The Rheology of Concentrated Suspensions of Fibers - Advances in

10 The Rheology of Concentrated Suspensions of Fibers Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 13, 2017 | http://pubs.acs.org Publication Date: June 1, 1974 | doi: 10.1021/ba-1974-0134.ch010

I.

Review of the Literature

RICHARD

O.

MASCHMEYER

and

CHRISTOPHER

T.

HILL

Materials Research Laboratory, Washington University, St. Louis, M o . 63130

The sparse literature on the rheological properties of con centrated suspensions is reviewed. Various authors have obtained widely different flow curves and have made con flicting observations regarding yieldstresses,fiberbreakage, extrusion forcefluctuations,and elastic effects. Most of the differences can probably be attributed to failure to control or measure fiber length distribution in suspension. Recent work in our laboratory is summarized, and suggestions are made for both experimental and theoretical research needed.

A

l a r g e p o r t i o n of short-fiber r e i n f o r c e d thermoset a n d t h e r m o p l a s t i c materials are p r o c e s s e d b y flow m o l d i n g t e c h n i q u e s i n c l u d i n g t r a n s -

fer-, i n j e c t i o n - , a n d c o m p r e s s i o n m o l d i n g .

E a c h processing

technique

i n v o l v e s t h e flow i n c o m p l e x geometries of suspensions of short

fibers

( u s u a l l y glass) a n d / o r r i g i d p a r t i c l e s i n fluids w h i c h a r e p o l y m e r melts or l i q u i d p r e p o l y m e r s . T h e s e suspensions are u s u a l l y h i g h l y c o n c e n t r a t e d ( 1 0 - 5 0 % solids b y v o l u m e ) , a n d t h e y often c o n t a i n trace amounts of a n i m m i s c i b l e s e c o n d p h a s e s u c h as w a t e r , a l u b r i c a n t , o r a w e t t i n g agent. T h e rational design of m o l d i n g equipment i n c l u d i n g plasticating devices, m o l d i n g m a c h i n e r u n n e r s a n d gates, a n d m o l d s r e q u i r e s a k n o w l edge o f the flow properties of the m a t e r i a l to b e m o l d e d at the p r o c e s s i n g c o n d i t i o n s of t e m p e r a t u r e , pressure, a n d shear rate.

These

properties

d e p e n d o n m a t e r i a l v a r i a b l e s s u c h as m a t r i x r h e o l o g y ; fiber l e n g t h , stiffness, a n d s t r e n g t h ; v o l u m e f r a c t i o n of fibers a n d / o r p a r t i c u l a t e

fillers;

a n d t h e n a t u r e a n d a m o u n t o f w e t t i n g agents, l u b r i c a n t s , o r other a d d i tives.

S i n c e w e cannot e v a l u a t e t h e flow properties f o r every m a t e r i a l

of interest, w e w o u l d p r e f e r sufficient e m p i r i c a l k n o w l e d g e a n d t h e o r e t i 95 Deanin and Schott; Fillers and Reinforcements for Plastics Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

96

FILLERS A N D R E I N F O R C E M E N T S FOR PLASTICS

c a l s u p p o r t to be able to p r e d i c t the flow b e h a v i o r of c o m m e r c i a l m o l d i n g c o m p o u n d s w i t h some certainty. M o s t of the d a t a a v a i l a b l e i n this area are c o n f o u n d e d b y w i t h resin a n d / o r

fiber

problems

d e g r a d a t i o n or l a c k of c o n t r o l of one or m o r e

i m p o r t a n t v a r i a b l e s . I n this l a b o r a t o r y w e are d e v e l o p i n g the r e q u i s i t e empirical background

concerning

the r h e o l o g y

of

concentrated

suspensions necessary to construct a w e l l - f o u n d e d m o d e l of

fiber

reinforced

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 13, 2017 | http://pubs.acs.org Publication Date: June 1, 1974 | doi: 10.1021/ba-1974-0134.ch010

