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An experimental investigation of thixotropy and flow of thixotropic suspensions through tubes

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An experimental investigation of thixotropy and flow of thixotropic suspensions through tubes

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Content A N EXPERIMENTAL INVESTIGATION OP THIXOTROPY A N D
PLO W OF THIXOTROPIC SUSPENSIONS TH R O U G H TUBES
A T h esis
P re s e n te d to
th e F a c u lty o f th e School o f E n g in eerin g
The U n iv e rs ity o f S outhern C a lif o r n ia
In P a r t i a l F u lf illm e n t
o f th e R equirem ents f o r th e Degree
M aster o f S cien ce in Chem ical E n g in ee rin g
• V . .
by
Mehdl M ehrali
Ju n e 1958
UMI Number: EP41760
All rights reserved
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q I 'S ? M W
This thesis, written by * 3 ^ ® i
Mehdi Mehrali
under the guidance of Faculty Committee
and approved by all its members, has been
presented to and accepted by the School of
Engineering in partial fulfillment of the re
quirements for the degree of
.......................Master o f ..Science., i n ......................
G hCTic^,£^inee^ng
Date ^ n e , 1958..................
of
Faculty Committee
Chairman
TABLE OF CONTENTS
CHAPTER ‘ PAGE
I . THE PROBLEM A N D RHEQLOGIGAL DEFINITIONS . . . . 1
A. The P ro b le m .................... . ........................ 1
S tatem en t o f th e P r o b l e m ................ 1
Im portance o f th e S t u d y .................... 1
B. R h e o lo g ic a l D e f in itio n s ................................. 1
I I . REVIEW A N D INTERPRETATION OF THE LITERATURE . . 4
A. G eneral . . ....................... 4
Newtonian L iq u id s .............................................. 4
Non-Newtonian F lu id s ..................................... 6
B. V isco m etric S tu d ie s ................................. 7
T h ix o tro p y ......................................... 7
T h ix o tro p ie Breakdown w ith Time . . . . 8
T h lx o tro p ic Breakdown w ith R ate o f
S h e a r .......................................................................... 10
I n t e r p r e t a t i o n .. .. . .. ................... 11
C. S tudy o f R h e o lo g ic a l P r o p e r tie s U sing
Tubes and P i p e s ........................... 13
T u rb u len t F l o w ........................................................15
I I I . EXPERIMENTAL METHODS...............................................17
M a te ria l U s e d ...........................................................17
V iscom eter Used . .................................... 17
P re p a r a tio n and D e s c rip tio n o f th e A pparatus 18
i l l
CHAPTER PAGE
I I I . EXPERIMENTAL M ETHODS (co n tin u e d )
P erform ance o f th e T e sts ...............................20
A dvantages and D isad v an tag es o f th e
A p p aratu s . . . . . . ................................................ 21
IV. THE RESULTS A N D THEIR DISCUSSION....................................23
A. C a lc u la tio n ...................... 23
B. The R e s u lts , E v a lu a tio n and D isc u ssio n . . 26
S hear D i a g r a m .......................................................... 29
R ate o f S hear - Time D ia g ra m .......................... 35
L im itin g D iam eter f o r V iscous Plow . . . 35
V. PRACTICAL APPLICATION A N D CONCLUSIONS .................... 42
A. P r a c ti c a l A p p l i c a t i o n ............................................ 42
B. C o n clu sio n s . .......................................................... 43
Recommendations . . . . . . . . . . . . 45
BIBLIOGRAPHY........................................................................ 47
APPENDIX .................................................................................50
LIST OP TABLES
TABLE PAGE
I . R e s u lts o f In s ta n ta n e o u s V olum etric R ate
o f P l o w .............................................................. 27
I I . R e s u lts o f C a lc u la tio n f o r Shear S tr e s s and
R ate o f S hear .................................................................... 28
