A study of dialyzer design

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A study of dialyzer design

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UNIVERSITY OF CINCINNATI

Ju L /2 -l9 d l

I hereby recommend that the thesis prepared under m y supervision by^ en titled

A

13- S m iii)_________________________

S tu d ij o j 1 J ) ia Jij-?er X te si^ n _______________

be accepted as fu lfillin g this part o f the requirements fo r the

A p p ro v e d by:

F o r m 668— G. S. a n d E d .— 1M— 7-37

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A STUDY OF DIALYZER DESIGN I A d i s s e r t a t i o n s u b m itte d to th e G rad u ate S chool o f th e U n iv e r s it y o f C in c in n a ti i n p a r t i a l f u l f i l l m e n t o f th e re q u ire m e n ts f o r th e d e g re e o f DOCTOR OF PHILOSOPHY 1942

,

by H enry Brow er S m ith , J r . B .S . M .S.

N o rth C a r o lin a S t a t e C o lle g e 1938 V i r g i n i a P o ly te c h n ic I n s t i t u t e 1939

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UMI Number: DP16066

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TABLE OF CONTENTS

I. II.

III.

IV.

V. V I.

Page 1

INTRODUCTION HISTORICAL

3

a.

L arg e S c a le U ses o f D ia l y s i s

b.

D if f u s io n T heory

11

c.

Osm osis

15

d.

Membrane T heory

18

e.

Membrane E l e c t r o k i n e t i c s

25

f.

D ia ly z e r K in e tic s

32

g.

D ia ly z e r s

34

THEORETICAL

5

39

a.

Case I

42

b.

C ase I I

45

c.

C ase I I I

48

d.

Case IV

50

e.

C ase V

53

f.

Case VI

56

g.

C ase V II

58

h.

C ase V I I I

61

i.

Case IX

65

EXPERIMENTAL

68

a.

D ata and G raphs

b.

D ia ly z e r C a l c u la t io n

74 107

DISCUSSION OB’ RESULTS

113

SUMMARY

122

k S ’42

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TERMINOLOGY

a Atoms o f a n io n s p e r m o le c u le A A rea, L c C ondenser c a p a c it y , L C C o n c e n tr a tio n , ML” ^ Cq R ich c o n c e n tr a ti o n , M L~/7 Cg D ilu te c o n c e n tr a tio n ML-0 Ca A nion c o n c e n tr a ti o n , e q u i v a le n t s / l i t e r Cjj C a tio n c o n c e n tr a ti o n , e q u i v a l e n t s / l i t e r D i e l e c t r i c c o n s ta n t D D i f f u s i v i t y c o e f f i c i e n t , L^T"-*d D is ta n c e betw een c o n d e n se r n l a t e s , L dq D e n s ity o f g a s , ML- ® i n E P o t e n t i a l d i f f e r e n c e , v o l t s , MsL3T_ Em Membrane p o t e n t i a l , v o l t s D if f u s io n p o t e n t i a l , v o l t s Eq. Thermodynamic p o t e n t i a l , v o l t s F The F a ra d a y F e F re e e n e rg y , ML f F o rc e , MLT-2 g W eight o f s o l u t e , M h Heigl.it o f th e l i q u i d l e v e l , L H P o t e n t i a l g r a d i e n t , v o lt s / c m . i R a tio o f t h e a c t u a l num ber o f p a r t i c l e s t o t h e number i f i o n i z a t i o n d id n o t ta k e p la c e I E l e c t r i c a l C u r r e n t, am peres k* B o ltzm an ’ s c o n s t a n t , e rg /d e g .A . 1 L en g th o f flo w p a t h , L L Lean l i q u o r flo w r a t e , L^T” ! m Atoms o f c a t i o n p e r m o le c u le M M o le c u la r w e ig h t n V alen c e o f th e r e v e r s i b l e io n Na A nion t r a n s f e r e n c e number He C a tio n t r a n s f e r e n c e number Up F r i c t i o n a l r e s i s t a n c e 0 Osmose, L^ 0 e E le c tro o s m o s e , L^ PQ O sm otic p r e s s u r e , ML“ ^ p V apor p r e s s u r e o f o f th e s o l u t i o n , m.m. Hg, Po V apor p r e s s u r e o f th e s o lv e n t , m.m. Hg. P P r e s s u r e , ML“ lT “ 2 q Q u a n tity o f s o lu tg t r a n s f e r r e d , M q C harge d e n s i t y , M§L“'sT “ l Q T o ta l e f f e c t i v e a r e a , L^ r R ad iu s o f a tu b e o r s p h e r e , L R R ic h l i q u o r flo w r a t e , L^T"1

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TERMINOLOGY (Cont.)

