Material Balance Considerations in an Electrocoating Tank

14 Material Balance Considerations in an Electrocoating Tank

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W I L L I A M V A N H O E V E N , JAMES E . L O H R , and W I L L E M Β. V A N D E R L I N D E Marshall Research and Development Laboratory, F & F Department, Ε . I. du Pont de Nemours & Co., Inc., 3500 Grays Ferry Ave., Philadelphia, Pa. 19146

A mathematical model has been developed which describes the time-dependent

concentration behavior of component(s)

in an operational electrocoating bath. C

T

The equation is:

= C e - ; + k V e~ > k

( )

T

k

2

n

n=0

where C is the component concentration at time, T , C is T

0

the initial concentration, k is the time-dependent first-order 1

rate constant for component removal, and k is the linearly 2

time-dependent

constant

for

component

addition.

The

model is based upon the addition being a stepwise process and removal being a continuous process. The validity and scope of the model are demonstrated in laboratory experi ments and field situations. Examples include application to the concentrations of solvent, amine, and water-soluble nonvolatiles.

The value of such information for assistance in

formulating,

controlling,

and

designing

electrodeposition

systems is shown. T t is a c r i t i c a l p r e r e q u i s i t e that t h e m a t e r i a l b a l a n c e i n a n e l e c t r o c o a t i n g tank b e k e p t w i t h i n set values to ensure satisfactory p e r f o r m a n c e at a n y t i m e d u r i n g t h e l i f e of t h e b a t h .

I n other w o r d s , t h e c o n c e n t r a t i o n

of a l l c o m p o n e n t s of t h e p a i n t , i n c l u d i n g c o n t a m i n a n t s , m u s t b e m a i n t a i n e d w i t h i n c e r t a i n l i m i t s to p e r m i t the d e p o s i t i o n of a c c e p t a b l e coat ings.

I n v i e w of the large n u m b e r of c o m p o n e n t s w h i c h go i n t o most

electrocoating f o r m u l a t i o n s , this is a c o m p l e x p r o b l e m . H i s t o r i c a l l y t h e attention g i v e n this p r o b l e m is as o l d as e l e c t r o d e p o s i t i o n itself.

Forty-

year o l d patents a n d j o u r n a l articles, c o n c e r n e d w i t h r u b b e r

electro-

207

Brewer; Electrodeposition of Coatings Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

208

ELECTRODEPOSITION

OF

COATINGS

d e p o s i t i o n , c o n s i d e r b a t h c o m p o s i t i o n a n d m a t e r i a l b a l a n c e ( 1 ).

Recent

l i t e r a t u r e contains n u m e r o u s articles d i s c u s s i n g d i f f e r e n t i a l d e p o s i t i o n of p i g m e n t s ( 2 ) , a c c u m u l a t i o n of solvents ( 3 ) , a n d the difficulties of m a i n t a i n i n g the p r o p e r a m o u n t of a m i n e s o l u b i l i z e r

(4).

P a i n t d e p o s i t i o n occurs w h e n d i s p e r s e d particles are

electrochem-

i c a l l y d e s t a b i l i z e d i n the r e g i o n of the substrate.

I n general, the t o t a l

system is v e r y sensitive to e l e c t r o c h e m i c a l changes.

S i n c e the c o m p o n e n t s

a n d c o n t a m i n a n t s i n a n e l e c t r o c o a t i n g t a n k c o n t r i b u t e i n different w a y s Downloaded by CHINESE UNIV OF HONG KONG on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0119.ch014

to the e l e c t r o c h e m i s t r y a n d the s t a b i l i t y of the d i s p e r s i o n , it is d i f f i c u l t to q u a n t i f y effects w i t h o u t extensive a n a l y t i c a l efforts. Nevertheless, c o m m e r c i a l e l e c t r o d e p o s i t i o n is a r e a l i t y despite d e l i c a t e n a t u r e of s u c h systems.

the

T h i s has b e e n m a d e possible because

the a d d i t i o n a n d r e m o v a l o f materials c a n be systematically a n d a c c u r a t e l y c o n t r o l l e d . T h e p u r p o s e of this p a p e r is to s h o w h o w the systematic changes o c c u r r i n g i n a n e l e c t r o c o a t i n g t a n k c a n be c a l c u l a t e d a n d u s e d to p r e d i c t a n d to c o n t r o l t h e concentrations of the c o m p o n e n t s i n the tank. T o m a i n t a i n a g i v e n l e v e l of a n y c o m p o n e n t i n a tank, it is necessary to k n o w , q u a n t i t a t i v e l y , the m o d e s of a d d i t i o n a n d r e m o v a l of that p a r t i c u l a r species.