I I I . R e s u lts o f V isco m etric M easurem ents ................... 31
IV . R e s u lts o f R esidence Time a s a F u n ctio n o f
R ate o f S hear .................................................... 37
V. Changes o f D0 w ith L ength ..................................... 40
LIST OP FIGURES
FIGURE PAGE
1 . S hear Diagram o f N ew tonian F lu id s . . . . . . . 5
2 . Shear Diagram o f Bingham P l a s t i c M a te ria ls . . 5
3. Shear Diagram o f P s e u d o p la s tic M a te ria ls . . . 5
4 . Shear Diagram o f D ila ta n t M a te ria ls . . . . . . 5
5 . S hear Diagram o f T h lx o tro p ic S u sp en sio n s . . . 5
6 . P l a s t i c V is c o s ity V ersus N a tu ra l L ogarithm of
Time « . . . ..................................................................... 9
7. R.P.M . V ersus Torque ........................................................ 9
8 . U - Ug V ersus I n Time . ................................................ 9
9 . Graph Showing Changes in Y ie ld V alue as a
F u n c tio n o f R.P.M .............................................................. 9
1 0 . Graph o f P l a s t i c V is c o s ity V ersus In R ate o f
S hear a t D if f e r e n t Time L e v e ls . . . .. . . 9
1 1 . D is tr ib u tio n o f S h earin g Force in a P ip e . . . 14
12. E xpected S hear Diagram of T h ix o tro p ic Suspen
sio n s O b tain ed from P ip e -L in e D ata . . . . . 14
1 3 . Shear Diagram o f Bingham P l a s t i c M a te ria ls f o r
V iscous and T u rb u len t Flow R e g i o n s ................... 14
1 4 . Main A p p aratu s Used f o r th e E xperim ent . . . . 19
1 5 . Graph o f D isch arg e R ate as a F u n c tio n o f H eig h t 24
1 6 . Time E q u ilib riu m V ersus W eight P e r Cent
B e n to n ite in W a t e r ............................................. 30
Vi
FIGURE PAGE
1 7 . Shear Diagram o f 8 P er Gent B e n to n ite
S u sp en sio n . ...................................................... 32
1 8 . L ogarithm o f Flow R ate V ersus Tube L ength . . . 34
1 9 . R ate o f S hear as a F u n ctio n o f R esidence Time . 36
20. Graph o f A ^ /L V ersus Tube L ength . . . . . . . 39
21. L ogarithm o f R esidence Time V ersus S hear
S t r e s s ........................... 41
CHAPTER I
THE PROBLEM A M D RHEOLOGICAL DEFINITIONS
A. The Problem
S tatem en t o f th e Problem : T his r e s e a rc h was an a t
tem pt to i n t e r p r e t th e r h e o lo g ic a l p r o p e r tie s o f th ix o -
t r o p ic su sp e n sio n s, b ased on a sim ple e x p e rim en ta l p ro c e
d u re o f flow o f th e s e m a te r ia ls th ro u g h tu b e s and p ip e s ,
o b ta in and e v a lu a te th e d a ta , and, f i n a l l y , f in d th e p ra c
t i c a l a p p lic a tio n o f th e r e s u l t s o f th o s e e n g in e e rin g flow
problem s where th ix o tro p y i s e n c o u n tered .
Im p o rtan ce o f th e S tudy: The p ro d u c ts o f many in
d u s t r i e s c o n s is t o f m a te r ia ls h av in g th ix o tr o p ic p r o p e r tie s
The q u a lity c o n tro l o f th e s e p ro d u c ts depends on how much
i s known ab o u t t h e i r b e h a v io r under d i f f e r e n t c o n d itio n s .
The d e sig n o f p ip e s iz e s and c a p a c ity o f equipm ent f o r con
v ey in g m a te r ia l o f t h i s n a tu re r e q u ir e s a knowledge o f
t h e i r flow c h a r a c t e r i s t i c s .
The a p p lic a tio n o f r e s u l t s , d e riv e d from a stu d y o f
a th ix o tr o p ic su sp en sio n , to i n d u s t r i a l problem s would,
th e r e f o r e , be o f r e a l v a lu e .
B. R h e o lo g ic al D e f in itio n s
P e r tin e n t r h e o lo g ic a l d e f in it io n s n o t g iv en in
2
l a t e r c h a p te rs a r e p re s e n te d as fo llo w s:
S tr e s s : S tr e s s i s th e a c tin g fo rc e p e r u n i t a re a
and may be th o u g h t o f as b ein g composed o f norm al ( t e n s i l e
and com pressive) and ta n g e n ti a l (s h e a rin g ) com ponents.
S tr a i n : The a l t e r a t i o n in shape due to a p p lie d
s t r e s s i s r e f e r r e d to a s s t r a i n .