Rp. s° t T Tc u U v V ! V1 V]_ Vg W

The Gas C o n s ta n t, s u i t a b l e u n i t s o f w ork p e r d eg . A. D is ta n c e from tu b e w a l l , L T h ic k n e s s o f t r a n s f e r p a th , L A b s o lu te te m p e r a tu r e , °A. T e m p e ra tu re , °C. M ig r a tio n v e l o c i t y o f c a t i o n , c m ^ ./s e c . v o l t L in e a r v e l o c i t y , LT” 1 M ig ra tio n v e l o c i t y o f th e a n io n , c m ^ ./s e c . v o l t Volume o f s o l u t i o n , L® *2 Volume o f s o lv e n t , I/Volume o f r i c h l i q u o r , L"5 Volume o f lean- l i q u o r , L^ Work, s u i t a b l e u n i t s o f work Mole f r a c t i o n o f s o lu te xc Donnan e q u ilib r iu m c o n c e n tr a tio n ., m o l e s / l i t e r x R a tio o f volum es T em p eratu re c o e f f i c i e n t , d e g ,-1 y O sm otic c o e f f i c i e n t , L^M- 1 T_1 /" L e e 's t r a n s f e r c o e f f i c i e n t , IT ” 1 o T h ic k n e ss o f e l e c t r i c a l d o u b le l a y e r , cm. C o n c e n tr a tio n d i f f e r e n c e , ML” 3 Mean p a th o f B row nian movement, cm. Io n m o b i lit y , c m ^ ./s e c . v o l t

I

I

I

Avts+m

F ig . 1 A T oxin D i a l y t i c C e ll I n th e s e c e l l s , a c e llo p h a n e o r p arch m en t p a p e r membrane i s em ployed.

The t o x i n o r serum i s a llo w e d t o rem ain s ta g n a n t i n t h e i r

co m p artm en ts, w h ile w a te r i s

lo w ly p a s s e d i n th e a d jo in in g com partm ent.

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T h is i l l u s t r a t e s a v e r y s im p le , b u t h i ^ i l y i n e f f i c i e n t m ethod. S u g ar p u r i f i c a t i o n p r e s e n t s a v e r y d i f f e r e n t . c a s e , more n e a r l y re s e m b lin g p r e f e r e n t i a l d i a l y s i s .

I n t h e s y ru p s from c r y s t a l l i z e d s u g a r ,

t h e r e re m a in s a q u a n t i t y o f su g a r w hich w ould be c r y s t a l l i z e d u n d e r extrem e c o n d i tio n s , b u t c a n n o t be removed i n p u re fo rm .

However, t h i s

s u g a r w i l l d ia ly z e i n p r e f e r e n c e t o th e n o n - e r y s t a l l i z a b l e s u g a r .

T h us,

i t i s p o s s i b l e t o r e c o v e r c o n s id e r a b le q u a n t i t i e s o f s u g a r t h a t o th e rw is e (4 2 ) w ould be w a s te d . The S te p h a n s p r o c e s s o f fo rm in g th e c a lc iu m s a c c h a r id e com petes w ith t h i s . The ru b b e r com panies o f G re a t B r i t a i n 1s Ea s t I n d i e s have en d ea v o red t o p u r i f y raw l a t e x by means o f d i a l y s i s b e f o r e th e l a t e x i s (2 6 ) c o n g e a le d . T h is rem oves an a c c e l e r a t o r and an o x id a n t. S ix te e n p e r c e n t o f th e t o t a l n i t r o g e n i s d i f f u s i b l e .

The f i l m from d ia ly z e d l a t e x i s

s tr o n g e r th a n t h a t fro m th e r e g u l a r p r o c e s s .

