Rheology of Emulsions - American Chemical Society

4 Rheology of Emulsions R. P a l , Y. Y a n , a n d J . M a s l i y a h Downloaded by NORTH CAROLINA STATE UNIV on December 7, 2012 | http://pubs.acs.org Publication Date: May 5, 1992 | doi: 10.1021/ba-1992-0231.ch004

1

☼

D e p a r t m e n t of C h e m i c a l E n g i n e e r i n g , University o f A l b e r t a , E d m o n t o n , A l b e r t a , C a n a d a T6G 2 G 6

This chapter presents a brief review of the rheological classification of fluids and instruments used for viscosity measurements. A discussion of the rheology of suspensions and how it relates to that of emulsions is given. Predictive correlations for emulsion viscosity are discussed in detail. The effect of added solids to an emulsion is fully treated, and its relation to a himodel system is discussed.

Rheological Classification of Fluids A fluid, that is, a l i q u i d o r a gas, is a substance that u n d e r g o e s c o n t i n u o u s d e f o r m a t i o n u n d e r the a c t i o n o f a n a p p l i e d shear force o r stress. I n o t h e r w o r d s , w h e n a fluid is s u b j e c t e d to shear, it flows. O n the o t h e r h a n d , a s o l i d d e f o r m s u n d e r the a c t i o n o f an a p p l i e d shear f o r c e a n d retains its o r i g i n a l shape u p o n the cessation o f the a p p l i e d shear f o r c e (J). T h e m a n n e r b y w h i c h a fluid obeys a g i v e n shear-stress-shear-rate r e l a t i o n s h i p d e t e r m i n e s its class w i t h i n the r h e o l o g i c a l classification o f a fluid.

Newtonian Fluids.

A fluid is said to b e N e w t o n i a n w h e n i t obeys

N e w t o n ' s l a w o f viscosity, g i v e n b y τ = -177

(1)

w h e r e τ is the shear stress ( P a o r N / m , f o r c e p e r u n i t area), 7 is the shear 2

rate e x e r t e d o n the fluid ( s ) , a n d η is constant a n d is r e f e r r e d to as the -1

fluid

d y n a m i c o r the shear viscosity (kg/m-s o r P a s ) . Current address: Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ^Corresponding author

1

0065-2393/92/0231-0131 $11.00/0 © 1992 American Chemical Society

In Emulsions; Schramm, L.; Advances in Chemistry; American Chemical Society: Washington, DC, 1992.

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A r h e o l o g i c a l i n s t r u m e n t s u c h as a v i s c o m e t e r c a n b e u s e d t o evaluate τ a n d 7 a n d h e n c e o b t a i n a value f o r t h e shear viscosity, η. E x a m p l e s o f N e w t o n i a n fluids are p u r e gases, mixtures o f gases, p u r e l i q u i d s o f l o w m o l e c u l a r w e i g h t , d i l u t e solutions, a n d d i l u t e e m u l s i o n s . I n some instances, a fluid m a y b e N e w t o n i a n at a c e r t a i n shear-rate range b u t deviate f r o m N e w t o n ' s l a w o f viscosity u n d e r e i t h e r v e r y l o w o r v e r y h i g h shear rates (2). T o b e m o r e p r e c i s e , t h e g e n e r a l tensor e q u a t i o n o f N e w t o n ' s l a w o f viscosity s h o u l d b e o b e y e d b y a N e w t o n i a n fluid (2); h o w e v e r , f o r o n e d i m e n s i o n a l flow, t h e a p p l i c a b i l i t y o f e q 1 is sufficient. F o r a N e w t o n i a n fluid, a l i n e a r p l o t o f τ versus 7 gives a straight l i n e whose slope gives t h e fluid viscosity. A l s o , a l o g - l o g p l o t o f τ versus 7 is l i n e a r w i t h a slope o f u n i t y . B o t h types o f plots are u s e f u l i n c h a r a c t e r i z i n g a N e w t o n i a n fluid. F o r a N e w t o n i a n fluid, t h e viscosity is i n d e p e n d e n t o f b o t h τ a n d 7, a n d i t m a y b e a f u n c t i o n o f t e m p e r a t u r e , p r e s s u r e , a n d c o m p o s i t i o n . M o r e o v e r , t h e viscosity o f a N e w t o n i a n fluid is n o t a f u n c t i o n o f the d u r a t i o n o f shear n o r o f the t i m e lapse b e t w e e n consecutive applications o f shear stress (3). F l u i d s that d o n o t o b e y N e w t o n ' s l a w o f viscosity c a n b e b r o a d l y g r o u p e d i n t o t i m e - i n d e p e n d e n t a n d t i m e - d e p e n d e n t n o n - N e w t o n i a n fluids. Subclassifications f o r each g r o u p are c o n v e n i e n t (3).

