Pq Usar Bubble

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    26 Moz ha e v , V . V . , Be c , N . a nd Ba lny , C. (1994) Biochem. Mol. Biol.Int. 34 , 191-199

    27 Kl iba nov , A . M. (1989) Trends Biochem. &i. 14 , 141-14428 Kirn , J . a nd Do rd ic k , J . S . (1993) Biotechnol. Bioeng. 42 , 772-77629 Na ka mura , K . (1990) Trends Biotechnol. 8 , 2 8 8 - 2 9 230 Ka ma t , S . V . , Be c km a n, E . J . a nd 1

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    G l o s s a r yN o m e n c l a t u r eA - Cross-sec t i ona l a rea (m 2)a - E f fec t i ve i n te r fac ia l a rea (m 1 )ab - Su r face a rea o f a gas bubb le (m 2 )B - Con stant in Eqn 1Cp - Hea t ca pac i ty (J kg 1 Kq )D - D i ffus ion co e f f i c i en t (m2s 1 )Dc - Co lumn d iam e te r (m)f - Func ti on de f i ned in Eqn 5 , Box 2g - Grav i ta t i ona l acce le ra t i on (ms 2 )h - Hea t - t rans fe r coe f f i c i en t (Wm 2 Kq )I - Ion ic s treng th (g- ion I-1)JG - Super f i c i a l gas v e loc i ty (m sq )k - T he rma l con duc t i v i ty (Wm q K q )kL - Vo lume t r i c mas s- t rans fe r coe f f i c i en t ( sq )LR A e r a te d r e a c to r h e ig h t ( m )n - Flow-behaviour indexn ' - M o l a r -f lo w ra te ( m o l s< )N 1 - F i rs t no rma l s t ress d i f fe rence (Pa )p - P r e s s u r e ( P a)p l , p 2 - P r e s s u r e a t t h e b o t t o m / to p o f t h ereac to r (Pa )R - Un i ve rsa l gas cons tan t (P a m3M -1K ~)T - Te m p e r a tu r e ( K )W - W o rk (J )

    G r e e k c h a r a c t e r s/3 - Exponent in Eqn 8, Box 2Eg - Gas holdup~, - Shea r ra te (s 1)~,' - Global shear-rate, as de fined b y Eqn 3 (s 1)r l - Genera l i zed newton ian v i sco s i ty (Pa .s )K - F lu id cons i s tency i ndex (Pa s , )/x - Visc osi ty (Pa.s)~e f f - E f fec t i ve v i sco s i ty (Pa .s )vL - K inemat i c v i sc os i ty o f the l i quid (m2s 1 )PL - Den si ty o f the l iqu id (kgm -3)o - - Su r face tens ion o f the l i qu id (kgs 2 )r - S h e a r s t r e s s ( P a)D i m e n s i o n l e s s g r o u p sBo - Bond nu mber (gDc2 PL ~-1)Ga - Gal i le i num ber (gDc3 pL2//%~2)Fr - Froude nu m ber (JG g~O.5 Dc-O.5Nu - Nusse l t numbe r (h Dc k -1)Pr - P rand tl nu mber (C p /~ k q )Pr* - Prandt l num ber o f non-newtonian l iqu ids (Eqn 8, Box 2)Re - Reynolds num ber (Dc JG v- l )Re* - Reynolds num ber o f non-newtonian l iqu ids (Eqn 8, B ox 2)Sc - Schm id t numb er (v L Dq )S h - S h e r w o o d n u m b e r ( k L D c D q ) o r ( k L D c 2 D < )Wi - W e issenberg num ber (N1 / r )

    ag i t a t ion , a s we l l a s the oxygen requ i red fo r the cu l -tu re , i s p rov ided by s pa rged a i r . In t e rna l s t ruc tu re st h a t m o d i f y t h e f l o w c h a r a ct e ri s ti c s w i t h i n t h e r e a c -t o r c a n b e i n st a ll e d; o n e s u c h m o d i f i c a t i o n , w h i c h i sga in ing inc rea s ing in dus t r i a l a ccep tance , i s t he a i r - l if treac tor(ALP. . ) (Ref . 4) . In th is a r t ic le , we review thep r inc ipa l cha rac te r i st i c s o f s imp le bubb le co lumn s tha td o n o t h a v e a n y i n t e r n a l s t ru c t u re s .AdvantagesMechanica l s impl ici tyT h e m o s t i m p o r t a n t a d v a n ta g e s o f b u b b l e c o l u m n sre s u l t f rom the i r s imp l i c i ty . As the re i s no need toi n t r o d u c e e n e r g y b y m e c h a n i c a l m e a n s , t h e s e a li n g o fthe s t i r re r - s ha f t a ss embly, w h ic h i s t he mo s t d i f f i cu l tp r o b l e m t o o v e r c o m e i n t h e m e c h a n i c a l d e s i g n o f ab io reac to r , i s e l imina ted . In add i t ion , t he abs ence o fa s haf t i n the head s pace o f the ve ss el g ive s more ro omf o r e n t r y p o r t s , a n i m p o r t a n t f a c t o r i n v e s s e l s w i t hre l a tive ly s ma l l d imens ion s .M e c h a n i c a l s i m p l i c i ty is p a r t ic u l a r l y i m p o r t a n t i nb io log ica l p roces s e s , whe re s t e r i l i t y ha s to be ma in -t a i n e d o v e r e x t e n d e d p e r i o d s . T h e a b s en c e o f sh af tse l i m i n a te s a v e r y e x p e n s iv e a n d e q u a l l y v u l n e r a b l ef e a t u re o f m e c h a n i c a l l y s t ir r e d b i o r e a c to r s , t h e r e b yincreasing process reliability.Mixing in viscousmediaI t i s gene ra l ly be l i eved tha t bubb le co lum ns a re l es ss u i t ed to p roces s e s invo lv ing h igh ly v i s cous l iqu ids .H o w e v e r , t h e r e i s e v i d e n c e t o t h e c o n t r a r y 5. In thec ase o f x a n t h a n p r o d u c t i o n , w h e r e t h e m e d i u m ish i g h l y n o n - n e w t o n i a n i n i t s r h e o l o g i c a l p r o p e r t i e s( see B ox 1 ) , me chan ica l ag i t a t ion was on ly e f fec t ive in

    a n a r r o w z o n e a r o u n d t h e i m p e l l e r , l e a v i n g a l a r g ep r o p o r t i o n o f t h e b i o r e a c t o r v o l u m e r e l at i v el yuns t i r red and , cons equen t ly , anox ic . In an ana logouss i t u a ti o n , h o w e v e r , t h e u s e o f a b u b b l e c o l u m nr e s u lt e d i n m o r e - h o m o g e n e o u s m i x i n g : t h e b u b b l esre l ea sed a t t he s pa rge r coa le s ced imm edia te ly to fo r mve ry l a rge bubb le s ( o f s imi lar d i ame te r to th a t o f thec o l u m n ) k n o w n a s sl ug s, w h i c h r o se r a p i d ly a l o n g t h ea xi s o f t h e c o l u m n , s e t t i n g t h e e n t i r e l i q u i d i n t oc i r cu l a t io n , w i t h u p w a r d m o v e m e n t n e a r t h e c y l i n d e ra xi s a n d d o w n w a r d m o v e m e n t n e a r t h e w a ll s.Shear damageM a n y c o m m e r c i a l ly im p o r t a n t b i o p r o c es s es i n v o l v eshear-sens i t ive cul tures of , for example , animal ce l ls .Shea r ing ac t ion in b io log ica l med ia i s neces s a ry fo rmix ing , mas s tr ans fe r and hea t e l im ina t ion : i ts im po r t -ance inc rea se s w i th s ca le -up . How eve r , excess ive s hea rcan dam age the ce ll s. M ech an ica l ly s t i r red b io reac to rsa r e p r o n e t o p r o d u c i n g h i g h - s h e a r r e g i o n s i n c e r t a i na re as o f t h e m e d i u m ( p a rt ic u l ar l y i n t h e v i c i n i t y o f t h ei m p e l le r , w h e r e m o s t o f t h e e n e r g y i n t r o d u c e d i s d is -s ipa ted ) , bu t l i t t l e mix ing e l s ewhe re . Howeve r , i nb u b b l e c o l u m n s , t h e t u r b u l e n c e i s d i s t r i b u t e d m o r eevenly.I n p r a c ti c e , A L R s a r e u s u al l y r e c o m m e n d e d f o rg ro win g s hea r - s ensi t ive ce ll s, becaus e o f the i r r ep u tedl o w e r s h e a r c o m p a r e d w i t h B C P ,.s . H o w e v e r , O n k e net al. s f o u n d n o p e r c e p t i b le d i ff e r en c e s i n t h e d o u b l i n gt i m e o f a n i m a l ce ll s c u l tu r e d i n B C I < s a n d A L R su n d e r t h e s a m e g r o w t h c o n d i t i o n s . T h e y a l s o h i g h -l i g h t e d t h e i m p o r t a n c e o f s p ar g e r d es i g n , a n d d i s -c u s s e d t h e r e d u c t i o n i n a n i m a l - c e l l d a m a g e c a u s e db y t h e a d d i t i o n o f b o v i n e s e r u m a l b u m i n ( B S A ).

