Extracellular Microbial Polysaccharides - American Chemical Society

11 Some Rheological Properties of G u m Solutions

Downloaded by UNIV OF ARIZONA on March 15, 2017 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0045.ch011

JOHN H. ELLIOTT Research Center, Hercules Inc., Wilmington, DE 19899

End-use applications of water-soluble polymers, including extracellular microbial polysaccharides, are almost exclusively based upon the rheological properties which they confer upon the final system. A rather detailed knowledge of the rheological behavior of aqueous solutions of such polymers is essential for selection of the most suitable gum for a given end use. This paper w i l l review some general rheological properties of aqueous gum solutions, including suitable experimental instrumentation. Supermolecular structure may be present in certain gum solutions, which gives rise to time dependent rheological behavior. Finally the use of rheological data in selecting gums for specific end uses w i l l be illustrated. Rheological Background In this paper, we shall be concerned primarily with data obtained in viscometric or simple shear flows (1). Here there is a non-zero velocity compo nent in only one direction in the medium. Familiar examples are the flows in capillary, concentric cylinder, and cone and plate instruments. The simplest case is that of the Newtonian l i q u i d , where the shear stress, S (dynes/cm. ) is directly propor tional to the shear rate, γ (sec. ); the constant of proportionality being the viscosity, η (poise), 2

-1

S = ηγ

(1)

Here, t h e v i s c o s i t y i s a c o n s t a n t independent o f s h e a r rate. Gum s o l u t i o n s show t h i s b e h a v i o r a t h i g h d i l u 144

Sandford and Laskin; Extracellular Microbial Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


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tions. As t h e c o n c e n t r a t i o n (or m o l e c u l a r weight) i s i n c r e a s e d t o t h e p o i n t where entanglement o c c u r s ( 2 0 , however, t h i s s i t u a t i o n no l o n g e r p r e v a i l s and t h e v i s c o s i t y becomes a f u n c t i o n o f t h e shear r a t e , d e c r e a s i n g w i t h i n c r e a s i n g shear r a t e . This i s called p s e u d o p l a s t i c i t y o r shear t h i n n i n g . The complete p s e u d o p l a s t i c c u r v e i s shown i n F i g u r e 1. I t s h o u l d be emphasized t h a t w i t h i n t h e time s c a l e o f conven t i o n a l l a b o r a t o r y measurements, p s e u d o p l a s t i c i t y i s a r e v e r s i b l e phenomenon. There a r e t h r e e p r i n c i p a l regions o f t h i s l o g η v s . l o g γ curve. A t v e r y low shear r a t e s , t h e v i s c o s i t y i s Newtonian. T h i s zero shear o r f i r s t Newtonian v i s c o s i t y , η , i s a f u n c t i o n o f t h e m o l e c u l a r w e i g h t , M, and c o n c e n t r a t i o n , C, o f the polymer. I t has been found t h a t a number o f p o l y m e r - s o l v e n t systems f o l l o w t h e r e l a t i o n s h i p ( 2 0 0

η

0

« c

3

Μ ·

5

3

(2)

4

4

The v a r i a t i o n o f η w i t h Μ · has been w e l l e s t a b l i s h e d f o r polymer m e l t s (_3) · As t h e shear r a t e i s i n c r e a s e d , a d e c r e a s e i n v i s c o s i t y i s observed. A f t e r a r e l a t i v e l y short t r a n s i t i o n r e g i o n , l o g η becomes l i n e a r i n l o g γ. T h i s i s t h e s o - c a l l e d power law r e g i o n and may c o v e r many decades i n s h e a r r a t e . T h i s i s g e n e r a l l y des c r i b e d by t h e f o l l o w i n g e q u a t i o n s 0

S = K(y)

n

and

1 1

η = K(^) "

(3a)

1

(3b)

The s l o p e o f t h e l o g η v s . l o g γ l i n e i n t h i s r e g i o n i s n-1. I f n i s one, t h e l i q u i d i s Newtonian; i f n i s l e s s t h a n one, i t i s p s e u d o p l a s t i c ; i f n i s g r e a t e r than one, t h e system i s d i l a t a n t o r shear t h i c k e n i n g . T h i s b e h a v i o r i s g e n e r a l l y o b s e r v e d i n systems c o n t a i n i n g a h i g h volume f r a c t i o n o f s o l i d s . The power law was c o n s i d e r e d as an e m p i r i c a l r e l a t i o n s h i p f o r many y e a r s ; however, S c o t t - B l a i r ( 4 ) has g i v e n a simple t h e o r e t i c a l d e r i v a t i o n based on t h e c o n c e p t o f t h e b r e a k i n g o f " l i n k a g e s " by s h e a r . As t h e shear r a t e i s i n c r e a s e d a n o t h e r t r a n s i t i o n zone i s o b s e r v e d , f o l l o w e d by a Newtonian r e g i o n , t h e i n f i n i t e shear o r second Newtonian v i s c o s i t y , nooT h i s r e g i o n i s o b s e r v e d a t v e r y h i g h shear r a t e s and i s very d i f f i c u l t t o study e x p e r i m e n t a l l y . The v a l u e of n appears t o show o n l y s l i g h t dependence on m o l e c u l a r w e i g h t , i n c o n t r a s t t o η and may be o r d e r s o f magnitude lower than η (5) . The η region i s of l i t t l e p r a c t i c a l importance and i s r a r e l y o b s e r v e d . O

