Electrochemical Measurement

8/9/2019 Electrochemical Measurement

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Corrosion science, Vol. 23, No. 4. pp. 391-430, 1983 0010-938X/83/040391-39 $03.00/0Printed in Great Britain. Pergamo n Press Ltd.

E L E C T R O C H E M I C A L M E A S U R E M E N T S I NF L O W I N G S O L U T I O N S

B R Y A N P O U L S O NN . E . I . P o w e r E n g i n e e r i n g L td . , G a t e s h e a d , T y p e a n d W e a r , U . K .

A b s t r a c t - - F l u i d f lo w c a n i n f l ue n c e b o t h t h e r a t e a n d t y p e o f co r r o s i o n . D e s p i t e t h i s m o s t c o r r o s i o nt e s ts e s p e c ia l ly t h o s e i n v o l v i n g el e c t ro c h e m i c a l m e a s u r e m e n t s a r e c a r r i e d o u t u n d e r p o o r l y c h a r a c -t e r i z e d a n d u n r e p r e s e n t a t i v e h y d r o d y n a m i c c o n d i t i o n s . T h i s p a p e r r e v i e w s t h e c h a r a c t e r i s t i c s o fe x i s ti n g s p e ci m e n s a n d t h e n d e s c r i b e s t h e d e v e l o p m e n t o f a n e w d e s ig n . B o t h t h e p r a c t i ca l , i n c l u d i n gm o n i t o r i n g , a n d m e c h a n i s t i c s i g ni f ic a n c e o f e l e c t r o ch e m i c a l m e a s u r e m e n t s i n f l o w i n g e n v i r o n m e n t sa r e t h e n d i s c u s s e d .I N T R O D U C T I O N

ELECTROCHEMICAL m eas ure m ent s are no w wid ely used in m os t f i e lds of c or ros ion .D e t a i l ed r ev iew s a r e ava i l ab l e w h i ch dea l w i t h t he a pp l i ca t i on o f e lec t r ochem i ca lt echn i ques i n gene r a l1,2,3 or speci f ical ly to pi t t ing 4 ga l van i c c o r r os i on , 5 in t e r g r an u l a rcor ros ion ,8 , 7 crevice cor ro s ion , s s t r es s co r ros io n crackingg, 1 an d h igh t em pe ra tu reh i g h p r e s s u r e s i t u a t i o n s ? ~ H o w e v e r c a u t i o n a r y r e m a r k s h a v e b e e n m a d e b y L a Q u e , 1~w h i c h s h o u l d b e d i g e s te d w i t h c ar e . T h e s e i n c lu d e : ( a ) t h a t m u c h o f w h a t i s t e r m e db a s i c c o r r o s i o n r e s e a r c h h a s n o t h i n g t o d o w i t h c o r r o s i o n , e . g . p u r e F e i n d e -oxy gen a t ed 1 N H 2SO 4. S i m i l a r l y t hos e i nvo l ved w i t h r ea l co r r os i on s i t ua t i ons a r eo f t e n n o t i n te r e s te d i n m e c h a n i s m s , (b ) t h a t f a s h i o n a b l e e q u i p m e n t ( h e m e n t i o n sp o t e n t i o s ta t s ) a r e u s e d t o g r i n d o u t i m p r e s s iv e l o o k i n g d a t a , o f t e n o f d o u b t f u lr e levance , and (c ) t ha t s ize e f fec t s an d t he s ep a r a t i on o f ano d i c an d c a t hod i c a r eashave a s i gn i fi cance t ha t i s o f t en o ve r l ooked .

M a n y i f n o t m o s t c a s e s o f c o r r o s i o n i n v o l v e s o m e r e l a t i v e m o t i o n b e t w e e n t h ec o r r o d i n g m e t a l a n d i t s e n v i ro n m e n t . S u c h m o v e m e n t c a n i n c r ea s e o r d e c r e as e p r o -ces ses occu r r i ng un de r s t a t ic cond i t i ons ; i t c an a l s o i n t r odu ce d i f f e r en t t ypes o f a t t ack ,e .g . e r o s i o n - c o r r o s i o n , o r c a u s e p r o b l e m s d u e t o d e p o s i ti o n . S o m e t y p i c a l e x a m p l e sa r e s h o w n i n F i g . 1 . O f t e n s o l u t i o n m o v e m e n t i s n e g l e c t e d o r m e a s u r e m e n t s a r ec a r r i e d o u t u n d e r p o o r l y c h a r a c t e r i z e d a n d / o r u n r e p r e s e n t a t i v e h y d r o d y n a m i cc o n d i t i o n s .

E l e c t ro c h e m i c a l m e a s u r e m e n t s i n f lo w i n g so l u t io n s c a n p r o v i d e d a t a o n ( a) t h er a t e o f g e n e ra l c o r r o s i o n a n d t h e p o s s i b il it y o f o t h e r f o r m s o f a t t a c k , ( b ) m e c h a n i s m ,by us i ng t he e f f ect o f f l ow as a d i agnos t i c c r i te r i on , ( c) t he cha r ac t e r i s t ic hy d r o dy na m i cpa r am e t e r s , e . g . t he r a t e o f m as s t r ans f e r , t he deg r ee o f t u r bu l enc e o r t he s u r f ace s hea rs tr e ss , a n d ( d) t h e c o m p o s i t i o n o f t h e s o l u t i o n b y e l e c tr o - a n a ly t i c al l y m o n i t o r i n gc o m p o s i t io n s o r m e a s u r i n g r e d o x p o t e n t i a ls , p H ' s , e tc .

Th i s pap e r i s i n t end ed t o r ev iew the ap p l i ca t i on o f e l ec t r ochem i ca l m e as u r em en t si n f low i ng env i r onm en t s .

M a n u s c r i p t r e c ei v e d 1 0 F e b r u a r y 1 98 2.P r e s e n t e d a t t h e M e e t i n g o n " E l e c t r o c h e m i c a l T e c h n i q u e s i n C o r r o s i o n T e s t i n g a n d R e s e a r c h "h e l d a t t h e C o r r o s i o n & P r o t e c t i o n C e n t r e i n t h e U n i v e r s i t y o f M a n c h e s t e r I n s t i t u t e o f S c i e n c e &

T e c h n o l o g y , 4 - 6 J a n u a r y 1 9 8 2 .39 1


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392 BRYAN POULSON

C O N C E P T S A N D T E R M I N O L O G YAt low relative velocities between metal and solution flow is laminar and at high

velocities it is turbulent. The transition occurs over a velocity range and depends on:the geometry, the viscosity of the liquid and the roughness of the surface. The dimen-sionless Reynolds number ( R e ) is used to take account of such effects and allows theprediction of transitions.

V dR e - - (1)Ywhere V is the relevant velocity (m s-l), d is the characteristic specimen length (m)and y is the kinematic viscosity (m 2 s-X).

In turbulent flow there is still a thin laminar sublayer (thickness 8h) close to themetal surface which results from viscous drag. If mass transport is occurring at thesurface there will also be a diffusional boundary layer (thickness 8d). The relationshipbetween the thickness of these two boundary layers is governed by the dimensionlessSchmidt number ( S c )

S c = - 7 - ( 2 )Dwhere D is the diffusivity of the relevant species (m2 s-X).

The higher S c is the thinner will be the diffusion layer and the more rapid will be itsformation. If both 8d and 8h start to develop together then ~ h / S d ~ S c t . Associatedwith the velocity gradient across these boundary layers is a frictional force whichmay be expressed as a surface shear stress (Ts). It has been suggested that this maycontrol the mechanical stability of surface films.

The overall transpor t to the surface consists of bulk convection and turbulentconvection. With the former there is a net transport of fluid involved, e.g. along thepipe: with the latter there is an exchange of fluid between the boundary layer and thebulk. Both depend on the concentration driving force: bulk convection on D, whileturbulent convection is a function of the eddy diffusivity ~ (m z s-X). With someapproaches the molecular diffusivity is added to the eddy diffusivity in a modifiedFicks law. In other approaches the overall resistance to mass transfer is seen as thesum of the resistances of the laminar and turbulent regions. Empirically this is by-passed by defining a mass transfer cofficient Kas

rate o f reactionK = ( 3 )concentration driving force.Mass transfer rates are also expressable in a non-dimensionless group in this case theSherwood number S h , though sometimes the Stanton number ( S t ) is used

K dS h - - ( 4 )D


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FIG. l(a). Car bon steel bolt after erosio n corrosion in pure water.Fl6. l(b). Surface morphology of erosion corrosion on carbon steel in pure water.


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FIG. l (c) .FIG. l (d). Depos i t ion o f magnet i t e on o r i f i ce p la te caus ing increased p ressu re d rop .De ndr i t i c m orpho logy o f depos i t suggest s e lec t rocrys ta l l i za t ion ra ther tha ns t ick ing par t i c les .


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E

GC~

G

C~


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Fro . 4 . Imping ing j e t ce l l showing cho ice o f j e t s and spec imens.


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( b )F I G . 1 9. D i s s o l u t i o n p a t t e r n s i n i m p i n g i n g j e t t e s ts . ( a ) C a r b o n s t e e l a f t e r 1 8 h i n4 M N H 4 N O 3 a t 7 5 C . ( b ) C o p p e r a f t e r 1 h i n 0 .1 N H C I c o n t a i n i n g 2 g 1 ] F e a~ a t3 5 C .


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Electrochemical measurem ents in flowing solutions 399

or

KS t - - (5 )V

S hS t - - . (6)R e S cI t c a n b e s h o w n b y d i m e n s i o n a l a n a l y s i s t h a t S h n m s t b e a f u n c t i o n o f R e a n d S c .S u c h r e l a t i o n s h i p s c a n b e d e r i v e d t h e o r e ti c a l ly , e .g . f o r t h e r o t a t i n g d i s c th i s p r e c e d e de x p e r i m e n t a t i o n . H o w e v e r t h e y a r e u s u a l l y o b t a i n e d a s e m p i r i c a l c o r r e l a t i o n s o fe x p e r i m e n t a l d a t a o b t a i n e d w i t h i n c e r t a i n li m i t s; t h e y a r e u s u a l l y o f t h e f o r m

S h = c o n s t a n t R e x S c y (7)x i s u s ua l l y b e t w e e n 0 . 3 a nd 1 , y i s typ i c a l l y 0 .33 .

F o r a r e a c t i o n t h a t i s d i f f u s io n c o n t r o l l e dr a t e = K . A C (8 )

w h e r e A C i s c o n c e n t r a t i o n d r i v i n g f o rc e .T h i s i s h o w K i s m e a s u r e d b y c h e m i c a l d i s s o l u t i o n , e . g . t r a n s c i n n a m i c a c i d i n

w a t e r . O r i n e l e c t r o c h e m i c a l t e r m s w h e n t h e r a t e = t h e l im i t i n g c u r r e n t d e n s i t y( L C D )

L C D = K n F A C . (9)T h u s t h e b a si s o f t h e L C D t e c h n i q u e in d e t e rm i n i n g K i s t o m e a s u r e L C D a t f ix e d AC .U s i n g a s m a l l e l e c tr o d e , fl u c t u a t io n s i n L C D a r e d i r e c t ly p r o p o r t i o n a l t o f l u c t u a ti o n si n v e l o c i ty a n d i n f o r m a t i o n a b o u t t u r b u l e n c e c a n b e o b t a i n e d . S i m i l a rl y i f K isk n o w n t h e n m e a s u r i n g L C D a l lo w s t h e d e t e r m i n a t i o n o f A C , w h i c h w i ll b e t h e b u l kc o n c e n t r a t i o n . T h i s i s t h e b a s is o f th e a n a l y t ic a l m e t h o d k n o w n a s v o l t a m m e t r y .

I f t h is a p p r o a c h c a n b e a p p l i ed t o a c o r r o s i o n p r o c e s s in w h i c h b o t h a n a n o d i ca n d a c a t h o d i c r e a c t i o n o c c u r , i f n e i th e r r e a c t io n i s d i ff u s io n c o n t r o l l e d t h e n t h e r a t e o fc o r r o s i o n w i ll b e g i v e n b y

c o r r o s i o n c u r r e n t = n F A C K . ( l o )T h e v a l u e o f A C w i ll b e th e b u l k c o n c e n t r a t i o n o f c a t h o d i c r e a c t a n t f o r s y s t em s w h i c ha r e c a t h o d i c a l l y c o n t r o l l e d a n d w i ll e q u a l t h e s o l u b i li t y li m i t o f t h e r e l e v a n t p r o d u c tw h e n t h e a n o d i c r e a c t i o n i s d if f u si o n c o n t r o l l e d ( F i g . 2 ).