    TIBTECHDECEMBER 994 VOL12)

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    B o x 1 . R h e o l o g yRheology is the study of f low and deformat ion of matter . Fluids tends to deform, more o r less cont inuously, when sub-jected to shear ing forces. The rate at which f lu ids deform is character ized by the shear rate (~,), and the she ar ing forceper un it area is known as she ar stress (r ) . The viscosity of a f lu id ( /~) s given by the shear stress d ivided by the shearrate ( i.e. r~ = r /7 ) . For a newtonian f lu id at a given temp erature, pressure and com posit ion, the viscosity is constant,independent of appl ied she ar, i .e. for newtonian f low: r = r~ ' (Eqn 1)where ~ is a constant. In other words, r = % Ho wever, there is another group of f lu ids, cal led non-newtonian f lu ids,for which the viscosity can change by a factor of 10 o r even 10 00 on appl ication of shear. Obviously, such an enor-mous change cannot be ignored. For such cases, i t is useful to def ine a modif ied viscosity (7) that var ies with shearrate. The rheological character izat ion of a 'generalized new tonian f lu id ' can then be descr ibed mathem atical ly as:

    r = ~/~, (Eqn 2)The beha viour of di f ferent non-newtonian flu ids is show nin the f igure The pseudoplast ic f lu ids, which f i t thebehaviour of polymers and therefore also descr ibe bio-logical exopolyme r s ystems, are of interest in biotech-nology. As can b e s een in the F ig. , the viscosity of thepseudoplast ic f lu id decreases with increasing shearrate; suc h l iquids are therefore cal led 'shear thinning' Ostwald 6, and de Waele7 suggested a mode l tha tdescr ibes the shear-rate-dependent viscosity by a'power law' :

    "q = K~ n-1 (Eqn 3)where the constants K and n are know n as the f lu id-con-sistency in dex and the f low-behaviour inde x, respect-ivelyThe power- law constants can be determined in suit -able viscometr ic apparatus, and should be carried outover the rang e of shea r exper ienced by the l iquids dur-ing the p rocess.

    00

    P s e u d o p l a s t i cN e w t o n i a n

    n t

    Shear ra te (~, )Rheology curves of newtonian and non-newtonian luids.

    T his e f fec t was a ls o obs e rved by Cr oug han e t a l . 9 o na d d i t i o n o f d e x t r an .T h e r e is e v i d e n c e t o s u g g e st th a t o n e o f t h e m a i ncaus es o f c e l l dama ge in s pa rged b io reac to rs i s r e l a tedt o t h e b u r s t i n g o f b u b b l e s t h a t d i s e n g ag e f r o m t h el i qu i d at th e t o p o f th e c o l u m n . T h i s p h e n o m e n o ng e n e r a t e s r a p i d , s u r f a c e - t e n s i o n - d r i v e n m o t i o n o ft h e l i q u i d ( A . H a n d a , P h D T h e s i s , U n i v e r s i t y o fB i r m i n g h a m , B i r m i n g h a m , U K , 1 9 78 ). I n a d d it i o n ,r u p t u r e o f t h e f il m a r o u n d t h e b u r s t i n g b u b b l e g e n -e ra te s s ma l l d rop le t s (30 -30 0 Ixm) tha t a re e j ec ted a th i g h v e l o ci t ie s 1. T h e a d d i t i o n o f P l u r o n i c F - 6 8 , apo ly me r ic add i t ive , t o BC R cu l tu re s s uppre s sed th ise f fec t r emarkab ly . T h i s i s a t t r ibu ted to the s t rong e l a s -t i c r e l axa t ion e f fec t o f the add i t ive . (T h e u s e o f add i -t ive s to redu ce s hea r dam age i s r ev iewe d in Re f . 11 .)Plant ce lls , w hi ch are a lso shear sensi tive, hav e bee ngrow n s uccess fu lly in BC R s (Re fs 12 ,13 ) . E xpe r -i m e n t a l o b s er v a ti o n s s h o w e d t h a t t h e g r o w t h o f p l a n t-cel l cu ltu re s in BC Rs , s t i r red - t ank reac to rs (ST R s ) an dshake f lasks was s imilar . B y contras t , T anaka TMr e p o r t e dtha t BC R s gave be t t e r r es u lt s t han S T R s and AL Rs a tconc entra t io ns o f ce l lu lar mater ia l up to 5 g 1-1 .I t appears , t he re fo re , t ha t the us e o f B C R s fo r s hea r -sensi tive cul tures m ay be a prac t ica l a l te rnat ive to o the rb i o r e a c t o r c o n f i g u r a t i o n s , p r o v i d e d t h a t a n a p p r o p r i -a t e p ro tec t ive agen t ( s uch a s P lu ron ic F-68 , BSA o rdex t ran ) i s employed .

    DisadvantagesT h e m a i n d i s ad v a n ta g e o f b u b b l e c o l u m n s is th a tag i t a t ion is coup led w i th th e ae ra t ion ra t e , s o ae ra t ionc a n n o t b e a l te r e d w i t h o u t c h a n g i n g t h e l e v el o f ag i -t a t ion , and v i c e v e r s a . ( T h e r a te o f o x y g e n a t i o n o f t h ec u l t u re c o u l d , h o w e v e r , b e c h a n g e d b y m o d i f y i n g t h ecom pos i t io n o f the ae ra t ion ga s s upp ly .) A no the r d i s -advan tage is tha t i t i s d i ff icul t to u se smal l -sca le expe r-imen t s to m ode l indus t r i a l p roces se s: a s the cha rac te r -i st ic s o f t h e h y d r o d y n a m i c s a r e, t o s o m e e x t e n t ,s c a l e - d e p e n d e n t , i t m a y b e d i f f ic u l t t o e x t r a p o la t efro m th e resul ts o f small -sca le exp erim ents . Final ly , therange o f ga s - f low ra te in th e b io rea c to r ha s a c l ea ru p p e r l i m i t , d e t e r m i n e d b y t h e p h e n o m e n o n o fd r o p l e t e n t r a i n m e n t . T h i s p r o b l e m i n c r e a s e s v e r ys h a r p ly a t v e r y - h i g h g a s - fl o w r at es , w h e n t h e l i q u i dm a y b e a l m o s t ' b l o w n - o u t ' o f th e r e a c to r .F l o w c o n f i g u r a t i o n s i n b u b b le c o l u m n sW i t h f e w e x c e p t io n s , t h e d i s cu s s io n o f f l o w r e g im e sand hea t and mass t r ans fe r in the pub l i s hed l i t e ra tu reare gener a l ly appl icable to l iquids wi th a v iscosi ty , o ra n e f f e c t iv e v i sc o si ty , < 5 0 m P a . s . T h e b e h a v i o u r o fbubb ly d i s pe rs ions in h igh ly v i s cous l iqu ids i s qu i t edifferent . Bubble s in suc h l iquids coalesce readi ly , andve ry l a rge bubb le s ( s ome a s l a rge a s the co lu m n d iam-e te r) fo rm in t al l co lum ns . In ad d i t ion , t he coa le s cenceo f b u b bl e s i n t h e b u l k v o l u m e o f su c h l i q u id s , a n d t h e