Time-Independent Non-Newtonian Fluids. T i m e - i n d e p e n d e n t n o n - N e w t o n i a n fluids are c h a r a c t e r i z e d b y h a v i n g t h e fluid viscosity as a f u n c t i o n o f t h e shear rate (or shear stress). H o w e v e r , t h e fluid viscosity is i n d e p e n d e n t o f the shear h i s t o r y o f the fluid. S u c h fluids are also r e f e r r e d t o as " n o n - N e w t o n i a n viscous fluids". F i g u r e 1 shows a t y p i c a l shear d i a g r a m for t h e various t i m e - i n d e p e n d e n t n o n - N e w t o n i a n fluids. Pseudoplastic Fluids. A p s e u d o p l a s t i c o r a s h e a r - t h i n n i n g fluid is one o f t h e most c o m m o n l y e n c o u n t e r e d n o n - N e w t o n i a n fluids. T h e v a r i a t i o n o f the shear stress, τ , versus t h e shear rate, 7 , f o r a p s e u d o p l a s t i c fluid is s h o w n i n F i g u r e 2. A p l o t o f τ versus 7 is c h a r a c t e r i z e d b y l i n e a r i t y at v e r y l o w a n d v e r y h i g h shear rates. T h e slope at v e r y l o w shear rate gives t h e

Bingham plastic Generalized plastic

ω ω φ

°°, respectively; a n d A is a n adjustable p a r a m e t e r . M o s t m a c r o m o l e c u l a r fluids a n d concentrated emulsions are p s e u d o p l a s t i c fluids. T h e y c a n also exhibit viscoelastic characteristics.


0

Dilatant Fluids. D i l a t a n t fluids o r s h e a r - t h i c k e n i n g fluids are less c o m m o n l y e n c o u n t e r e d t h a n p s e u d o p l a s t i c (shear-thinning) fluids. R h e o l o g i c a l d i l a t a n c y refers to an increase i n the apparent viscosity w i t h increas i n g shear rate (3). I n m a n y cases, v i s c o m e t r i c data f o r a s h e a r - t h i c k e n i n g fluid c a n b e fit b y u s i n g t h e p o w e r l a w m o d e l w i t h n > 1. E x a m p l e s o f fluids that are s h e a r - t h i c k e n i n g are c o n c e n t r a t e d solids suspensions. Fluids with a Yield Stress. B o t h p s e u d o p l a s t i c a n d dilatant fluids are c h a r a c t e r i z e d b y the fact that n o finite shear stress is r e q u i r e d to m a k e t h e fluids flow. A fluid w i t h a y i e l d stress is c h a r a c t e r i z e d b y t h e p r o p e r t y that a finite shear stress, τ , is r e q u i r e d to m a k e t h e fluid flow. A fluid o b e y i n g 0

τ =

TQ —

%7

(6)

is c a l l e d a B i n g h a m plastic. H e r e the p a r a m e t e r % is a constant. η is n o t a r e a l viscosity b u t a viscosity d e f i n e d after t h e 7-axis is s h i f t e d to τ (see F i g u r e 1). F o r most p r a c t i c a l fluids w i t h a y i e l d stress, t h e plastic viscosity, % , is a f u n c t i o n o f shear rate. S u c h fluids are r e f e r r e d t o as g e n e r a l i z e d plastic. D r i l l i n g m u d is a g o o d e x a m p l e o f a g e n e r a l i z e d plastic fluid. Β