D eform atlont T his term i s u sed b o th f o r a r e l a
t i v e d isp lace m en t in p ro g re s s and f o r th e s t a t e o f d i s
p lacem en t re a c h e d d u rin g t h i s p ro c e s s a t any i n s t a n t of
tim e .
Q onslstenc.v: The flow n a tu re o f a f l u i d w hich i s
due to i t s i n t e r n a l s t r u c t u r e i s r e f e r r e d to a s c o n s is te n
cy . I t i s th e r e s is ta n c e o f fe re d by a r e a l f l u i d to de
fo rm a tio n when s u b je c te d to a sh e ar s t r e s s . T his p ro p e rty
o f f l u i d s i s re p re s e n te d by a c o n s is te n c y cu rv e ( r a t e o f
sh e a r v e rsu s sh e a r s t r e s s f o r non-N ew tonian f l u i d s ) , and
n o t by a s in g le v a lu e (N ew tonian f l u i d s ) .
C o e ff ic ie n t o f V is c o s ity : C o e ff ic ie n t o f v is c o s
i t y , a b s o lu te v is c o s ity , o r sim ple v is c o s ity i s th e r e
s is ta n c e o f f l u i d s to flo w . I t i s d i r e c t l y p ro p o rtio n a l
to th e c o ta n g e n t o f th e a n g le made by th e c o n s is te n c y
cu rv e and th e fo rc e a x is .
Y ie ld V alue: T h is i s th e minimum t a n g e n ti a l
sh e a rin g f o rc e p e r u n it a r e a r e q u ir e d to cau se flo w .
P lu g Flow: T h is term r e f e r s to t h a t p a r t o f th e
3
flo w where th e sh e a rin g s t r e s s i s l e s s them th e y ie ld
v a lu e .
A pparent V is c o s ity ; T his i s an im ag in ary q u a n tity
a p p lie d to non-N ew tonian f l u i d s ; i t i s th e v i s c o s ity a non-
N ew tonian f l u i d would have a t a g iv e n r a t e o f sh e a r i f i t
w ere a N ew tonian. A pparent v i s c o s i t i e s a re n o t com parable.
P l a s t i c V is c o s ity : T his i s d e fin e d as th e sh e a r
in g s t r e s s in ex cess o f th e y ie ld v a lu e th a t w ill produce
a u n i t r a t e o f s h e a r. P l a s t i c v i s c o s i t i e s a re com parable.
The co n cep t o f p l a s t i c v is c o s ity i s u se d and a c c e p te d
r a t h e r th a n t h a t o f a p p a re n t v is c o s ity .
S lip Flow : T his phenomenon e x i s ts o n ly in suspen
s io n s h av in g y ie ld v a lu e . I t o cc u rs a t th e w a ll o f a cap
i l l a r y tu b e , and to a n e g lig ib le e x te n t in r o t a t i o n a l v is
co m eters. The suspended p a r t i c l e s a r e h e ld to g e th e r, due
to fo rc e o f f lo c c u la tio n , a s a s o li d p lu g w hich i s l u b r i
c a te d by a t h i n l iq u i d la y e r c a u sin g s lip p a g e , o r g lid in g ,
a lo n g th e w a ll. T h is flow , not b ein g la m in a r, i s c a lle d
s lip p a g e flo w .
F .o ta tio n a l V iscom eter: T his ty p e of v isco m eter i s
u se d to o b ta in th e c o e f f ic ie n t of v is c o s ity and y ie ld
v a lu e . The speed o f r o t a t i o n and th e to rq u e im posed by
v isc o u s d rag can be m easured, and th e y ie ld v a lu e may be
c a lc u la te d .
CHAPTER I I
REVIEW ARB INTERPRETATION OF THE LITERATURE
A. G eneral
The stu d y o f th e m echanics o f flow o f l i q u i d s and
su sp e n sio n s comes u n d er th e sc ie n c e o f Rheology. In a
h ro a d sen se, Rheology i s d e fin e d as th e sc ie n c e o f flow
an d d efo rm atio n o f m a tte r ( 2 ,7 ,1 1 ); h u t, in p r a c t ic e , i t
r e f e r s to th e stu d y o f th e r h e o lo g ic a l p r o p e r tie s o f th o se
m a te r ia ls w hich behave in a manner in te rm e d ia te to s o lid s
and li q u i d s . Rheology i s p r im a r ily concerned w ith th e
s t r e s s - s t r a i n - t i r a e r e la tio n s h i p s in such m a te r ia ls .