    TIBTECH DECEMBER 1994 (VOL 12)

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    C o a l e s c e d - b u b b l e r e g i m eS lug g ing / -. .. .. .. .~ - ~ ( he t e r og ene ous )r eg im e ~ - " "- - -~ - " ~ I oO o e lI ~ o / ' - ~ " - - - J I < >< >Q I

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    C o l u m n d i a m e t e r D C ( m )F i g u r e 1

    F low r eg im es i n bubb le c o lum ns ( fr om Re f . 21 ) . T he d i s pe r s ed - bubb le r eg im e , c ha r -ac t e r iz ed by bubb les tha t hav e m or e o r l es s t he s am e s i z e as thos e p r oduc ed by t h es pa r ge r , i s obs e r v ed i n a ll c o lum ns , r ega r d les s o f t he i r d iam e t e r , whe n t he s upe r -f ic i a l gas v e loc i t y i s low ( < O . 04m s q) . T he c oa les c ed - bubb le r eg im e , c ha r ac t e r iz ed bybubb le coalescen ce and bu lk - l iqu id c i rcu la t ion, is observe d in co lumn s wi th a d iam-e t e r o f 0 . 2 m o r m o r e a t h i ghe r s up e r fi c ia l gas v e loc i t i es ( > 0 . 075 m s - i ) . F ina l l y, s l ug -g ing r eg im e , c ha r ac t e r i z ed by t he c y l i nd r i c a l bubb les b r idg ing t he c o lum n , i sobs e r v ed i n c o lum ns w i t h s m a l l e r d i am e t e r s ( _< 0 . 1m ) , a t s upe r f ic i a l gas v e loc i t i es> 0 . 0 4 m s 4 .

    break up o f bubb le s a t t he s u r face , gene ra te s ve ry t in ybubb le s , r e s u l t ing in an appa ren t ly b imoda l d i s t r i -b u t i o n o f b u b b l e s i ze . H y d r o d y n a m i c s a n d m a ss t r a n s-f e r i n t h e s e h i g t d y v i s c o u s n e w t o n i a n a n d n o n -n e w t o n i a n l i q u id s is a n i m p o r t a n t a r ea o f c u r r e n tresearch a c t iv i ty s

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    i n cr e as e s a t th e e x p e n s e o f t h e c e n t r al p a t h w h i c h ,un de r the s e con d i t ions , cons is ts o f the l a rge s t bubb le s .A c l ea r d o w n w a r d f l o w o f h q u i d d e v e l o p s, b r i n g i n gt h e s m a l le s t b u b b l e s t o t h e b o t t o m o f t h e c o l u m n . A th igh e r va lue s o f s upe r f ic i a l ga s ve loc i ty , t he wav y f lowa l o n g t h e c o l u m n a x is is d a m p e d , a n d m o s t o f t h e g aspas s e s rap id ly th rough the cen t re . A t the s ame t ime ,t h e l o o p o n e i t h e r s id e b e c o m e s e v e n m o r e t u r b u l e n t ,a n d t h e d o w n w a r d f l o w o f r e c i r c u la t i n g l i q u i d isc lear ly vis ib le a lo ng the co lu m n wal ls (Fig . 2c).T h e c h a n g e i n f l o w p a t te r n ( d e p i ct e d b y t h e t r a n -s i t ion f rom F ig. 2b to F ig. 2c ) co r re s ponds to the ' t r an -s i t i o n r e g i m e ' , a p h e n o m e n o n r e p o r t e d i n b u b b l eco lum ns wi t h a s pa rge ho le

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    reviewsBox 2. Dimensionless corre lations

    Di m ens ion l es s c o r r e l a t i ons a r e a s t and a r d t oo l us ed i n c hem i c a l eng i nee r ing to gene r a l i z e and c o r r e la t e r es u l t s ov e r a w i de r ange o fgeom e t r i c d i m en s i ons and phy s i c oc hem i c a l v a r i ab les . W hen the r e l a ti ons h i p be t ween t he p r oc es s v a r i ab l es is c l ea r ly unde r s t ood , i ti s pos s i b l e to de r iv e , f r om f i r s t p r i nc i p l es , an equa t i on o r a s e t o f equa t i ons r e l a t ing t hes e v a r i ab les , wh i c h a r e d i m ens i ona l l y c ons i s t -en t . D i v is ion by o ne o f t he t e r m s w i l l t hen gene r a t e a s e r i es o f d i m ens i on l es s g r oups , eac h w i t h a c l ea r ly unde r s t ood phy s i c a l m ean -i ng . Howev e r, i n p r ac t ic e , w e do no t und e r s t and how d i f f e r en t p r oc es s v a r iab l es a r e r e la t ed . I ndeed , we s e l dom k now l i t tl e m o r e t hant he f ac t t ha t t he v a r iab l es unde r c on s i de r a t ion a r e r e l a ted . I n s uc h s i t ua t i ons , whe r e l im i ted k now l edge o f t he phenom enon s t ud i eddoes n ot a l low ex p l i c i t d ime ns iona l l y con s i s ten t equ at i ons to be ded uced , the pr i nc i p l es o f d imens iona l ana l ys is , es tab l i shed by R ay le ighand B uc k ingham , a r e us ed ( s ee Re f . 38 ) . D i m ens ion les s g r oups us ua l l y r ep r es en t t he r a t i o o f t wo c o m pe t i ng phenom ena . A h i gh v a l ueo f t he ex pon en t o f the d i m ens i on l es s g r oup i n t he c o r r e l a t i on i nd i c a t es t ha t t he r e l ev an t phenom ena a r e o f c ons i de r ab l e s i gn i f ic anc ei n t he p r oc es s .I t has bec om e c u s t om a r y t o nam e t h e d i m e ns i on l es s g r oup s a f t e r the s c i en t i s t wh o m ade t he m o s t s i gn i f ic an t c on t r i bu t i on t o t hedev e l opm en t o f t he r e l a t ed f i e ld o f s c i enc e and t ec hno l ogy . F o r ex am p l e , m as s - t r ans f e r c oe f f ic i en t s a r e us ua l l y ex p r es s ed i n t e r m so f S he r wood num ber s , hono u r i ng t he A m er i c an s c i en t i s t T hom as K . S he rwood :

    S h = kLDD (Eqn 1)A s k L c anno t be d e t e r m i ned ex p l i c i tl y in p r ac t i c e , i t i s p r ude n t t o us e t he v o l um e t r i c m as s - t r ans f e r c oe f fi c ien t , k La , and c o ns eq uen t l ym od i f y t he S he r wood num ber as :

    Sh* - kLaDc2D ( E qn 2 )T he S he r wood num ber ev i den t l y r ep r es en t s t he r a t i o o f m as s - t rans f e r r a t e t o m o l ec u l a r d if fus iv it y, and i t has p r ov en v e r y us e f u l i nt he c o r r e l a t i on o f ex p e r i m en t a l r es u l t s in m as s t r ans f e r .C o r r e l a t i o n s f o r m a s s - t r a n s f e r c o e f f i c i e n t(1) Ak i ta and Yosh ida 's cor re l a t i on 39