plastics processing. Significance

of Rhéologieal Measurements in Concentrated Suspensions

V i s c o s i t y is a true m a t e r i a l p a r a m e t e r o n l y for h o m o g e n e o u s m a t e rials, a n d s h o r t - f i b e r - r e i n f o r c e d plastics c a n s e l d o m be treated as h o m o geneous. T h u s , the m e a s u r e d viscosity of a suspension m a y d e p e n d

upon

b o t h the flow g e o m e t r y a n d the geometry of the s u s p e n d e d m a t e r i a l . A p a r t i c u l a r suspension m a y h a v e different properties i n s i m i l a r geometries of different size—e.g., the viscosity of a suspension i n c a p i l l a r y flow m a y d e p e n d u p o n the d i a m e t e r of the c a p i l l a r y . T h e d e p e n d e n c e of viscosity o n g e o m e t r y is the result of b o t h the o r i e n t a t i o n of the fibers d u r i n g flow a n d t h e i n t e r a c t i o n of particles w i t h the w a l l of the m e a s u r i n g i n s t r u m e n t . W a l l i n t e r a c t i o n , w h i c h has b e e n

Table I.

Research Group S t a n k o i et al. (24)

Thomas & H a g e n (25) Newman & Trementozzi (26) Carter & G o d d a r d (27) M i l l s (28) B e l l (29) Ziegel (30)

Takano (31-32) K a r n i s et al. (33)

Viscometer Dimension (inch) Viscometer (dia/gap) Matrix capillary capillary capillary

Previous Measurements on

Material

0.35-0.47 polyester a n d kaolin clay 0.06 polypropylene 0.5

styreneacrylonitrile (copolymer) cone & 0.16 polybutene plate oil capillary ? polyethylene capillary 0.12-0.25 B - s t a g e d epoxy couette ? various polymers, l i q u i d at R T capillary 1 to 1/4 B-staged rectangular epoxy couette & 0.076castor o i l capillary 0.40

Fiber Type and Length, inch glass, 0.8 glass, 0.18-0.44 wollastonite, 10~

glass, 0.008-0.03 glass, 0.25 glass, 0.125 glass, 0.24

glass, 0.125-0.5 n y l o n , 0.049

Deanin and Schott; Fillers and Reinforcements for Plastics Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

3

10.

MASCHMEYER AND

Suspensions

HILL

of

97

Fibers

t h o r o u g h l y s t u d i e d for spheres a n d d i l u t e suspensions, is d e s c r i b e d i n terms of

(a)

m e c h a n i c a l i n t e r a c t i o n i n v o l v i n g p h y s i c a l contact of

p a r t i c l e w i t h the w a l l (1, 2);

(b)

the

hydrodynamic interaction, i n w h i c h

the presence of the w a l l alters the v e l o c i t y profile a r o u n d t h e p a r t i c l e ( 3 , 4);

a n d ( c ) r a d i a l m i g r a t i o n i n w h i c h p a r t i c l e s i n t u b e flow m i g r a t e

either t o w a r d or a w a y f r o m the flow axis ( 5, 6, 7, 8, 9 ). A l t h o u g h the m a g n i t u d e of these effects i n d i l u t e fiber suspensions


does not seem l a r g e ( 1 0 ) , t h e i r i m p o r t a n c e i n c o n c e n t r a t e d

suspensions

of fibers is u n k n o w n . T h u s , a l t h o u g h s u m m a r i z i n g short-fiber r e i n f o r c e d p l a s t i c flow d a t a i n terms of v i s c o s i t y is u s e f u l for i n t e r p r e t a t i o n i n terms of past experience, the d a t a m a y b e v a l i d o n l y for the g e o m e t r y i n w h i c h it was measured. Concentrated Suspension Viscosity

Data

T h e flow of c o n c e n t r a t e d suspensions of s p h e r i c a l particles has b e e n s t u d i e d for m a n y years ( I I , 12, 13).

W h i l e c l a s s i c a l studies w e r e

con-

c e r n e d p r i m a r i l y w i t h the effect of v o l u m e f r a c t i o n of solids o n suspension viscosity, m o r e recent w o r k has c o n s i d e r e d effects of 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 (8,14),

w e t t i n g a n d second fluid phases ( 1 5 , 1 6 ,

a n d v i s c o e l a s t i c i t y of the fluid phase ( I S , 19, 20, 21,

17),

22,23).