Q

0

0

0

0


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The f o l l o w i n g i s a q u a l i t a t i v e r a t i o n a l i z a t i o n o f the g e n e r a l p s e u d o p l a s t i c curve shown i n F i g u r e 1(60 . In the n r e g i o n , the time s c a l e o f the measurement i s s u f f i c i e n t l y l o n g t h a t s t r u c t u r e o r entanglements a r e not d i s r u p t e d and Newtonian f l o w i s o b s e r v e d . As the shear r a t e i s i n c r e a s e d , the time s c a l e becomes s h o r t e r and the p o l y m e r i c u n i t s cannot r e l a x . Struc t u r e i s broken down and the polymer m o l e c u l e s tend t o become o r i e n t e d i n t h e f l o w d i r e c t i o n . These e f f e c t s i n c r e a s e w i t h i n c r e a s i n g shear r a t e , g i v i n g r i s e t o power law b e h a v i o r . As t h e shear r a t e i s i n c r e a s e d t o v e r y h i g h v a l u e s , breakdown and o r i e n t a t i o n have gone as f a r as p o s s i b l e and a f u r t h e r i n c r e a s e i n shear r a t e does n o t a f f e c t them. The f l o w i s then Newtonian, the η region. The η and power law r e g i o n s a r e most i m p o r t a n t i n c h a r a c t e r i z i n g aqueous gum systems. Some g e n e r a l i z a t i o n s can be made about b e h a v i o r i n these r e g i o n s . F i g u r e 2 shows l o g η v s . l o g γ p l o t s f o r xanthan gum i n aqueous s o l u t i o n . A t the h i g h e r c o n c e n t r a t i o n s , 2500 and 1500 ppm., the η r e g i o n l i e s a t shear r a t e s below 10~2 sec."" . T h i s region i s q u i t e apparent, however, a t the lower c o n c e n t r a t i o n s , 500 and 250 ppm. I t i s a l s o a p p a r e n t t h a t as the polymer c o n c e n t r a t i o n i s i n c r e a s e d , the t r a n s i t i o n from η t o non-Newtonian f l o w o c c u r s a t lower v a l u e s o f the shear r a t e . The power law s l o p e a t h i g h e r c o n c e n t r a t i o n s i s q u i t e steep and not v e r y s e n s i t i v e t o c o n c e n t r a t i o n . As c o n c e n t r a t i o n i s r e d u c e d , t h i s s l o p e becomes l e s s s t e e p , and, w h i l e not shown i n F i g u r e 2, a t v e r y low c o n c e n t r a t i o n s Newtonian b e h a v i o r i s o b s e r v e d . S o l u t i o n s o f polymers, h a v i n g a l o n g - c h a i n branched s t r u c t u r e , w i l l show a lower η than a l i n e a r polymer o f the same weight average m o l e c u l a r w e i g h t . T h i s has been e x t e n s i v e l y s t u d i e d i n the case o f l i n e a r and l o n g - c h a i n branched p o l y e t h y l e n e s . A c l a s s i c study i n t h i s f i e l d i s t h a t o f Busse and Longworth (7_) . The e f f e c t o f s a l t s on the r h e o l o g i c a l p r o p e r t i e s o f aqueous gum s o l u t i o n s i s a m a t t e r o f c o n s i d e r a b l e p r a c t i c a l importance. The p r e s e n c e o f s a l t s markedly lowers the v i s c o s i t y o f d i l u t e s o l u t i o n s o f p o l y e l e c t r o l y t e s ; i n f a c t , we have o b s e r v e d a d e c r e a s e o f o v e r t h r e e decades i n the η v a l u e o f a 2500 ppm. s o l u t i o n of a polyacrylamide, having a n i o n i c f u n c t i o n a l i t y , i n g o i n g from d i s t i l l e d water t o a 2.2% b r i n e . T h i s e f f e c t may be l a r g e l y a t t r i b u t e d t o the p o l y e l e c t r o l y t e e f f e c t , t h a t i s , the i o n i c s t r e n g t h o f the medium r e d u c e s t h e r e p u l s i o n between a d j a c e n t c h a r g e s on t h e polymer c h a i n . T h i s r e s u l t s i n a conforma-


Q

σ ο

σ

0

1

0

0

0


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Solutions


LOWER NEWTONIAN REGION

LOG SHEAR RATE Figure 1. Viscosity as a function of shear rate for a pseudoplastic or shear thinning system

American Chemical Society Library 1155 16th St., N.W.