I f w e t h e n s u b s t i tu t e f o r K w e o b t a i nD ( V d _ ) X ( D ) Y x c o n s t a n t ,c o r r o s i o n c u r r e n t = n F A C D ~ \ ? / (11)

i .e . c o r r o s i o n r a t e s c a n b e p r e d i c t e d w k h o u t a n y t e s ts i f r e l ev a n t p a r a m e t e r s a r e k n o w n .


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400 BRYAN POULSON

STEEL

CATHODIC REDUC TION RATEi,(j MILD STEEL N SEAWATER

SE/~ATER

CONTROLLING

02] :BLLK VALUE

ANO DIC REA CTION R AT E CONTROLLINGaa H im ST EE L IN CONCENTRATEDSULPHURICACID

I[ F e s o 4 ] i = S A T D ~A T IO N . U Ed ~ CONCENTRATED H2SOOl,

1IFFUSION.__t|LAYERAnodic and cathodically controlled corrosion reaction.

S T E E L

FIG. 2.

H o w e v e r t h i s w o u l d p r e d i c t n o c o r r o s i o n a t z e r o v e l o c it y a n d n a t u r a l c o n v e c t i o nw ou l d have t o be added a t l ow t o ze r o f l ow ve l oc i t i e s .

A P P A R A T U S F O R E L E C T R O C H E M I C A L M E A S U R E M E N T S INF L O W I N G S O L U T I O N SApparatus

A p p a r a t u s f o r e x a m i n i n g t h e e f fe c ts o f f lo w o n c o r r o s i o n i s s im i l a r t o t h a t u s e d i ns t a t i c t e s ts excep t t ha t e i t he r t he s pec i m en ( r o t a t i ng d i s c s and cy l i nde r s ) o r t he s o l u t i onm u s t b e m o v e d , a n d m o r e t h o u g h t m u s t be g i v e n t o t h e p l a c e m e n t o f r e fe r en c e a n dcou n t e r e l ec t rodes . W r ang l en 13 has a r gue d s t r ong l y t ha t t he r o t a t i ng d i s c and pa r -t i c u l a r l y t h e r o t a t i n g c y l i n d e r h a v e a d v a n t a g e s o v e r f l o w i n g s y s t e m s w h e n e l e c t r o -c h e m i c a l m e a s u r e m e n t s a r e t o b e m a d e . T h e s o l u t io n v o l u m e t o s p e c im e n a r e a r a t i oa f f ec t s t he s ens i t i v it y o f chem i ca l ana l ys i s t o m on i t o r co r r os i on bu t t h i s s hou l d i n anycas e be r e levan t t o t he p r ac t i ca l p r ob l em . A s I s ee i t t he adv an t age s o f r o t a t i n g s ys t em sa r e conven i ence bas ed , i. e. t hey a r e cheap an d eas y to u s e , s m a l l , e t c . The adva n t ageso f a f l ow i ng s ys t em a r e t he ab i l i t y t o t e s t r ep r e s en t a t i ve geom et r i e s and r ea l i s t i cm a t e r i a ls an d t he ab i l i t y t o m a i n t a i n a co ns t a n t env i r on m en t i f t h i s is des ir ab l e .

A d e s c r ip t io n o f a r i g u s e d t o m a k e e l e c tr o c h e m i c a l m e a s u r e m e n t s i n f lo w i n gac i d c l e an i ng s o l u t i ons s hou l d i l lu s t r a t e s om e r e l evan t cons i de r a t i ons . Th e r e s t o ft h i s s ec t ion w i l l t hen be a r ev iew o f t he ch a r ac t e r is t ic s o f va r i ous s pec i m en s w h i ch a r eus ed ( F i g . 5 ) . The m as s t r an s f e r cha r ac t e r is t i c s o f p i pes and o r if ice s t oge t he r w i t h s om eo t he r geom et r i e s encou n t e r ed i n p r ac t i ce have r ecen t l y been com pr ehe ns i ve l y r ev i ew edby Con ey . 14

The r i g i s s how n i n F i g . 3 and i s cons t r uc t ed nea r l y en t i r e l y ou t o f Po l yv i ny l i denf l uo r i de ( PV D F) . Th i s w as cho s en becaus e i t s chem i ca l r e si s tance i s nea r l y a s go od a sP T F E , i t c a n b e u s e d u p t o 1 40 C , it c a n b e w e l d e d a n d m a c h i n e d e a s i ly a n d is r e a d il y


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Electrochemical measurem ents in'flowing solutions 401a va i l a b l e a s va l ve s , pum ps , e l bow s , be nds a nd o t he r f i t t i ngs . S o l u t i on i s s t o r e d i n a2 0 1. P V D F g l as s f i b re r e i n f o r c e d t a n k w i t h f a ci li ti e s f o r d e - o x y g e n a t i o n , p o s i ti o n i n g o fa u x i l i a ry e l e c tr o d e s a n d a l e v el c o n t r o l . T e m p e r a t u r e i s c o n t r o l l e d ( d : 0 . 2 5 C ) b y as il ic a e n c l o s e d 1 .5 k W h e a t e r w i t h a c o n t a c t t h e r m o m e t e r o p e r a t i n g a r e l a y . T e m p e r a -t u r e s in v a r i o u s p a r t s o f t h e l o o p c a n b e m e a s u r e d o r r e c o r d e d u s in g t h e r m o m e t e r so r t h e r m o c o u p l e s . T h e p u m p is a P V D F c e n t r i fu g a l p u m p w i t h a H a s t a l l o y C s h a f t ;s i m i la r m a g n e t i c a ll y c o u p l e d p u m p s i n P V D F a r e n o w a v a i l a b le . S o l u t i o n f lo w ism e a s u r e d u s i n g a r o t o m e t e r b e c a u s e th e y a r e s im p l e , c h e a p , c le a r a n d c o m p a t i b l e w i t ha w i de r a n ge o f f lu i d s.

T h e c e ll f o r ho l d i n g s t r a i gh t t ube s , be nd s a nd o r i f ic e s pe c i m e ns i s s ho w n i n F i g . 3 .B o t h a r e m o t e o r c o - a x i a l c o u n t e r e l e c t r o d e c a n b e u s e d d e p e n d i n g o n t h e s p e ci fi cr e q u i r e m e n t s . A v e r s a t il e P V D F i m p i n g i n g j e t c e ll is a l so i n c l u d e d in t h e l o o p a n ds h o w n i n F i g . 4 a l lo w i n g a v a r i e t y o f n o z z l e a n d s p e c i m e n t y p e s t o b e u s e d . T h e t h r e en o z z l e s s h o w n i n c l u d e t h e c o n v e n t i o n a l j e t p r o d u c i n g a w i d e r a n g e o f m a s s t r a n s f e rr a t e s a c r o s s a s pe c i m e n , a s i m i l a r j e t ha v i ng a l a r ge r d i a m e t e r p r od uc i n g r e l a t i ve l yc o n s t a n t m a s s t r a n s f e r a c r o s s a sm a l l s p e c im e n u n d e r l a m i n a r c o n d i t i o n s a n d f in a l ly am u l t i p l e j e t w h i c h i t is h o p e d w i l l p r o d u c e c o n s t a n t m a s s t r a n s f e r a c r o s s a s m a l ls p e c i m e n u n d e r h i g h l y t u r b u l e n t c o n d i t i o n s . S o i t w il l b e p o s si b le t o e x a m i n e c o r r o s i o nu n d e r c o n d i t i o n s o f e q u a l m a s s t r a n s f e r w i t h l a m i n a r o r t u r b u l e n t c o n d i t i o n s .

ROTATINGD I S C

R O T A T I N GC Y C L I N D E R

i IM R N O I N GJ E T

N O Z Z L EO RO R I F I C E

TUBE

o

x,~ j ~ T j

* . . . . L - . . . . J o

R e : ~ ) r 2-yRec =1"7-35x10

Rec ,,.2O0Re=~R e ~2000

Reo =~LY~yRe ,,, 600Re =- (:I~YRe ~ 2 0 0 0

S-"hL = .6205 R e s Sc~S"hT : "00"/8 Re" Sc:~ ~ , ~ . . 0 7 9 Re SC~'~

. . . . . (1.25*5"76100od/F-i Re Sc, 6S-"h,;A : 1.12 Re Sc~(Hld)~Shw; : .65 Re ~" (x/d) ~

51%, : = "276 Re : i Sc ~ ~ "h , . : 1 * A , I + .~6_ _ B , [ ~ - 2Sh,~ L 0165 Re~ ' !~hL =}61LIReSc d/L) ~ ~-h~ : .2?6R~Id/L)3~S'h,~ ='0165 Re~ ~

FIG. 5. Sum mary of specimen types examined in detail.

The rotating discA s t he d i s c is r o t a t e d s u r f a c e d r a g c a us e s s w i r l ing o f t he f l u i d w h i c h is f o r c e d

r a d i a l l y ove r i t s s u r f a c e ; a x i a l f l ow b r i ng i ng f r e s h s o l u t i on t o t he d i s c . W i t h t h i sc e n t r i f uga l f l ow t he s u r f a c e i s un i f o r m l y a c c e s s ib l e . H o w e ve r , a t l ow Re v a l u e s( < l 0 s ) a l t e r n a t iv e f lo w p a t t e r n s ( r e v e rs e a n d t o r o i d a l f l o w ) h a v e b e e n p r o p o s e d f o r


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40 2 BRYAN POULSON

b o t h N e w t o n i a n x5 a n d n o n - N e w t o n i a n f lu i d s 15 b u t t h e s e a r e u n i m p o r t a n t i n t h i sc o n t e x t .

A t h i g h e r R e v a l u e s t h r e e f l o w r e g i m e s c a n e x i s t s i m u l t a n e o u s l y o n t h e s u r f a c eo f t h e d is c. T h e p o s i t i o n o f e a c h w i l l d e p e n d o n R e b u t w i ll b e m o d i f i ed b y , a m o n go t h e r t h i n g s , t h e s u r f a ce r o u g h n e s s . T h e m o s t d e t a i l e d s t u d y o f s u c h t ra n s i t i o n s h a sb e e n b y C h i n a n d L i t t x7 u s i n g f l u c t u a t io n s i n t h e l i m i ti n g d i f f u s i o n c o n t r o l l e d c u r r e n tde ns i t y a t a po i n t e l e c t r ode . B r i e f ly i t w a s f ou nd i f R e < 1 .7 105 f low was l am ina r ;i f R e > 1 .7 105 < 3 .5 105 f low i s t r ans i t ion a l an d i f R e > 3.5 105 f low ist u r bu l e n t ( s e e F i g . 6 a nd T a b l e 1 ) .

T h e r o t a t i n g d i s c i s i m p o r t a n t i n t h a t t h e o r y p r e c e d e d e x p e r i m e n t a l r e s u l t s a n de x a c t s o l u t i o n s t o t h e t h e o r e t i c a l e q u a t i o n s h a v e b e e n o b t a i n e d f o r m a s s t r a n s f e ru n d e r l a m i n a r c o n d i t io n s b y L e v i c h~a w h o s ho w e d

S h ---- 0.6 20 5 R e .5 S c .33. (12)T h i s w a s d e r i v e d a ss u m i n g a r e a s o n a b l y h i g h v a l u e o f S c . M o d i f i c a t io n s h a v e b e e n

p r o p o s e d b y S p a r r o w a n d G r e g g , ~9 R i d d i f o r d ~ a n d N e w m a n n . 2~ R e c e n t l y M i s h r aa nd S i ngh ~2 r e v i e w i ng a l l t he d a t a p r o po s e d

S h = S c [0.5657 q- Sc .] 0.62048 R e .5 (13)b u t t h e d e g r e e o f im p r o v e m e n t , i f a n y , t h a t t h i s g i ve s w a s n o t q u a n t i f i e d a n d t h es i m p l e r L e v i c h e q u a t i o n i s a d e q u a t e f o r u s e in c o r r o s i o n s t u d ie s . O t h e r m o d i f i c a ti o n sh a v e b e e n p r o p o s e d f o r d i s c e c ce n t r ic i t y o r e d g e e f f e ct s. T h e s i t u a t io n w h e r e m a s st r a n s f e r i s l i m i te d t o p a r t o f t h e d i s c h a s b e e n t r e a t e d b y C h i n a n d L i t t, ~3 t h e y s h o w e dt h a t m a s s t r a n s f e r c o u l d b e t e n t i m e s g r e a t e r a t a p o i n t e l e c t r o d e f o r a g i v e n r o t a t i o n a ls pe e d .