Concentrated Suspensions of Fibers Shear Rate, sec'

Volume Fraction, Aspect

Ratio

?

1

15

Force Fluctuation

Yield Stress

Fiber Breakage

5-150

yes

yes

no

yes

no

perhaps

?

0-40

0.38-386

10

0-50

3-3000

?

?

no

no

?

yes

yes

52-228

0.5-2.2

0.167-167

400 200

20 45-63

30 & 900 8-100

500

2

0.5-1.2

200-800

0-60

?

8

8

yes ?

yes

yes

yes

yes

no force m e a s u r e ments


98

FILLERS A N D R E I N F O R C E M E N T S FOR PLASTICS

A synopsis of e x p e r i m e n t a l l i t e r a t u r e o n the r h e o l o g y of c o n c e n t r a t e d fiber

suspensions d o n e o u t s i d e o u r l a b o r a t o r y is s h o w n i n T a b l e I.

c o l u m n s are m o s t l y s e l f - e x p l a n a t o r y ; force vation by

fluctuation

The

refers to the obser-

some that the force r e q u i r e d to extrude

fiber

suspensions

t h r o u g h c a p i l l a r i e s fluctuates w i t h t i m e . Insufficient d a t a w e r e a v a i l a b l e to c o m p a r e the flow curves f r o m a l l researchers o n the same basis, so the q u a l i t a t i v e c o m p a r i s o n of F i g u r e 1 w a s c o n s t r u c t e d .

O n l y the r e l a t i v e


shapes a n d shear-rate ranges are significant.

CAPILLARY 15% (35)

CAPILLARY

^sS.

0 - 40% ^S^s. (48, 55)

_

CONE AND PLATE 0 - 2 % (57)

COUETTE 2% (15)

°·

1

CAP. 0-60% (36)

. >O - ^

I

.. J -

1

10

CAP. 20% (56)

w

1 100

1000

SHEAR RATE (SEC ) -1

Figure

1.

Qualitative comparison of viscosity data suspensions of fibers

for

N o n e of these w o r k s p r o v i d e a firm basis for u n d e r s t a n d i n g melt-state r h e o l o g y of r e i n f o r c e d plastics. T h e t h r u s t of the w o r k s of B e l l T a k a n o (31,

32)

a n d K a r n i s et al

v a r i o u s parameters

on

fiber

(33)

(29),

was to m e a s u r e the effect of

orientation i n

flow,

and no

viscosity d a t a w e r e p u b l i s h e d . T h e d a t a of M i l l s (28)

quantitative

are f r a g m e n t a r y

since o n l y t w o c a p i l l a r y v i s c o s i t y points for fiber suspensions w e r e p u b l i s h e d . C a r t e r a n d G o d d a r d (27)

a n d Z i e g e l (30)

m e a s u r e d suspensions

w i t h fiber concentrations w e l l b e l o w those of c o m m e r c i a l interest. m a n a n d T r e m e n t o z z i (26) fillers

New-

w e r e p r i m a r i l y interested i n the effects of

o n d i e s w e l l . T h e y p u b l i s h e d one specific viscosity-t>s.-fiber

con-

c e n t r a t i o n c u r v e a l t h o u g h the fibers i n v o l v e d w e r e q u i t e s m a l l a n d h a d l o w aspect ratios. T h o m a s a n d H a g e n (25)

d i d a m o r e t h o r o u g h s t u d y of short-fiber

r e i n f o r c e d t h e r m o p l a s t i c r h e o l o g y w i t h v a r i a b l e s i n the r e g i o n of m e r c i a l interest for suspensions of glass fibers i n p o l y p r o p y l e n e . flow

curves fit a p o w e r l a w m o d e l , a n d n o y i e l d stresses w e r e

comTheir

observed.


10.