Sandford and Laskin; Extracellular Microbial Polysaccharides Washington, O.C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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t i o n a l change from an extended c o n f i g u r a t i o n toward t h a t o f a random c o i l . In g e n e r a l , s a l t s o l u t i o n s a r e p o o r e r s o l v e n t s f o r w a t e r - s o l u b l e p o l y s a c c h a r i d e s than d i s t i l l e d water. As a consequence, t h e v i s c o s i t i e s o f d i l u t e s o l u t i o n s o f t h e s e polymers and t h e i r i n t r i n s i c v i s c o s i t i e s a r e lower i n s a l t s o l u t i o n s than i n pure water. It i s f r e q u e n t l y o b s e r v e d , however, t h a t c o n c e n t r a t e d s o l u t i o n s show h i g h e r v i s c o s i t i e s when s a l t s a r e p r e s e n t . Tager ( 8 J has c a r r i e d o u t e x t e n s i v e s t u d i e s o f t h e v i s c o s i t i e s of concentrated solutions of organic s o l u b l e polymers i n good and poor s o l v e n t s . In t h e case o f p o l a r polymers, v i s c o s i t i e s i n poor s o l v e n t s may be s e v e r a l decades h i g h e r t h a n those i n good s o l vents. T h i s i s a consequence o f t h e f o r m a t i o n o f r e l a t i v e l y s t r o n g s u p e r m o l e c u l a r s t r u c t u r e s by t h e polymer m o l e c u l e s i n t h e p o o r e r s o l v e n t . The same c o n s i d e r a t i o n s a r e a p p l i c a b l e t o w a t e r - s o l u b l e gums. I t i s apparent from t h e e a r l i e r d i s c u s s i o n t h a t a r e a l i s t i c r h e o l o g i c a l c h a r a c t e r i z a t i o n o f gum s o l u t i o n s r e q u i r e s t h e d e t e r m i n a t i o n o f i t s v i s c o s i t y as a f u n c t i o n o f shear r a t e o v e r a t l e a s t s e v e r a l decades o f shear r a t e . C o n c e n t r i c c y l i n d e r o r cone and p l a t e rheometers, c o v e r i n g a wide range o f shear r a t e s , a r e the most s u i t a b l e i n s t r u m e n t s . In our own work, when the v i s c o s i t y - s h e a r r a t e c u r v e was needed o v e r more than s i x decades o f shear r a t e , i t was n e c e s s a r y t o use t h r e e d i f f e r e n t i n s t r u m e n t s , t h e Weissenberg rheogoniometer, t h e Haake R o t o v i s c o , and t h e H e r c u l e s Hi-Shear V i s c o m e t e r , t o c o v e r t h e low, i n t e r m e d i a t e and h i g h shear r a t e r a n g e s , r e s p e c t i v e l y . Excellent agreement between i n s t r u m e n t s was found i n t h e r e g i o n s of o v e r l a p . Gum s o l u t i o n s show e l a s t i c as w e l l as v i s c o u s properties. These a r e r e a d i l y determined by imposing a s i n u s o i d a l s t r a i n o f s m a l l amplitude upon t h e sample, f o r example, u s i n g a cone and p l a t e i n s t r u m e n t . The r e s u l t i n g s t r e s s wave i s s i n u s o i d a l and has t h e same f r e q u e n c y as t h e imposed s t r a i n wave (9) . I t i s , however, o u t o f phase w i t h t h e s t r a i n wave, t h e phase a n g l e , δ, l y i n g between 0° and 9 0 ° . T h i s may be r e s o l v e d i n t o a component i n phase w i t h t h e s t r a i n , from which t h e dynamic modulus, G', may be c a l c u l a t e d . The s t r e s s wave component i n q u a d r a t u r e w i t h t h e imposed s t r a i n y i e l d s t h e dynamic v i s c o s i t y , η * . In and near t h e η r e g i o n , η and t h e v i s c o s i t y i n s t e a d y shear a r e i n good agreement when t h e s t e a d y shear i s p l o t t e d a g a i n s t γ and η' a g a i n s t t h e f r e q u e n c y , ω, i n radians/second, i . e . , considering ω i n o s c i l l a t i o n equal t o γ i n steady shear(10). A t higher frequen1

0


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c i e s η- g e n e r a l l y i s lower than the c o r r e s p o n d i n g steady shear v i s c o s i t y . F i g u r e 3 shows η, η , and G' f o r a 2% s o l u t i o n o f sodium c a r b o x y m e t h y l c e l l u l o s e (CMC) i n water. It i s seen t h a t η' l i e s somewhat below η. G increases with f r e q u e n c y w h i l e η' d e c r e a s e s , which i s the expected behavior. S u p e r m o l e c u l a r s t r u c t u r e , which i s o f t e n p r e s e n t i n gum s o l u t i o n s , g i v e s r i s e t o a v a r i e t y o f r h e o l o g i c a l phenomena. In c o n t r a s t w i t h p s e u d o p l a s t i c b e h a v i o r , t h e s e e f f e c t s a r e time dependent. The most common i s t h i x o t r o p y , which has been d e f i n e d as a reversible gel-sol transition. I t i s observed e x p e r i m e n t a l l y as a d e c r e a s e i n v i s c o s i t y w i t h time a t a c o n s t a n t shear r a t e . E v e n t u a l l y an e q u i l i b r i u m v i s c o s i t y value i s reached. I f s h e a r i n g i s s t o p p e d , the v i s c o s i t y w i l l r i s e t o i t s o r i g i n a l v a l u e , as the s t r u c t u r e i n the system r e f o r m s . A d i f f e r e n t and w i d e l y used method o f c h a r a c t e r i z i n g t h i x o t r o p y , developed some y e a r s ago by Green and Weltman(11), i n v o l v e s programmed i n c r e a s e s i n shear r a t e from r e s t t o a h i g h v a l u e (the up c u r v e ) , f o l l o w e d by a r a p i d d e c r e a s e back t o z e r o shear r a t e (the down c u r v e ) . A t y p i c a l example o f such a shear r a t e - s h e a r s t r e s s c u r v e i s shown i n F i g u r e 4. The a r e a o f the l o o p i s a measure o f the work p e r u n i t volume p e r second f o r t h i x o t r o p i c breakdown, under the c o n d i t i o n s o f the experiment. The e x t r a p o l a t e d i n t e r c e p t of the down c u r v e on the shear a x i s can be c o n s i d e r e d as a y i e l d stress. I t must be emphasized t h a t i f the programmed r a t e o f i n c r e a s e i n shear r a t e used i n o b t a i n i n g the up c u r v e i s changed, the a r e a o f the h y s t e r e s i s l o o p and the v a l u e o f the e x t r a p o l a t e d y i e l d s t r e s s w i l l , i n g e n e r a l , be d i f f e r e n t . The concept o f a y i e l d s t r e s s i s v e r y u s e f u l i n the r h e o l o g i c a l c h a r a c t e r i z a t i o n o f systems h a v i n g supermolecular s t r u c t u r e . I t was proposed some time ago by Bingham(12). Whether o r not i t r e a l l y e x i s t s has been debated i n the i n t e r v e n i n g y e a r s . Bingham's original definition is 1