W h e n R e > 2 x 105 t he ove r a l l m a s s t r a ns f e r r a t e c om pr i s e s a c on t r i bu t i on f r omt h e l a m i n a r a n d t r a n s i t i o n r eg i o n s a n d a b o v e 3 .5 1 05 t h e t u r b u l e n t r e g i o n . A b o v eR e ~ 105 t h is d o m i n a t e s t h e o v e r a l l r a t e a n d v a r i o u s e q u a t i o n s h a v e b e e n p r o p o s e ds uc h a s :

S h = 0 .0078 R e .9 Sc .3 (24) ( 1 4 )S h = 0.0 11 7 Re 0 .896 Sc ~.46 (25) (15)

S h = 317.16 S c .3 3 0.00838 R e .9 S c .8311 -- (2.6 105/Re).~-5](22) (16)I n c o r r o s i o n s t u d i e s i t i s m o r e i m p o r t a n t t o k n o w h o w t h e m a s s t r a n s f e r r a t e v a r i e sloca l ly . A t R e v a l u es u p t o R e c r it m a s s t r a n s f e r i s u n i f o r m a n d a s g i v en b y t h e L e v i t c he q u a t i o n . A b o v e R e c r i t a c e n t r a l l a m i n a r r e g i o n is s u r r o u n d e d b y t r a n s i t io n a n dt u r b u l e n t z one s w he r e m a s s t r a n s f e r w i ll be i nc r e a s i ng w i t h inc r e a s i ng r a d i a l d i s t a nc e ;t h is h a s b e e n t r e a t e d b y N e w m a n ~4 a n d F r e n c h w o r k e r s . ~6T h e r o t a t i n g c y l i n d e r

L i ke t he r o t a t i ng d i s c, a r o t a t i ng c y l i nde r w i l l c a us e s w i r l ing o f t he f l u i d be c a us eo f s u r fa c e d r a g . T h e e x t e n t w i ll d e p e n d o n t h e e x a c t g e o m e t r y , p a r t i c u l a r l y t h e d e g r e e


13/40

Electrochemical mea sureme nts in flowingsolutions 403

FIG. 6.

"1

0 8 - -

' 0 6

.o 4

.O 2

O

L A M I N A R TRANSITION JVORTEX INTEI:~4EDIATEoO TURBU LENT

T U R B U L E N T

Probe dmmo oA,~ o "381& d - + " 3 8 1

d ' + ^ " .381- - b .254

. a o . 2 5 #+ o o r & J o e O e O

~u o +_ _ ~ , . , . ~ ~ % o o o o o- - 1 ' 7 + a I

I+ o o 3"5O t 3 T A A !

2 3 4 S 6 7R e * 1 6~

Transitions on the rotating disc electrode using variations in the LCD (Chinand Litt).

P w f r

6 0 . 15 447.76O'34 1 3

of ba f f l i ng . A f avour ed expe r i m en t a l a r r angem en t i s one i nvo l v i ng t he p r e s ence o f acon cen t r i c s t a t i on a r y ou t e r cy l i nde r a r o un d t h e i nne r r o t a t i ng cy l i nde r . E i s enbe r g 27e t a L s how ed t ha t t he c r i t i ca l d i m ens i on , a t l ea s t f o r m as s t r ans f e r i n t he t u r bu l en tr e g io n , w a s t h e d i a m e t e r o f t h e i n n e r r o t a t i n g c y l in d e r . L a m i n a r f lo w o n l y o c c u r s a tlow ro ta t io na l speeds , e .g . 10 r .p .m , g iv ing a cr i t ica l R e of -~ 200 ; t h is m ay be i nc r eas edi f t he ou t e r cy l i nde r is a l s o r o t a t ed . N ew m an 28 cons i de r s t ha t t h r ee f l ow r eg im es needt o be de f i ned : (1 ) a t l ow r o t a t i on a l s peeds f low is tange n t i a l and l am i na r , (2 ) s econd l y ,above a c r i ti ca l va l ue o f T a * (s ee F i g . 7 ) f l ow rega i ns l am i na r b u t T ay l o r vo r ti ce s deve l opg i v i ng s upe r i m pos ed r ad i a l and ax i a l m o t i on , ( 3 ) t h i r d l y , above a c r i t i ca l R e t r uet u r bu l ence deve l ops .

T h i s h a s b e e n e x a m i n e d i n d e ta i l b y M i z u s h i n a29 us i ng t he L C D T t echn i que w i t h71 - po i n t e l ec t r odes i n t he s t a t i ona r y ou t e r cy l i nde r . H i s r e s u l t s a r e s um m ar i zed i nF i g . 7 a n d s h o w t h e s i t u a t i o n i s e v e n m o r e c o m p l i c a t e d t h a n t h a t p o s t u l a t e d b yN e w m a n . T h e n o n - u n i f o r m i t ie s in m a s s t r a n s f e r a t i n t e r m e d i a t e sp e e ds w e r e a l so f o u n db y H o l m a n a n d A s h e r . a I n t h e i r e x p e r i m e n t s T a y l o r v o rt ic e s p r o d u c e d p e a k s a n dt r oughs i n t he i r benzo i c ac i d cy l i nde r s r o t a t i ng i n w a t e r .

Re l a t i ve l y l i tt l e m as s t r ans f e r da t a is ava i lab l e on t he l am i n a r r eg i on . C or ne t andK a p p e s s e r 3~ f o u n d t h a t f o r S c = 46S h = 37 (between 5 < R e < 200) (17)

w h i ch s ugges t s t ha t t he f l u i d i s r o t a t i ng w i t h t he i nne r cy l i nde r and no t con t r i bu t i ngt o m as s t r ans f e r . Th i s s i m p l e p i c t u r e does no t ag r ee w i t h t heo r e t i ca l p r ed i c t ions 3~ o rs om e w or k us i ng a r o t a t i ng w i re . z3 H ow ever , t h i s r eg i on has l i tt le p r ac t i ca l s i gn if icance .

A b o v e a R e of ~ 200 i t is s u r p r i s i ng i n v i ew o f t he com pl i ca t ed t r ans i t i ons an dapp a r en t n on - un i f o r m i t i e s o f t he p r oces s t ha t a s i ng le m as s t r ans f e r co r r e l a t i on ex i s ts .


14/40

404 BRYANPOULSON

E A M I N A R

T a = R e F d o - d i "L d i . }. ,u A S h / S 3 3 T o

. 4 "4 1 ' 2. 0 1 i i i I

L AM IN A R .1 [ _ _ 2 0 ~ ~ ( 8 O OV O R T E X I I I ~

T R A N S I T I O N" 3 ~ 1 . , ~ " V ' I 5 0 i ~ t ~ ~ . 10oO

TURBULENTVORTEX1 ~ ~ ~ 1 0 0 ~ ~ 2000, lSOOOt / 1 I I

2 ~ ~ 1 I 6 0 t ,~ 1 5 0 0 0U R B U L E N T IO 1 2 3 0 50T I M E D IS T A N C E mFlO. 7. Transition on the rotating cylinder electrode usin g LC DT (M izushina).E i s e n b u r g e t a L w e r e t h e f i r s t t o s t u d y t h i s c o m p r e h e n s i v e l y u s i n g b o t h c h e m i c a ld i s s o l u t i o n a n d L C D T a n d s u g g e s t e d ?7

S h = 0.079 R e .~ ScO .aSe . ( 1 8 )I t h a s b e e n p o i n t e d o u t u t h a t t h i s c o r r e l a ti o n i s r e m a r k a b l e i n t h a t i t c a n b r i n g

t o g e t h e r d a t a o n h e a t t r a n s f e r , m a s s t r a n s f e r a n d f r i c t i o n o n c y l i n d e r s r o t a t i n g i ng a s es a n d l iq u i d s o v e r r a n g e s o f S c a n d R e o f 4 a n d 5 o r d e r s o f m a g n i t u d e r e sp e c ti v e ly .

N e w m a n 35 h a s s u g g e s te d t h a t t h e r a t i o o f i n n e r t o o u t e r d i a m e t e r s s h o u l d b ei n c o r p o r a t e d i n t h e c o r r e l a ti o n b y m o d i f y i n g R e , i .e. [R e dl /do] .~ bu t t he e f f ec t w i l l bes m a l l i n m o s t c a s e s. G a b e a n d R o b i n s o n 3s h a v e p o i n t e d o u t t h e r e a r e s l ig h t v a r ia t i o n si n t he R e a n d S c pow er i nd i ces bu t aga i n t hes e a r e s m a l l . K i ng sT, sa has i n s i s ted t h a tin ~ t wel l baf f l ed sys tem the R e i n d e x s h o u l d a p p r o a c h u n i t y . S i n ce m o s t o f K i n g s 'expe r i m en t s have be en w i t h d i s s o l v i ng cy l i nde r s i t is p r obab l e t ha t i nc r eas i ng f r ic t i ona lf o r ces have been r e s pons i b l e f o r t he e f f ec t s . Th i s has been exam i ned i n de t a i l byK a p p e s s e r e t a l . ~9 w h o i n t r o d u c e d a d i m e n s i o n l e s s r o u g h n e s s t e r m ( d / e ) . This i s ther a t io o f s p e c i m e n d i a m e t e r t o r o u g h n e s s h e i g h t . T h e i r r e s u lt s a r e s h o w n i n F i g . 8 .Es s en t i a l l y : ( a ) f o r s m oo t h s pec i m ens t he E i ns enbur gh co r r e l a t i on ho l ds , ( b ) w i t hi nc r eas ing r ough nes s a de c r eas i ng c r i ti ca l R e i s r e a c h e d a b o v e w h i c h m a s s t r a n s f e r isa b o v e t h e s m o o t h v a l u e , a n d ( c) a b o v e t h e c r i ti c a l R e va l ue


15/40


I o '

ldSh S ~

" d/t Sh:{1.2S.STSlogd,~ fr~ e S~ , d / * x j- o \' , ls6 \ ~ ' / / o 3 /

o ~ 2 x I O

_ - - < d o 4 -_ u o . O -:_ o , ~

1 - % f " , 1 "~" , t , l ] l I t , J I I I I1 0 ~ 1 0 I 0 sRe

Mass transfer correlations for rough and smooth rotating cylinders usingLCDT (Kappesser et al.) .FIG. 8,

S h = (1.25 + 5.76 loglo d / c ) -2 R e S c .3 3B , (19)i .e . t he m a s s t r a ns f e r r a t e i s d i r e c t l y p r o po r t i o na l t o R e . G a b e 4 ha s r e c e n t l y r e -e x a m i n e d t h e e f f ec t s o f r o u g h n e s s a n d f o u n d m a s s t r a n s f e r c a n b e i n c r e a s e d b y u p t o5 0 t i m e s b y a c o m b i n a t i o n o f in c r e a s in g s u r f a ce a r e a a n d m i c r o t u r b u l e n c e .T h e i m p i n g i n g j e t

T hi s c o m p r i s e s a s ubm e r ge d j e t i m p i ng i ng , u s ua l l y a t 90 , on t o a f l a t s pe c i m e n .T h e h y d r o d y n a m i c s o f t h is g e o m e t r y h a v e b e e n e x t e n si v e ly e x a m i n e d4~.42 an d ares u m m a r i z e d i n F i g . 9 .

I n g e n e r a l m a s s t r a n s f e r d e p e n d s o n b o t h t h e j e t t o p l a t e d i st a n c e ( H / d ) a n d t h er a d i a l p o s i t i o n o n t h e p l a t e ( x / d ) , i.e.

S h = ~ R e ~ S cY f ( H / d ) f ( x / d ) . (20)F o r b o t h r o u n d a n d s l o t n o z z le s th e l o c al v a r i a t i o n i n m a s s t r a n s f e r c o e f fi c ie n t

i s t he s a m e . A t ( H / d ) v a l u e s g r e a t e r t h a n a p p r o x 5 a m o n o t o n i c a l l y d e c r e a s i n g b e l l -s h a p e d c u r v e i s o b t a i n e d 43 (F ig . 10). Fo r sm a l le r ( H i d ) v a l u e s o n e o r t w o p e a k s a t( x / d ) va l ue s o f ~ 0 . 5 a nd 2 a s s how n i n F i g . 1 1 . 44 T he s e pe a ks h a ve no t be e n f ou ndb y a ll w o r k e r s ( e .g . F i g. 1 0) a n d a r e a l so p r o m o t e d b y h i g h R e va l ue s . I t i s t hou ghO ~t h a t t h e o u t e r p e a k i s c a u s e d b y t h e s u d d e n r i s e i n tu r b u l e n c e d u e t o t h e d i s a p p e a r a n c eo f t he s t a b i l iz i ng p r e s s u r e g r a d i e n t .

