Intrinsic Membrane Compaction and Aqueous ... - ACS Publications

10 Intrinsic Membrane Compaction and Aqueous Solute Studies of Hyperfiltration (ReverseOsmosis) Membranes Using Interferometry 1

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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: May 21, 1981 | doi: 10.1021/bk-1981-0153.ch010

DAVID MAHLAB , NISSIM BEN YOSEF, and GEORGES BELFORT

School of Applied Science and Technology, Hebrew University of Jerusalem, Israel

This paper is the third in a series and a direct continuation of our first publication. In the first paper, we described the theory and a nominal experiment to show the goodness of fit of the concentration polarization for dissolved species for an unstirred batch system with a plane infinite membrane. An explicit general solution was derived and presented for the time-dependent connec tive diffusion equation for the case π^«ΔΡ. Interferometry was used to measure the steady state feed-side concentration build-up at 28+1°C for a constant applied differential pressure of 30 atm for a dilute solution of 62 mg/£ NaCl. Theoretical analysis of the electromagnetic wave propagation in an inhomogeneous medium (i.e. ray tracing of the bended beam) was analytically solved for the JbtcutLonaJiy form of the diffusion equation. The second paper is concerned with the numerical solution to the general tMjdvib^ZWt form of the diffusion equation and its ^ parametric fit to the changing interferometric fringe pattern. Here we are concerned with applying the same model and optical methods to analyze (1) the influence of -applied pressure on intrinsic compaction, and (2) aqueous solution effects on intrinsic transport parameters and concentration polarization. The reader is referred to our first paper for details including ^ the relevance of the work and previous significant developments. The major significance of this work is that iy\&LWikAjl c o m p a c t i o n for one solute and aqueooo AoZuutlon e^eato for different solutes are measured for a commercial hyperfiltration membrane as a function of applied differential pressure. The results are obtained via simulation of the steady state concentra tion profile adjacent to the planar surface of the membrane for 7 ί « ΔΡ. 1,2

σ

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This is the third in a series of papers dealing with this particular topic. Current address: Ormat Turbines, P.O. Box 68, Yavne, Israel.

Current address : Department of Chemical Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12181. To whom correspondence should be addressed. 2

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0097-6156/81/0153-0147$05.00/0 i t tmé © 1981 American Chemical Society M * - —

Λ

Λ .

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

148

II.

SYNTHETIC

MEMBRANES:

DESALINATION

Theory

BoundaAy VaZlid Vhoblm. The r e l e v a n t transformed boundary value problem and s o l u t i o n s w i l l be presented without d e r i v a t i o n s i n c e the d e t a i l s have been published p r e v i o u s l y (Mahlab e t a l . , 1977). Thus, the problem can be s t a t e d as f o l l o w s :

2


jty

3 IP

with the boundary

(1)

M

conditions,

iKS.O) = 0 and and

3]Jj 3?

+

RT|/(0,T)

t

) = 0

(2a)

= -R

(2b)

5-0 T=T

with the f o l l o w i n g T

and

transformations

= V t/V, w o 2

? = V x/P w o

iK?,t) - c ( x , t ) / c

(3a)

- 1

Q

(3b)

A f t e r taking the Laplace Transform of E q s ( l ) and (2) and rearranging the s o l u t i o n i n t o p a r t i a l f r a c t i o n s , the i n v e r s e Laplace transformation r e s u l t s i n a s o l u t i o n d i v i d e d i n t o 3 cases: where R =

2

l V l

).

0.19

A1C1

P RT/(P

-0.7

2.500

-8.0

0.30

0.56

0.36

MgCl?6H?0

Solute

And S p e c t r o s c o p i c Results o f Aqueous S o l u t i o n s

Parameters From the S o l u t i o n - D i f f u s i o n M o d e l

Table I I I


3

- -

--

- -

42.0

32.5

Urea

MAHLAB ET AL.

10.