L iq u id s and su sp e n sio n s of s o li d s in liq u i d s a re
one o f two g e n e ra l ty p e s ( 2 ,7 ,9 ) ;
1. N ew tonian L iq u id s: These a r e c h a ra c te riz e d by
h av in g a c o n s ta n t v is c o s ity , in d ep en d en t o f the
r a t e o f sh e a r (F ig u re 1 ) ; th a t i s ,
/* = ~ iv f * c o n s ta n t
< JL r
Where:
y “ » V is c o s ity
T = Shear s t r e s s
Ra te o f sh e a r
otr
3c® C onversion f a c to r ,
3 2 .1 7 J ik s 1 ..( — 0 . 4 ..
l b . fo rc e S e c .2
*
: : : :
6
V is c o s ity i s th e m easure o f th e r e s is ta n c e to
flo w o r d efo rm atio n o f a f l u i d .
2. Non-Newtonian F lu id s! The v is c o s ity o f th e se
m a te r ia ls a t c o n s ta n t te m p e ra tu re i s a fu n c tio n
o f th e sh e a r s t r e s s .
Non-Newtonians a re d iv id e d in to f iv e groups!
a . Bingham P l a s t i c : The flow o f t h i s ty p e o f
m a te r ia l i s c h a ra c te riz e d by a " y ie ld v a l
u e, " s in c e a c e r t a in fo rc e must he a p p lie d
to th e m a te r ia l b e fo re any flow ta k e s p la c e .
The c o n s is te n c y cu rv e o f Bingham b o d ies
in te r c e p ts th e s t r e s s a x is and u s u a lly
shows a c u rv a tu re a t th e low er end (F ig u re
2 ), w hich i s th e r e s u l t o f th e t r a n s i t i o n
from p lu g to la m in a r flo w .
b . P s e u d o p la s tic ! The v is c o s ity o f t h i s type
o f f l u i d w ill d e c re a se a s th e r a t e o f sh e a r
a t w hich th e m a te ria l i s m easured in
c re a s e s (F ig u re 3 ).
c . D ila ta n t! A d i l a t a n t m a te r ia l shows in
c re a s e in v is c o s ity w ith in c re a s in g r a t e
o f s h e a r, o f te n re a c h in g a p o in t a t which
th e f l u i d becomes s o li d (F ig u re 4 ) .
d . R h eo p ectic: The s tr u c t u r e o f th e s e sus
p e n sio n s b re a k s and r e b u ild s i t s e l f v ery
?
r a p id ly d u rin g rh y th m ic sh a k in g ,
e. T h ix o tro p ic : The a p p a re n t v is c o s ity o f
t h i s m a te r ia l changes w ith tim e and r a t e
o f sh e ar (F ig u re 5 ). The flo w o f th ix o
tr o p ic m a te r ia ls i s a ls o c h a r a c te r iz e d by
a " y ie ld v a lu e ."
B. V isco m etric S tu d ie s
T h lx o tro p y : Some su sp en sio n s p o sse ss a ty p e of
s tr u c tu r e w hich i s d e s tro y e d when shaken and w hich r e
b u ild s i t s e l f when s ta g n a n t. T his is o th e rm a l and non-chem -
i c a l tra n s fo rm a tio n i s c a lle d th lx o tro p y ( 2 ). Some o i l s a t
h ig h r a t e o f sh e a r, p r in tin g in k s (1 3 ), p a in ts , and ben
t o n i t e su sp e n sio n in w ater a re exam ples o f th ix o tr o p ic
m a te r ia ls . The v is c o s ity o f th e s e m a te r ia ls , c a lle d p la s
t i c v is c o s ity , d e c re a se s w ith an in c re a s e in th e r a t e o f
s h e a r and th e tim e o f i t s a p p lic a tio n .