T h e d e t a i le d a n a ly s i s o f s u c h b e h a v i o u r h a s t e n d e d t o c o n c e n t r a t e o n t h e r e g i o no f u n i f o r m a c c es s ib i li ty ( x / d < 0 . 5 o r 1 ) a nd t he w a l l j e t r e g i on ( x / d > 5) . A pre-l i m i n a r y a n a ly s i s 45 o f t h e s e c o n d a r y p e a k s a t ( x / d ~ 2 ) s u g g e s t s a d e p e n d e n c y o nR e . vS , b u t i n g e n e r a l li t tl e a t t e n t i o n h a s b e e n p a i d t o s u c h f e a tu r e s .


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4 0 6 BRYAN POULSON

C O N I C A L P O T E N T I A L C O R E

~'6.-1.4d I W A L L J E T R E G I O N\ ~5-4 d! S T A G N A T I O NI R E G I O N

F I o . 9 .

Yx oV

P x P

""b/ / - - ' 25

9[- - - - -~ ,o '4b-~.,o /~ nI - \ d o - . . ,,81 \ 4 :" "~t 2" F - P ? ' - vAs 1 / , ' I~ " '. , m ) ' V '/ ' \ ' = m / ' b " ' - 8 " " m I - :/ ~ t ~ ', l / = ",,....~..,~ 5 nI . . . . / " . . . .h-1 ' , o ,s / . . . o - . , ) ' i .. .. . . . ~ . ~ ' V ~I . / , &~ /3 1 ; / ' 4 /\ , ,I-" . . ~ / 4 x / I L - ~ . - . o " P

R A D I A L D I ST A N C E (x / d )I m p i n g i n g je t e le c t ro d e : t e r m i n o l o g y a n d h y d r o d y n a m i c s ( L u s h e t a l . ,G o r d o n e t a l . ) .

I n t he un i f o r m l y acces s ib l e r eg i on m as s t r ans f e r is p r opo r t i ona l t o R e a n d d e c r ea s e sw i t h i nc r eas i ng ( H / d ) , hav i ng a d i f f e ren t con s t an t i n d i f f e r en t f l ow r eg i ons . Ch i n a ndT s a n g 46 s u g ge s te d f r o m L C D T m e a s u r e m e n t f o r H i d v a l u es b e t w e e n 0 . 2 a n d 6 .

L a m i n a r j e t: S h = 1.51 R e .~ Sc .33 ( H /d ) - '~4( i f R e < 2000, x / d be t w een 0 .1 a nd 0 .5 )

(21)

T u r b u l e n t j e t : S h = 1.12 R e '5 Sc '38 ( H /d ) - '~7( i f R e be t w een 4000 and 16 ,000 an d x / d be t w een 0 . 1 and 1 ) .

(22)

The w a l l j e t r eg i on beg i ns a t ~ 3 - 5 nozz l e d i am e t e r s an d i n th i s r eg i on m as st r ans f e r f a i l s w i t h r ad i a l d i s t ance a s ( x / d ) - l . Pa t r i ck et al . 47 u t il iz i n g L C D T s u g g e s te d


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FIG. 10 .

l o '

Sh3lO

"-0~-"'~ d =-156"" ~ ~ n ~ . O Re:- 114300

u ~ u ~ 5 c = 9 0 0

_ u ~ 8- - A 1 9 . 2

I I I I I I I I I1 2 3 4 5 6 7 8 1 0RADIAL DISTANCE (x /d }

M ass transfer from impinging et ob tained b y chemical dissolution of trans-cinnamic acid into water (Rao and Trass).Sh - 1.14 Re .s2 (x/d)-1.5 ( 5120 < Re ~< 13498; 8


18/40

408 BRYANPouLSoN

51Re

37~X~0

FIG. 11.

250000

1240007 8 0 0 03 4 0 0 01O0O05 0 0 0VO 2 4 6 8 500

RADIA l - D ISTANCE (x /d )Mass transfer from impinging jet showing characteristic secondary peaks(Martin).

T A B L E ] . D E T A I L S O F F L O W R EG IM E S O N R O T A T IN G D IS C AF TE R C H I N A N D L I T T

Reynolds No.Region range CommentsLamin ar < 1.7 105 Some impri nted spirals at 60 to the radiu shave been found possibly caused by pro-trusions or gas bubbles.

~ Vor tex > 1.7 < 2.6 x 10 sOInt ermedi ate > 2.6 < 3.5 10 ~t- turbulent

Turbulent > 3.5 x 10 ~

Stationary vortices are amplified producingspirals a t 76 to th e radius .Stationary vortices are breaking down intosmaller eddies.Stable eddies have been formed.


19/40

Electrochemical mea sureme nts n flow ingsolutions 409d i s t u rb a n c e s a n d i t is p r o b a b l y t h a t t h e f l o w w il l a l w a y s be t u r b u l e n t w h e n Re ~ 105.T h i s h a s b e e n e x a m i n e d in d e t a il b y a n u m b e r o f w o r k e r s , R e i s s a n d H a n r a t t y49 usedt h e L C D T a t a p o i n t e le c t ro d e , t h e y f o u n d : ( a) a t lo w Re f lo w is l a m i n a r a n d t h e r e a r eno cu r r en t f l uc t ua t i ons , ( b ) a t a Re of 2140 a s l i gh t w a vy d i s t u r banc e w as n o t ed , ( c )a t s l i gh tl y h i ghe r Re i n t e r m i t t e n t p a tc h e s o f t u r b u l e n t f lo w ( tu r b u l e n t p l u g s) a n d n o n -t u r bu l en t fl ow w as i nd i ca t ed ( F i g . 12a), ( d ) a s Re i nc r eases t he f r ac t i on o f t i m e t hem o t i o n i s t u r b u l e n t - - k n o w n a s t h e i n t e r m i t t e n c y f a c t o r - - i s i n c r e a s e d , ( e ) a t a Renu m be r o f 3740 t he f l ow is com pl e t e l y t u r bu l en t ( F i g . 12b ), and ( f ) f u r t he r i nc r easesin Re i nc r eas e t he f r eque ncy o f t he f l uc t ua t i ons i n t he L C D ( F i g . 12c).

The r e i s ve r y l i t t l e m as s t r ans f e r da t a ava i l ab l e f o r f u l l y deve l oped l am i na r f l ow .F i r s t ly , becaus e i t i s no t o f p r ac t i ca l in t e r e s t an d s eco nd l y , becaus e o f t he l ong en t r y

, , o l - .

F I I I I~10 20 30 . 40 50

ev ercx~]

FIG. 12.

T I M E s

100 - - :t . . . . . ,8O

611111111111111 2 3 4 5 6 7 8 9 10 11

, o F , ' , , , , I-II 0

-

1 2 3 4 5 6 7 8 9 1 01

O ~ O~o //

1 6 ~ I 0 , I I ] I ] [ I I [ I10 ~ 10sReTransitions in pipe flow obtained using LCD T and effect of Re on turbulence(Reiss and Hap.ratty).


20/40

41 0 BRYAN POUt,SONl e n g t h s i n v o lv e d . H o w e v e r , b o t h t h e o r y a n d a v a i la b l e h e a t t r a n s f e r d a t a s u g g e s t it isi n d e p e n d e n t o f R e : t h e t h e o r e t i c a l c o n s t a n t N u v a l u e ( h e a t tr a n s f e rs e q u i v a l e n t o f S c )o f 4.1 i s t o b e c o m p a r e d w i t h t h e e x p e r i m e n t a l v a l u e o f 3 .6 5.5

F o r t h e c a s e o f f u ll y d e v e l o p e d t u r b u l e n t f lo w i n s m o o t h s t r a ig h t t u b e s t h e re i s al a rg e c h o i ce o f c o r re l a ti o n s t o c h o o s e f r o m ( T a b le 2 ), th e m o s t c o m m o n b e in g t h eC h i l t o n - C o l b u r n a n a l o g y ? 1

S h = 0 . 0 2 3 R e .8 S c . 3~ . ( 26 )C o n e y t4 h a s r e v ie w e d s u c h c o r re l a ti o n s p o i n t i n g o u t h o w t h e C h i l t o n - C o l b u r n

a n a l o g y g i v e s r e s u l t s w h i c h d i v e r g e f r o m m o r e r e c e n t c o r r e l a t i o n s a t h i g h R e v a l u e sa n d p r e d i c t s l o w v a l u e s a t h i g h S c n u m b e r s . C o n e y t4 r e c o m m e n d s t h e B e r g e r a n dH u e s2 c o r r e l a t i o n w h i c h w a s b a s e d o n t h e i r o w n L C D T r e s ul t s a n d o t h e r a v a i l a b l ed a t a

S h = 2 + c R e 2 S c .3 ( 26 )w h e r e c : 0 . 0 1 6 5 + 0 . 0 1 1 S c e -S O ; a = 0 .86 - - 10 / ( 4 .7 + S c ) ~ ( 27 )

w h i c h i s v a l i d 0 . 6 < S c < 104 , 104 < R e < 10e.T h e y a l s o p r o p o s e d a s i m p l er e q u a t i o n f o r h ig h S c v a l u e s

TABLE 2. SOM ECORRELATIONS OR FU LLYDEVELOPEDTUBEFLOWOrigin ator Co rrelat ion Origin

Chi l t on - Co l bur n S h = 0.023 R e '8 S c '3 a An alogy with hea t t ransfer.Be r ge r - H ue S h = 2 + c R # S c 'ac ---- 0.016 5 + 0.011 S c e - s oa = 0.86 - 10/(4.7 + S c ) 3

T he i r ow n L CD T da t a a ndother experimental data .

Be r ge r - H ue S h = 0.0165 Rc '8 ~ S c ' a n F o r S c > 10 only 3%error .H a r r i o t - H a mi l t on

Notter-Sleicher

S h - - 0.0096 Re'91a S c 's46

S h --- 0.0149 R e ' Ss S c '8 3

Sh - -- Sho + 0.079 a/[ R e S c( I + S c ' S ) ' a s sS h = R e S c2 7 .81]where P = F(Sc)

Churchill

Jayattilleke

From their chemicaldissolution experimentsinvolving ben zoic acid inglycerine-water mixtures.Theo retical e diffusivitywith constants f romexperimental work.Empir ical a nalo gy withfriction.Bo und ary layer integrat ion.Tota l resistance to m asstransfer is sum ofresistances in lam inar an dturbulent regions.


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Electrochemical measurem ents in flowing solutions 411S h = 0.016 5 Re .se SC0'33. (28)

T h i s f i t t e d a l l t he i r da t a b e t w e e n R e 8 0 0 0 - 2 0 0 , 0 0 0 a n d S c 1000- 6000 . A t a S c o f 1 0 t h em a x i m u m d i f fe r e n c e b e t w e e n s i m p l e a n d f u l l e q u a t i o n is o n l y 3 ~ o.Entry e f fec t s

O n a n y t e s t sp e c i m e n i f t h e r e i s a l o w c o n c e n t r a t i o n o f t h e d i ss o l v in g s u b s t a n c ea t t h e b e g i n n i n g e n h a n c e d m a s s t r a n s f e r w i l l o c c u r . T h i s i s p a r t i c u l a r l y i m p o r t a n tw i t h t u b u l a r s p e c im e n s a n d i t h a s b e e n c o m m o n p r a c t i c e t o p r o v i d e s e p a r at e l en g t h s o ft u b e s p r i o r t o t h e s p e c i m e n s o t h a t e s t a b l i s h e d m a s s t r a n s f e r c o n d i t i o n s w i l l b eo b t a i n e d b e f o r e th e s p e c i m e n is r e a c h e d . T h i s m a k e s i t e a s ie r t o o b t a i n d a t a p e r t i n e n tt o f u l l y e s ta b l i sh e d c o n d i t i o n s i f f o r e x a m p l e s p e c i m e n s a r e s i m p l y w e i g h e d o r c o r r o s i o nr a t e s o b t a i n e d f r o m s o l u t i o n a n a l y si s .