    / - , 0 5 / ~ 2 - ~ 0 . 6 2 / ~ 3 " ~ 0 '3 1kLaDc2 _ 0 6 ( V L ) ' l g U c ~ P L I / g U c l E : g l . 1D t J t , " 2 Jo r i n t e r m s o f d i m ens i on l es s g r oups :

    Sh = 0. 6 Sc 0.5 Bo 0.62G a0.31Egt.1whe r e t he gas h o l dup was c o r r e l a t ed f o r pu r e l iqu i ds and non - el ect ro l yt e s o l u t i ons as:

    (Eqn 3)

    o r :

    / D 2 , , 1 / 8 / D 3 - , 1 / 1 2 / ~ , 1 . 0_ _ 0 2 / g c p L / [ g o / [ JG |~ g ) 4 t j t - -C JE 0.2 Bo 1 /8 Ga 1/12 Fr 1(1 E ) 4 ( E qn 4 )

    F o r s a l t s o l u t ions , t he c oe f f i c i en t 0 . 2 i s rep l ac ed by 0 . 25 .(2) Hiki ta e t al . cor re l a t i on 4o [ j "~ 1 "7 6 " # 4 g " ~ - 0 2 8 4 ~ 0 ' 2 4 3 / I ,L / - 0 , 6 0 4k L a = 1 4 " 9 g f l G / ~- ~LL / / ~ / / ~ - - ~ / ( E qn 5 )

    whe r e t he v a l ue o f f c hange s ac c o r d i ng t o t he i on ic s t r eng t h o f t he e l ec t r o l y t e s o l u t ion . F o r non -e lec t ro l yt e s o l u t ions , f = 1 . 0 , an d f o re l ec t r o l y te s o l u t ions , f depe nds on t he i on i c s t reng t h as f o l lows :For 0 < I < 1 .0 g- i o nH , f= 1 0 o .o681F o r I > 1 . 0 g - i o n H , f = 1.1 14 .10 o .o211(3) Suh et a l . correlat ion5For non-newton ian li qu ids w i th e f fec t i ve v isco s i t i es h i gher than 4m Pa .s , Suh et a l . 5 p r opos ed t he f o l low i ng c o r r e l a ti on :

    S h = 0 . 0 18 S c o -5 B oo.2 Gao.62 Fr o.51 1+ 0.1 2W i ] -1t he e f f ec t iv e v i s c os i t y is c a l c u l a ted f r om E qn 3 , B ox 1 , and 1 ' i s ob t a i ned f r om E qn 1 t ak i ng B = 280 0 .

    (Eqn 6)

    T I B T E C HD E C E M B E R 9 9 4 (V O L 1 2 )

  • 8/9/2019 Pq Usar Bubble

    7/11

    5 0 7reviews

    Bo x 2 . D i me n s i o n l e s s c o r re l a t i o n s ( c o n t i n u e d )Hea t - transfer corre la t ionsF or t he c o r r e l a t ion o f t he hea t -t rans fe r c oe f f i c ien t s , t he d i m e ns i on l es s g r oup us ed m o s t f r equen t l y has been nam ed a f t e r t he G e r m ans c i en t i s t E r ns t K r a f t W i lhe lm N us s e l t ( 18 82 - 19 57 ) . T he N us s e l t num be r i s de fi ned as :

    N u = h D ck (Eqn 7)and i t s i gn if ie s t he r a t i o o f t u r bu l en t hea t tr ans f e r t o pu r e hea t c onduc t i v i ty . I t i s , t he r e f o r e , a na l ogous t o t he S he r wood num ber( wh ic h i s a l s o c a l l ed t he N us s e l t num be r f o r m as s t r ans f e r ).K awas e and M oo - Y oung 's c o r r e l a t ion f o r hea t t r ans f e r c o e f f ic i en t 41

    Nu = 0 . 075 ( 10 . 3 n - O . 63 ) n l / 3 (Pr* ) l /3 Fr "# (Re*)~+3(n+1)w h e r e :

    # = ( 4 - n ) / [ 6 ( n + 1 ) ] ; P r* = ( K D l - a C p ) / ( k JGl -" ) ; and Re* = (p Dc"JG2-n) /KT h i s equa t i on r educ e s f o r new t on ian l iqu i ds to :

    Nu = 0 . 13 4 p r l / 3 F r -1 / 4 Re3 /4

    (Eqn 8)

    (Eqn 9)

    t h e v o l u m et r i c m ass - t r an s fe r co ef f i c i en t i n c reases l i n -ea r l y wi th i n c reas in g su p er f i c i a l g as v e lo c i t y . Th ei n c r e a s e i n g a s - f l o w r a t e i n c r e a s e s t h e n u m b e r o fb u b b l es , b u t n o t t h e i r sh ap e as, u n d er t h ese co n d i t i o n s ,t h e r e a r e n o i n t e r a c t i o n s b e t w e e n b u b b l e s . F u r t h e rincreases in th e sup erf icial gas velo ci ty resu lt s in a less-t h a n - l i n e a r i n c r e a s e i n t h e v o l u m e t r i c m a s s - t r a n s f e rco ef f i c i en t , as a r esu l t o f co a l escen ce , wh ic h ch an g est h e i n te r r a ci a l a re a p e r u n i t v o l u m e o f g as .T h e s p a r g er d e t e r m i n e s t h e i n i ti a l b u b b l e s i z e a n dsh ap e i n a g iv en li q u id . A sp arg er wi th smal l d i am-e t e r h o l es , su ch as a p e r fo ra t ed o r s i n t e r ed p l a t e , w i l lg en era t e smal l e r b u b b l es t h a n a s i n g l e o r i f i ce sparg er ,a n d w i l l t h e r e f o r e p r o v i d e a h i g h e r i n t e r r a c i a l g a s -l i q u id co n t ac t a r ea i n t h e v i c in i t y o f t h e sp arg er.

    T h e m e a n b u b b l e s iz e i n t h e c o l u m n a s a w h o l e i sd e t e r m i n e d b y t h e e q u i l i b r i u m b e t w e e n b u b b l e c o -a l e s c e n c e a n d b r e a k u p , w h i c h d e p e n d s b o t h o n t h ep h y s i c o c h e m i c a l p r o p e r t ie s o f t h e l i q u i d a n d t h e t u r b u -lenc e levels. T he re i s a cr i t ical bub ble s ize that c an ex is ti n a g iv en l i q u id u n d e r g iv en f l u id -d y n amic co n d i t i o n s ,su ch t h a t an y b u b b l e l a rg e r t h an t h i s s i ze wi l l t en d t ob r e a k d o w n . I n n o n c o a l e s c i n g li q u id s , t h e b u b b l e sr e l eased b y t h e sp arg er, i f smal l e r t h an t h e c r i t i ca l si ze ,w i l l d e t e r m i n e t h e m e a n s i z e . I f , o n t h e o t h e r h a n d ,t h e r e l eased b u b b l es a r e la rg e r t h an t h e c r i t i ca l s i ze ,t h e y w i l l b re a k , a n d t h e m e a n s iz e w i l l b e c l o s e to t h ec r i t i ca l v a lu e . By co n t r as t , f o r co a l esc in g li q u id s , t h em ea n b u b b l e s i ze wi l l b e c lo se to t h e c r i t ica l b u b b l esize, regard less o f the in i t ia l s ize d is t r ibu t ion .