MASCHMEYER

A N D HILL

Suspensions

of

99

Fibers

M i c r o s c o p i c i n s p e c t i o n of the extrudate s h o w e d no fiber m i g r a t i o n a n d possible fiber b r e a k a g e o n l y at the highest shear rates. T h e i r q u a n t i t a t i v e results, h o w e v e r , are o b s c u r e d b y r e s i n d e g r a d a t i o n i n c u r r e d i n m i x i n g . S t a n k o i et al. (24)

m e a s u r e d viscosities of suspensions of glass

a n d k a o l i n c l a y i n a polyester p r e p o l y m e r .

fibers

T h e i r flow curves, w h i c h d i s -

p l a y e d y i e l d stresses, w e r e consistent w i t h a B i n g h a m plastic m o d e l .

They

o b s e r v e d no fiber m i g r a t i o n or breakage. Since t h e y d i d not r e p o r t m a t r i x


resin r h e o l o g i c a l d a t a , it is difficult to generalize t h e i r q u a n t i t a t i v e data to other systems. Elastic Effects and Normal Stresses in Concentrated Suspensions C o n t r a d i c t o r y observations h a v e b e e n m a d e c o n c e r n i n g elastic a n d n o r m a l - s t r e s s - d r i v e n p h e n o m e n a i n fiber suspensions. m e n t o z z i (26)

Newman and Tre-

f o u n d that the a d d i t i o n of w o l l a s t o n i t e filler to a v i s c o -

elastic r e s i n g r e a t l y r e d u c e d the c a p i l l a r y d i e s w e l l . C a r t e r a n d G o d d a r d (27)

d e t e c t e d no phase l a g i n d y n a m i c o s c i l l a t o r y testing of a suspension

of short fibers i n a cone a n d plate i n s t r u m e n t , b u t t h e y m e a s u r e d large p r i m a r y n o r m a l stress differences.

A s d i s c u s s e d later, R o b e r t s (34,

35)

o b e s e r v e d massive W e i s s e n b e r g r o d c l i m b i n g a n d large c a p i l l a r y entrance corrections for a suspension (glass fibers i n a n i n e l a s t i c o i l ) w h i c h d i s p l a y e d no d i e s w e l l a n d no elastic r e c o v e r y w h e n r a p i d l y d e f o r m e d . Recent Study of Fiber Suspension Rheology T h e r e v i e w a b o v e indicates that there is little agreement researchers a b o u t the flow b e h a v i o r of c o n c e n t r a t e d

fiber

among

suspensions,

e v e n o n a q u a l i t a t i v e l e v e l . T h e i r results d o suggest, h o w e v e r , the f o l lowing points: ( a ) C o n c e n t r a t e d fiber suspensions are h i g h l y n o n - N e w t o n i a n , a n d they m a y h a v e h i g h y i e l d stresses ( b ) F o r c e vs. d i s p l a c e m e n t curves i n c a p i l l a r y rheometers fluctuations, p r o b a b l y f r o m l o g - j a m m i n g at the c a p i l l a r y entry

show

( c ) F l o w p r o p e r t i e s m a y b e sensitive to fiber o r i e n t a t i o n a n d , hence, to v i s c o m e t e r g e o m e t r y (d) F i b e r breakage during changes i n suspension v i s c o s i t y

flow

c a n be

severe a n d cause

large

( e ) B r o d n y a n s t h e o r y (36) of fiber suspension r h e o l o g y p r e d i c t s viscosities w h i c h are orders of m a g n i t u d e too large for c o n c e n t r a t e d suspensions of h i g h aspect r a t i o fibers ( f ) O b s e r v a t i o n s of elastic effects are c o n t r a d i c t o r y . I n v i e w of the difficulties i n w o r k i n g d i r e c t l y w i t h short-fiber r e i n f o r c e d plastics, w e h a v e s t u d i e d the r h e o l o g y of a m o d e l system of glass fibers

i n silicone o i l (34,

35, 37, 38, 39).

V i s c o s i t y measurements


were

100

FILLERS

AND

REINFORCEMENTS FOR

PLASTICS

d o n e w i t h the l a r g e b o r e c a p i l l a r y r h e o m e t e r s h o w n i n F i g u r e 2.