T h e r e q u i r e d m a s s t r a n s f e r e n t r y l e n g t h s c a n b e e s t i m a t e d f r o m t h e o r e t i c a l o re m p i r i c a l c o r r e l a t i o n s o b t a i n e d o v e r v a r i o u s ( d / L ) r a ti o s . F o r l a m i n a r f l o w s t h i s h a sb e e n e x a m i n e d b y R o s s a n d W r a g g 57 w h o s h o w e d g r a p h i c a l ly b o t h t h e G r a e t z 5s a n dL e v e q u e ~9 s o l u t io n s . O n l y t h e f o r m e r p r e d i c t s a n a p p r o a c h t o c o n s t a n t Sh , or f u l l yde v e l ope d m a s s t r a ns f e r , a t s u f f ic i e n tl y l ong t ube s . F o r a t yp i c a l s o l u t i on w i t h S =2 0 0 0 a n d R e = 500 t he r e qu i r e d e n t r y l e ng t h w ou l d be 125 ,000 t ub e d i a m e t e r s , i .e .f o r a 1 c m d i a . t u b e i t w o u l d b e a b o u t a m i le . U p t o l e n g t h s o f a b o u t 5 0 0 t u b e d i a -m e t e rs m a s s t r a n s f er s h o u l d b e o b t a i n e d f r o m t h e L e v e q u e e q u a t i o n

S h = 1.614 (Re Sc d /L ) .33. (29)

I n t u r b u l e n t f l ow , u s in g t h e L C D T B e r g e r a n d H a e s2 f o u n d :S h = 0 .276 R e .5~3 S c .33 ._d'Z3 (3 0)L

C o n e y 14 d i f f e r e n t i a t e d th i s w r t L t o ob t a i n l oc a l S h va l ue sS h L = 0 .184 R e .ss3 Sc .33 (d /L ) 0"33. (31)

T h e n b y d i v i d i n g t h i s b y t h e s i m p l i f i e d B e r g e r a n d H a e e q u a t i o n f o r f u l l y d e v e l o p e dt u b e f l o w h e o b t a i n e d

S hS h f d -- 11.15 R e -0"277 (d /L ) 'a3. (32)

T h i s p r e d i c t s e n t r a nc e e f f ec t s de c r e a s e w i t h i nc r e a s i ng R e a n d e v e n a t a n R e of 104t he y w i ll ha ve d i s a p pe a r e d b e f o r e 1 t ub e d i a . I t is i n t e r e s t i ng t ha t t h i s s ugge s t s e n t r ye f fec t s w i l l b e S c i n d e p e n d e n t . H o w e v e r , C o n e y 14 p o i n t s o u t a t l o w S c t h i s i s no t s oa nd e n t r y e f f e c t s w i l l be l a r ge r a nd e x t e n d f u r t he r . I n l a m i na r f l ow t he r e ve r s e i s t r uea n d a t a S c o f 1 o n l y ~ 1 m w o u l d b e r e q u i r e d as c o m p a r e d t o ~ 1 m i l e a t a S c o f2000.


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412 BRYAN POULSON

It is also necessary to provide a sufficient length of straight tube prior to the speci-men so the hydrodynamic boundary layer may be fully established. Ross and Jones6summarized these requirements as being"

For laminar flow L min = 0.035 Re d (Re < 2000). (33)For turbulent flow L min = 0.693 R e '~5 d (R e > 3000). (34)

This gives entry lengths of 3.5-70d for R e between 100 and 1000 and 5.2-12.3d for R ebetween 3000 and 100,000.Orifices, ferru les and f lo w expansions

Recently it has been realized that such geometries provide in many environmentsthe necessarily severe hydrodynamic conditions to produce erosion corrosion. Theyare thus useful specimens for studying the effects of varying hydrodynamic factors oncorrosion as well as being relevant to practical situations.

In the ease of a ferrule or sudden expansion, fluid emerges as a round turbulentjet and, being unable to satisfy its entrainment appetite with ambient fluid, causescirculation of fluid from further downstream (Fig. 5). The downstream limit of therecirculation zone is marked by the attachment of the separated streamlines to the pipewall. The flow downstream then slowly readjusts until after about 7 tube dia it isfully re-established. The case of an orifice differs slightly in that a vena contractor isproduced the area of which is typically only 60 ~ of the orifice, thus increasing Reo.Both the heat transfer data of Krall and Sparrowel (KS) and the mass transferdata, using LCDT, of Tagg, Pattrick and Wragg62 (TPW) show that the maximummass transfer rate can be obtained from

[ \ ]hm ax = 0.276 Reo'e6 S c '3z where R e o R e (35)as shown in Fig. 13. This will be reduced slightly if mass transfer is taking place priorto the orifice, probably reducing the numerical factor to 0.2 under conditions mini-mizing mass transfer. 14 This enhancement over fully developed pipe values increaseswith increasing d ido values and decreasing R e values and occurs at approx. 2 tubediameters downstream of the orifice. The enhancement can be obtained by dividingthe correlation equat ion for the maximum mass transfer downstream of an orifice bytha t for fully developed flow. After simplification this becomes

Shmax__ 0.2 7 (_ dy .e8 1S h f d 0.0165 do ~ Re 0"19 (36)

The actual mass transfer profile has been examined in some detail by Coney payingparticular attention to the KS and TPW data he obtained.[ R e c O 3 _ 2 1 ) ] 3 7 ,

S h f d - - [ + A ~ I + B x \ S h f d


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Elec t rochem ica l measu rements in f lowing solut ions 413

FIG. 13.

ld

ShS

1 8

1 0 3

~,,~B ~ w/ S , 27R g SE

I I1 0 4 1 0 SR e

M a ss a n d he a t t r a ns f e r c o r r e la t ions fo r pe a k r a t e f o l lowing a sudde n e xpa n-s ion (Ta gg , P a t t r ic k a nd W r a gg , Kr a l l a nd S pa r r ow) .

V a l u e s o f t h e c o n s t a n t s A a n d B a t d i ff e r en t t u b e d i a m e t e r s f r o m t h e o r if ic e , o b t a i n e df r o m g r a p h s o f C o n e y a r e g i v e n i n T a b l e 3 . T h e f it o f s u ch a n a p p r o a c h c a n b e j u d g e di n F i g . 1 4 t a k e n f r o m C o n e y ' s p a p e r . F u r t h e r s i m p l i f i c a ti o n c a n b e o b t a i n e d b y s u b -s t i t u t in g f o r S h f d , f r o m t h e s i m p l i f i e d B . H . e q u a t i o n .

S h xS h f a

( R e o " 2 1 ) ]- - [ -}- A x [ I B x \ 0 . 0 i 6 5 ~ e e 0 . 8 6 (38 )

A s u m m a r y o f o t h e r s p e c i m e n s t h a t h a v e b e e n u s e d i s g i v e n i n F i g . 15 .TABLE 3. VALUES OF CONSTANTS IN CONEY'S EQUATION FOR MASS TRANSFER

PROFILES OF ORIFICESDis ta nc e f r om o r i fi c e A Bi n t u b e d i a m e t e r K S T P W K S T P W

0.5 2.72 2.12 0.057 0.0731.0 3.67 3 0.051 0.0491.5 4.52 3.75 0.059 0.0622.0 4.7 4.2 0.066 0.0722.5 4.5 4.17 0.068 0.0793.0 4 3.74 0.067 0.0783.5 3.15 2.92 0.065 0.0734.0 2.45 2.25 0.064 0.0694.5 1.72 1.62 0.063 0.0645.0 i .45 1.27 0.062 0.0635.5 1.22 0.98 0.059 0.0626.0 1 0.77 0.058 0.0626.5 0.82 0.6 0.056 0.0627.0 0.67 0.45 0.055 0.062

K S d a t a v a l i d : 2 ~ < d /d o ~ 4 , 104 ~< Re ,< 1.3 105; 3 ~P r


24/40

4 1 4 B RY AN P O ~ N

il5 m

Sh

d / d , R en 6 1 5 6 7 2o 3 10126A 3 21700

o / O O \ o \ Io o/ A A -A 'A \_ _ , C \

A / A ~ n . 1+ + '~ 1A "~-.9 o

1 2 3 4 5 6 7T U B E D I A M E T E R S F R O M ' N O Z Z L E ( x /d )

Fie . 14. Enhancement of ma ss transfer downstream of a nozzle: comparison ofexperimental LCD data (Tagg, Pattrick and W ragg) wi th Coney's correlation.

Relationship between corrosion rates fo r different specimen geom etriesT h e p u r p o s e o f u s i ng w e l l c h a r a c t e r i z e d sp e c i m e n s is t o b e a b l e t o c o m p a r e r e s u l ts ,

w i t h t h a t p r e d i c t e d f r o m t h e m a s s t r a n s f e r c o r r e l a t i o n , w i t h t h a t o b t a i n e d w i t hd i f f e re n t s p e c im e n s , a n d m o r e i m p o r t a n t l y t o b e a b l e t o r e l a t e th e r e s u l ts t o p r a c t i c a lg e o m e t r i e s , e . g . b e n d s , p u m p i m p e l l e r s , e t c . H o w e v e r , t h e m a s s t r a n s f e r c h a r a c t e r is t i c so f s u c h c o m p o n e n t s a r e n o t a l w a ys k n o w n .

B e c a u s e r o t a t i n g d i s cs a n d c y l in d e r s a r e e a s y t o u s e a n u m b e r o f w o r k e r s h a v es u g g e s te d e i t h e r e m p i r i c a l c o r re l a t i o n s o r c o r r e l a t i o n s b a s e d o n a n e q u a l i t y o f m a s st r a n s f e r .

P o l u b o y a r t s e v a83 c a r r i e d o u t a n e x t e n s i v e i n v e s t i g a t i o n u s i n g l a m i n a r r o t a t i n gd is c s a n d t u r b u l e n t p i p e f l ow w i t h a n u m b e r o f d i ff e r en t m a t e r i a l / e n v i r o n m e n t c o m -b i n a t io n s . E m p i r i c a l e q u a t i o n s o b t a i n e d a r e g i v e n i n T a b l e 4 t o g e t h e r w i t h t h e i rt h e o r e t i c a l e q u a t i o n s . T h e d i f f e r en c e s b e t w e e n t h e tw o , i .e . t h e n u m e r i c a l c o n s t a n ti s t h e r e s u l t o f n a t u r a l c o n v e c t i o n .

H e i r # 4 u s e d t h e r e a c t i o n Z n + I s = Z n I ~ , w h i c h i s d i f f u s i o n c o n t r o l l e d , t o s t u d yt h e r e l a t i o n s h i p b e t w e e n t u r b u l e n t c o r r o s i o n o n d i s c s a n d c y l i n d e r s a n d t u b e s , h eo b t a i n e dv e l o c i t y i n t u b e ( m / s ) = 6 .6 x r o t a t i o n s p e e d ( r p m ) x [ d is e r a d i u s ( em ) ] 4

= 37 x ( rpm ) '~ x [cy l inde r rad iu s cm] 'L (39 )


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E l e c t r o c h e m i c a l m e a s u r e m e n t s i n f l o w i n g s o l u t i o n s 4 1 5

FIG. 15 .

ROTATING DISC IN HOU SING ROTA TINGRING DISC

I 1

PLATES IN ANNULUSSINGLE PLATE DUCT WAL L

. . . . . . . . . . . . . . P [p

I V . H . . . H . ~ I

BOILER WATEREROSION-CORROSION TEST

i

i

P L A N O E A

M U L T I P L E PLATES IN PIPE

l . . . . . . . . r / ~ , . ,[ r i iI , , , J

BNFRA IMPINGINGJET TEST

S u m m a r y o f s o m e o t h e r s p e c i m e n s t h a t h a v e b e e n u s e d in f lo w e x p e r i m e n t s .

W r a n g l e r 18 u s i n g t h e E i s e n b e r g c o r r e l a t i o n ( fo r c y l in d e r s ) a n d t h e C h i l t o n - C o l b u r na n a l o g y ( f o r t u b e s ) e q u a t e d m a s s t r a n s fe r s a n d o b t a i n e d

l o g R e t u b e : 0 . 6 7 + 0 . 8 3 3 l o g R e c y l i n d e r . ( 4 0 )

TABLE 4. P I P E T O D I S C C O R R E L A T I O N S P R O P O S E D B Y P O L U B O Y A R T S E V A e l d .T e m p e r a t u r eM a t e r i a l E n v i r o n m e n t C E m p i r i c a l e q u a t i o n T h e o r e t i c a l e q u a t i o n

S t e e l 9 4 - 9 8 % H ~ S O 4 6 0 V = - 0 . 0 5 + V ---- 0. 7 S e ~ ' e 6 v / T n0 .7 C ~tn30 V = 0 .5 Set'=s~/?n4 0 V = 0 .9 Sc,'=SCyn

Cu 0 .1 N HC1 + V = - 0 .21 +198 g 1-1 Fe 3 . 0 . 5 ~ / 7 nP b 2 M N a O H + V = - 0 . 9 4 0 .1 N N a N O a 0 . 6 C ~ ' n

V i s p i p e v e l o c i t y i n m s - 1, n i s n u m b e r o f r p m t o g i v e s a m e c o r r o s i o n r a t e , S c t i s t u r b u l e n t Scn u m b e r ( r a t i o o f ~ d i f fu s i v i ty f o r m o m e n t u m t r a n s f e r t o t h a t f o r m a s s t r a n s p o r t ) .