    P r o p e r t i e s o f t h e l i q u i d m e d i u m , s u c h a s v i s co s i tyan d su r f ace t en s io n , a f f ec t k L a . As gas i s sparged ,l i q u i d m o v e m e n t i s i n i ti a t e d a n d a g a s - l i q u i d i n t e rf a c ei s c r e a te d . T h e n a t u r e o f t h e o p e r a t i o n o f p n e u m a t i -ca l l y ag i t a t ed r eac to r s su ch as b u b b l e co lu m n s d o es n o tp e r m i t t h e a e r a t i o n p ro c e s s t o b e s e p a r a te d f r o m t h emix in g p ro cess . Ch an g es i n t h e su p er f i c i a l g as v e l -

    o c i t y w i l l t h e r e f o r e al t er b o t h h q u i d - p h a s e m o m e n -t u m a n d m a s s t r an s fe r . T h e v i s c o s it y o f t h e l i q u i d ,w h i c h is a p r o p e r t y a f f e c t in g t h e l i q u id - p h a s e m o m e n -tu m , w i l l al so h av e a s t ro n g e f f ec t o n v o lu me t r i c masst r ans fe r . A l t h o u g h k i s a f f ec t ed b y v i sco s i t y t o so m eex t en t , t h e e f f ec t i v e i n t e r r ac i a l a r ea ( a) is mu c h m o resen s i ti v e t o i t. I n ad d i t i o n , t h e su r f ace t en s io n a f f ec t sb u b b l e c o a l e s c e n c e a n d b r e a k u p , a n d t h e r e f o r e a ls oaf f ect s t h e i n t e r r ac i a l a r ea , a l t h o u g h t h e me ch a n i sm b yw h ic h t h is o cc u r s i s st il l n o t c l ear . I n t h e case o f smal lb u b b l e s ( d < 1 0 m m ) , t h e p r e s e n c e o f s u r f a c e - a c ti v eagents wi l l a l so af fect kL b y c o n t r o l l i n g t h e r i g i d it y o ft h e b u b b l e s u r fa c e34.

    T h e a c t u a l m e c h a n i s m o f m a s s tr a n s f e r f r o m ab u b b l e i n to l i q u id h as n o t y e t b ee n e lu c id a t ed ful ly .E a r l y w o r k b y B a i r d a n d D a v i d s o n 35 a s s u m e d t h a t t h emass t r an s fe r f ro m a sp h er i ca l , cap - sh ap ed b u b b l e ( t h es h a p e c o m m o n l y o b s e r v e d i n b i o lo g i c a l m e d i a ) t ak e sp l a ce t h r o u g h t h e b o u n d a r y l ay e r s u r r o u n d i n g t h eb u b b l e ; t h is d o e s n o t i n c l u d e t h e r e a r o f th e b u b b l ei n t e r f a c i n g w i t h t h e w a k e , a n d t h e c o n t r i b u t i o n o f t h ewa k e r eg io n t o mass t ran s fe r i s t h u s i g n o red . B y co n -t ra s t, C o p p u s a n d R i e t i m a 36 s h o w e d t h a t t h e c o n t r i -b u t i o n o f t h e w a k e r e g i o n c a n n o t b e n e g l e c te de n t i r e l y . T h e y c o n c l u d e d t h a t m a s s t r a n s f e r o c c u r ss i m u l t a n e o u s ly f r o m t h e f r o n t a n d r e a r , a n d t h e c o n -t r i b u t i o n o f t h e r ea r t o t h e t o t a l mass t r an s fe r can b eas h ig h as 2 0 -3 0 % in ce r t a i n cases . R ec en t i n v es t i -g a t io n s b y S c h m i d t a n d L u b b e r t 37 also suggest that thew a k e b e h i n d t h e b u b b l e p l a y s a m o r e i m p o r t a n t r o l ei n m a ss t r a n s f e r t h a n p r e v i o u s l y t h o u g h t . T h e yo b serv ed t h a t t h e mass t r an s fe r r ed ac ro ss t h e b u b b l eb o u n d a r y l a y e r a l m o s t i n v a r i a b l y f o u n d i t s w a y i n t oth e wak e , f ro m wh ere i t was d i s s i p a t ed i n to t h e b u lk .I f t h is i s e s t ab l ish ed co n c lu s iv e ly , t h en we can v i su a l -ize mass t ransfer as tak ing p lace in two s tages: t ransferac ro ss t h e b u b b l e i n t e r f ace i n to t h e wak es ; an d

    TIBTECHDECEMBER1994(VOL12)

  • 8/9/2019 Pq Usar Bubble

    8/11

    5O 8reviews

    su b seq u en t d i s s i p a t i o n i n to t h e b u lk . Th i s wo u ld l eadto s i g n i f i can t mo d i f i ca t i o n o f cu r r en t , we l l - es t ab l ish edth eo r i e s o f mass t r an s fe r .Scale-upT h e p r o b le m s e n c o u n t e r e d i n t he s c a l e- u p o f b i o -r e a c t o r s c a n b e c a t e g o r i z e d i n t o t w o g r o u p s . O n ec o v e r s t h e c a se s w h e r e a h i g h p o w e r i n p u t p e r u n i tv o l u m e i s u s e d a t t h e l a b o r a t o r y s ca le , b u t c a n n o t b ea t t a i n ed a t an in d u s t r i a l sca le , b ecau se o f ec o n o m ic o rme ch an i c a l limi t a t i o n s . Ob v io u s ly , th i s g ro u p d o es n o ti n c l u d e p l a n t o r a n i m a l c u l t u r e s , w h e r e h i g hs p e c if i c p o w e r i n p u t c a n n o t b e t o l e r a t e d b e c a u s e o fc e l l f ra g il it y . T h e o t h e r g r o u p c o m p r i s e s p r o b l e m sr e l a ti n g to a l a c k o f k n o w l e d g e o f h y d r o d y n a m i c s i nl a rg e -v o lu me v essel s.In general , b ioprocesses invo lve several s teps: masso r h e a t t r a n s f e r b y c o n v e c t i o n ; t r a n s f e r b y d i f f u s i o nme ch an i sms ( f ac i l it a t ed o r o th e rwi se ) ; an d ca t a ly t i cr eac t i o n s . I n t h e case o f ca ta ly t ic r eac t i o n s , h ea t an dmass t r an s fe r a re i n t eg ra l t o t h e p ro cess , a s mo lecu l esm u s t e n c o u n t e r e a c h o t h e r i n o r d e r t o r e a c t , a n de n e r g y ( h e at ) t r a n s f e r w i l l a c c o m p a n y t h e r e a c t i o n .D e p e n d i n g o n w h e t h e r t h e s e st ep s a r e i n p a ra ll e l, o ri n se r i es, an d o n t h e i r r e l a t i v e v e lo c it i e s , t h e o v era l lr a t e o f t h e p ro cess m ay b e l im i t ed b y a s i n g le s tep . Th ee q u i l ib r i u m b e t w e e n t h e i n d i vi d ua l c o m p o n e n t r a te scan b e ( an d u su a l l y i s) a l t e r ed b y a ch an g e i n t h e sca leo f t h e s y s te m : a l t h o u g h a c h a n g e i n s c a l e d o e s n o tc h a n g e t h e p h y s i c o c h e m i c a l o r k i n e t i c p a r a m e t e r s( sca l e - i n d ep en d en t v a r i ab l es ) , i t d o es a f f ec t t h e o v er -a ll co n v ec t i v e mass - an d h ea t - t r an s fe r r a t es ( sca l e -d e p e n d e n t v a r i ab l es ) . T h u s , f o r t h e s a m e s y s te m , o n ad i f fe r e n t s c al e, a n e w e q u i l i b r i u m b e t w e e n t h e r a t eso f t h e m a n y s te p s o c c u r r i n g m a y b e e s t a b li s he d , a n dt h e i n t e r p l a y o f a ll t h e p a r a m e t e r s m a y l e a d t o a r e g i m ew h er e a d i f f e r en t s t ep is co n t ro l l i n g t h e p ro cess r a t e .