1

(S - σ ) 0

= ηγ

(4)

where the shear s t r e s s , S, must exceed the y i e l d v a l u e , σ , b e f o r e f l o w can o c c u r . T h i s i s shown i n F i g u r e 5. In p r a c t i c e , t h i s type o f b e h a v i o r i s never s t r i c t l y observed. The e x p e r i m e n t a l f l o w c u r v e does not i n t e r s e c t the a b s c i s s a s h a r p l y but c u r v e s i n toward the o r i g i n , as shown by the d o t t e d l i n e . A s t r a i g h t por t i o n o f the c u r v e , a t h i g h e r shear r a t e s , however, may be e x t r a p o l a t e d t o the a b s c i s s a t o g i v p a v a l u e o f σ . 0

0



2 % C M C - 7 H 4 F IN W A T E R

CO

3 _J 10 3 Û ο 2 ~ ol0

3


2 Ο Ο CO

10

10"

10

10

10*

10*

S H E A R R A T E ( S E C * ) OR F R E Q U E N C Y ( R A D I A N S / S E C ) 1

Figure 3. Dynamic viscosity and modulus and steady shear viscosity as functions of frequency or shear rate for 2.0% CMC in water

Figure 4. Hysteresis loop treatment. Stress vs. shear rate for a thixotropic ma terial—arrows indicate in creasing and decreasing shear rate

SHEAR S T R E S S



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Perhaps what may be o p e r a t i o n a l l y c o n s i d e r e d as a y i e l d s t r e s s i s m e r e l y the p r e s e n c e o f a r e l a x a t i o n time which i s v e r y much g r e a t e r than the time s c a l e o f the e x p e r i m e n t a l measurement. There i s a fundamental d i f f e r e n c e between steady s h e a r and dynamic measurements i n the case o f systems e x h i b i t i n g a time dependent r h e o l o g i c a l r e s p o n s e . The t o t a l s t r a i n , t o which the sample i s s u b j e c t e d i n s t e a d y shear, i s d e t e r m i n e d by the shear r a t e and the time t h a t i t i s a p p l i e d . The t o t a l s t r a i n can thus be v e r y l a r g e , l e a d i n g t o e x t e n s i v e s t r u c t u r e breakdown and polymer o r i e n t a t i o n . Dynamic measurements, on the o t h e r hand, are c a r r i e d out a t low s t r a i n a m p l i t u d e s . Under t h e s e c o n d i t i o n s , t h e r e i s l i t t l e o r no s t r u c t u r e breakdown o r polymer o r i e n t a t i o n , and the p r o p e r t i e s o f the sample are measured e s s e n t i a l l y a t r e s t . Dynamic and s t e a d y shear measurements supplement each o t h e r t o g i v e a more complete r h e o l o g i c a l c h a r a c t e r i zation. I t must be remembered, however, t h a t the r h e o l o g i c a l s t a t e o f the system may be q u i t e d i f f e r e n t i n the two t y p e s of measurements. Rheological