0

Time-Dependent Non-Newtonian Fluids. T i m e - d e p e n d e n t n o n - N e w t o n i a n fluids are c h a r a c t e r i z e d b y t h e p r o p e r t y that t h e i r viscosities are a f u n c t i o n o f b o t h shear rate a n d shear history. Thixotropic Fluids. T h i x o t r o p i c fluids are c h a r a c t e r i z e d b y a d e crease i n t h e i r viscosity w i t h t i m e at a constant shear rate a n d fixed t e m p e r a t u r e . W h e n shear rate is steadily i n c r e a s e d f r o m 0 to a m a x i m u m value a n d t h e n i m m e d i a t e l y decreased t o w a r d 0, a hysteresis l o o p is f o r m e d , as s h o w n i n F i g u r e 3. T h e shape o f t h e hysteresis l o o p is also a f u n c t i o n o f the rate b y w h i c h the shear rate, 7, is c h a n g e d . O i l - w e l l d r i l l i n g m u d s , greases, a n d f o o d materials are examples o f t h i x o t r o p i c fluids. Eheopectic

Fluids.

Rheopectic

fluids

are c h a r a c t e r i z e d b y a n i n

crease i n t h e i r viscosity w i t h t i m e at a constant shear rate a n d fixed t e m p e r a t u r e . A s f o r a t h i x o t r o p i c fluid, a hysteresis l o o p is also f o r m e d w i t h a r h e o p e c t i c fluid i f i t is sheared f r o m a l o w to a h i g h shear rate a n d b a c k to a l o w shear rate. H o w e v e r , a d i f f e r e n t rate is u s u a l l y f o l l o w e d u p o n l o w e r i n g the shear rate, as is s h o w n i n F i g u r e 3. B e n t o n i t e clay suspensions a n d sols are t y p i c a l examples o f r h e o p e c t i c fluids (3).


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Rheology of Emulsions

Thixotropic


Rheopectic

Ο

Figure 3. Flow curves for thixotropic and rheopectic fluid in a single continuous experiment.

Shear rate, y Viscoelastic

A f u l l d e s c r i p t i o n o f viscoelastic fluids was g i v e n

Fluids.

b y S k e l l a n d (3): T h e s e materials e x h i b i t b o t h viscous a n d elastic p r o p e r t i e s . I n a p u r e l y H o o k e a n elastic s o l i d , t h e stress c o r r e s p o n d i n g to a g i v e n strain is i n d e p e n d e n t o f t i m e , whereas f o r viscoelastic substances the stress w i l l g r a d u a l l y dissipate. I n contrast to p u r e l y viscous l i q u i d s , o n t h e o t h e r h a n d , viscoelastic fluids flow w h e n s u b j e c t e d to stress, b u t p a r t o f t h e i r d e f o r m a t i o n is g r a d u a l l y recov e r e d u p o n r e m o v a l o f the stress. F l o u r d o u g h , N a p a l m , j e l l i e s , a n d c o n c e n t r a t e d e m u l s i o n s are t y p i c a l e x a m ples o f viscoelastic

fluids.

I n t h e p r e v i o u s sections, t h e n o n - N e w t o n i a n viscosity (η) was u s e d t o c h a r a c t e r i z e t h e r h e o l o g y o f t h e fluid. F o r a viscoelastic fluid, a d d i t i o n a l coefficients are r e q u i r e d t o d e t e r m i n e t h e state o f stress i n a n y flow. F o r steady s i m p l e shear flow, t h e a d d i t i o n a l coefficients are g i v e n b y -ΨΙ(Ί)ΊΙΙ

(7a)

T22 - T33 = - ^ 2 ( 7 ) 721 !

(7b)

Tu - T

2 2

=

T h e f u n c t i o n s φ a n d ψ are k n o w n as t h e p r i m a r y a n d s e c o n d a r y n o r m a l τ

2

stress coefficients (7). S u b s c r i p t s 1, 2, a n d 3 f o r τ a n d 7 r e f e r t o t h e flow d i r e c t i o n , shear axis, a n d n e u t r a l axis, respectively. I n g e n e r a l , t h e p r i m a r y a n d secondary n o r m a l stress coefficients are s t r o n g f u n c t i o n s o f the shear rate 7 , a n d ψ is u s u a l l y about 1 0 % o f φ 2

ν

M o r e o v e r , ψ is a p o s i t i v e q u a n t i t y , λ

w h e r e a s ψ is a negative q u a n t i t y . N o n z e r o values o f ψι a n d ψ give rise to the 2