    K n o w l e d g e o f t h e m i x i n g , h e a t - a n d m a s s - t ra n s fe rr a te s , a n d t h e i r d e p e n d e n c e o n t h e d i m e n s i o n s o f t h eb io reac to r a r e t h e re fo re b asi c r eq u i r emen t s fo r p ro cesssca l e -u p . Th i s i n fo rmat io n , a s we l l a s t h e en erg y r e -qu i rem ents fo r a g iven ope rat ion , i s available in the fo rmo f co r r e l a t i o n s th a t ca n b e u se d i n d es ig n eq u a t i o n s .M a s s - t r a n s f e r c o r r e l a t i o n s

    Th e v o lu met r i c mass - t r an s fe r r a t e (k t a ) i s , p e rh ap s ,t h e k e y p a r a m e t e r t o c o n s i d e r i n t h e d e s i g n a n d s c a l e-u p o f a r e a c t o r. T h i s p a r a m e t e r m a y b e e v a l u a t e d u s in gco r r e l a t i o n s t h a t a r e av a i l ab l e i n t h e t ech n i ca l l i t e r a -t u r e ( s ee ' :' B o x 2 ) , o r b y e x t r a p o l a t i n g f r o m e x p e r -i m e n t a l d a t a . I t i s , h o w e v e r , n o t u n c o m m o n t o f i n dth a t d i f f e r en t co r r e l a t i o n s p red i c t d i f f e r en t v a lu es fo rk t a . T h e s e d i f f e re n c e s ar e s o m e t i m e s r e l a t e d to t h ee x p e r i m e n t a l m e t h o d s u s e d t o d e t e r m i n e t h e m . M a s s -t r a n s f e r c o e f f i c i e n t s c a n b e d e t e r m i n e d f o r e i t h e rl a b o r a t o r y - o r i n d us t r ia l - sc a l e e q u i p m e n t u s i n g a n y o fsev era l ex p er im en ta l met h o d s ( fo r d e t ai l s, s ee Bo x 3 ) .N e w t o n i a n l i q u i d s

    Ak i t a an d Yo sh id a 39 r ep o r t e d a co r r e l a t i o n fo r k L ad e d u c e d f r o m e x p e r i m e n t a l d a ta o b t a i n e d u s i ng w a t er ,

    v a r i o u s a q u e o u s i o n i c s o l u t i o n s , a n d m e t h a n o l a n dg ly co l so lu t i o n s i n b u b b l e co lu m n s o f d i f f e r en t si zes( see Bo x 2 ) . Th i s i s t h e m o s t r e l i ab l e an d w id e ly u se dc o r r e l a t i o n to d a t e , a n d it is r e c o m m e n d e d f o r a c o n -se rv a t iv e es t imat e o f k L a . T h i s c o r r e l a t i o n p e r m i t s t h ee v a l u a ti o n o f k L a i n a c o l u m n o f d i a m e t e r / ) o f o r a g asw h o s e m o l e c u l a r d i f fu s i vi ty i n t h e l i q u i d i s D . T h e s et h r e e v a r ia b l es a r e c o m b i n e d i n t o a s i n g le d i m e n s i o n -l e s s g r o u p , t h e S h e r w o o d n u m b e r , w h o s e v a l u e c a nb e ca l cu l a t ed as a fu n c t i o n o f t h e su p er f i c ia l g as v e l -o c i t y i n t h e c o l u m n , t h e c o l u m n d i a m e t e r , a n d th ephysical p rope r t ies o f the l iq u id - v iscosi ty , d i f fusiv ity ,d en s i t y an d su r f ace t en s io n .Hik i t a e t al . 4 measu red t h e v o lu m et r i c mass - t ran s fe rco ef f i c i en t i n b u b b l e c o lu mn s wi th e l ec t ro ly t e an dn o n e l ec t ro ly t e so lu t io n s , u s in g v a r i o u s g ases (B o x 2 ) .T h e y i n t r o d u c e d a t e r m f o r t h e g a s d e n s i t y i n t o t h eexpression . However , gas-phase proper t ies are general lyd e e m e d n o t t o b e o f c ri ti c al c o n c e r n i n t h e d e s i g n o fb ioreactors , un l ike in cer tain chemica l reactors , a l thou ghin t e res t in t h e ro l e o f gas p ro p er t i e s o n t h e p e r fo r ma n ceo f b u b b l e co lu mn s h as r ecen t l y b ee n r ev iv ed44.N o n - n e w t o n i a n l i q u i d s

    B i o l o g i c a l m e d i a a r e o f t e n vi s c o u s a n d n o n -n e w t o n i a n , a n d t h u s c o m p l i c a t e t h e m a t h e m a t i c a lt r e a t m e n t o f m a ss t r a n sf e r, b e c a u s e o f t h e v a r i a t i o n o fv i sco s i t y wi th sh e ar - r a t e ( see Bo x 1 ) . An ap p ro a ch t h a ti s f r e q u e n t l y u s e d t o p r e d i c t k L a i n n o n - n e w t o n i a nl iq u id s w a s p r o p o s e d b y N i s h i k a w a e t al . 45. T h e y s t ud -i e d t h e p r o b l e m o f h e a t t r a n sf e r i n b u b b l e c o l u m n san d c o r r e l a t ed t h e sh ear r a t e wi th t h e su p er f i c ia l gasv e l o c i t y f o r / G > 0 . 0 4 m s -1 a s:

    T = B.JG (Eq n 1)w he re T is the shear rate i n s-1 ,. /G is the superf icial gasv e lo c i t y i n m s -1 , an d B i s a co n s t an t e s t im at ed as 5 0 0 0 .T h i s s h e a r r a t e is th e n u s e d i n t h e p o w e r l a w ( se e B o x1 fo r d e f i n i t i o n ) t o ca l cu l a t e a me an v a lu e o f ap p are n tv i s c os i ty f o r t h e w h o l e r e a c t o r ( s ee B o x 1 ). H e n z l e re t a l . 46 , K a w a s e a n d M o o - Y o u n g 41, S c h u m p e a n dD e c k w e r47, Za idi e t a l . 4 8 , D e c k w e r e t al . 49 a n d G o d b o l ee t aL s o h av e a l l ap p l i ed Eq n 1 t o d ev e lo p t h e i r r e sp ec t iv ec o r r e l a t io n s f o r k t a , b y t ak in g v ar i o u s v a lu es o f B i nth e r an g e Dc < B < 3 0 0 0 fo r ca l cu l a ti n g t h e ap p a ren tv i sco s i t y . S imi l a r co r r e l a t i o n s fo r v i sco e l as t i c n o n -n e w t o n i a n l iq u i ds i n c l u d e t h e r e l a x a t i o n t i m e o f t h el i q u id i n t e r m s o f th e D e b o r a h n u m b e r s l, o r t h e ' f ir s tn o r m a l s tr es s' d e r i v e d f r o m t h e e q u a t i o n o f c o n s e r -v a t io n o f m o m e n t u m i n t h e f o r m o f t h e W e i s s e n b er gn u m b e r s ( s e e B o x 2 ).

    Th e co n s t a n cy o f B i n Eq n 1 i s q u es t i o n ab l e , a s i tp r ed i c t s t h a t l i q u id s t h a t h av e d i f f e r en t rh eo lo g i ca lp r o p e r t i e s h a v e t h e s a m e s h e a r r a t e a t a g i v e n s u p e r -f i ci a l g as v e lo c i t y . Hen c e , sh ear r a t es ca l cu l a t ed f ro mE q n 1 s h o u l d o n l y b e u s e d i n r e le v a n t e q u a t i o n s t oca l cu l a t e k L a , a n d s h o u l d n o t b e u s e d t o d e s c r i b eh y d r o d y n a m i c s .