T h i s is possible o n l y w i t h a t h o r o u g h u n d e r s t a n d i n g of

the m e c h a n i s m of e l e c t r o d e p o s i t i o n a n d the d i s t r i b u t i o n of the c o m p o nents b e t w e e n the c o n t i n u o u s a n d d i s c o n t i n u o u s phases i n the

electro

c o a t i n g b a t h . T h e rates of a d d i t i o n a n d r e m o v a l of e a c h c o m p o n e n t of the e l e c t r o d e p o s i t i o n b a t h m u s t also b e k n o w n .

F o r t u n a t e l y m a n y of these

i n p u t a n d r e m o v a l rates are restricted w i t h i n fixed l i m i t s b y the e q u i p m e n t d e s i g n , t u r n o v e r rates, p a i n t f o r m u l a s , etc. is

F u r t h e r m o r e the

treatment

s i m p l i f i e d b y the fact that e l e c t r o c o a t i n g tanks are m a i n t a i n e d

at

constant v o l u m e . T h e p r o p o s e d m a t e r i a l b a l a n c e m o d e l takes i n t o a c c o u n t the rates of c o m p o n e n t a d d i t i o n a n d r e m o v a l , b y w h a t e v e r means, a n d a l l o w s the c a l c u l a t i o n of the c o n c e n t r a t i o n of that c o m p o n e n t at a n y g i v e n t i m e . R e m o v a l of b a t h c o m p o n e n t s i n v o l v e s several factors. C e r t a i n species —e.g., solvents, crosslinkers, e t c . — m a y p a r t i t i o n b e t w e e n the o r g a n i c a n d aqueous phases so that t h e y w i l l be p a r t i a l l y r e m o v e d b y d e p o s i t i o n of p a i n t (3, 5 ) .

If c o m p o n e n t s d o not p a r t i t i o n i n t o t h e aqueous phase b u t

r e m a i n associated w i t h the o r g a n i c b i n d e r , they are r e m o v e d i n d i r e c t p r o p o r t i o n to the rate of d e p l e t i o n of p a i n t solids. If a n e l e c t r o d e p o s i t i o n t a n k is e q u i p p e d w i t h a n u l t r a f i l t r a t i o n u n i t , or some other d e v i c e w h i c h selectively removes the aqueous phase, species d i s s o l v e d i n this phase w i l l be r e m o v e d at a rate w h i c h d e p e n d s o n the instantaneous concentrations i n the bath—i.e., the rate of r e m o v a l of s u c h species is first o r d e r w i t h respect to t h e i r c o n c e n t r a t i o n .

dt -

-

k

l

That is:

c


(1)

14.

Material Balance Considerations

VAN HOEVEN ET AL.

209

I n t e g r a t i o n over t h e l i m i t s t = 0 a n d t = T g i v e s : C = Co e - V

(2)

t

W h e r e C is the c o n c e n t r a t i o n at t i m e T, C is t h e c o n c e n t r a t i o n at t = 0, t

0

a n d Zci is the slope of a p l o t o f In C vs. T. A d d i t i o n of materials to t h e b a t h is m o r e s t r a i g h t f o r w a r d . F o r a n y species w h i c h enters t h e p a i n t b a t h as p a r t of the r e p l e n i s h m e n t , or w i t h the w o r k , there is a rate of increase i n c o n c e n t r a t i o n , fc , w h i c h is t i m e Downloaded by CHINESE UNIV OF HONG KONG on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0119.ch014

2

dependent only. That is: C = Co + k (T t

2

(3)