The c r i t e r i o n o f th lx o tro p y , when th e m a te r ia l i s
ru n in a r o t a t i o n a l v isc o m ete r, i s th e h y s te r e s is lo o p
form ed by p l o t t i n g r .p .m . v ersu s to rq u e . T h lx o tro p y has
n o t been d e fin e d in such a way a s to make i t m easurable,
b u t th e e x te n t o f th ix o tr o p ic breakdown can be d eterm in ed
by th e a r e a o f th e h y s te r e s is lo o p . The l a r g e r th e a re a
o f t h i s lo o p , th e more breakdown (2 ).
There a r e two methods o f th ix o tr o p ic breakdown:
8
(1) "Breakdown w ith tim e" o cc u rs when th e m a te ria l
i s s u b je c te d to a c o n s ta n t sh e a rin g r a t e o v er a p e rio d o f
tim e . The breakdown i s r& pid a t f i r s t , and th e n slow s
g r a d u a lly u n t i l i t re a c h e s an e q u ilib riu m p o in t.
(2) F u rth e r breakdown, o r "breakdown w ith r a t e of
s h e a r ," o c c u rs when th e energ y in p u t i s in c re a s e d .
T h ix o tro p ic Breakdown w ith Time: The r e la tio n s h i p
betw een tim e and th ix o tr o p ic breakdown a t c o n s ta n t r a t e o f
s h e a r i s g iv e n by Weltmann ( 2 ,1 2 ).
B = - i!2 t or U = -B i n t + In k 1
d*
Where:
T - '7 V
U = P l a s t i c v is c o s ity =
t = Time
B » C o e ff ic ie n t o f th ix o tr o p ic breakdown
w ith tim e
k'; ss I n te g r a ti o n c o n s ta n t
r ss S hear s t r e s s
% - X ie ld v a lu e , -d.v/d.r = R ate o f sh e a r
B i s c o n s ta n t f o r each m a te r ia l and k* changes
w ith r a t e o f s h e a r. F ig u re 6 shows th e p l o t o f U v ersu s
I n t . The slo p e o f th e l i n e s i s g iv e n as B = ^ •
tl
The c o n c lu sio n s re a c h e d by Weltmann (2 ,1 2 ) a re :
.1) The y ie ld v a lu e i s in d ep en d en t o f th e tim e o f
a p p lic a tio n o f th e s h e a rin g s t r e s s , p ro v id ed th e r a t e o f

10
s h e a r rem ains c o n s ta n t, F ig u re 7.
2) The r a t e o f breakdown i s in d ep en d en t o f r a t e
o f s h e a r. In o th e r w ords, th e tim e i t ta k e s to re a c h th e
e q u ilib riu m p l a s t i c v is c o s ity , Ug, a t any r a t e o f sh e ar, i s
c o n s ta n t. T his i s co n firm ed by F ig u re 8, w hich i s a graph
o f U-Ug v e rsu s tim e.
3) The tim e r e q u ir e d to re a c h a c e r t a i n p o in t,
su ch a s t^ (F ig u re 7) i s th e same w hether th e m easurem ents
commence a t Tg and p ro c ee d to t^ , o r s t a r t a t th e p o in t o f
maximum to rq u e and p ro ceed to t^ by a h o r iz o n ta l p a th .
T h ix o tro n ic Breakdown w ith R ate o f S h ear: A fte r
e q u ilib riu m i s e s ta b lis h e d a t a c o n s ta n t r a t e o f sh e ar,
f u r t h e r breakdown can be o b ta in e d by in c re a s in g th e r a t e
o f energy in p u t. The e q u a tio n o f th lx o tr o p lc breakdown
w ith r a t e o f sh e a r I s o b ta in e d on th e b a s is o f th e assump
tio n th a t th e l o ss i n to r q ue i s p r o p o r tio n a l, to_jthe r a t e
o f sh e ar ( 2 ,5 ) . The s im p lif ie d form o f th e fo rm u la i s
v / m l
Where: 00 » to p a n g u la r v e lo c ity = . rpm /9.55
M a — coefficient o f th ix o tr o p ic
breakdown w ith r a t e o f sh e a r
k = i n t e g r a tio n c o n s ta n t w hich changes
w ith tim e and becomes eq u a l to u >
when U = 0.
11
A graph o f U v e rsu s In c o g iv e s a s t r a i g h t l i n e w ith M as
th e slo p e .