C e r t a in d i f f i c u l t i e s a r o s e ,

how ever, due t o th e fo rm a tio n o f a l i g h t l y c o a g u la te d g e l i n th e v i c i n i t y o f th e membrane. By p r o p e r ly c o n t r o l l i n g c o n d i tio n s , t h i s was p a r t i a l l y (2 7 ) a l l e v i a t e d . I t i s a p p a r e n t t h a t th e c o n d itio n was n o t c o m p le te ly t r e a t e d , s in c e t h e r e was no m ethod o f l a t e x c i r c u l a t i o n em ployed, and a t c e r t a i n l i m i t s , th e l a t e x s t a b i l i t y c o u ld b e e x p e c te d t o be a f f e c t e d . th e a p p a r a tu s em ployed w as v e r y c r u d e .

F u rth e rm o re ,

The B r i t i s h I n d i a Company h a s

dropped t h e i r e x p e rim e n ts s in c e th e n , b u t t h e r e i s no a p p a r e n t r e a s o n why a m odern d i a l y z e r c o u ld n o t e f f e c t th e p u r i f i c a t i o n . P ro b a b ly th e g r e a t e s t d i a l y s i s ad v an ces and t h e m o st s u c c e s s f u l a p p l i c a t i o n s have b een i n th e v is c o s e m a n u fa c tu rin g i n d u s t r i e s .

F or

t h a t r e a s o n , and b e c a u se o f th e a v a i l a b l e in f o r m a tio n , t h i s c a s e w i l l be tr e a te d in d e t a i l . V is c o s e i s m a n u fa c tu re d by c a u s t i c i z i n g wood p u lp ( e s s e n t i a l l y

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9

a lp h a c e l l u l o s e ) w i t h sodium h y d r o x id e , w h ich c a u s t i c c e l l u l o s e i s th e n r ip e n e d , t r e a t e d w ith c a rb o n d i s u l f i d e , and th e n d is s o lv e d i n d i l u t e (1 7 ) sodium h y d ro x id e s o l u t i o n . F ig u r e (2 ) r e p r e s e n t s th e flo w s h e e t t h a t i s em ployed by th e T u rb iz e C h a t i l l o n C o r p o r a tio n o f Rome, G e o rg ia . The m a n u fa c tu re o f v is c o s e r e q u i r e s 1 ,2 5 l b s . o f NaOH p e r l b . o f v is c o s e p r o d u c ts , 65 p e r c e n t ( o r 0 .8 1 3 l b . ) o f w hich i s em ployed i n (1 7 ) th e s te e p in g b a t h s . A ll o f th e c a u s t i c i s n o t d ia ly z e d a f t e r each s te e p in g s in c e th e d e g re e o f c o n ta m in a tio n does n o t r e q u i r e p u r i f i c a t i o n .

The

fo llo w in g p ro c e d u re i s em ployed; 220 l b s . o f wood o u lp ( d r y b a s i s ) i s p la c e d i n a s te e p in g b a t h , to w hich i s added 2 ,9 9 8 l b s . o f 17 -1 8 p e r c e n t c a u s tic s o lu tio n .

A f t e r th e s p e c i f i e d p e r io d o f s te e p i n g , th e

e x c e s s c a u s t i c s o l u t i o n i s d r a in e d o f f .

Im m e d ia te ly f o llo w in g t h i s ,

p r e s s u r e i s a p p lie d t o t h e c a u s t i c i z e d c e l l u l o s e by means o f a h o r i z o n t a l screw ja c k , th u s l i b e r a t i n g a q u a n t i t y o f 17 p e r c e n t NaOH s o l u t i o n , w hich i s known a s th e " 1 s t p r e s s " .

The d r a in and " 1 s t p r e s s " a r e

com bined and s e n t to a p u r i f i c a t i o n u n i t i n w h ich su sp en d ed m a tte r i s rem oved.

T h is h a s com bined w ith i t 0 .7 0 l b . o f h e m ic e l lu lo s e .

The

c a u s t i c i z e d c e l l u l o s e m ass i s th e n p r e s s e d a g a in t o y i e l d th e "2nd p r e s s " . T h is c o n s i s t s o f 298 l b s . o f 17 p e r c e n t c a u s t i c w hich i s c o n ta m in a te d w ith 1 .9 l b s . o f h e m ic e l lu lo s e .