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416 BRYANPOULSONEllison and SchmeaP ~ appear to have confirmed this approach in a study of carbonsteel dissolving in concentrated sulphuric acid. They used both rotating cylinders andpipe flow measuring corrosion both electrochemically and by weight loss. Their resultsare shown in Fig. 16 together with the predictions using known or measured data onthe solubility of FeSO4, the diffusivity of ferrous ions, and the kinematic viscosity ofHzS04 with the Eisenborg and the Harriot Hamilton correlations. The agreementbetween predicted and measured corrosion rates was impressive.

However there are a number of pieces of evidence tha t such simple approaches do

1 ~ ~ _ _ _ C A R B O N S T E E l _ P I P E 6 8 % w t H 2 S O I , 6 0 c J- - F R I E N Dn d E T Z N E ]- - H A R R I O T o n d H A I t i - T O N / / / / |S h s " c x ~ R ' ~ /LIN ~ DEISSL.ER I

, O o , , , , l , l l , ,Re

Sh~

ld - - * 2 0 % - "S h - '0 7 9 R e ' S ~ s 6 " " ' " i ~ " ' - 2 0 / o_ _ " . . . = ' " / ~ . . . . . A 6 0 C

- - x .. ' o . / ~ . . . . . . . . ~ . . . . .. .. .. . o 4 0 C~ ' ~- - . ~ , . , , ' ~ ..o'" o_ / ' " J ~ .. " a 2 7 C

i . ,, ~ . . j~ . .. .. .. .. " o . '" ^ R O T A T I N G S T E E l _ C Y L I N D E R 6 O O /o w t, z $ O t," " ~ : / " i " "" ~ ' J ' J[ ' l l ' I J I ' ['I C I 0 3 1 0 ~ 1 0R e

FIo. 16. Data for carbon steel pipe and rotating cylinders exposed to 68% HaSO,compared o predictedbehaviourfrommass ransfer correlations(Ellisonand Schmeal).


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Electrochemical measurem ents in flowing solutions 417n o t a lw a y s w o r k . F o r e x a m p l e L a Q u e 66 s h o w e d t h a t t h e r e s p o n s e o f r o t a t i n g i r o na n d c o p p e r d i s cs r o t a t i n g i n s e a w a t e r w a s r a d i c a l ly d i f fe r e n t. B i g n o l d e t a l . e e x a m i n e dt h e e r o s i o n - c o r r o s i o n b e h a v i o u r o f c a r b o n s te e l i n p u r e w a t e r a t a r o u n d 1 50 C u s in ga n o r if ic e s p e ci m e n g e o m e t r y . T h e y f o u n d t h a t t h e e r o s i o n c o r r o s i o n r a t e u n d e r t h e i rt e s t c o n d i t i o n s v a r i e d a s t h e c u b e o f t h e m a s s t r a n s f e r (F i g . 1 7 ) r a t e i n s t e a d o f b e i n gd i r e c t l y r e l a t e d t o i t . T h i s w a s e x p l a i n e d i n t e r m s o f a m o d e l b a s e d o n t h e e l e c t r o -c h e m i c a l d i s s o l u t i o n o f m a g n e t i t e . W e h a v e e x a m i n e d t h i s u s i n g d i f f e r e n t m a t e r i a l ,e n v i r o n m e n t a l c o m b i n a t i o n s w i t h b o t h o r if i ce a n d i m p i n g i n g je t g e o m e t ri e s . T y p i c a lc o r r o s i o n r a t e p r o f i le s f o r i ro n a n d c o p p e r s p e c im e n s d i s so l v i n g i n 0.1 N H C 1c on t a i n i n g 2 g 1 -* f e r r i c i on ( a s F e C I a) a r e s how n i n F i g . 18 . 45 I n t h i s s o l u t i on c o r r o s i o ni s t h o u g h t t o b e c o n t r o l l e d b y t h e r a t e o f r e d u c t i o n o f f e rr i c t o f e r r o u s i o n s, s o th ep r o f il e s f o r t h e t w o m a t e r i a ls s h o u l d b e t h e s a m e a n d s i m i l a r t o th e m a s s t r a n s f e rp r o f il e . T h i s i s th e c a s e w i t h c o p p e r , b u t i r o n b e h a v e s a n o m a l o u s l y . I n p a r t i c u l a r i ta p p e a r s t h a t i r o n d i s s o l u t i o n d o w n s t r e a m o f t h e p e a k is l es s t h a n p r e d i c t e d , p r o -d u c i n g a h i g h a p p a r e n t e n h a n c e m e n t f a c t o r . A p o s s i b le r e a s o n f o r t h i s is th e l o c a l -i z a t i o n o f a n o d i c a n d c a t h o d i c a r e a s . C r o s s s e c t io n s t h r o u g h i m p i n g i n g j e t e le c t r o d e sa r e s h ow n i n F i g . 19. W i t h C u e xp os e d t o t h e 0 .1 N H C 1 + 2 g 1 -1 F e 3+ t he p r o f i l e

FIo. 17.

E

U J

rzo

8ZO8EZu.I

1 0 ~ " DECgYGENATED PU RE WATERmn

m

~- - FLOW RATES

d = 8-34mmdo= 2 .72mm

p H 9 0 5 1 5 7 C

I I l l l l l [ I I i l l l l1 10MASS T RAN SFER COEFFICIENT (ms~g) )Effect of m ass transfer rate on erosion-corrosion rate o f carbon steel orificespecimens exposed to p ure w ater (Bignold).

k g ha 9 2 0o 574

2 8 7

[~3 SL.OPE =37 h

AA ~ 66o 7


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418 BRYAN POULSON

|tu

zoU~0,v3 m6

DISTANCE c r .I 2 3 4 5 6 7 8 9I I I I I I I I I

0_ _ , q " , , 0 O 0

M

0 C A R B O N COPPER

I 0 I I 12 13 14 15 .16/ I I I 1 1 1EMCAt~EHENTFACTORS T E E L | 0 3

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O oo oo

o0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

I I II 2 3DISTANCE DOWNSTREAM OF

O

4 5 6 7 8 9 O l l 12 13ORIFICE IN TUBE DIAMETERS

FIG. 18. Effect of mater ial on enhancement of corrosion in 0.1 N HC1 conta ining2 g 1-1 Fe =+ at 50C, following on or if ice. Rey nolds num ber was 27,309, d/dOof 2 .67,giving predicted enhancem ent of 4.6.

i s a g a i n s i m i la r t o t h a t e x p e c t e d f r o m t h e m a s s t r a n s f e r p r o f il e (F i g . 1 1 ) . W i t hc a r b o n s te e l e x p o s e d t o N H 4 N O 8 w h i c h is a s o l u t i o n th a t p r o d u c e s a p r o t e ct iv ef il m th e c o r r o s i o n is m u c h m o r e l o c a li z e d a t t h e r e g i o n o f h ig h e s t m a s s t r a n s f e r w h i c his a lso t h e r e g i o n o f h i g h e s t t u rb u l e n c e .

I n c o r r o s i o n s i tu a t i o n s , i n w h i c h b o t h a n o d i c a n d c a t h o d i c r e a c t io n s o c c u r , o f t e no n s e p a r a t e a r e a s - - s i m p l e r e l a t i o n s h i p w i t h m a s s t r a n s f e r d o n o t a l w a y s h o l d . T h er e l a ti o n s h i p b e tw e e n c o r r o s i o n r a t e a n d m a s s t ra n s f e r , o r o t h e r h y d r o d y n a m i c p a r a -m e t e r , n e e d s t o b e d e t e r m i n e d f o r e a c h s y s t e m o f in t e re s t.

T H E A P P L I C A T I O N O F E L E C T R O C H E M I C A L M E A S U R E M E N T S I NF L O W I N G S O L U T I O N SPractical corrosion situations

E a r l y u s e s o f e l e c t ro c h e m i c a l t ec h n i q u e s i n m e a s u r i n g c o r r o s i o n r a t e s w e r e b a s e do n u n s o u n d t h e o r y . E x a m p l e s i n c l u d e d T o d t ' s C o r r o s i m e t e r ( w h i ch m e a s u r e d t h e


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Electrochemical mea suremen ts in flowingsolutions 419g a l v a n ic c u r r e n t b e t w e e n t h e s p e c i m e n a n d a P t e l e ct ro d e ) a n d t h e P o l a r i z a t i o n b r e a km e t h o d ( w h i c h d e p e n d e d o n a r b i t r a r y b r e a k s i n p o l a r i z a t i o n c u r v e s ) . T h e b a s i ce q u a t i o n f r o m w h i c h t h e c o r r o s i o n r a t e I~ o,~ c a n b e o b t a i n e d f r o m t h e c u r r e n t Im e as u r e d a t po t en t i a l E is . a s

[ E - E o o ,1 i - E o r - E 1I = lor, ex p L-0.4-3~,~ _1 -- I~~ ex p L 0~-34-b~- d (41)f r o m t h i s h a v e d e v e l o p e d a n u m b e r o f d i f fe r e n t a p p r o a c h e s :(a) Tafe l ex t rapo la t ion . W i t h t h is m e t h o d t h e l i n e a r p o r t i o n o f c u r v e is e x tr a p o l a t e df ro m high pote nt i a l s to Ecor r to obta in /cor r . 69(b ) Po lariza tion resistance. 7Thi s m e t h od u t il ize s the s l ope o f the E l i curve (Rp) c loset o Eco r~ ( o r i m p edan ce t echn i ques ) 71 i n r e l a t i on o f t he f o r m

Icorr = ba be I2.303 (ba 4- b~) Rp.U n k n o w n s a r e o b t a i n e d e m p i ri c a ll y , b y o t h e r t e c h n iq u e s ( e.g . a ) o r b y e d u c a t e dguess ing .

(c ) Curve f i t t ing or B arna r t t ' s 3 po in t t echnique . T h i s m e t h o d u s e s d a t a a t b o t h h i g ha n d l o w v a l u e s o f E w i t h g r a p h i c a l, TM co m pu ter 7z,74 or uniq ue so lu t ion s . 7sBef o r e any c on f i dence is g i ven t o t h e u s e o f e lec t r ochem i ca l t echn i qu es i n a g i ven

m e t a l / e n v i r o n m e n t s y s t e m , t h e v a l u e s o b t a i n e d s h o u l d b e p l o t t e d a g a i n s t a c t u a lco r r os i on r a t e s ( w e i gh t l o s s , s o l u t i on ana l ys i s , e t c . ) and a r ea s onab l e deg r ee o fco r r e l a t i on be ob t a i n ed ove r t he r ange o f i n te r e s t.

A s l o n g a g o a s 1 9 6 9 S o u t h i n a M T e c h t h e s isTM m a d e a n e x t e n s i ve s t u d y o f t h eco r r os i o n o f m i l d s tee l t ubes i n f l ow i ng i nh i b i t ed H C1 i n a r i g ve r y s i m i l a r t o t h a t s h ow ni n F i g . 3 . A n exce l l en t co r r e l a t i on be t w een po l a r i za t i on r e s i s t ance an d co r r os i on r a t e sw a s o b t a i n e d w i t h d i f fe r e n t i n h ib i to r s , te m p e r a t u r e s a n d r e d o x p o t e n t i a l s a s s h o w ni n F i g . 20 and an em pi r i ca l r e l a t i ons h i p be t w een t he t w o de f i ned a s "log co r ros io n r a t e (mg cm -2 hr -1) = 1 .903 - - l og polar i z a t ion r es i s t ance ( f~cm : ) . (42)

P o t e n t i a l d e p e n d e n t a d s o r p t i o n e f f e c t s o c c u r i n t h i s s y s t e m s o b e a r i n g i n m i n dt he i r e f fec ts i n o t he r s y s t em s ( H ~SO , p l u s p r opa r gy l i c a l coho l ) s uch a go od co r r e l a t i onis s u rp r is i ng . S o u t h t h e n w e n t o n t o e x a m i n e t h e e f fe c t o f v a r y i n g R e . O v e r t h e r a n g e10 z ~< R e ~< 5 10a t h e c o r r o s i o n r a t e w a s a l in e a r f u n c t i o n o f lo g R e . A t h i g h e rva l ues o f R e a l og / l og f it w as ob t a i n ed a s expec t ed f r o m m as s t r ans f e r co r r e l a t i ons .