2

die-swell phenomenon,

fluid

c l i m b i n g u p a r o t a t i n g shaft

(Weissenberg

effect), a n d s e c o n d a r y flow b e t w e e n m o v i n g surfaces. F o r steady-state

s h e a r i n g flows, t h e r e l a t i o n s h i p b e t w e e n t h e shear-

stress tensor a n d t h e shear-rate tensor is g i v e n b y C r i m i n a l e - E r i e k s e n -


136



F i l b e y e q u a t i o n (7). F o r cases o f s m a l l d e f o r m a t i o n a n d d e f o r m a t i o n g r a d i ents, the g e n e r a l l i n e a r viscoelastic m o d e l c a n be u s e d f o r unsteady m o t i o n o f a viscoelastic fluid. S u c h a m o d e l has a m e m o r y f u n c t i o n a n d a relaxation m o d u l u s . B i r d a n d c o - w o r k e r s (6, 7) gave details o f the available m o d e l s . I n the p r e v i o u s sections, fluids w e r e classified i n d i s t i n c t categories. H o w e v e r , some e m u l s i o n s cannot be fitted i n t o any one category. S o m e dispersions o r e m u l s i o n s e x h i b i t various n o n - N e w t o n i a n behaviors d e p e n d i n g o n the l e v e l o f the shear rate. F o r e x a m p l e , dispersions o f latex particles exhibit a N e w t o n i a n b e h a v i o r at v e r y l o w shear rate; a r a n d o m t h r e e - d i m e n sional structure is f o r m e d , a n d the B r o w n i a n m o t i o n is d o m i n a n t . T h i s c o n d i t i o n is s h o w n as a r e g i o n A i n F i g u r e 4. A t still a h i g h e r shear rate, the t h r e e - d i m e n s i o n a l structure changes to a t w o - d i m e n s i o n a l one a n d the vis cosity decreases w i t h shear rate. I n this r e g i m e , the fluid exhibits a sheart h i n n i n g b e h a v i o r . T h i s is r e g i o n B . A t still h i g h e r shear rate, the threed i m e n s i o n a l structure lends i t s e l f to a c o m p l e t e l y t w o - d i m e n s i o n a l structure a n d the suspension behaves as a N e w t o n i a n fluid (regime C ) . W h e n the shear rate is i n c r e a s e d f u r t h e r , the t w o - d i m e n s i o n a l o r d e r e d structure be c o m e s unstable a n d the s u s p e n s i o n viscosity increases (8, 9). I n this r e g i m e ( D ) , the fluid has a s h e a r - t h i c k e n i n g b e h a v i o r . A s w i l l be discussed i n the section " V i s c o s i t y o f E m u l s i o n w i t h A d d e d S o l i d s " , this b e h a v i o r was o b s e r v e d f o r a b i t u m e n - i n - w a t e r e m u l s i o n w i t h a d d e d solids. R e f e r e n c e s 10 a n d 11 give m o r e details 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 fluids.

Viscosity Measurements: Instruments T h e d i r e c t l y m e a s u r e d variables are not the fluid p r o p e r t i e s s u c h as viscos ity, b u t the forces, torques, a n d rate o f r o t a t i o n p e r t a i n i n g to a g i v e n a p p a ratus (7). I n some cases, the m e a s u r e d shear stress, τ, a n d shear rate y data c a n b e u s e d to construct a m o d e l o r use an established m o d e l to fit the data. S o m e o f the t y p i c a l apparatus u s e d to measure the r h e o l o g i c a l b e h a v i o r o f fluids w i l l be discussed i n the f o l l o w i n g section. A d e t a i l e d c o m p i l a t i o n o f c o m m e r c i a l r h e o l o g i c a l e q u i p m e n t is g i v e n i n r e f e r e n c e 12.

Capillary Tube. B a s i c a l l y , f o r these devices, the f r i c t i o n a l pressure d r o p associated w i t h the l a m i n a r flow o f the fluid o f interest is m e a s u r e d i n à c a p i l l a r y t u b e . N o r m a l l y , various t u b e lengths a n d diameters are u s e d to e l i m i n a t e e n d effects (13, 14). A p p e n d i x 1 (taken d i r e c t l y f r o m ref. 7) gives the i n t e r r e l a t i o n s h i p b e t w e e n the m e a s u r e d flow rate, pressure d r o p , shear stress, a n d shear rate (equations A - l to A - 3 ) . T h e c a p i l l a r y t u b e v i s c o m e t e r is not suitable f o r settling suspensions. T h i s i n s t r u m e n t suffers f r o m the fact that the shear rate is not constant across the t u b e radius a n d the fluid cannot b e sheared as l o n g as d e s i r e d . It is


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137

log -

·| ι » ι * i ' » * ' ί [Scale 1

Fluid -

Figure 5. Concentric cylinders

arrangement.