Properties

i n End

Uses

Jeanes (13) has r e c e n t l y p u b l i s h e d an e x t e n s i v e r e v i e w on the a p p l i c a t i o n s o f e x t r a c e l l u l a r m i c r o b i a l polysaccharide-polyelectrolytes. In t h i s p a p e r , r h e o l o g i c a l p r o p e r t i e s i n end uses w i l l be i l l u s t r a t e d by s e v e r a l examples w i t h which the w r i t e r has had f i r s t - h a n d experience. These, u n f o r t u n a t e l y , have not been i n v o l v e d p r i m a r i l y w i t h e x t r a c e l l u l a r m i c r o b i a l p o l y s a c c h a r i d e s ; however, they do i l l u s t r a t e the a p p l i c a t i o n o f r h e o l o g i c a l c h a r a c t e r i z a t i o n t o end uses. Food Systems Sodium c a r b o x y m e t h y l c e l l u l o s e , often c a l l e d c e l l u l o s e gum o r CMC, i s a w i d e l y used component o f food systems. I t may a c t as a suspending agent, t h i c k e n e r , p r o t e c t i v e c o l l o i d , humectant, and t o c o n t r o l the c r y s t a l l i z a t i o n o f some o t h e r component. CMC i s c l a s s i f i e d by the Food and Drug A d m i n i s t r a t i o n under " s u b s t a n c e s t h a t are g e n e r a l l y r e c o g n i z e d as safe" (Gras). CMC i s p r e p a r e d by the r e a c t i o n o f a l k a l i c e l l u l o s e w i t h sodium c h l o r o a c e t a t e and i s a polyelectrolyte. Important parameters i n c h a r a c t e r i z i n g CMC are the average degree o f p o l y m e r i z a t i o n (DP), the average number of a n h y d r o g l u c o s e u n i t s per m o l e c u l e ; and the average degree of s u b s t i t u t i o n (DS),



152


the average number o f c a r b o x y m e t h y l groups per anhydroglucose u n i t . I t was e a r l y r e c o g n i z e d i n our r h e o l o g i c a l c h a r a c t e r i z a t i o n o f CMC s o l u t i o n s and g e l s t h a t samples h a v i n g the same nominal c h e m i c a l c o m p o s i t i o n and s o l u t i o n v i s c o s i t y c o u l d show markedly d i f f e r e n t r h e o l o g i cal properties. E a r l i e r work showed t h a t CMC p r e p a r e d under c o n d i t i o n s g i v i n g more u n i f o r m s u b s t i t u t i o n gave pseudoplastic solutions. I f t h e s e c o n d i t i o n s were not followed, t h i x o t r o p i c solutions r e s u l t e d . This i s p a r t i c u l a r l y t r u e f o r the lower DS l e v e l s . Our work l e d t o the c o n c l u s i o n t h a t a v e r y s m a l l q u a n t i t y o f unsubstituted c r y s t a l l i n e c e l l u l o s e residues, e x i s t i n g as f r i n g e m i c e l l e s , a c t as c r o s s - l i n k i n g c e n t e r s and e n a b l e a t h r e e - d i m e n s i o n a l network t o be formed(14,15). N i j h o f f was g r a n t e d a U.S. p a t e n t ( 1 6 ) on the use of CMC, h a v i n g low DS, t o form unctuous g e l s f o r low c a l o r i e spreads. T h i s prompted a study o f the r h e o l o g i c a l p r o p e r t i e s o f unctuous m a t e r i a l s . I t was found t h a t when such m a t e r i a l s (e.g., b u t t e r , mayonnaise and ointments) were s u b j e c t e d t o an imposed s i n u s o i d a l s t r a i n , which was g r e a t e r than the l i n e a r v i s c o e l a s t i c l i m i t , the r e s u l t i n g s t r e s s wave was not s i n u s o i d a l , but i n many c a s e s approached a square w a v e ( 1 7 ) . S i m i l a r o b s e r v a t i o n s have been r e p o r t e d by Komatsu, e t a l . (18). Our r e s u l t s were i n t e r p r e t e d i n terms o f a m o d i f i e d Bingham body, c o n s i s t i n g o f an e l a s t i c , a f r i c t i o n a l and a v i s c o u s element connected i n s e r i e s . The r e s p o n s e o f t h i s model t o s t e a d y shear and t o imposed s i n u s o i d a l shear has been c a l c u l a t e d ( 1 9 ) , and the model has p r o v e d t o be u s e f u l i n c h a r a c t e r i z i n g s t r u c t u r e d systems(20). Komatsu e t a l . i n t e r p r e t e d t h e i r e x p e r i m e n t a l r e s u l t s u s i n g the Casson e q u a t i o n , which w i l l be d i s c u s s e d l a t e r . F i g u r e 6 shows the e f f e c t o f DS on the s t e a d y shear p r o p e r t i e s o f 5% CMC s o l u t i o n s and g e l s . Curve A f o r the sample h a v i n g a DS o f 0.7 i s t y p i c a l o f a v i s c o e l a s t i c system, and t h i s was c o n f i r m e d by dynamic measurements. Curve Β f o r a sample o f DS 0.4 shows a s t e e p e r r i s e i n the s t r e s s and a l s o a s t r e s s o v e r s h o o t . The Curve C f o r an e x p e r i m e n t a l sample h a v i n g a DS o f 0.18 shows the v e r y sharp peak and r a p i d s t r e s s decay, c h a r a c t e r i s t i c o f unctuous systems. Curve D shows dynamic measure ments on the DS 0.18 sample. The square n a t u r e o f the s t r e s s curve i s obvious. T a b l e I i l l u s t r a t e s the t y p e s o f CMC used i n a number o f food p r o d u c t s . The c o n n e c t i o n between the t y p e used i n a g i v e n system and the s o l u t i o n r h e o l o g i c a l p r o p e r t i e s d i s c u s s e d above w i l l be a p p a r e n t . The y i e l d s t r e s s , as a u s e f u l r h e o l o g i c a l con c e p t , was d i s c u s s e d e a r l i e r . It i s frequently d i f f i -