The f i n a l e q u a tio n o f th ix o tr o p ic breakdown i s
c o n s ta n t. M and B a re c o n s ta n t and dependent o n ly on th e
m a te r ia l.
y ie ld v a lu e (2) w hich g iv e s th e t h i r d c o e f f ic ie n t o f t h i
xo tr o p ic breakdown B V#. "V1 ! g iv e s th e In c re a s e i n y ie ld
v a lu e p e r u n it d e c re a se in p l a s t i c v is c o s ity due to change
i n r a t e o f s h e a r. I t i s g iv e n as V = , where f]_ an
X 2
fg a re y ie ld v a lu e s (F ig u re 9 ).
I n t e r p r e t a t i o n : From th e fo re g o in g l i t e r a t u r e
su rv ey , we c o u ld o u tlin e a p ro ced u re f o r o b ta in in g th e
p l a s t i c v is c o s ity o f a th ix o tr o p ic su sp e n sio n a t any r a te
o f sh e ar and tim e o f i t s a p p lic a tio n .
p l a s t i c v is c o s ity o f a th ix o tr o p ic m a te r ia l d e c re a se s w ith
in c r e a s e in tim e . Beyond a c e r t a in tim e, tg , th e v is c o s
i t y , Ug, rem ains c o n s ta n t and would not change u n le s s th e
r a t e o f sh e a r w ere a l t e r e d . At a second sh e a r r a t e and
a f t e r th e la p s e o f a d e f i n i t e tim e, tg , w hich i s th e ch a r
a c t e r i s t i c o f th e su sp e n sio n , th e e q u ilib riu m would ag ain
b e e s ta b lis h e d . A cu rv e o f Ug v e rsu s In rpm, d e s ig n a te d
w hich c o u ld be s im p lif ie d
g iv e n by Green (2 ,5 ) as e
, K b e in g a
A change i n th e r a t e o f sh e a r does change th e
1) When c o n s ta n t r a t e o f sh e a r i s a p p lie d , th e
12
i n F ig u re 10 a s “e q u ilib riu m lim itin g v is c o s ity curve" w ith
s lo p e M , i s made w hich g iv e s th e low er li m it o f p l a s t i c
v is c o s ity a t tg f o r d i f f e r e n t r a t e s o f s h e a r. T h erefo re ,
th e p l a s t i c v i s c o s ity o f th e p a r t i c u l a r th ix o tr o p lc su s
p e n sio n , a t any tim e and r a t e o f s h e a r, f a l l s to th e r i g h t
s id e o f t h i s cu rv e .
2) T h e o r e tic a lly sp eak in g , th e p l a s t i c v is c o s ity
o f a th ix o tr o p ic su sp e n sio n i s i n f i n i t e a t zero r a t e of
sh e a r and zero tim e. T h is means t h a t th e v is c o s ity lo s e s
i t s m eaning and th e m a te r ia l a c ts a s a s o li d and does n o t
flo w u n le s s a sh e a r s t r e s s g r e a te r th a n y ie ld v a lu e i s
a p p lie d . The p l a s t i c v is c o s ity , how ever, h as a d e f in it e
v a lu e a t lo w e st p o s s ib le r a t e o f sh e a r and tim e o f ab o u t
1 - 2 seeo n d s. T his v a lu e co u ld be ta k e n as th e upper
l i m i t o f p l a s t i c v is c o s ity o f th e su sp e n sio n .
3) E x p erim en tal d a ta f o r h ig h r a t e s o f sh e a r a re
n o t a v a ila b le . I t i s re a s o n a b le to b e lie v e t h a t beyond th e
a p p lic a tio n o f a c e r t a in r a t e o f sh e a r th e p l a s t i c v is c o s
i t y o f a th ix o tr o p ic su sp e n sio n does n o t change. There
f o r e , th e e q u ilib riu m lim itin g v is c o s ity cu rv e o f F ig u re 10
becomes d is c o n tin u o u s a s soon as t h i s h ig h r a t e o f s h e a r i s
re a c h e d .
The o r d in a te o f F ig u re 10 i s U =-B in t + In k 1 =
- T z . Tp— . S in ce B i s a c o n s ta n t and k ' i s a f u n c tio n o f
-dL V /cL r
r a t e o f sh e a r, th e p l a s t i c v is c o s ity o f th e su sp e n sio n
13
c o u ld be o b ta in e d a t any r a t e o f sh e a r and tim e o f i t s
a p p lic a tio n .