This

d e v i c e , w h i c h is d e s i g n e d for r o o m t e m p e r a t u r e o p e r a t i o n , a l l o w s m e a s u r e m e n t of steady flow viscosity a n d c a p i l l a r y e n t r a n c e corrections the shear rate r a n g e 0.055-5500 sec" . 1

over

C a p i l l a r i e s are a v a i l a b l e w i t h


l e n g t h - t o - d i a m e t e r ratios f r o m 1 to 32 a n d diameters of Vs a n d *4 i n c h .

Capillary

Instron Compression Cell

Figure 2.

Capillary

viscometer

T y p i c a l n o n - N e w t o n i a n viscosity curves for 15 a n d 30 v / o

suspensions

of glass fibers i n 600-poise s i l i c o n e o i l are s h o w n i n F i g u r e 3 as o b t a i n e d in our rheometer (39).

T h e s e d a t a w e r e c o r r e c t e d for c a p i l l a r y entrance

losses b y the m e t h o d of B a g l e y (40),

b u t the R a b i n o w i t s c h c o r r e c t i o n for

n o n - N e w t o n i a n effects was not u s e d .

The median

fiber

lengths

were

a p p r o x i m a t e l y 0.005 i n c h i n e a c h case, a n d t h e suspensions w e r e so w e l l m i x e d that n o f u r t h e r fiber d e g r a d a t i o n o c c u r r e d d u r i n g testing. A p a n e l ( 3 7 ) a n d S h e l t o n ( 3 8 ) s t u d i e d the effect of r e p e a t e d c a p i l l a r y extrusion o n t h e v i s c o s i t y a n d fiber l e n g t h d i s t r i b u t i o n s of 15 v / o % - i n c h glass fibers i n silicone oils.

Photomicrographs

of a t y p i c a l suspension

t a k e n after v a r i o u s runs ( F i g u r e 4 ) c l e a r l y s h o w that b r e a k a g e


occurs.

10.

MASCHMEYER AND

Suspensions

HILL

of

101

Fibers


10"

Q_ Q_

10°

ίο

ίο

1

ίο

2

10 *

3

1

APPARENT SHEAR RATE (SEC* ) 1

Figure 3. Apparent non-Newtonian viscosity of suspen sions of glass fibers in 600-poise oil (O, Vi-inch capillary; A, V8-inch capillary)

Figure 4. Photomicrographs of glass fibers after repeated extrusion through the capillary viscometer. Left to right, after 0, 10, and 20 runs. Dark bar is a bundle of fibers Vs-inch long (37). F i g u r e 5 shows t y p i c a l extrusion d a t a . T h e curves for the 1- a n d 6 - i n c h c a p i l l a r i e s , w h e n n o r m a l i z e d , s u p e r i m p o s e to y i e l d one c u r v e , i n d i c a t i n g that fiber d a m a g e occurs i n the c a p i l l a r y e n t r y r e g i o n a n d not d u r i n g passage t h r o u g h the c a p i l l a r y . T h e extent of d a m a g e is h i g h e r at h i g h e r e x t r u s i o n rates, b u t a suspension w h i c h s h o w e d no m e a s u r a b l e d e g r a d a t i o n after m u l t i p l e passes at l o w shear rates s h o w e d a c o n s i d e r a b l e d r o p i n v i s c o s i t y w h e n tested at h i g h rates ( F i g u r e 5 ) .

Therefore, a drop i n

extrusion f o r c e m a y not be a sufficient test of fiber d a m a g e . Roberts

(34,

35)

has c o m p l e t e d

s t u d y of the v i s c o s i t y of m i x e d

suspensions of v a r i o u s ratios of % - i n c h glass fibers to 30-μ glass spheres, at a constant t o t a l solids v o l u m e f r a c t i o n of 1 5 % i n the 600-poise s i l i c o n e


102

FILLERS


2000

AND

REINFORCEMENTS FOR

PLASTICS

-

6" CAPILLARY 5 IN/MIN

1000

10

15

20

25

NUMBER OF EXTRUSIONS

Figure 5. Effect of repeated extrusion on extrusion force for suspensions of 15 v/o glass fibers in silicone oil. Legends indicate capillary length and Instron crosshead speed (37). o i l . H i s d a t a are s h o w n i n F i g u r e 6, a n d plots of the B a g l e y e n d c o r r e c t i o n , e (40),

vs. shear stress are s h o w n i n F i g u r e 7. E v e n t h o u g h these

e n d corrections are large, the suspensions e x h i b i t e d n o d i e s w e l l u p o n e x i t i n g f r o m the c a p i l l a r y . T h e y d o e x h i b i t a v e r y s t r o n g W e i s s e n b e r g r o d c l i m b i n g effect, as s h o w n i n F i g u r e 8.