Rotating cup

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139


type o f a v i s c o m e t e r is not v e r y suitable f o r viscosity m e a s u r e m e n t o f s u s p e n sions. S u c h viscometers c a n give f a i r l y l o w a n d h i g h shear rates. T h e p e r t i n e n t r h e o l o g i c a l expressions f o r t h e cone a n d plate are g i v e n i n A p p e n d i x 1, equations B - l t o B - 5 .


Parallel

T h i s i n s t r u m e n t resembles t h e cone a n d

Plate Viscometer.

plate v i s c o m e t e r , except that i t has a flat h o r i z o n t a l r o t a t i n g plate i n p l a c e o f the c o n e . T h e shear rate w i t h i n t h e n a r r o w gap o f t h e t w o plates is n o t as u n i f o r m as f o r t h e c o n e a n d plate v i s c o m e t e r . T h e l i m i t i n g shear rates f o r t h e p a r a l l e l plate v i s c o m e t e r are s i m i l a r t o those o f t h e c o n e a n d plate i n s t r u m e n t . T h i s type o f a v i s c o m e t e r is suitable f o r r h e o l o g i c a l m e a s u r e m e n t s o f suspensions a n d e m u l s i o n s . T h e equations d e f i n i n g t h e various r h e o l o g i c a l quantities are g i v e n i n A p p e n d i x 1 b y equations C - l t o C - 5 .

Rheology of Emulsions The rheological behavior o f an emulsion can be Newtonian or n o n - N e w t o n i a n d e p e n d i n g u p o n its c o m p o s i t i o n . A t l o w t o m o d e r a t e values o f d i s -

Rotating cone with angular velocity W ' 1 "

1

1

κ

11 I i * l

I I I

\ h\

Fixed plate

Pressure—sensing devices

Figure 6. Cone and plate viscometer. (Reproduced with permission from refer ence 7. Copyright 1987 Wiley.)


140



persed-phase c o n c e n t r a t i o n , e m u l s i o n s g e n e r a l l y e x h i b i t N e w t o n i a n behav i o r . I n the h i g h - c o n c e n t r a t i o n range, e m u l s i o n s behave as s h e a r - t h i n n i n g fluids (17-21). F i g u r e 7 shows t h e r h e o g r a m s (shear stress versus shear rate plots) o f a t y p i c a l e m u l s i o n system at d i f f e r e n t values o f dispersed-phase c o n c e n t r a t i o n . T h e v o l u m e - s u r f a c e m e a n d i a m e t e r o f the o i l d r o p l e t s f o r t h e system s h o w n is 10 μιτι. F o r a g i v e n c o n c e n t r a t i o n , the v a r i a t i o n o f l o g τ against l o g y is l i n e a r , a result i n d i c a t i n g that t h e e m u l s i o n s f o l l o w a p o w e r l a w ( e q 2). T h e r h e o g r a m s s h o w n i n F i g u r e 7 i n d i c a t e that t h e e m u l s i o n s c o n s i d e r e d are N e w t o n i a n u p to a dispersed-phase c o n c e n t r a t i o n o f 4 0 % b y v o l u m e as t h e slope o f t h e r h e o g r a m s is u n i t y . A t dispersed-phase c o n c e n t r a tions above 4 0 % , t h e slope o f t h e rheograms is less t h a n u n i t y , a result i n d i c a t i n g a p s e u d o p l a s t i c o r s h e a r - t h i n n i n g b e h a v i o r ; that is, t h e apparent viscosity (the ratio o f t h e shear stress to t h e shear rate) decreases w i t h a n increase i n t h e shear rate. I n t h e c o n c e n t r a t i o n range i n w h i c h e m u l s i o n s behave as n o n - N e w t o n i a n fluids, the d e v i a t i o n o f the slope o f the rheograms f r o m u n i t y increases w i t h t h e increase i n t h e dispersed-phase c o n c e n t r a t i o n . A l s o , q u i t e l i k e l y at v e r y h i g h c o n c e n t r a t i o n s o f the d i s p e r s e d phase, e m u l sions m a y d e v e l o p a y i e l d stress ( y i e l d stress is t h e stress that m u s t b e e x c e e d e d b e f o r e any flow o f m a t e r i a l c a n take p l a c e ) . H a n a n d K i n g (22) h a d s h o w n that c o n c e n t r a t e d e m u l s i o n s c a n exhibit viscoelastic b e h a v i o r e v e n t h o u g h the d i s p e r s e d a n d t h e c o n t i n u o u s phases are b o t h N e w t o n i a n . F o r a g i v e n shear stress, t h e p r i m a r y n o r m a l stress