T h is h a s re a c h e d a c e l l u l o s e c o n te n t to o

h ig h f o r f u r t h e r s te e p in g o p e r a t i o n s , and i s , t h e r e f o r e , s e n t to th e d ia ly z e rs f o r p u r if ic a tio n .

F our h u n d red l b s . o f 1 6 .7 p e r c e n t c a u s t i c (42) i s r e t a i n e d by th e c a u s t i c i z e d c e l l u l o s e . I t i s th e "2 n d p r e s s " l i q u o r w hich i t i s d e s ir e d to d is c u s s i n

d e ta il.

T h is l i q u o r h a s th e f o llo w in g a p p ro x im a te co m p o sitio n s D e n s i t y ------------------1 .2 gm./cm^ C a u s t i c ------------------16% NaOH

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10

C a r b o n a t e s ------------- 4$ (C a, Mg, N a, K) O rg an ic M a t t e r

2% (m o s tly h e m ic e llu lo s e )

Suspended s o l i d s , s i l i c a t e s , m e t a l l i c i m p u r i t i e s , e t c . T h is l i q u i d p a s s e s i n t o a s to r a g e ta n k , w here p a r t o f t h e s u s ­ pended s o l i d s p a s s o u t.

From h e r e t h e l i q u o r p a s s e s t o d i a l y z e r s o f th e

C e r in i t y p e , w here 90 p e r c e n t o f th e d is s o lv e d h e m ic e llu lo s e i s rem oved, n e a r l y a l l c a r b o n a te s , and a l l th e s h re d s and m e t a l l i c i m p u r i t i e s . T h is i s d e l iv e r e d a s 8 p e r c e n t NaOH s o l u t i o n , t h e im pure l i q u i d b e in g re d u c e d t o 1 ,5 p e r c e n t NaOH. The r e c o v e ry e f f i c i e n c y i s s p e c i f i e d a s (4 2 ) 90 p e r c e n t . T h ere i s some i n c r e a s e i n th e im pure l i q u o r volum e, w h ile th e p u re l i q u i d h a s a volume tw ic e t h a t o f t h e im pure s o l u t i o n .

The

c o n c e n tr a ti o n o f th e s o lu ti o n m u st be b u i l t up b e f o r e f u r t h e r u s e i n th e s te e p in g b a t h s , o r re d u c e d i n s tr e n g t h f o r u s e i n m ix in g w ith tr e a te d c e llu lo s e .

I n c i d e n t a l l y , some p l a n t s hav e fo u n d i t a d v a n ta g e o u s

t o d ia ly z e some o f t h e f i r s t p r e s s l i q u o r e x o r e s s ly f o r th e p u rp o s e o f th e m ix in g s o l u t i o n , th u s d e r i v i n g th e a d v a n ta g e o f h ig h p u r i t y o f th e d ia ly z e d s o l u t i o n s . The v a lu e o f d i a l y s i s a s a r e c la m a tio n p r o c e s s i s e s t a b l i s h e d by th e r e c o r d o f i t s r a p i d grow th i n th e c a u s t i c - v i s c o s e i n d u s t r y . Some o f t h e im m ediate f e a s i b l e i n d u s t r i e s w h ere d i a l y s i s c o u ld (1 ) be p r o f i t a b l y em ployed a r e g iv e n by B a s s e t, a w o rk er i n t h e f i e l d . These a r e a s f o llo w s : (1 ) S ugar r e f i n i n g - l a r g e p e r c e n t o f c r y s t a l l i z a b l e s u g a r may b e o b ta in e d from m o la s s e s . (2 ) T e x t i l e in d u s tr y - r e c o v e ry o f w a ste m e r c e r iz in g c a u s t i c , w a s te sodium s u l f a t e , e t c . (3 ) Gel p u r i f i c a t i o n - a lu m in a , s i l i c a g e l , g lu e s , g e l a t i n s , e t c .

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11

(4 ) O rg an ic w a s te s

m ay

be f l o c c u l a t e d by rem oving s o lu b le s a l t s .

(5 ) T a r t a r i c and c i t r i c a c id r e c o v e ry . O th e r th a n su g a r r e c la m a tio n , t h e r e h a s b een l i t t l e work done in any o f t h e s e f i e l d s .