T h e e n d corrections r e s u l t

f r o m the l a r g e forces r e q u i r e d to r e o r i e n t the fiber mass as i t enters the c a p i l l a r y a n d not f r o m the u s u a l effect of storage of e n e r g y i n a n elastic polymer network. Research Needs D e s p i t e the r a p i d g r o w t h i n the use of short fiber r e i n f o r c e d c o m posites, r e l a t i v e l y f e w w o r k s o n the r h e o l o g y of c o n c e n t r a t e d fiber sus-


10.

MASCHMEYER

AND

Suspensions

HILL

1G°

of

103

Fibers

1

1 % SPHERES/% FIBERS 0/15v

10',4

3/12 6/9

-


12/3

S

10

10

>v

-

V

15/0

3

^ ^ · \ \ ,

0/0

f

z

1

10

100

1000

SHEAR RATE (SEC ) -1

Figure

40

% SPHERES/% FIBERS

6.

Viscosities of glass sphere/glass silicone oil suspensions (34).

40

fiber/

SPHERES/% FIBERS

15/0

12/3

20

20

0

1

h ο

2

ο

3

4 9

/

5

6

5

6

6

ο

1? 0

1

2

3

4

3/12 •Ω—Û

0

1

2

3

4

ο-

5

6

0

1

2

H0RIZ0NAL AXIS:

SHEAR STRESS, PSI

VERTICAL AXIS:

END CORRECTION

3

4

5

6

Figure 7. End corrections for glass sphere/glass fiber/silicone oil sus pensions (34)

pensions h a v e a p p e a r e d . M o r e e x p e r i m e n t a l w o r k is n e e d e d to e l u c i d a t e the d e p e n d e n c e of suspension r h e o l o g y u p o n t h e properties of the c o m ponents, the n a t u r e of t h e i r interface, t h e c o n d i t i o n s u n d e r w h i c h t h e y



104

FILLERS

AND

REINFORCEMENTS F O RPLASTICS

Figure 8. Rod climbing during mixing of 3 v/o glass fibers, 12 v/o ghss beads in silicone oil at 2 rpm (34) are m i x e d , a n d the flow geometry.

W h i l e v o l u m e f r a c t i o n o f the

fiber

phase is i m p o r t a n t , there is a c l e a r i n d i c a t i o n that t h e fiber l e n g t h d i s t r i b u t i o n m a y p l a y a k e y role i n d e t e r m i n i n g t h e m a g n i t u d e o f suspension viscosity. T h e r e is also a n e e d for t h e o r e t i c a l analysis o r m o d e l i n g o f the flow

properties o f c o n c e n t r a t e d suspensions o f fibers i n w h i c h t h e m e

c h a n i c a l interactions o f the fibers are c o n s i d e r e d t o b e large. A c o m p l e m e n t a r y effort t o p r e d i c t t h e d e p e n d e n c e o f the fiber l e n g t h d i s t r i b u t i o n o n m i x i n g c o n d i t i o n s a n d t i m e is also n e e d e d .

Literature Cited 1. 2. 3. 4. 5. 6.