10

10

2

10

3

10

4

Figure 7. Rheograms of oil-in-water emulsions at different values of oil con centration. (Reproduced with permission from reference 21. Copyright 1990.)


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coefficient, ψ

Rheology of Emulsions ΐ9

141

was m a x i m u m at a dispersed-phase v o l u m e f r a c t i o n o f about

0.3. T h e system u s e d was I n d o p o l L l O O - g l y c e r i n e (22).

Viscosity of Emulsions. T h e viscosity o f an e m u l s i o n , d e f i n e d as the ratio o f shear stress to shear rate, d e p e n d s u p o n several factors: 1. the viscosity o f the c o n t i n u o u s phase


2. the v o l u m e f r a c t i o n o f the d i s p e r s e d phase 3. the viscosity o f the d i s p e r s e d phase 4. the average p a r t i c l e size a n d p a r t i c l e size d i s t r i b u t i o n 5. shear rate 6. the nature a n d the c o n c e n t r a t i o n o f the e m u l s i f y i n g agent 7.

temperature

T h e viscosity o f an e m u l s i o n is d i r e c t l y p r o p o r t i o n a l to the c o n t i n u o u s - p h a s e viscosity (η ), a n d therefore, a l l the viscosity equations p r o p o s e d i n the literature are w r i t t e n i n terms o f the relative viscosity (i7 ). I f an e m u l s i f y i n g agent is p r e s e n t i n the c o n t i n u o u s phase, as is the case w i t h e m u l s i o n s , rj is t h e n the viscosity o f the e m u l s i f i e r s o l u t i o n rather t h a n the viscosity o f the p u r e fluid phase (i.e., o i l o r w a t e r alone). W h e n an e m u l s i o n is p r e p a r e d , s o m e o f the e m u l s i f y i n g a g e n t b e c o m e s a d s o r b e d at the o i l - w a t e r interface; this a d s o r p t i o n tends to l o w e r the o r i g i n a l c o n c e n t r a t i o n o f e m u l s i f i e r i n the c o n t i n u o u s phase a n d cause a n associated decrease i n η . H o w e v e r , the a m o u n t o f e m u l s i f i e r a d s o r b e d is usually v e r y l o w c o m p a r e d w i t h the total a m o u n t present, a n d t h e r e f o r e any decrease i n c o n c e n t r a t i o n o f the e m u l s i fier c a n easily be n e g l e c t e d (23). 0

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T h e v o l u m e f r a c t i o n o f the d i s p e r s e d phase is the most i m p o r t a n t factor that affects the viscosity o f e m u l s i o n s . W h e n particles are i n t r o d u c e d i n t o a g i v e n flow field, the flow field b e c o m e s d i s t o r t e d , a n d c o n s e q u e n t l y the rate o f energy d i s s i p a t i o n increases, i n t u r n l e a d i n g to an increase i n the viscosity o f the system. E i n s t e i n (24, 25) s h o w e d that the increase i n the viscosity o f the system d u e to a d d i t i o n o f particles is a f u n c t i o n o f the v o l u m e f r a c t i o n o f the d i s p e r s e d particles. A s the v o l u m e f r a c t i o n o f the particles increases, the viscosity o f the system increases. Several viscosity equations have b e e n p r o p o s e d i n the literature r e l a t i n g viscosity to v o l u m e f r a c t i o n o f the d i s p e r s e d phase. W e discuss these equations i n a later s e c t i o n . U n l i k e a s o l i d - i n - l i q u i d suspension, the viscosity o f an e m u l s i o n m a y d e p e n d u p o n the viscosity o f the d i s p e r s e d phase. T h i s d e p e n d e n c e is espe c i a l l y t r u e w h e n i n t e r n a l c i r c u l a t i o n occurs w i t h i n the d i s p e r s e d d r o p l e t s . T h e p r e s e n c e o f i n t e r n a l c i r c u l a t i o n reduces the d i s t o r t i o n o f the flow field a r o u n d the droplets (26), a n d c o n s e q u e n t l y the o v e r a l l viscosity o f an e m u l sion is l o w e r t h a n that o f a suspension at the same v o l u m e f r a c t i o n . W i t h the