Rheological


ELLIOTT

Properties

of Gum

Figure 5. Stress vs. shear rate for a Bingham body

SHEAR STRESS (S-*OO|f)

0 Figure 6.

10

20

Solutions

30

40

50

Five percent CMC in water; effect of degree of substitution on stress response


154


c u l t t o e s t a b l i s h even s e m i - q u a n t i t a t i v e l y , u s i n g Bingham's r e l a t i o n s h i p (equation 4 ) . The Casson equation, - σ ^ = A γ*

(5)

0

which was d e r i v e d f o r s u s p e n s i o n s , has p r o v e d t o be v e r y u s e f u l i n d e t e r m i n i n g s m a l l v a l u e s o f σ from a plot of against γ^(24). As an example, c n o c o l a t e m i l k i s f o r m u l a t e d witK~~about 0.03% κ-carrageenan which p r e v e n t s s e t t l i n g o f t h e cocoa. The κc a r r a g e e n a n causes a c o n s i d e r a b l e i n c r e a s e i n t h e v i s c o s i t y o f t h e m i l k - s u g a r system and t h e e x i s t e n c e o f a y i e l d s t r e s s has been p o s t u l a t e d . Plots of S vs. γ c o u l d n o t be e x t r a p o l a t e d t o g i v e a v a l u e o f σ ; however, t h e Casson p l o t s , shown i n F i g u r e 7, a r e l i n e a r f o r values of between zero and one and p e r mit a r e l i a b l e e x t r a p o l a t i o n .


ρ

0

Friction

Reduction

R h e o l o g i c a l b e h a v i o r , d i s c u s s e d so f a r , has been c o n f i n e d t o systems i n l a m i n a r f l o w . The phenomenon o f drag r e d u c t i o n i s o b s e r v e d o n l y i n t u r b u l e n t f l o w . The t r a n s i t i o n from l a m i n a r t o t u r b u l e n t f l o w i n a p i p e o c c u r s when t h e Reynolds Number, R, f o r t h e system becomes g r e a t e r t h a n about 2000 R

=

QZSL

(6)

y

d i s the pipe diameter, ν i s the l i n e a r v e l o c i t y of the f l u i d h a v i n g a d e n s i t y , p , and v i s c o s i t y y . R i s d i m e n s i o n l e s s when s e l f c o n s i s t e n t u n i t s a r e used, and i s the r a t i o o f i n e r t i a l t o v i s c o u s f o r c e s i n the fluid. Note t h a t t h e symbol f o r v i s c o s i t y has been changed from η t o y , which i s commonly used i n engineering. The phenomenon o f f r i c t i o n r e d u c t i o n has been known f o r some time, t h e f i r s t s c i e n t i f i c d e s c r i p t i o n h a v i n g been g i v e n by Toms i n 1948 (2!5) and i t i s o f t e n r e f e r r e d t o as t h e Toms e f f e c t . When s m a l l q u a n t i t i e s (10-500 ppm.) o f a h i g h m o l e c u l a r weight polymer a r e added t o a l i q u i d i n t u r b u l e n t f l o w , t h e r e i s a d r a m a t i c r e d u c t i o n i n t h e power n e c e s s a r y t o m a i n t a i n the same f l o w r a t e . When t h e same c o n c e n t r a t i o n o f polymer i s added t o t h e l i q u i d i n l a m i n a r f l o w , t h e only e f f e c t observed i s a s l i g h t i n c r e a s e i n v i s c o s i t y , which may be s c a r c e l y d e t e c t a b l e . I f p r e s s u r e drop i s measured a l o n g a tube, t h e f l u i d v e l o c i t y o r Reynolds


11.

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Rheological

Properties

of Gum

155

Solutions

TABLE I SOME USES OF CMC IN FOODS


FOOD PRODUCT

PROPERTY CONFERRED BY CMC

DP

REFERENCE

CMC TYPE S**) DS

BAKED GOODS

WATER RETENTION, CONTROL OF BATTER VISCOSITY

H, M

0.7

NO

21 , 22, 23

DOUGHNUTS

GREASE HOLDOUT

H M

0.7

NO

21. 22. 23

STARCH SYSTEMS, WHIPPED TOPPINGS

INHIBITION OF SYNERESIS

H M

0.7

NO

21 , 22

SYRUPS, BEVERAGES, JUICES

THICKENER, VISCOSIFIER

H M

0.7

NO

21, 22, 23

ICE CREAM

TEXTURE, BODY, CONTROL OF SUGAR AND ICE CRYSTALLIZATION

H M

0.7

NO

21 , 22, 23

PET FOODS (SEMIMOIST)

BINDER

H M

0.7

NO

21 . 22, 23

CONFECTIONS

CONTROL OF SUGAR CRYSTALLIZATION

L

0.7

NO

21, 22, 23

LOW CALORIE SYRUPS

VERY SMOOTH TEXTURE

H

0.7

YES

21, 22, 23

LOW CALORIE SPREADS

UNCTUOUSNESS

H M

0.4

NO

16, 17

*) H.M.L, HIGH, MEDIUM, OR LOW VISCOSITY

**) S, UNIFORM SUBSTITUTION


EXTRACELLULAR MICROBIAL

156

number b e i n g h e l d c o n s t a n t , t h e p e r c e n t r e d u c t i o n , % FR, i s g i v e n by %FR = 100 ; .