I n a s i m i l a r w ay P r aza k v7 exam i ned b o t h s t a t ic an d r o t a t i n g s tee l d is c s in con -cen t r a t e d s u l phu r i c ac i d w i t h t he r e s u l ts s how n i n F i g . 21. A go od co r r e l a t i on be t w eene l e c tr o c h e m i c a l a n d w e i g h t l os s m e a s u r e m e n t s w a s o b t a i n e d o v e r 3 o r d e rs o f m a g n i t u d ew i t h th e s a m e r e l a ti o n s h i p f o r f lo w i n g a n d s t a ti c c o n d i t i o n s in a s y s t e m w h i c h h a sr e l a t i ve l y t h i ck co r r os i on p r oduc t s .

V e r y f e w e l ec t r o c h e m i c a l m e a s u r e m e n t s h a v e b e e n c a r r i e d o u t i n f l o w i n g s o l u ti o n sw i t h t h e a i m o f p re d i c ti n g o r m e a s u r i n g lo c a l iz e d f o rm s o f c o r r o s io n . A n u m b e r o f


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420 BRYAN POULSON100C

' E>uJoz

e~zore,

tO C

m

m

m

m

m

m

m

m

m

m

m

m

" I

X A V A R I O U S I N H IB I TO R SV I N F L O W I N G 5 O lo H C l~o.~ A T 8 0 Cs t o ~ = - I % . e . X o

co r re la t ion m,~ ic ie~ t= , 9 9 ~ A

% " \ , \t J t l a l t t I == l t l t t . i i i J J lo.1 1 10C O R R O S I O N R A T E ( m g c m I~1 }

Fro. 20. Correlation between polarization resistance and corrosion rate in flowinginhibited 5~o HC1 at 80C (South).

Flo. 21.

1(2~'S 5

1 4 0 0 ~

iu F e 9 6 O / o H2SO. at 22c o ~

" O 5 1 ~ - L 2 0 ~ 5 0 0 1 O O O 2 O C X ) 5 0 0 0POLA RISATION RES ISTANC E (V ,~1 cn~2 )

Correlation between corrosion rate and polarization resistance for rotatingsteel discs in 96 ~o HsSO4 at 22C (Prazak).


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Electrochemical measurements in flowing solutions 421

workers have suggested that monitoring the free corrosion potential and its relation-ship to values known to cause SCC, pitting, erosion-corrosion etc. is a valuabletechnique). ~s Such techniques should be examined in practical situations. The recentanalysis of electrochemical noise and its empirical relation to corrosion ratC 9 is mostinteresting especially in view of similar effectss when acoustic emission techniquesare used to monitor noise. It would be valuable to see if such approaches could beused in practical flowing systems.M echanistic applicationsThere are a number of situations in which differentiation can be made betweendifferent corrosion mechanisms by moving the corrosive environment in some pre-determined way; this has been sadly neglected as a diagnostic technique.

Dissolution mechanisms. The effect of flow has been used in a number of instancesto determine if corrosion is under activation, diffusion or mixed control. A strikingexample is provided by the work of Zemburasx examining the corrosion of Cu discsrotating in air-saturated 0.1 N H2SO4 at different temperatures (Fig. 22).At a more fundamental level the rotating disc and in particular the rotating ring-disc electrode has been used by MiUers~ and Picketings3 to study the dissolution ofmetals and alloys. For example a Cu 10 9/o Au disc electrode was subjected to anodicdissolution and the ring was kept at a potential when it would only detect the dischargeof Au *+. At all currents applied to the disc the ring current was less than 2 vtA (i..e.Au was not dissolving from the disc in accord with expectations from its potential), s3Mech anism o f passivation

There are two general, postulated mechanisms of passivation: (a) dissolution and10

FIG. 22.

8

oc0u 2

/Cu In a ir saturated .1N H:SO~75 C

sOcI I I I0 1 2 3 4

ANG ULAR VELO CITY ( rod /sec i sE f fec t o f ang u la r ve loc i ty and tempera ture on Cu d iscs ro ta t ing in a i r -sa tu ra ted

0. ! N H=SO4 (Zembu ra) .


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422 BRYAN PO ~N

s u b s e q u e n t p r e c i p i t a t i o n , ( b ) s o l i d s t a t e r e a c t i o n ( o x i d e o r a d s o r p t i o n ) i n p a r a l l e lw i t h m e t a l d i s s o l u t io n . A r m s t r o n g a4 h a s e x a m i n e d p o s s i b le c r i t e r i o n f o r d e c i d i n gb e t w e e n t h e t w o a n d s u g g e s t e d t h a t t h e a c t i v e - p a s s iv e tr a n s i t i o n s h o u l d b e r o t a t i o n( o r f lo w ) d e p e n d e n t i f ( a ) o c c u r s as l o n g a s t h e n u c l e i a r e f o r m e d a t a d i s t a n c e f r o m t h es u r f a c e w h i c h a l lo w s t h e m t o b e s w e p t a w a y : n o e f fe c t s h o u l d o c c u r i f ( b ) w a s o p e r a -t iv e . T h i s w a s u s e d b y T u r n e r a n d B r o o k 85 e x a m i n i n g t h e b e h a v i o u r o f C u i n H C 1s o l ut io n s a n d f o u n d n o e f fe c t o f f lo w o n t h e f o r m a t i o n o f C u C I~ ; t h e y c o n c l u d e d i tf o r m e d b y a s o l id s t a t e m e c h a n i s m . W i l d e sa e x a m i n i n g t h e b e h a v i o u r o f i r o n i n1 M L i C I h a s s h o w n t h e r e v e r se s i tu a t i o n . I n s t a ti c s o l u t io n s n o p a s s i v a t i o n o c c u r sb e c a u s e o f a c id i t y b u i ld u p w h i c h i s r e m o v e d b y u s i n g a r o t a t i n g c y l i n d e r a n d p a s s iv a -t i o n o c c u r s.

T h e r e a r e t w o i n t e r e s ti n g a d h o c o b s e r v a t i o n s : R i c h a r d s o n 87 s h o w e d t h a t T y p e 3 0 4s t a i n l e s s s t e e l w a s pa s s i ve i n ho t s t r ong H N O 3 o r N a O H o r m i x t u r e s o f t h e t w o .H o w e v e r if i t w a s e x p o s e d t o e a c h i n t e r m i t t e n t l y i t w a s n o t a n d c o r r o d e d a t 5 r a m / y e a r .T h i s c l e a r l y s ugge s ts t ha t d i f f e r e n t ox i de s a r e r e s p ons i b l e f o r pa s s i v i t y i n e a c h c a s e .T h e e f f e c t o f e m p t y i n g a n d r e fi ll in g a c e ll c o n t a i n i n g a m i l d s t ee l s p e ci m e n p o t e n t i o -s t a ti c a ll y c o n t r o l l e d i n l i q u i d a m m o n i a w a s e x a m i n e d , ss I t w a s f o u n d t h a t l a r g e c u r r e n tt r a n s i e n ts o c c u r r e d a t e a c h f lu s h / re f il l c y c l e b u t t h e m a g n i t u d e d e c r e a s e d w i t h t i m e .I t w a s s u g g e s t ed t h a t i n i ti a ll y t h e c u r r e n t d e c a y w a s d u e t o a n a d s o r b e d s p e ci es w h i c hw a s l o s t d u r i n g t h e f l u s h c y c l e . H o w e v e r a t l o n g e r t i m e s a p a s s i v e f i l m d i d f o r m ,i n d i c a t e d b y i n t e r f e re n c e c o l o u r s , p r e v e n t i n g t h e h i g h i n i t ia l c u r r e n t s .M e c h a n i s m o f p i t ti n g

T h e r e a r e a n u m b e r o f p o s t u l at e d m o d e l s f o r th e b r e a k d o w n o f p as s iv i ty a n d t h ei n i t i a t i o n o f p i tt in g . O n e s u c h m o d e l s u g g e st s p a ss i v it y b r e a k d o w n i s a s so c i a t e d w i t ht h e l o c a l i z e d b u i l d - u p o f a c id i t y a t t h e m e t a l s u r f ac e . I t w a s s u g g e s t e d t h a t t h i s c o u l db e t e s t ed b y e x a m i n i n g t h e e f f ec t s o f f lu i d fl o w o n t h e b r e a k d o w n p o t e n t i a l. T h i sh a s b e e n d o n e b y a n u m b e r o f w o r k e r s w h o s e r e su l ts a r e s u m m a r i z e d i n T a b l e 5 a n dt y p i f ie d b y t h e r e s u l t s o f M a n s f e l d s9 s h o w n i n F i g . 2 3 . I t w o u l d a p p e a r t h a t t h e f l o w

TABLE 5. SUMMARYOF EFFECTS OF "FLOW" ON PITTING POTENTIALS

Meta l Envi ronment Spec imenype Effect Ref.AI 3.5 Yo NaC I Rotating cylinder No ne Man sfeld304SS 3.5 % NaC1 Rotating cylinderIron 1 M LiC1 Rotating cylinder No ne WildeAl 0.1 N NaC I Rotating cylinder Increase p by Fra nz et al.50 mV304L 0.2 M NaC 1 + Rotating cylinder Almo st o effect S ato et al.

0.I M NaISO~304 0.1 NaC i Flat specimen in solution ,,, 200 mV more Nakay amavibrated with 200 kH~ noble

waves


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FIG. 23.

tt lt )03

E_J

Z

oO.

30G

2 0 ~ m

10(

10C

2013

P I T T I N G

j o o/ o \o / \~ ~ o / P R O T E C T I O N o

I IO 4 8 12 16A N GU LA R V E LOC ITY (rad / s c i s

Effect of rotation on pitting o f Typ e 304 stainless ste el in 3~ NaC1(Mansfeld).

c o n d i t i o n s e x a m i n e d s o f a r h a v e l it tl e e f f ec t o n t h e p i t t i n g p o t e n t i a l a l t h o u g h t h eu l t r a s o n i c v i b r a t i o n s c l e a rl y d o .

P i t g r o w t h i s c e r t a i n ly m a r k e d l y i n f l u e n c e d b y s o l u t i o n f l o w , in t h a t s o l u t i o n f lo wm i n i m i z e s t h e g r o w t h o f p i ts . T h i s i s r e c o r d e d 93 a n d s h o w n b y t h e g e n e r a l r e c o m -m e nd a t i o n 94 t ha t ve l oc i t i e s g r e a t e r t h a n 5 f t . / s a r e r e qu i r e d t o a vo i d p i t t i ng o f s t a in l e s ss te e l i n s e a w a t er . M o r e r e c e n t l y B e c k a n d C h a n 95 h a v e e x a m i n e d t h e e f f e c t o f f l o wo n t h e g r o w t h o f p it s. T h e y c o n c l u d e d t h a t a s a l t f i h n is m o r e i m p o r t a n t t h a n l o w p Hi n m a i n t a i n i ng p i t t i ng a n d a bo ve a c r i t i c a l ve l oc i t y (m a s s t r a n s f e r r a t e ? ) t he s a l t f i lmi s r e m o v e d a n d r e p a s s i v a t io n o c c u r s . T h e y d e v e l o p e d a t h e o r y t h a t s u g g es ts t h a ts u c h p r o c e s s e s d e p e n d o n t h e s iz e o f t h e p i t a n d t h e h i g h e r t h e v e l o c i ty t h e s m a l l e rw i l l be t he c r i t i c a l p i t s i ze a t w h i c h r e pa s s i va t i on oc c u r s ( V c r i t i c a l ~ P i t r a d i u s4 / 3 ).Stress-corrosion cracking

I t w o u l d a p p e a r f r o m a n u m b e r o f p a p e r s t h a t c o n t r o l o f p H b y u s in g a l a rg ev o l u m e o f s o l u t io n a n d p u m p i n g t h is t h r o u g h t h e n o r m a l l y s m a l l ( ~ 5 0 c m 3) t e stc e ll w o u l d b e w e l l w o r t h w h i l e i n m e c h a n i s t i c st u d ie s . A l t h o u g h t h e m e c h a n i s m o fe n v i r o n m e n t a l c r a c k g r o w t h h a s n o t y e t p r o v e d a s s e s s a b l e b y f l o w c o n t r o l t h e o c c u r -r e n c e o f c r a c k i n g h a s. U n d e r c o n d i t i o n s o f c o n s t a n t p o t e n t i a l i t h as b e e n s h o w n t h a t