142



increase i n dispersed-phase viscosity, the i n t e r n a l c i r c u l a t i o n is r e d u c e d , a n d c o n s e q u e n t l y the viscosity o f an e m u l s i o n increases. T h e p h e n o m e n o n o f i n t e r n a l c i r c u l a t i o n is i m p o r t a n t o n l y w h e n the e m u l s i f i e r is not present at the d r o p l e t surface. T h e p r e s e n c e o f an e m u l s i f i e r greatly i n h i b i t s i n t e r n a l c i r c u l a t i o n (27), a n d the e m u l s i o n d r o p l e t s behave m o r e l i k e r i g i d particles. T h u s , i n the p r e s e n c e o f e m u l s i f i e r s , the effect o f dispersed-phase viscosity o n the o v e r a l l e m u l s i o n viscosity is n e g l i g i b l e . F o r m o n o d i s p e r s e o r u n i m o d a l d i s p e r s i o n systems (emulsions o r sus pensions), some l i t e r a t u r e (28-30) indicates that t h e relative viscosity is i n d e p e n d e n t o f the p a r t i c l e size. T h e s e results are a p p l i c a b l e as l o n g as the h y d r o d y n a m i c forces are d o m i n a n t . I n o t h e r w o r d s , forces d u e to the p r e s e n c e o f an e l e c t r i c a l d o u b l e layer o r a steric b a r r i e r (due to the a d s o r p t i o n o f m a c r o m o l e c u l e s onto the surface o f the particles) are n e g l i g i b l e . I n g e n e r a l the h y d r o d y n a m i c forces are d o m i n a n t (hard-sphere interaction) w h e n t h e s o l i d particles are relatively large (diameter >10 μ ι η ) . F o r particles w i t h diameters less t h a n 1 μ ι η , the c o l l o i d a l surface forces a n d B r o w n i a n m o t i o n c a n b e d o m i n a n t , a n d the viscosity o f a u n i m o d a l d i s p e r s i o n is n o l o n g e r a u n i q u e f u n c t i o n o f the solids v o l u m e f r a c t i o n (30). I n systems w h e r e B r o w n i a n m o t i o n is significant, the relative viscosity decreases w i t h t h e increase i n t h e p a r t i c l e size. F i g u r e 8 shows K r i e g e r ' s data (31 ) f o r a 5 0 % m o n o d i s p e r s i o n o f polystyrene spheres i n b e n z y l a l c o h o l i n t h e absence o f b o t h steric a n d electroviscous forces. A t a g i v e n shear stress, the relative viscosity decreases w i t h the increase i n the p a r t i c l e size. T h i s result i m p l i e s that the i m p o r t a n c e o f the B r o w n i a n m o t i o n decreases w i t h increase i n p a r t i c l e size. K r i e g e r (31) s h o w e d that t h e effect o f t h e

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X Figure 8. Relative viscosities vs. shear stress for 50% monodispersions of four different particle sizes of cross-linked polystyrene spheres in benzyl alcohol. (Reproduced with permission from reference 31. Copyright 1972 Elsevier.)