A P

A p N

o" ΔΡ

\ - 100

(1 -

POLYSACCHARIDES

friction

i

(7)

0

where Δ Ρ i s t h e p r e s s u r e drop f o r t h e pure l i q u i d and ΔΡ i s t h e p r e s s u r e drop f o r t h e same l i q u i d c o n t a i n i n g a low c o n c e n t r a t i o n o f polymer. Percent f r i c t i o n r e d u c t i o n s as h i g h as 70-80% have been o b s e r v e d . The importance o f t h i s e f f e c t t o those i n d u s t r i e s where l a r g e q u a n t i t i e s o f l i q u i d s must be pumped i s o b v i o u s . E x t e n s i v e r e s e a r c h s t u d i e s have a l s o been c a r r i e d by U n i t e d S t a t e s and f o r e i g n n a v a l l a b o r a t o r i e s ( 2 6 , 2 7 ) . Many w a t e r - s o l u b l e polymers, i n c l u d i n g c e l l u l o s i c s and m i c r o b i a l p o l y s a c c h a r i d e s have been t e s t e d as f r i c t i o n r e d u c t i o n a d d i t i v e s (2*8 ) . The mechanism by which t h e s e polymers produce f r i c t i o n r e d u c t i o n i s n o t c l e a r l y understood. In g e n e r a l , h i g h m o l e c u l a r weight and a l i n e a r s t r u c t u r e g i v e a more e f f i c i e n t polymer. The diameter o f t h e t e s t s e c t i o n i s a v e r y important parameter; g r e a t e r f r i c t i o n r e d u c t i o n s u s u a l l y a r e o b s e r v e d i n s m a l l e r diameter t u b e s . I t i s known t h a t these a d d i t i v e s t h i c k e n the v i s c o u s sub-layer a t the pipe w a l l . V i s c o e l a s t i c e f f e c t s almost c e r t a i n l y p l a y an e f f e c t and i t may be t h a t e l a s t i c energy s t o r a g e by the polymer m o l e c u l e i n t e r a c t s w i t h t h e s m a l l , energy d i s s i p a t i n g , turbulent eddies. Polymer s u p e r m o l e c u l a r s t r u c t u r e may a l s o p l a y a r o l e and i t has been sug g e s t e d t h a t t h i s c o u l d be a s i g n i f i c a n t f a c t o r i n t h e d i a m e t e r e f f e c t (2_9). The shear i n t u r b u l e n t f l o w can degrade the polymer m o l e c u l e s . Guar gum and sodium c a r b o x y m e t h y l c e l l u l o s e a r e more shear r e s i s t a n t b u t l e s s e f f e c t i v e f r i c t i o n r e d u c e r s than p o l y - ( e t h y l e n e oxid e ) and p o l y - ( a c r y l a m i d e s ) (27) . The f i e l d o f f r i c t i o n r e d u c t i o n i s v e r y a c t i v e , and t h e f o l l o w i n g r e v i e w s a r e recommended(24,30,31).


0

Flow Through Porous Media T h i s i s a n o t h e r s i t u a t i o n i n which t h e f l o w i s not l a m i n a r . The b a s i c e q u a t i o n f o r f l o w through porous media i s Darcy's law: Q A

_ k ΔΡ " μ Δ1

Q i s t h e f l o w r a t e i n cm.^/sec. through 9

s e c t i o n a l area o f A

(8) a cross

ΔΡ

(cm/) , ^ j - i s the pressure


11.