0 . Study o f R h e o lo g ic a l P r o p e r tie s
U sing Tubes and P ip e s
Tubes and p ip e s can be u se d to stu d y rh e o lo g ic a l
p r o p e r tie s . The flow p r o p e r tie s o f th ix o tr o p ic su sp en sio n s
have n o t been s tu d ie d a s e x te n s iv e ly a s o th e r non-H ew tonian
m a te r ia ls , and in o rd e r to stu d y th e flo w c h a r a c t e r i s t i c s
o f th ix o tr o p ic su sp e n sio n s th ro u g h tu b e s and p ip e s , a b r i e f
su rv ey o f flo w o f Bingham p l a s t i c would be b e n e f i c ia l.
The t o t a l fo rc e p ro d u cin g flo w i n a p ip e o f le n g th
L, d ia m e te r D, betw een s e c tio n 1 and 2 i s n..............
S in ce th e re i s no a c c e le r a tio n in ste a d y , u n ifo rm floi*,
t h i s fo rc e i s opposed by an equal f o rc e tw •
riD L T w = nx»aW / ^
hence Tw = and % - ra(^ ~
f 7w * S hear s t r e s s a t th e w a ll.
Tr = S hear s tr e s s a t r a d iu s r .
The slu d g e flo w in g in th e c e n te r o f th e p ip e moves
a s a s o li d p lu g w ith r a d iu s r 0 shown in F ig u re 11. T his
phenomenon r e s u l t s from th e f a c t th a t th e sh e ar betw een
moving la y e r s in c re a s e s from zero a t th e c e n te r o f th e
p ip e to a maximum a t th e p ip e w a ll, and a t some d is ta n c e
I f l i w
m
15
betw een th e c e n te r and th e w a ll, th e sh e a r w ill be equal
to y ie ld s t r e s s o f th e slu d g e ( 1 ) . T h e re fo re :
7- = *_(*£)_ _
3 Z L
Where th e sh e a r i s l e s s th a n th e y ie ld v a lu e , th e r e w ill be
no r e l a t i v e m otion betw een a d ja c e n t p a r t i c l e s w hich w ill
th e r e f o r e , flo w to g e th e r a s a s o lid p lu g .
The mean v e lo c ity o f flow i n f e e t p e r second i s
g iv e n a s :
v = - 2 |- ^ - - 5 - r a)
The v a lu e s o f /* and T ]j depend o n ly on th e n a tu re
o f th e slu d g e and a re in d ep en d en t o f m easuring a p p a ra tu s
c h a r a c t e r i s t i c s . On th e b a s is o f t h i s e q u a tio n , i f a graph
i s p lo tt e d w ith 7w a s o rd in a te , v e rsu s zV /fib a s a b s c is s a ,
th e slo p e o f th e r e s u l t i n g l i n e w ill re p re s e n t th e co e f
f i c i e n t o f r i g i d i t y , w hich i s analogous to th e c o e f f ic ie n t
o f v is c o s ity , and i n te r c e p t i s 4 /3 o f y ie ld s t r e s s ( 1 ,7 ) .
T h is one l i n e r e p r e s e n ts th e flow o f a g iv e n Bingham p la s
t i c m a te r ia l i n a p ip e o f any d ia m e te r.
The sh e a r diagram o f th ix o tr o p ic su sp e n sio n s ob
ta in e d from p ip e l i n e d a ta cannot be re p re s e n te d by one
l i n e f o r any p ip e d ia m e te r and le n g th . The ex p ected sh e a r
diagram o f a th ix o tr o p ic su sp en sio n , showing th e e f f e c t o f
p ip e d ia m e ter and le n g th (7 ), i s g iv e n i n F ig u re 12.
T u rb u le n t Flow: The sh e a r diagram f o r th e tu rb u
l e n t flow o f a Bingham ty p e p l a s t i c i s shown in F ig u re 13.