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B r o w n i a n m o t i o n c a n b e taken i n t o account b y p l o t t i n g η against the r e τ

d u c e d shear stress τ , g i v e n as Γ


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w h e r e k is the B o l t z m a n n constant a n d Τ is the absolute t e m p e r a t u r e . T h e data f o r the d i f f e r e n t s i z e d particles t h e n f a l l o n a single c u r v e , as s h o w n i n F i g u r e 9. F i g u r e 10 shows the v a r i a t i o n o f the relative viscosity w i t h the c o u n t e r i o n m o l a r i t y at d i f f e r e n t r e d u c e d shear stress values f o r m o n o d i s p e r s e polystyrene latex h a v i n g a d i a m e t e r o f 0.192 μ ι η at d i s p e r s e d phase v o l u m e f r a c t i o n φ = 0.509. C l e a r l y , η is a f u n c t i o n o f the electrolyte c o n c e n t r a t i o n i n a d d i t i o n to the r e d u c e d shear stress. F i g u r e 11 shows the r e l a t i v e - v i s c o s i t y - c o n c e n t r a t i o n b e h a v i o r f o r a v a r i ety o f h a r d - s p h e r e suspensions o f u n i f o r m - s i z e glass beads. E v e n t h o u g h the p a r t i c l e size was v a r i e d substantially (0.1 to 440 μ ι η ) , the relative viscosity is i n d e p e n d e n t o f the p a r t i c l e size. H o w e v e r , w h e n the p a r t i c l e d i a m e t e r was s m a l l (~1 μ ι η ) , the relative viscosity was c a l c u l a t e d at h i g h shear rates, so that the effect o f B r o w n i a n m o t i o n was n e g l i g i b l e . F i g u r e 8 shows that η b e c o m e s i n d e p e n d e n t o f the p a r t i c l e size at h i g h shear stress (or shear rate). τ

τ

T h e effect o f p a r t i c l e size d i s t r i b u t i o n o n the viscosities o f suspensions a n d e m u l s i o n s has b e e n investigated (28, 32-35). M o s t o f these studies i n d i c a t e that the effect o f p a r t i c l e size d i s t r i b u t i o n is o f e n o r m o u s m a g n i t u d e

Figure 9. Relative viscosities vs. reduced shear stress for 50% monodispersions of polystyrene spheres of various sizes in different media. Points are taken from Figure 8. (Reproduced with permission from reference 31. Copyright 1972 Elsevier.)


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Counterion Molarity Figure 10. Variation of relative viscosity of monodisperse polystyrene latex with electrolyte concentration at different reduced shear stress. (Reproduced with permission from reference 31. Copyright 1972 Elsevier.)

at h i g h values o f dispersed-phase c o n c e n t r a t i o n . A t l o w c o n c e n t r a t i o n s , h o w e v e r , the effect is s m a l l . F i g u r e 12 shows C h o n g et a l . (28) data f o r m o n o d i s p e r s e a n d b i d i s p e r s e ( b i m o d a l ) s u s p e n s i o n systems. I n a b i d i s p e r s e s u s p e n s i o n , t h e v o l u m e frac t i o n o f s m a l l spheres (diameter d) i n t h e m i x t u r e is k e p t constant at 2 5 % o f the total solids. T h e figure shows that t h e viscosity o f a b i d i s p e r s e s u s p e n s i o n is a strong f u n c t i o n o f the p a r t i c l e size ratio, d/D, w h e r e D is the d i a m e t e r o f the large particles. T h e viscosity decreases substantially b y d e c r e a s i n g d/D at a g i v e n total solids c o n c e n t r a t i o n . T h e data f o r the u n i m o d a l system f a l l w e l l above the b i m o d a l suspensions. A l s o , t h e effect o f p a r t i c l e size d i s t r i b u t i o n decreases at l o w e r values o f total solids c o n c e n t r a t i o n . F i g u r e 13 illustrates a n o t h e r v e r y i n t e r e s t i n g p o i n t . H e r e the relative viscosity o f a b i m o d a l suspension is p l o t t e d as a f u n c t i o n o f v o l u m e p e r c e n t o f s m a l l spheres i n total solids. A t any g i v e n total solids c o n c e n t r a t i o n , t h e relative viscosity decreases i n i t i a l l y w i t h the increase i n v o l u m e p e r c e n t o f s m a l l spheres, a n d t h e n i t increases w i t h f u r t h e r increase i n s m a l l spheres. T h e m i n i m u m o b s e r v e d i n the relative viscosity plots o f a b i m o d a l s u s p e n s i o n is q u i t e t y p i c a l . T h e r e are n o f u n d a m e n t a l reasons w h y a s i m i l a r b e h a v ior w o u l d not be true for emulsions.


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Rheology of Emulsions - American Chemical Society

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