ELLIOTT


g r a d i e n t i n atmospheres/cm., μ i s t h e v i s c o s i t y i n c e n t i p o i s e , and k i s t h e p e r m e a b i l i t y i n d a r c i e s . In cgs u n i t s , p e r m e a b i l i t y has t h e u n i t s cm. and one d a r c y e q u a l s 9 . 8 7 x l 0 - cm. . The d a r c y i s t h e commonly used u n i t o f p e r m e a b i l i t y i n g e o p h y s i c a l work. The r a t i o k/μ i s the m o b i l i t y . T h i s i s a most i m p o r t a n t parameter i n porous media s t u d i e s , and w i l l be d i s c u s s e d i n terms o f the use o f polymer s o l u t i o n s as m o b i l i t y b u f f e r s i n enhanced o i l r e c o v e r y . The economics o f enhanced o i l r e c o v e r y t e c h n i q u e s a r e now f e a s i b l e , i n view o f t h e energy s h o r t a g e and t h e h i g h c o s t o f imported p e t r o l e u m . The importance o f the m o b i l i t y i n such an o p e r a t i o n a r i s e s from t h e f a c t t h a t i f one l i q u i d , e.g., o i l , i s t o be pushed o u t by a n o t h e r i m m i s c i b l e l i q u i d , e.g., water o r a polymer s o l u t i o n , the l a t t e r must have an e q u a l o r lower m o b i l i t y t o p r e v e n t f i n g e r i n g o r water b r e a k t h r o u g h , which would bypass r e c o v e r a b l e o i l i n the f o r m a t i o n ( 3 2 ) . C o n s i d e r a t i o n o f Darcy's e q u a t i o n i n d i c a t e s two mechanisms by which a d d i t i o n o f a polymer t o water can lower the m o b i l i t y . I t can i n c r e a s e the v i s c o s i t y and/or i t can lower the perme a b i l i t y o f the porous medium t o t h e aqueous s o l u t i o n . The l a t t e r i s brought about by polymer a d s o r p t i o n o r entrapment. In g e n e r a l , both mechanisms appear t o be o p e r a t i n g , however, one o r t h e o t h e r tends t o predominate. The f l o w o f a polymer s o l u t i o n t h r o u g h a porous medium i s n o t a l a m i n a r o r v i s c o m e t r i c f l o w and u n u s u a l e f f e c t s may be o b s e r v e d . F o r example, p o l y ( a e r y l a m i d e ) s o l u t i o n s show p s e u d o p l a s t i c b e h a v i o r i n viscometric flows. In porous media, however, such s o l u t i o n s appear t o e x h i b i t d i l a t a n t p r o p e r t i e s (33^) . Indeed a p o l y ( a e r y l a m i d e ) s o l u t i o n i n water showed b o t h p s e u d o p l a s t i c and d i l a t a n t r e s p o n s e s , depending upon t h e f l o w r a t e { 3 4 ) . As a polymer m o l e c u l e moves t h r o u g h the p o r e s o f a porous medium, i t i s s u b j e c t e d t o a c c e l e r a t i o n s and decelerations. These, t o g e t h e r w i t h the s t r e t c h i n g d e f o r m a t i o n which o c c u r s as i t p a s s e s t h r o u g h a f i n e p o r e , i n t r o d u c e e l a s t i c and r e l a x a t i o n e f f e c t s which are absent i n v i s c o m e t r i c f l o w s . Thus the f l o w b e h a v i o r o f polymer s o l u t i o n s i n a porous medium cannot be p r e d i c t e d from v i s c o m e t r i c measurements, but, i n g e n e r a l must be d e t e r m i n e d i n the s p e c i f i c porous medium o f i n t e r e s t . Xanthan gum i s b e i n g c u r r e n t l y t e s t e d f o r use i n m o b i l i t y c o n t r o l f o r enhanced o i l r e c o v e r y . Available i n f o r m a t i o n i n d i c a t e s t h a t i t o p e r a t e s t o lower m o b i l i t y p r i m a r i l y by i n c r e a s i n g v i s c o s i t y . As shown 9


157

2



158

i n F i g u r e 2, xanthan s o l u t i o n s show p s e u d o p l a s t i c b e h a v i o r down t o q u i t e low c o n c e n t r a t i o n s . This i s d e s i r a b l e , g i v i n g low v i s c o s i t i e s a t t h e h i g h shear r a t e s encountered d u r i n g i n j e c t i o n , but s i g n i f i c a n t l y h i g h e r v i s c o s i t i e s when moving t h r o u g h t h e o i l b e a r i n g f o r m a t i o n , where shear r a t e s a r e i n t h e range o f 0.1 t o 10 s e c . " . 1

Literature Cited


(1) (2)

(3) (4) (5) (6) (7) (8) (9) (10) (11)

(12) (13) (14) (15) (16) (17) (18) (19) (20)

Middleman, S., "The Flow of High Polymers", p. 8, Interscience, New York, 1968. Peterlin, Α . ,"Non-NewtonianViscosity and the Macromolecule", p. 225, Advances in Macromolecular Chemistry, Volume 1, W. M. Pasika, E d . , Academic Press, New York, 1968. Reference 1, p. 172. Scott-Blair, G. W., Rheol. Acta (1965) 4, 53. Reference 1, p. 101. Lenk, R. S., "Plastics Rheology", p. 12, Wiley Interscience, New York, 1968. Busse, W. F., and Longworth, R., J. Polymer S c i . (1962) 58, 49. Tager, Α. Α . , Rheol. Acta (1974) 13, 831. Ferry, J. D . , "Viscoelastic Properties of Polymers", p. 12, Wiley, New York, 1970. Bueche, F., "Physical Properties of Polymers", p. 220, Interscience, New York, 1962. Green, H . , and Weltman, R. Ν . , Ind. Eng. Chem., Anal. Ed. (1943) 15, 201. Also Green, H . , "Industrial Rheology and Rheological Structures", Wiley, New York, 1949. Bingham, E. C . , "Fluidity and Plasticity", p. 217, McGraw-Hill, New York, 1922. Jeanes, Α . , J. Polymer S c i . (1974) Symposium No. 45, 209. Ott, Ε., and E l l i o t t , J . Η., Makromol. Chem. (1956) 18/19, 352. deButts, Ε. Η., Hudy, J. Α . , and Elliott, J . Η., Ind. Eng. Chem. (1957) 49, 94. Nijhoff, G. J. J., U.S. Patent 3,418,133. E l l i o t t , J . H . , and Ganz, A. J., J. Texture Studies (1971) 2, 220. Komatsu, Η., Mitsui, T . , and Onogi, S., Trans. Soc. Rheol. (1973) 17:2, 351 E l l i o t t , J . H . , and Green, C. E., J. Texture Studies (1972) 3, 194. E l l i o t t , J . H . , and Ganz, A. J., Rheol. Acta (1974) 13, 1178.



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