T) 0

or:

w h e r e AC is the a m o u n t of that c o m p o n e n t b r o u g h t i n t o t h e t a n k i n AT t i m e units. F o r e a c h o p e r a t i o n , AT is t h e n u m b e r of days r e q u i r e d f o r one turnover—i.e., the n u m b e r o f days r e q u i r e d to r e m o v e a n a m o u n t of p a i n t solids e q u a l to t h e a m o u n t o r i g i n a l l y present i n the tank. O f course if there is n o r e m o v a l m e c h a n i s m , t h e species continues to increase i n c o n c e n t r a t i o n . A t l o w concentrations, i o n i c contaminants a p p r o x i m a t e this b e h a v i o r . I n a n o p e r a t i n g system, the a d d i t i o n a n d r e m o v a l expressions c a n b e c o m b i n e d to o b t a i n c o n c e n t r a t i o n at a n y t i m e Τ > T . I n t h e c o m b i n e d expression i t is a s s u m e d that Τ is i n d a y s a n d that t h e t a n k is oper a t e d s u c h that a n a m o u n t of the species sufficient to p r o d u c e a concentra t i o n change of m a g n i t u d e k (== AC/AT) is a d d e d at t h e e n d of e a c h o p e r a t i n g d a y . T h u s at the e n d of t h e first day's o p e r a t i o n , f o l l o w i n g the r e p l e n i s h m e n t a d d i t i o n , the c o n c e n t r a t i o n of t h e c o m p o n e n t i n q u e s t i o n w i l l b e C i = C e~\ -f- k>; at the e n d of t h e second d a y , C = (C éT i -f k )e~ i + k ; etc. A t a n y t i m e T, 0

2

0

fc

2

0

2

k

C

2

T

= C e~ i 0

k

T

+ k

2

T-l X 71 =

0

e-*i"

(5)

w h i c h c a n be m o d i f i e d t o :

(5a)


210

ELECTRODEPOSITION

OF

COATINGS

U s i n g E q u a t i o n 5,

as Τ C^

ι 1 —e

(6)

*i

w h e n the t i m e f o r i n c r e m e n t a l a d d i t i o n s equals one d a y . I n the i d e a l case, w h e r e a d d i t i o n a n d r e m o v a l are s i m u l t a n e o u s l y


c o n t i n u o u s , the c o n c e n t r a t i o n c h a n g e w i t h t i m e i s : dc — = k

2

-

h

c(t)

I n t e g r a t i o n of this f u n c t i o n g i v e s : C

t

= C β-*i< + ^ ( l - e - * i ' )

(50

0

It is e v i d e n t that i n this case the a s y m p t o t i c v a l u e of C

t

Ceo = Since 1 — e~ i « k

k

l9

is:

p

(60

E q u a t i o n 6' c a n b e u s e d i n process d e s i g n to deter

m i n e kx for g i v e n values of

and k. 2

T o s i m p l i f y the use of rate E q u a t i o n 5, a H e w l e t t - P a c k a r d 9100 c a l c u l a t o r / p l o t t e r system has b e e n p r o g r a m m e d to give C vs. Τ plots d i r e c t l y , f o r preselected k values a n d i n i t i a l c o n d i t i o n s . T h e rate e q u a t i o n i n t h e " s t e p - w i s e " f o r m is e s p e c i a l l y u s e f u l for s i m u l a t i n g a c t u a l o p e r a t i n g situations.

B y u s i n g a s u m m a t i o n i n s t e a d of

a n i n t e g r a l s o l u t i o n , c o m p e n s a t i o n f o r u n e x p e c t e d r a n d o m a d d i t i o n s of a n y species c a n b e m a d e . accommodated.

A l s o , variations i n rates of r e m o v a l c a n

be

If a c o m p o n e n t is b e i n g r e m o v e d b y m o r e t h a n one first-

order concentration dependent mechanism, & i can be replaced b y a com posite ki w h i c h

is s i m p l y the

s u m of i n d i v i d u a l

first-order

fc/s.

In

p r a c t i c e a c o m p o s i t e ki is often necessary, as i n the case of solvents, w h e r e d e p o s i t i o n w i t h the c o a t i n g , e v a p o r a t i o n , a n d u l t r a f i l t r a t i o n m u s t a l l b e c o n s i d e r e d . W e h a v e f o u n d e x p e r i m e n t a l l y that w h e n electrocoati n g f o r m u l a t i o n s c o n t a i n i n g less t h a n 1 5 % solvent are h e l d i n c o n t r o l l e d e n v i r o n m e n t s , plots of In C ( s o l v e n t ) vs. Τ are essentially l i n e a r ; the slope of s u c h a p l o t is the kx c a u s e d b y e v a p o r a t i o n . T h e s e e x p e r i m e n t a l l y d e r i v e d e v a p o r a t i o n rate constants are u s e f u l components

of the

c o m p o s i t e kis u s e d i n subsequent c o n c e n t r a t i o n vs. t i m e calculations. F i g u r e 1 demonstrates the u t i l i z a t i o n of the m o d e l . I n this example, a r b i t r a r y b u t realistic values of C

0>

ki, a n d k> have b e e n used. C u r v e A



14.

