l e r , K.S. Trans. Faraday Soc. 1958, 54, 1408-1428.

9.

Jonsson, G.; Boesen, C.E. D e s a l i n a t i o n 1975, 17, 145-165.



314

SYNTHETIC

MEMBRANES*.

HF

AND

UF

USES

10.

Boesen, C.E.; Jonsson, G. 5 t h I n t e r n . Symp. on Fresh Water from the Sea 1976, 4, 259-266.

11.

Boesen, C.E.; Jonsson, G. 6 t h I n t e r n . Symp. on Fresh Water from the Sea 1978, 3, 157-164.

12.

Jonsson, G. D e s a l i n a t i o n 1978, 24, 19-37.

13.

S p i e g l e r , K.S.; Kedem, O. D e s a l i n a t i o n 1966, 1, 311-326.

14.

Sherwood, T.K.; B r i a n , P.L.T.; F i s h e r , R.E. Ind. Eng. Chem. Fundamentals 1967, 6 ( 1 ) , 2-12.

15.

Pusch, W. Ber. Bunsenges. Physik. Chem. 1977, 81, 269-276.

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S o u r i r a j a n , S.; Matsuura, T. in "Reverse Osmosis and S y n t h e t i c Membranes"; S o u r i r a j a n , S., Ed.; N a t i o n a l Research C o u n c i l of Canada: Ottawa, 1977; Chapter 3.

17.

S o u r i r a j a n , S. "Reverse Osmosis"; Academic P r e s s : New York, 1970; Chapter 3.

18.

Matsuura, T.; Dickson, J.M.; S o u r i r a j a n , S. Ind. Eng. Chem. Process Des. Dev. 1976, 15(1), 149-161.

19.

T a f t , R.W., J r . in " S t e r i c E f f e c t s in Organic Chemistry" Newman, M.S., Ed.; Wiley: New York, 1956; p. 556-675.

20.

Small, P.A. J . A p p l . Chem. 1953, 3, 71-80.

21.

Matsuura, T.; S o u r i r a j a n , S. Ind. Eng. Chem. Process Des. Dev. in press.

22.

Matsuura, T.; S o u r i r a j a n , S. J. A p p l . Polymer Sci. 1973, 17, 3683-3708.

23.

Dickson, J.M.; Matsuura, T.; S o u r i r a j a n , S. Ind. Eng. Chem. Process Des. Dev. 1979, 18(4), 641-647.

24.

Pageau, L.; S o u r i r a j a n , S. J. A p p l . Polymer Sci. 1972, 16, 3185-3206.

25.

S o u r i r a j a n , S. "Reverse Osmosis"; Academic Press: New York, 1970; Chapter 2.

26.

Matsuura, T.; Pageau, L.; S o u r i r a j a n , S. J. A p p l . Polymer S c i . 1975, 19, 179-198.

27.

W i l k e , C.R.; Chang, P. AIChE J . 1955, 1, 264-270.

RECEIVED

December 4, 1980.


Solute Preferential Sorption in Reverse Osmosis - ACS Publications

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