(

)

(

RO

Membrane

Studies Using Interferometry

157

)

f / l C i v a r i e s i n the same d i r e c t i o n as s t r u c t u r e temperature (T ~*)20°q* l° gitudinal r e l a x a t i o n T^, and chemical s h i f t 6, r e s p e c t i v e l y . Thus, i t appears that the same p r o p e r t i e s of aqueous i n o r g a n i c s o l u t e s that e f f e c t water s t r u c t u r e and m o b i l i t y (as measured by the s p e c t r o s c o p i c parameters above) a l s o e f f e c t the a b i l i t y of a s o l u t e to move or d i f f u s e through a membrane. D i f f u s i o n of e l e c t r o l y t e s i s u s u a l l y dependent on t h e i r c o n c e n t r a t i o n , hydrated s i z e and i o n i c atmosphere, t h e i r e f f e c t on water s t r u c t u r e , and t h e i r d i s s o c i a t i o n . A l s o , the i n t e r n a l s u r f a c e p r o p e r t i e s or s t r u c t u r a l p r o p e r t i e s of the membrane w i l l d i r e c t l y i n f l u e n c e the e l e c t r o l y t e m o b i l i t y . These d e t a i l s have yet t o be c l a r i f i e d w i t h respect to the mechanism of d e s a l t i n g . Na

n


str

effects

ABSTRACT

A previously reported interferometric method is used to study the effects of both intrinsic compaction andaqueoussolution on transport through a commercial cellulose acetate hyperfiltration membrane. By fitting the theoretical model to the experimental interferogram, the intrinsic solute rejection R and the reduced flux v(=v /D,cm ) thus obtained, are studied as a function of applied pressures from 5 to 30 atm. and for six different solutes (NaCl, KCl, MgCl, NaNO , A l C l , and urea). For the pressure studies, two phase compaction behavior is observed with an inflection point between 7 and 11 atms. For the aqueous solution studies, the hydraulic permeability K and the g-ratio are hardly effected by solute type (within experimental error). The solute diffusive permeability P , however, varies with solute type in good qualitative agreement with free energy parameters, infrared overtone shifts, and spin echo and continuous wave nuclear magnetic resonance spectroscopy results from the literature. -1

wo

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ACKNOWLEDGEMENTS The authors thank Amotz Weitz f o r t e c h n i c a l a s s i s t a n c e and advice. T h i s work was sponsored by the U S - I s r a e l B i n a t i o n a l Foundation under Grant No. 186. LITERATURE CITED

1.

Mahlab, D., Ben-Yosef N. and Belfort G., "Interferometric Measurement of Concentration Polarization Profile for Dissolved Species in Unstirred Batch Hyperfiltration (Reverse Osmosis)", Chem. Eng. Commun. 6, 0-000. (1980)

2.

Mahlab, D., Ben-Yosef N. and Belfort G., "Concentration Polarization Profile for Dissolved Species in Unstirred Batch Hyperfiltration (Reverse Osmosis) - II Transient Case." Desalination, 24, 297-303 (1978)



158

SYNTHETIC MEMBRANES:

DESALINATION

3.

Yasuda, H . , and Lamaze, C . E . , J . Polym. S c i . , A-2, 9, 1537 (1971).

4.

Thau-Alexandrowicz G., Bloch R. and Kedem O., Desalination 1, 66 (1966).

5.

Lonsdale H.K., Chap 4, p.93-160, in Desalination by Reverse Osmosis (ed. U. Merten) The MIT Press, Mass. (1966).

6.

Sourirajan S., Reverse Osmosis, Logos Press, London (1970).

7.

Sourirajan S. and Matsuura T . , Chap 3 of Reverse Osmosis and Synthetic Membranes (ed. S. Sourirajan), National Research Council Canada, NRCC No. 15627 (1977).

8.

Luck W.A.P., Chap iii.3 of Structure of Water and Aqueous Solutions (ed. W.A.P. Luck) Verlag Chemie Physik Verlag (1974).

9.

Hertz, H.G., Chap VII.2 of Structure of Water and Aqueous Solutions (ed. W.A.P. Luck) Verlag Chemie Physik Verlag (1974).

RECEIVED

December 4, 1980.


Intrinsic Membrane Compaction and Aqueous ... - ACS Publications

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