    A n o v e l a p p r o a c h w a s s u g g e s t e d b y M e r c h u k a n dB e n - Z v i s2, w h i c h i n v o l v e d th e e v a l u a t io n o f a m e a nTIBTECH DECEMBER 1994 (VOL 12)

  • 8/9/2019 Pq Usar Bubble

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    5 0 9reviews

    B o x 3 . M e a s u r e m e n t o f t h e m a s s - t ra n s f e r c o e f fi c ie n t

    The f i gu re shows the methods used to de te rmine themass-transfer coeff ic ient kLa. I t shows that: (1) a l l themethods compare the pe r fo rmance o f the rea l sys temwi th tha t expec ted f rom a mathem at i ca l mode l ;(2 ) mode ls rep resen t a s imp l i f i ed (amenab le to ma th -emat i ca l t rea tmen t ) desc r ip t i on o f the sys tem; and(3 ) k L a i s n o t a r e a l p r o p e r t y o f t h e s y s te m , s u c h a stempera tu re , p ressure o r su r face tens ion , bu t i s aparamete r o f the mode l .Mode ls fo r gas - l i qu id m ass t rans fe r do no t on l y con-s ide r the mic roscop ic descr ip t i on o f gas- l i qu id i n te r -face where mass t rans fe r takes p lace , bu t a l so thema croscop ic d escr ip t ion of the reactor , including thelevel of mix ing in both the gas and l iqu id phases ( i .e .whe the r these phases have a un ifo rm com pos i t ion o rno t ) . I f a me thod to de te rmine the mass- t rans fe r coe f -f i c i en t i s be ing s ough t fo r a g i ven b io reac to r , i t isex t reme ly impor tan t to cons ide r the assumpt ions under -p inn ing the method and to check the i r app l i cab i l i t y tothe s i tuat ion under considerat ion.Regard less o f the assumpt ions under l y ing the mode l ,the methods use d to de te rmine m ass- t rans fe r coe f -f ic ients can be c lassi f ied in to those based on steady-s ta te measurem ents and those based on t rans ien tresponses . De ta i l ed descr ip t i ons o f va r i ous methodsare g i ven by Atk inson an d M av i tuna42 .In bubb le -co lumn b io reac to rs , the ga s p hase ( i .e . a i r )i s a lways con t i nuous , w h i le the l iqu id phase m ay e i the rbe con t inuous o r (more o f ten ) ba tch . T rans ien t me thodsare based on app ly ing a change in the concen t ra t i on o fthe oxygen in the gas phase , and con t i nuous l y reco rd -ing the con centrat ion of d issolved oxyg en in the l iqu id

    In p u t f ( c )

    /

    R e s p o n s ef(kLa)

    \

    ~ _ _ _ ~ C o m p a r e a n d c h o o s e t h e k L a t h a t ~g i v e s t h e b e s t fit

    kk aThe s tep s involved in the determinat ion of the mass-transfercoefficient, kLa.

    phase . The resu l ts p red i c ted by the m ode l re la ti ng d i sso lved oxyge n w i th t ime a re then compared w i th those ob ta inedexper imen ta l ly and , as show n in the F ig . above , the va lue o f the m ode l pa rame te r , kLa , ha t g i ves the bes t f i t i s se lec ted .One o f the m a in p rob lems w i th the t rans ien t m e thod i s the l ag t ime o f the oxygen e lec trodes used to de te rmine theleve l o f d i sso lved oxygen . The d i s to r ti on i n the me asured va lues , resu l t ing f rom p robe- response dyna mics , tends tocomp l i ca te the uns teady-s ta te m ethods used to de te rmine kLa . Param ete rs tha t descr ibe the p robe- response dy-namics w i l l become an i n f l uen ti a l fac to r i n the ca l cu la t i on o f kLa , pa r t icu la r ly wh en the va lue o f kLa i s approx ima te l yequa l to o r g rea te r than the i nve rse o f the p robe- response t ime . I t has been sugges ted 43 tha t th i s can be so l ved i nsome cases b y trunca t ing the i n i ti a l po r t ion o f the e lec t rode response .Whatever the method used to ca l cu la te k L a , he bas i s o f the techn ique i s the com par i son o f the m easured va r iab lew i th the va lue (o r va lues) tha t a mathema t ica l mo de l o f the p roce ss p red i c ts . I t has been po in ted o u t tha t the cho iceo f the m ode l i s ve ry imp or tan t and p oor assum pt ions on f low charac te r is t i cs and mix ing l eve ls in gas o r l i qu id phasesmay lead to s ign i f ican t e r ro rs 3 .

    sh ear - r a t e , a l so k n o wn as t h e g lo b a l sh ear - r a t e , o v ert h e e n t i re v o l u m e o f t he b u b b l e c o l u m n , b a s ed o n ktam e a s u r e m e n t s . T a k i n g t h i s a p p r o a c h , a s u r p r i s i n g l ys i m p l e e q u a t i o n w a s f o u n d t o c o r r e l a t e th e v o l u m e t r i cmass - t r an s fe r co ef f i c i en t wi th t h e g lo b a l sh ear - r a t e fo rb o t h n e w t o n i a n a n d n o n - n e w t o n i a n l iq u id s :

    kLa = 1 .4 X 1 0 6 T '1 .7 0 (Eq n 2 )wh ere t h e g lo b a l sh ear r a t e i s g iv en b y :

    T ' =~ l / n( N J g l n ( p ] / p 2 )

    (Eq n 3 )

    A c o m p a r i s o n o f t he p r e d i c ti o n s o f E q n 2 w i t hsev era l s e ts o f ex p er im en ta l d a t a i s sh o wn in F ig . 4 .E v e n t h o u g h s o m e o f t h e d a ta , p a r t ic u l a r ly t h o s e o fN a k a n o h a n d Y o s h id a s l, d e v i a t e c o n s i d e r a b l y f r o mt h e m o d e l , t h e v a r i a t i o n o f kLa w i t h t h e g l o b a lsh ear - r a t e sh o ws t h e same t r en d fo r a l l t h e d a t a se t s ;t h i s i n c l u d e s n e w t o n i a n a s w e l l a s n o n - n e w t o n i a nsy s t ems . I t i s ev id en t t h a t t h i s ap p ro ach can l ead t ot h e d e v e l o p m e n t o f a g e n e r a l c o r r e l a t i o n fo r t h em a s s - t r a n sf e r c o e f f i c i e n t i n t e r m s o f t h e g l o b alsh ear - r a t e , ap p l i cab l e t o an y l i q u id , r eg ard les s o fw h e t h e r i t is n e w t o n i a n o r n o n - n e w t o n i a n . A d d i -t i o n a l d a t a a r e r e q u i r e d t o s t r e n g t h e n t h i s p r o m i s -i n g a p p r o a c h , i n o r d e r t o e x p a n d i t s r a n g e o fappl icab i l i ty .

    TIBTECH DECEMBER 1994 (VOL 12)

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    0 . 1 a008 /0 . 0 6 -0 . 0 4 -0 . 0 2 - , ~ , b c . -

    0 ~ ' ~ , ,, , ~)0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0G l o b a l s h e a r r a t e ( s - 1)