211


VAN HOEVEN ET AL.

TIME -DAYS Figure 1. Curve A Β C D Ε

Concentration vs. time curves according to Equation 5 h, % day' 0.3 0.3 0.3 0.6 0

h, % day0 0.05 0.05 0.1 0.05

Co, %

1

1

5 5 5 5 5

represents t h e increase i n c o m p o n e n t

concentration

when no removal

m e c h a n i s m is o p e r a t i n g (i.e., C = 5 % , k = 0, a n d k = 0 . 3 % d a y " ) . 0

x

1

2

C u r v e Ε represents t h e opposite extreme of r e m o v a l w i t h o u t a d d i t i o n (C

0

= 5 % , & i = 0.05 d a y " , k = 0 ) . C u r v e C is the result of c o m b i n 1

2

i n g these t w o extreme situations

a n d represents t h e c o n c e n t r a t i o n vs.

t i m e b e h a v i o r o f a n y species w h i c h is subject t o these selected a d d i t i o n a n d r e m o v a l rates a n d i n i t i a l c o n c e n t r a t i o n k = 0.3% day" ). 2

1

(C

0

1

1

Q

2

2

x

C u r v e Β shows t h e c h a n g e w h i c h occurs w h e n C

a n d & i are h e l d constant, a n d k is d o u b l e d (C k = 0.6% day" ).

= 5 % , fc = 0.05 d a y ,

0

= 5 % , & i •= 0.05 d a y , - 1

T h i s is e q u i v a l e n t t o d o u b l i n g t h e p r o d u c t i o n rate,


212

ELECTRODEPOSITION

OF

COATINGS

g o i n g to a t w o - s h i f t o p e r a t i o n , etc. C u r v e D shows the effect of d o u b l i n g kx w h i l e h o l d i n g C a n d k at the o r i g i n a l v a l u e ( C — 5 % , kx = 0

k

2

=

0.3%

day" ).

0.1 d a y " , 1

0

2

T h i s s i t u a t i o n w o u l d arise i f the e v a p o r a t i o n r a t e

1

w e r e d o u b l e d or i f t h e u l t r a f i l t r a t i o n rate w e r e increased. A l t h o u g h the rate at w h i c h a c o m p o n e n t approaches its e q u i l i b r i u m c o n c e n t r a t i o n , C*» is o f t e n i m p o r t a n t , the v a l u e of the e q u i l i b r i u m c o n c e n t r a t i o n is g e n e r a l l y of e v e n greater c o n c e r n . If, f o r e x a m p l e , C u r v e Β of F i g u r e 1 represents a c o m p o n e n t c o n c e n t r a t i o n b e h a v i o r f o r a g i v e n Downloaded by CHINESE UNIV OF HONG KONG on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0119.ch014

p a i n t f o r m u l a t i o n , the e q u i l i b r i u m c o n c e n t r a t i o n c a n b e c a l c u l a t e d to b e 1 2 . 3 % . If this l e v e l of the c o m p o n e n t a d v e r s e l y affects t h e e l e c t r o c o a t i n g process, the m o d e l c a n b e u s e d to c a l c u l a t e the v a l u e of kx necessary to m a i n t a i n a n y t o l e r a b l e c o n c e n t r a t i o n of the species.

F o r example, if the

e q u i l i b r i u m c o n c e n t r a t i o n of C u r v e C is a n a c c e p t a b l e v a l u e , t h e p a i n t m u s t b e r e f o r m u l a t e d w i t h a different b u t s i m i l a r c o m p o n e n t w i t h t w i c e the e v a p o r a t i o n rate, or t h e t a n k d e s i g n m a y be a l t e r e d to a c h i e v e the same goal, or u l t r a f i l t r a t i o n m a y b e i n c r e a s e d .