D if f u s io n T h eo ry . D if f u s io n o f a s o lu te i n th e l i q u i d s t a t e i s g o v ern ed by m u l t i p l e f a c t o r s , a w o rk in g r e l a t i o n b etw een w hich h a s n e v e r b e e n s a t i s f a c t o r i l y re a liz e d .

However, c e r t a i n fu n d a m e n ta l r e l a t i o n s h o ld r a t h e r w e ll f o r

lim ite d c a se s. The r a t e o f d i f f u s i o n i n lo n g p a t h s i s d e f in e d by

(i)

T h is r e l a t i o n i n d i c a t e s t h a t th e d i f f u s i v i t y c o e f f i c i e n t i s a f u n c ti o n o f t h e c o n c e n tr a ti o n .

However, w here th e d i f f u s i o n p a t h i s r e l a t i v e l y s h o r t ,

th e c o n c e n tr a ti o n g r a d ie n t a c r o s s t h e p a th may b e assumed t o be l i n e a r ( 8) i n p a th le n g th . T h e re fo re we may w r i t e

-

{2)

F u rth e rm o re , f o r any sy stem , i t may be w r i t t e n t h a t Ji

& =

(3 )

S u b s t i t u t i n g (3 ) i n (2 ) ■ a)

(4 )

The e q u a tio n (4 ) i s th e m ost c o n v e n ie n t t o u s e i n th e c a s e o f d i a l y s i s , and w i l l b e em ployed i n some o f th e s u b se q u e n t w ork.

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E q u a tio n s

12

(l)

and (2 ) o n ly d e f in e th e d i f f u s i v i t y c o e f f i c i e n t . An a n a lo g y f o r d i l u t e s o l u t i o n s may b e draw n fro m G raham 's

e f f u s io n la w , w hich i s g iv e n as (5 ) and (6)

T h is r e l a t i o n i s o b j e c t i o n a l b e c a u se M d o es n o t c o n s id e r s o l u t e s o lv a t io n . ( 21) N e r n s t fo u n d t h a t th e d i f f u s i o n o f e l e c t r o l y t e s c o u ld be r e l a t e d to t h e i r io n i c m o b i l i t i e s , and g iv e s t h e f o llo w in g e q u a tio n (V)



C om parison o f e q u a tio n s ( ? ) and (2 ) i n d i c a t e s t h a t /Z 7 -

( 8)

(24) U sin g th e d a ta o f W. Oholm, th e f o llo w in g c a l c u l a t i o n s i n d i c a t e th e a p p l i c a b i l i t y o f e q u a tio n ( 8 ) . TABLE I

S u b sta n c e

.D { C a lc .} • D ( o b s .) ) s D ( C a lc .) » .S u b s ta n c e : 18° C. : 18° C. : 18°C.

I • •

KC1 NaCl L iC l HC1 U o te:

: s s s



1 .4 6 0 1 .1 7 0 1 .0 0 0 2 .3 2 4

1 .4 6 0 i 1 .1 7 3 : 0 .9 9 4 • « 2 .4 3 1 • •





:K0H :Na0H :K I :CH3C00H

: : : :

• •

1 .9 0 3 1 .4 3 2 1 .4 6 0 0 .9 3 0

: : s :

2.109 1 .5 5 8 1 .4 6 7 1 .3 7 0

A ll v a lu e s o f D w ere m easu red a t N o rm a lity z 0 .0 1 D i s e x p re s s e d i n c m .^ /d a y .

E q u a tio n (8 ) was l a t e r m o d if ie d , and fo u n d t o g iv e b e t t e r r e s u l t s ,

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IS

The m o d ifie d form i s g iv e n a s

0) I n g e n e r a l, i t may be s a id t h a t th e above e q u a tio n h o ld s f o r e l e c t r o l y t e s , w here th e i o n i z a t i o n i s n e a r l y c o m p le te , o v e r a ran g e o f te m p e r a tu r e s i n th e v i c i n i t y o f 18 d e g re e s C, I n an e f f o r t to c o r r e l a t e D w ith th e v a r i a t i o n o f te m p e r a tu r e , (2 3 ) Oholm co m p iled th e f o llo w in g t a b l e f o r th e ap p ro x im a te v a lu e o f o< , t h e te m p e r a tu r e c o e f f i c i e n t p e r d e g re e f o r v a r io u s ra n g e s o f t h e d iffu s io n c o e f f ic ie n t. TABLE I I D =