    e

    F i g u r e 4V o l u m e t r i c ma s s - t r a n s fe r c o e f f i c i e n t f o r n e w to n i a n a n d n o n - n e w -to n i a n l i q u i d s a s a f u n c t i o n o f s h e a r -r a te i n b u b b l e c o l u mn s . ( a ) Th eg l o b a l a p p r o a c h ; ( b ) , ( e ) , ( d ) a n d ( e ) a r e c u r v e s d e d u c e d f r o m th ec o r r e l a t i o n s o f G o d b o l e e t a L s o , S c h u m p e a n d D e c k w e r 4 7 , D e c k w e re t a l . 4 9 a n d N a k a n o h a n d Y o s h i d a 51, respec t ive ly . In each case , thes h e a r r a te u n d e r g i v e n e x p e r i me n ta l c o n d i t i o n s w a s c a l c u l a te d f r o mE q n 3 ( i n t e x t ) . E x p e r i me n ta l d a ta r e p o r te d i n t h e l i te r a tu r e v a r y c o n -s i d e ra b l y , d e p e n d i n g o n : ( 1 ) t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f t h ete s t l i q u id s u s e d ; ( 2 ) t h e m e th o d s e mp l o y e d to d e te r m i n e th e r a te so f ma s s t r a n s fe r ; a n d ( 3 ) t h e a s s u mp t i o n s ma d e w i th r e g a r d t o t h ep a t te r n o f m i x i n g i n t h e g a s a n d l i q u i d p h a s es . W h e n a n y c o r r e l a t i o ni s u s e d fo r d e s i g n p u r p o s e s , i t mu s t b e a s c e r ta i n e d th a t t h e c o n -d i t i o n s e x p e c te d i n p r a c t i c e a r e a s c l o s e a s p o s s i b l e t o t h e o n e su n d e r w h i c h t h e c o r r e l a t i o n w a s d e d u c e d . Th e g l o b a l a p p r o a c h ( a )a t t e m p ts t o r e c o n c i l e d a ta p u b l i s h e d b y v a r i o u s a u th o r s . W h i l e a llt h e r e p o r te d d a ta d o n o t c o l l a p s e i n to a s i mp l e c o r r e l a t i o n o f t h efo r m s h o w n i n E q n 2 i n t e x t , t h e a d v a n ta g e o f u s i n g g l o b a l s h e a r-r a te a s t h e p r i m a r y c o r r e l a t i n g f a c to r i s e v id e n t : t h e v a r i a t i o n o f v o l u -me t r i c ma s s - tr a n s fe r c o e f f i c i e n t w i t h t h i s s h e a r r a te s h o w s th e s a met r e n d fo r a ll d a ta s e t s .

    Heat-transfer correlationsT h e h e a t - t r a n s f e r r a t e s a c h i e v a b l e i n b u b b l ec o l u m n s a r e m u c h h i g h e r t h a n t h o s e a c h i e v e d i n

    s in g l e -p h ase f l o w s3 . Th i s i s b ecau se o f t h e b u b b l e -d r i v e n t u r b u l e n c e a n d h q u i d r e c i r c u l a ti o n , w h i c h a r ec h a r a ct e r is t ic s o f t h e f l o w i n b u b b l e c o l u m n s . S e v e ra lc o r r e l a t io n s h a v e b e e n p r o p o s e d f o r t h e p r e d i c t i o n o ft h e h ea t - t r an s fe r co ef f i c i e n t i n t h ese r eac to r s ; t h e o n ed e d u c e d b y K a w a s e a n d M o o - Y o u n g 54 is s h o w n i nB o x 2. T h e m o d e l , w h i c h a p p e a r s t o f it m o s t p u b -h s h e d d a t a , c a n t a k e n o n - n e w t o n i a n b e h a v i o u r o fl i q u id s i n to co n s id e ra t i o n , an d i t p red i c t s th e en h an ce-men t i r~ - ,h ea t t r an s fe r r esu l t i n g f ro m sh ear - t h in mn ge f fe c ts . K a w a s e - M o o - Y o u n g ' s c o r r e l a t i o n a ls o e n a b le st h e h e a t - t r a n s fe r c o e f f i c i e n t t o b e e s t i m a t e d a s a f u n c -t i o n o f t h e p h y s i c a l p r o p e r t i e s o f th e l i qu i d , t h ec o l u m n d i m e n s i o n s a n d t h e o p e r a t iv e v a ri a bl e s.P o w e r inpu tF r o m a c o m m e r c i a l p o i n t o f vi ew , t h e r e q u i r e dp o w e r i n p u t is a k e y c o n s i d e r a t i o n i n t h e d e s i g n o f an e w p r o ce s s . I n t h e c a se o f h i g h - v a l u e p r o d u c ts , t h ec o n t r i b u t i o n o f p o w e r i n p u t t o t h e t o ta l c o s t o f p r o d -u c t m a n u f a c t u r e i s u s u a l l y n e g l i g i b l e . H o w e v e r , f o r

    l o w - v a l u e b u l k p r o d u c t s , t h e c o s t o f p o w e r i n p u t c a nb e c r i t ica l .

    A c o m p a r i s o n o f p o w e r - i n p u t r e q u i r e m e n t s i nm e c h a n i c a l l y a n d p n e u m a t i c a l l y a g i ta t e d r e a c t o r s w a sc a r r i e d o u t b y S i g u r d s o n a n d 1 L o b i n s o n5 s . Th e i rr esu l t s su g g es t t h a t i n o rd er t o ach i ev e k ta v a lu es u pt o 0 . 0 7 s -1, t h e t o t a l p o w e r c o n s u m e d b y a b u b b l ec o l u m n i s l e s s t h a n t h a t c o n s u m e d b y a s t i r r e d t a n kreac to r fo r i n d u s t r i a l - sca l e o p era t i o n . F o r kL a v a lu esr a n g i n g f r o m 0 . 0 7 t o 0 . 1 0 sq , t h e p o w e r c o n s u m e d b yb o t h t y p e s o f r e a c t o r w a s c o m p a r a b l e . I f h i g h e r v a lu e sOfkLa a r e r eq u i r ed , a s t i r r ed - t an k co n f ig u ra t i o n wo u ldb e p r e f e r a b l e , de s p i te t h e h i g h e n e r g y c o st s b e c a u s e o fp rac t i ca l co n s id e ra t i o n s : t o ach i ev e su ch h ig h k tav a l ue s in a b u b b l e c o l u m n , t h e g a s v e l o c i t y w o u l dh a v e t o b e s o h i g h t h a t t h e r e w o u l d b e t h e p o s s i bi l it yo f l i q u i d e n t r a i n m e n t i n t o t h e o u t g o i n g g as .C o n c l u d i n g r e m a r k s

    B u b b l e c o l u m n s h a v e m a n y a d v a n t a g e o u s c h a r a c -t e r i s t i c s t h a t mak e t h em an a t t r ac t i v e ch o i ce fo r t h es c a l in g - u p o f b i o l o g ic a l p ro c e ss e s . T h e i r m e c h a n i c a ls imp l i c i t y en ab l es a mo re s t e r i l e o p era t i o n . P erh ap smo re imp o r t an t l y , i t i s p o ss ib l e t o co n t ro l l ev e l s o fs h e a r w i t h i n t h e r e a c t o r - a c ru c i a l f a c t o r f o r t h eg ro wth o f p l an t an d an ima l ce l ls i n p a r t i cu l a r .Re l i ab l e d es ig n co r r e l a t i o n s a r e a l so av a i l ab l e fo rm o m e n t u m , m a ss a n d h e a t t ra n s fe r , m a k i n g i t p o s s -i b l e t o co n s t ru c t l a rg e r eac to r s r a t i o n a ll y .

    E v e n t h o u g h t h e e f f e c t iv e n e s s o f s im p l e b u b b l eco lu m n s fo r h ig h ly v i sco u s l i q uid s (v i sco s it y ~1 P a .s )h a s b e e n q u e s t i o n e d , r e c e n t e v i d e n c e i n d i c a t i n g t h a tt h is t y p e o f r eac to r h as ce r t a i n ad v an t ag es i n t h e h ig hv i sco s i t y r an g e i s en co u rag in g 5 ,s6. Th e mass - t r an s fe rr a t e i n su ch l i q u id s i s , h o wev er , ad v er se ly a f f ec t ed .M o s t o f t h e m a ss t r a n s f e r o c c u r s i n t h e v i c i n i t y o f t h eg as sp arg er wh ere b u b b l es a r e r e la t i v e ly smal l; t h eu p p e r s e c t i o n s c o n t a i n i n g v e r y l a rg e b u b b l e s o f f e rn eg l i g ib l e i n t e r f ac i a l a r ea . No twi th s t an d in g so me d i s -a d v a nt a ge s , b u b b l e c o l u m n s w i l l c o n t i n u e t o f i n d n e wap p l i ca t i o n s i n b io p ro cess in g .R e f e r e n c e s

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    TIBTECH DECEMBER 1994 (VOL 12)