Maude, Α., Whitmore, R., Brit. J. Appl. Phys. (1956) 7, 98. Maude, Α., Brit. J. Appl. Phys. (1959) 10, 371. Vand, V., J. Phys. Chem. (1948) 52, 287. Goldman, Α., Cox, R., Brenner, H., Chem. Eng. Sci. (1967) 22, 637. Segre, G., Silberberg, Α., J. Fluid Mech. (1962) 14, 136. Karnis, Α., Goldsmith, H., Mason, S. G., Can. J. Chem. Eng. (1966) 44, 181. 7. Seshadri, V., Sutera, S., J. Colloid Interface Sci. (1968 ) 27, 101. 8. Seshadri, V., Sutera, S., Trans. Soc. Rheol. (1970) 14, 351. 9. Cox, R., Brenner, H., Chem. Eng. Sci. (1968) 23, 147. 10. Attansio, Α., Bernini, U., Galloppo, P., Segre, G., Trans. Soc. Rheol. (1972) 6, 147. 11. Rutgers, I. R., Rheol. Acta (1962) 2, 202, 305; (1963) 3, 118. 12. Frankel, Ν. Α., Acrivos, Α., Chem. Eng. Sci. (1967) 22, 847. 13. Brenner, H., Ann. Rev. Fluid Mech. (1970) 2. 14. Eagland, D., Kay, M., J. Colloid Interface Sci. (1970) 34, 249. 15. Woods, M. E., Krieger, I. M., J. Colloid Interface Sci. (1970) 34, 91. 16. Papir, Y. S., Krieger, I. M., J. Colloid Interface Sci. (1970) 34, 126. 17. Kao, S. V., D.Sc. Thesis, Washington University, St. Louis (1973). 18. Highgate, D. J., Whorlow, R. W., Rheol. Acta (1970) 9, 569.


10.

MASCHMEYER AND HILL

Suspensions of Fibers

Agarwal, P. K., M.S. Thesis, Washington University, St. Louis (1971). Nazem, F., D.Sc. Thesis, Washington University, St. Louis (1973). Schmidt, L. R., M.S. Thesis, Washington University, St. Louis (1967). Nazem, F., Hill, C. T., Trans. Soc. Rheol. (1974) 18, 87. Onogi, S., Matsumoto, T., Warashina, Y., Trans. Soc. Rheol. (1973) 17, 175. 24. Stankoi, G. G., Trostyanskaya, E. B., Kazanski, Tu. Ν., Okorokov, V. V., Mikhasenok, Ya., Soviet Plastics (Sept. 1968), 47. 25. Thomas, D. P., Hagan, R. S., Ann. Meetg. Reinforced Plastics Div., Soc. Plastics Ind., 1966. 26. Newman, S., Trementozzi, Q. Α., J. Appl. Polymer Sci. (1965) 9, 3071. 27. Carter, L., Goddard, J., NASA Rept. N67-30073 (1967). 28. Mills, N., J. Appl. Polymer Sci. (1971) 15, 2791. 29. Bell, J., J. Composite Material (1969) 3, 244. 30. Ziegel, K.D.,J. Colloid Interface Sci. (1970) 34, 185. 31. Takano, M., "Flow Orientation of Short Fibers in Rectangular Channels," Report #HPC-70-116. Monsanto/Washington University Association, February 1974. 32. Takano, M., unpublished data. 33. Karnis, Α., Goldsmith, H. L., Mason, S. G., J. Colloid Interface Sci. (1966) 22, 531. 34. Roberts, K. D., M.S. Thesis, Washington University, St. Louis (1973). 35. Roberts, K. D., Hill, C. T., Ann. Tech. Conf., Soc. Plastics Engrs., Montreal, May 1973. 36. Brodnyan, J. G., Trans. Soc. Rheol. (1959) 3, 61. 37. Apanel, G., Undergraduate Research Report, Washington University, St. Louis (1971). 38. Shelton, R. D., Undergraduate Research Report, Washington University, St. Louis (1971). 39. Maschmeyer, R. O., D.Sc. Thesis, Washington University, St. Louis (1974). 40. Bagley, E. B., Schreiber, H. P., "Rheology," Vol. V, F. R. Eirich, Ed., Aca demic, New York, 1969. RECEIVED October 11, 1973. Part of this work conducted under the Monsanto/ Washington University Association sponsored by the Advanced Research Proj ects Agency, Department of Defense, Office of Naval Research contract N0001467-C-0218 (formerly N00014-66-C-0045). Other portions supported by Na tional Science Foundation grant No. GH34594. Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 13, 2017 | http://pubs.acs.org Publication Date: June 1, 1974 | doi: 10.1021/ba-1974-0134.ch010

19. 20. 21. 22. 23.

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The Rheology of Concentrated Suspensions of Fibers - Advances in

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