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424 BRYAN POUL~N

solution flow increased the initiation time and it was suggested that micro-turbulencedecreased local concentrating effects? However it can be speculated that underfreely corroding condit ions flowing solutions would increase the rate of transport, 97of (say) oxygen, and this could increase or reduce the susceptibility depending on theeffect on the free corrosion potential and the potential cracking zone.E r o s i o n - c o r r o s i o n

A paper by Lush e t al . 41 examined the relationship between erosion-corrosion(EC) and the hydrodynamics modelled in an air rig with a hot wire anemometer.With an impinging jet electrode, using both current measurements between concentricrings and corrosion depth measurements, they looked at the behaviour of Cu discs insea water. It was suggested that the corrosion rate was dependent on the diffusion ofcopper ions away from the surface and that this was proportional to rs. In the centrallaminar region this could be obtained from mean velocities measured near the walland was in fact constant: in the turbulent region it was assumed that rs could beobtained from the T1 (because distribution of TI and corrosion were similar). Theradial distribution of attack at a single jet velocity agreed very well with their pre-dictions. However the effect of varying jet velocity on the rate of laminar (V '~) andturbulent (V.') was less than predicted (V '5) and (V 'ee) respectively. It was suggestedthat this was because the reaction was under mixed control. Further it was showntha t it was only at high values o f T1 (above 0.75 ms -1 rms) that the surface remainedfilm free and impingement attack occured; this could it was suggested be a designparameter. However it is not clear (a) why the available or measured mass transferrates (and also incidentally Tl 's using the LCDT), were not correlated with the experi-mental profile, and (b) since the mass transfer rate peaks in the same region as the TIit is not clear if the surface is kept clean for electrochemical (i.e. it dissolves away)or mechanical (i.e. it breaks away) reasons. The mechanical stability could be examinedby using a solution saturated w.r.t, the film, e.g. saturat ing cone. H~SO4 with FeSO4.

Some preliminary work has examined the effect of potential and environment insystems where stress corrosion cracking (SCC) occurs, i.e. carbon steels in nitrateand carbonate solutions.45 Interestingly the potential range over which EC occurs(Fig. 24) is similar, but wider, than that causing SCC. Furthermore the maximumrates of attack are similar to the crack velocities suggesting that in these systems,similar electrochemical parameters may be importan t in both cases. It would appearthat potential moni toring might be a valuable tool for predicting the possibility of EC.H y d r o d y n a m i c a p p l i c a t i o n s

The application of electrochemical techniques to determining hydrodynamicparameters has been the subject o f two excellent reviews. ~9,9s The basis is that manyelectrode reactions are controlled by diffusion if they are driven at a fast enough rate,their limiting current density (LCD). This is obtained in practice by slowly increasingthe potential driving the reaction and measuring the current until the plateau is reached.The mass transfer coefficient can then be obtained from the time averaged local (ona small electrode) or average LCD

L C DK -- - - . (43)n F A C


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UJ

>E.dI -zI- -0o..

Fro. 24.

-50C

-600

-700

- 8 0 0

- 9 0 0

MILD STEEL in solution 1Nwrt NotCO3r,N a H C O 3at 8 0 C w i t h 3m m j e t i m p In ~ g a t 7 m / s o n to25rnm dla speclrnen 3ram awe ,

/ e ~ e

A V E R A G E C O R R O S I O N R A T E ( ra g c n i2 fil )E f f e c t o f p o t e n t i a l o n e r o s i o n - c o r r o s i o n o f m i l d s t e e l i n c a r b o n a t e s o l u t io n .

T h e i n t e n s i ty o f tu r b u l e n c e ( T 1 ) ca n b e o b t a i n e d i n a m a n n e r a n a l o g o u s t o t h e h o tw i r e a n e m o m e t e r , w i t h c e rt a i n a s s u m p t i o n s , " f r o m t h e R M S v a l u e o f f l u c t u a ti o n s i nt h e L C D a n d is u s u a ll y q u o t e d a s :

T l = V ' ~ -C ~~ (44)V Kw h e r e v a n d k a r e f l u c t u a t i o n s i n v e l o c i ty o r m a s s t r a n s f e r c o e f f ic i e n t f r o m m e a n v a l ue s .

T h e l o c a l v e l o c i ty i n a s y s t e m c a n b e o b t a i n e d b y e m p i r i c a l l y c a l i b r a ti n g a s m a l lp r o b e u n d e r i m p i n g e m e n t c o n d it io n s o b t a i n i n g : "

L C D = ~ -~- ~ V''5 (45)w h e r e 0c i s a c o n s t a n t r e p r e s e n t i n g n a t u r a l c o n v e c t i o n a n d ~ is a n e m p i r ic a l c o n s t a n t .T h e s u r f a c e s he a r s t r es s c a n a l s o be ob t a i n e d . 47,1

A t y p i c a l e x p e r i m e n t a l s e t- u p i s s h o w n i n F i g . 2 5. P r e c a u t i o n s w h i c h m u s t b e t a k e ni nc l ude ( a ) ope r a t i ng a t a f l ow r a t e w he r e t he r e i s a l i m i t i ng c u r r e n t , ( b ) c hoos i ng a ne l e c t r o l y t e h a v i n g a n e x c es s o f ( + ) a n d ( - - ) i o n s s o t h a t r e a c t in g s p e ci es d o n o tm i g r a t e i n t h e e l e c t r ic f ie ld , (c ) c h o o s i n g a p o t e n t i a l a t w h i c h o n l y t h e r e a c t i o n o fi n t e re s t is o c c u r r i n g , ( d ) p o s i t i o n i n g t h e e l e c t r o d e s s o t h a t t h e c u r r e n t d i s t r i b u t i o n i sa s e ve n a s pos s i b l e a n d ne i t he r e f f e c t s t he f l ow , a nd ( e ) i f l oc a l m a s s t r a n s f e r c oe f f i c i e n t sa r e t o b e o b t a i n e d t h e s m a l l e l e ct r o d e s m u s t b e s u r r o u n d e d b y l a r g e a c ti v e e l e c t ro d e s .

T h e t w o c o m m o n s o l u ti o ns u s e d i n th e L C D T a r e :


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4 2 6 B R Y A N P O U L $O N

FOR RfT..,O~NOLeD/lRECORDER

I_..~ECTRUM ANALYZER ~ ' - -"FOR RECORDING N D ANALYZING

FLUCTUATIONS N LCD ON APOINT ELECTRODE TO GET Tldc

POTENTIOSTAT

COUNTER ELECTRODE

I

F IG . 2 5 . Typical experimental set-up for LCD measurements.

( a) T h a t b a s e d o n t h e f e r r o c y a n i d e /f e r r ic y a n i d e c o n t a i n i n g a n e x c e ss o f s o d i u m a n dh y d r o x y l io n s , e .g . 2 M N a O H p l u s e q u i m o l a r K a F e ( C N ) s a n d K 4 F e ( C N ) e t o0 .0 0 5 M d e - o x y g e n a t e d a n d s h ie l de d f r o m t h e l ig h t. T h e L C D f o r t h e r e d u c t i o n

F e ( C N ) ~ - q - 6 e ~ F e ( C N ) ~ - ( 4 6)is u s u a ll y m e a s u r e d o n a n i n e r t N i e l e c t r o d e ( g la s sy c a r b o n w o u l d s e e m a p o s s i b l ea l t e r n a t i v e ) a t t h e a n o d e t h e o x i d a t i o n

F e ( C N ) ~ - --~ F e ( C N ) g - q - 6e ( 47 )o c c u r s k e e p i n g t h e s o l u t i o n u n c h a n g e d .

( b ) T h e d e p o s i t i o n o f C u f r o m a n a c i d c o p p e r s u l p h a t e s o l u t io n , e .g . 1 .5 M H 2 SO 4 q -0 . 05 M C u S O 4. 57 M i z us h i na ~a ha s s ugge s t e d a c o r r e c t i on t o a l l ow f o r t he c om -m i t t a l r e d u c t i o n o f h y d r o g e n i o n s b u t e a r l i e r r e su l t s 57 o f R o s s s h o w a c l e a rp l a t e a u . T h e r e a c t i o n s o c c u r r i n g a r e :

A t t he c a t h od e : C u 2+ + 2e --~ C u ( 48 )A t t h e C u a n o d e : C u ~ C u 2 + 2 e . ( 4 9)

O t h e r w o r k e r s h a v e u t i l iz e d t h e r e d u c t i o n o f o x y g e n i n a 3 .5 ~o N a C I s o l u t i o n . 2sA l l t h e r e a c t io n s d i s c u s s e d s o f a r a r e u s e d s o t h a t t h e s u r f a c e d o e s n o t c h a n g e w i t h


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Electrochemical measurements n flowingsolutions 427time, indeed this is usually given as an advantage of the LCDT. However duringcorrosion both dissolution and deposition can occur leading to surface roughnessand overall shape changes. Gabe 11 has presented some results using a Cu cylinderdissolving at its LCD, and this approach would be valuable with other geometries.Similarly we are examining the possibility of modelling deposition processes (e.g.Fig. 1) using Cu deposition but allowing it to proceed and develop thick deposits.

Numerous examples of the use of the LCDT have been given in the specimencharacteristics section.Analytical applicationsAs indicated the LCD of an electrode reaction depends on both the mass transfercoefficient and the concentration driving force which is the bulk concentration whenthe transport of the relevant species to the electrode is rate controlling. Thus in voltam-metry a given geometry is used and LCD obtained in solutions of known strengths. Acalibration curve then allows the determination of any unknown concentration. Forsome geometries a theoretical curve can be obtained if solution parameters are known.There are a number of factors which in the past have limited this technique: (a)difficulty in keeping the solid electrode clean, (b) sensitivity, and (c) interfering currentsfrom reactions not of direct interest.This has led to a number of modifications to the simple voltammetric approach.Pulse vol tammetry, in which the electrode is kept clean by a programmed pulsesequence, x02Anodic str ipping vol tamm etry, in which the species are preconcentrated by cathodicdeposit ion then anodically stripped using either a one or two electrode arrangement. 13Normally the ring-disc set-up is used but other hydrodynamic geometries, i.e. aseries of concentric rings in the impinging jet, could be used.Hydrodynamic modulat ion, or by varying the rotat ion speed about a certain valuethe convective-diffusion component can be extracted in extremely unfavourable

P L AT IN U M E L E C T R O D E A N D E X IT T U B E

o ~ IG L A S S Y C A R B O N D I S C 3 ,4 r a m d i a lI

. 2mm d i0 in te t j e t ....

F IG . 26 . Ce l l used fo r vo l t am m et ry s tud ies (F lee t) .


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4 2 8 B RY AN P O ~ N

112

O .

J

_

I I I101 107 106

C O N C E N T R A T I O N C d 2"FIG. 27.

I i1 05

Typical calibration cu rve for voltamm etry (Fleet).c i r c u ms t a n c e s , s2 I t wo u l d i n p r i n c i p l e b e p o s s i b le t o d o t h i s u s i n g o t h e r g e o m e t r ie sa n d v a r y i n g f lo w r a te .

I S O s u r f a c e v o l t a m m e t r y ( I S C V A ) , o r c o n t r o l l i n g t h e s u r f a c e c o n c e n t r a t i o n ( Cs )b y s i m u l t a n e o u s l y s c an n i n g id a n d r o t a t i o n to wh i l e k e e p i n g t h e r a t i o id too, 5 c o n s t a n tc a n g i v e b o t h k i n e ti c a n d t h e r m o d y n a m i c i n f o r m a t i o n a b o u t t h e s y s t e m ,s2A n e x a m p l e o f th e t y p e o f ce ll t h a t h a s b e e n u s e d i n s u c h a p p l i c at i o n s is s h o w n i nF i g . 2 61 ~ a n d a t y p i c a l c a l i b r a t i o n c u r v e f o r t h i s c e ll u s i n g a n o d i c s t r ip p i n g v o l t a m -me t r y i s s h o wn i n F i g . 2 7 . Th e r e a r e n o t ma n y e x a mp l e s wh e r e s u c h t e c h n i q u e s a r eu s e d i n s i t u a t i o n s r e l e v a n t t o c o r r o s i o n . W e a r e c u r r e n t l y e x a m i n i n g t h e p o

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