T h u s the m o d e l c a n be

u s e d to p r e d i c t f u t u r e difficulties a n d , b y k n o w i n g the m a g n i t u d e of the p r o b l e m s , assist i n p r e p a r a t i o n s to correct these difficulties. P e r h a p s the biggest

p r o b l e m i n e l e c t r o d e p o s i t i o n has b e e n

con

t r o l l i n g the c o n c e n t r a t i o n of the amines u s e d to s o l u b i l i z e the r e s i n . A p proaches

have

i n v o l v e d the

use

of v o l a t i l e amines,

amine

deficient

r e p l e n i s h m e n t s , a n d flushed cathodes. T h e m a t h e m a t i c a l m o d e l d i s c u s s e d h e r e is d i r e c t l y a p p l i c a b l e to the first t w o a p p r o a c h e s . If flushed cathodes are u s e d , this m o d e l does not a p p l y since t h e rate of r e m o v a l of a m i n e does not d e p e n d o n its c o n c e n t r a t i o n b u t o n l y u p o n the a m o u n t of c u r r e n t u s e d f o r c o a t i n g . T h e use of v o l a t i l e amines is exactly analogous to the p r e v i o u s d i s c u s s i o n w h e r e the m o d e l w a s s h o w n to b e v e r y u s e f u l . M o t o y a m a et al. h a v e p u b l i s h e d results of the a m i n e b a l a n c e i n a system u t i l i z i n g a m i n e deficient r e p l e n i s h m e n t ( 6 ) .

B y using a non-vol

a t i l e a m i n e , e v a p o r a t i o n is d i s r e g a r d e d , a n d r e m o v a l is l i m i t e d to the a m o u n t c a r r i e d out o n the w o r k p i e c e i n t h e c o m b i n e d film p l u s d r a g o u t ) .

Since this a m i n e i n c l u s i o n has a

film

(deposited

first-order

concen

t r a t i o n d e p e n d e n c e , it is a m e n a b l e to treatment b y o u r m o d e l . I n this system, the i n i t i a l a m i n e c o n c e n t r a t i o n , C , is 8.6 0

meq/20

grams solids. R e m o v a l of a m i n e b y t h e e l e c t r o c o a t i n g process is a l i n e a r f u n c t i o n of a m i n e c o n c e n t r a t i o n i n the tank.

T h e ratio of t h e

amine

c o n c e n t r a t i o n i n the c o m b i n e d film to a m i n e c o n c e n t r a t i o n i n the b a t h is 0.34.

T h e average

t u r n o v e r p e r 13.26

t u r n o v e r rate is 2.3

days).

Therefore,

turnovers p e r m o n t h

E q u a t i o n 1, dc dt

0.34 13.26 d a y s

(one

w i t h no amine addition, using

c(t)

(t i n days)

or, ki = 0.0256 d a y . 1


14.

VAN HOEVEN

213


ET AL.

T h e a m o u n t of a m i n e a d d e d i n o n e t u r n o v e r increases t h e c o n c e n t r a t i o n 5.5 m e q / 2 0 grams solids i f n o a m i n e is r e m o v e d . T h a t i s : 5.5 meq/20 g r a m s solids

k

=

k

= 0.4135 (meq/20 g r a m s solids) d a y

2

13.26 d a y s

or 2

U s i n g these values of C , k


0

u

_

1

a n d k , t h e change i n a m i n e c o n c e n t r a t i o n 2

i n the b a t h w i t h time c a n b e calculated. F i g u r e 2 compares the computed c o n c e n t r a t i o n vs. t i m e c u r v e w i t h M o t o y a m a ' s d a t a .

U s i n g E q u a t i o n 6,

Co, = 16.35 m e q / 2 0 grams solids, w h i c h c o m p a r e s f a v o r a b l y w i t h 16.18 m e q / 2 0 grams solids c a l c u l a t e d b y M o t o y a m a .

40

80

120

160

TIME- DAYS

240

200

Figure 2. Comparison of amine concentration vs. time accord ing to the data of Motoyama (6) and calculation using Equation 5. For the curve, C = 8.6 meq/20 grams solids, k = 0.0256 day , k = 0.4135 (meq/20 grams solids) day' . 0

1

2

t

1

I n c o m m e r c i a l e l e c t r o c o a t i n g systems there a r e o f t e n a c o n s i d e r a b l e n u m b e r of o p e r a t i o n a l inconsistencies, o n a d a y t o d a y basis, i n the a d d i t i o n a n d r e m o v a l o f materials. D a i l y a d d i t i o n s o f r e p l e n i s h m e n t c o m p o -


214

ELECTRODEPOSITION


2.0r

1

1

1

1

1

1

1

1

1

O F COATINGS

r

TIME - DAYS Figure 3. Comparison of data and calculated component concentration vs. time when addition rate, k varies. C = 1.60%, k = 0.331 day (constant throughout). Initial k — 0.231% day- ; after day I , k = 0.0% day ; after day 6, k = 0.231% day ; after day 7, k = 0.112% day . 0

2

1

1

1

2

1

2

1

2

2

1

nents m a y v a r y , as does t h e a m o u n t of c o a t i n g . A s m e n t i o n e d p r e v i o u s l y , r a n d o m events c a n b e t a k e n i n t o a c c o u n t w h e n u s i n g this m o d e l . F i g u r e 3 is a p l o t of c o m p o n e n t c o n c e n t r a t i o n vs. t i m e f o r s u c h a s i t u a t i o n . C w a s 0

d e t e r m i n e d a n a l y t i c a l l y to b e 1 . 6 0 % . I n this case, kx r e m a i n e d

constant

(0.331 d a y " ) t h r o u g h t h e entire t i m e i n t e r v a l of 10 days. T h e v a l u e of 1

k v a r i e d f o u r times d u r i n g this t i m e p e r i o d , r a n g i n g f r o m zero to 0 . 2 3 1 % 2

d a y " , d e p e n d i n g o n t h e a m o u n t of r e p l e n i s h m e n t a d d e d . T h e p o i n t s are 1

a c t u a l d a t a b a s e d o n a n a l y t i c a l d e t e r m i n a t i o n s of t h e c o m p o n e n t tration.

concen

T h e agreement o f t h e c a l c u l a t e d a n d a n a l y t i c a l l y d e t e r m i n e d

values demonstrates

that t h e a p p l i c a t i o n of this m o d e l to c o m m e r c i a l

operations is p r a c t i c a l . T h e m o d e l d e s c r i b e d i n this p a p e r is a n o r g a n i z e d , m a t h e m a t i c a l a p p r o a c h to t h e m a t e r i a l b a l a n c e of a n e l e c t r o c o a t i n g tank. T h e a p p r o a c h recognizes t h e stepwise m o d e s o f a d d i t i o n a n d t h e

first-order

n a t u r e of

d e p l e t i o n s a n d incorporates b o t h i n t o a single e q u a t i o n w h i c h

describes

the instantaneous a n d e q u i l i b r i u m c o n c e n t r a t i o n of a n y c o m p o n e n t i n t h e e l e c t r o c o a t i n g b a t h . T h e m o d e l c a n b e a p p l i e d to b o t h p a i n t f o r m u l a t i o n a n d process d e s i g n .

Acknowledgments T h e authors t h a n k R . E . W h e e l e r f o r h i s assistance w i t h t h e m a t h e matics, L . F . N o n e m a k e r f o r his g u i d a n c e a n d assistance i n t h e p r e p a r a t i o n of this m a n u s c r i p t , a n d Ε . I. d u P o n t d e N e m o u r s & C o . , I n c . f o r p e r m i s s i o n to p u b l i s h this p a p e r .


14.

VAN

HOEVEN ET AL.


215

Literature Cited 1. 2. 3. 4.

Sheppard, S. E., Trans. Electrochem. Soc. (1927) 52, 47. Robinson, F . D., Tear, B . J., J. Oil Col. Chem. Assoc. (1970) 53, 265. Tsou, I. H., U. S. Patent 3,434,952 ( 1 9 6 9 ) . Burnside, G. L., Brewer, G . E. F., Strosberg, G . G., J. Paint Technol. (1969) 41 (534) 431. 5. K o r a l , J . N., Blank, W . J., Falzone, J . P . , J. Paint Technol. (1968) 40 (519) 156. 6. Motoyama, Y . , Kusano, H., Ohe, O . , J. Paint Technol. (1969) 41 (533) 402.


RECEIVED

M a y 28, 1971.


Material Balance Considerations in an Electrocoating Tank

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