16
The low er p a r t o f th e cu rv e i s f o r th e v isc o u s flo w and
th e upper p a r t f o r tu r b u le n t flow , and I t i s n o te d th a t
t h i s p o r tio n b ran ch es o f f somewhat s h a rp ly from th e r e
m ainder o f th e c u rv e . The b ra n c h -o ff p o in t o cc u rs a t
lo w er r a t e o f sh e a r v a lu e s as th e d ia m e te r o f th e p ip e i n
c r e a s e s . The v e lo c ity a t w hich th e flow changes from v is
cous to tu r b u le n t flow i s c a lle d th e c r i t i c a l v e lo c ity
( 1 ) . The same f a c t o r s may be assum ed to a f f e c t tu r b u le n t
flo w f r i c t i o n a l lo s s e s o f a slu d g e flo w in g in a s t r a i g h t
p ip e as a f f e c t th e la m in a r flow f r i c t i o n a l lo s s e s .
The v is c o s ity o f th e d is p e rs io n medium can be sub
s t i t u t e d f o r th e v is c o s ity o f th e su sp en sio n in o rd e r to
c a lc u la te th e Reynolds number ( 1 ). The f r i c t i o n f a c t o r
c h a r t so c o n s tru c te d would be ap p ro x im a tely th e same as
th e c h a r t o b ta in e d f o r a Newtonian l i q u i d .
T his method i s p r a c tic a b le b ecau se in tu r b u le n t
flo w th e f r i c t i o n a l lo s s e s a re due e s s e n t i a l l y to im pact
lo s s e s w hich depend o n ly on d e n s ity and v e lo c ity . The
p re se n c e o f b e n to n ite o r o th e r in c r e a s e r s o f d e n s ity , would
i n no way a f f e c t th e b a s ic v is c o s ity o f th e d is p e rs io n
medium. I t i s th e v is c o s ity o f th e d is p e rs io n medium
w hich ca u ses a r e l a t i v e l y th in la y e r o f m a te r ia l to move
In la m in a r flo w alo n g th e w a lls o f th e p ip e , w h ile th e
m a te r ia l in th e c e n te r o f th e p ip e i s flo w in g tu r b u le n tly .
CHAPTER I I I
EXPERIMENTAL M ETHO DS
M a te ria l Used: A ll t e s t s w ere perform ed on th e
same m a te r ia l, b e n to n ite , w hich was e a s ily a v a ila b le from
B raun Chem ical C o rp o ra tio n o f Los A ngeles. B e n to n ite su s
p e n sio n in w a te r i s an e x c e lle n t example o f m a te r ia l h av in g
th ix o tr o p ic p r o p e r tie s .
S e v e ra l sam ples w ere p re p a re d i n o rd e r to e s ta b li s h
th e w eight p e rc e n t c o n c e n tra tio n o f b e n to n ite su sp en sio n
r e q u ir e d to o b ta in v isc o u s flow w ith tu b e s iz e s to be em
p lo y e d . F iv e, s ix , seven, and e ig h t p e rc e n t su sp e n sio n s
w ere o b ta in e d by m ixing d ry b e n to n ite w ith a known q u a n tity
o f w ater in a m ixer f o r o n e -h a lf h o u r. They w ere s to re d
and aged a t l e a s t o v e rn ig h t b e fo re u se .
V iscom eter Used: P re lim in a ry t e s t s f o r v is c o s ity
m easurem ents o f th e su sp e n sio n s were p erform ed w ith th e
B ro o k fie ld M S y n c h ro -L e c tric " v isco m eter o f th e Chem ical
E n g in e e rin g L a b o ra to ry . The to rq u e on th e r o t a t i n g s p in d le
o f t h i s v isc o m e ter i s m easured by a c a lib r a te d s p rin g .
T here w ere two g ra d u a te d s c a le s from 0 to 500 and 0 to 100,
and a c a l i b r a t i o n was g iv e n f o r each s p in d le d i r e c t l y in
c e n tip o is e s . However, t h i s i s th e v is c o s ity o f a Newtonian
m a te r ia l th a t would g iv e th e same s c a le re a d in g . T his
p a r t i c u l a r v isc o m eter had a o n e-sp eed m otor and th e re fo r e
o n ly one R.P.M . c o u ld be o b ta in e d . A lthough n o t a s ______
18
f l e x i b l e and a s a c c u ra te a s o th e r ty p e s o f r o t a t i o n a l v is
co m eters, i t p ro v id e d a q u ick means o f d e te rm in in g th e
p re se n c e and e x te n t o f th e v a rio u s T h e o lo g ic a l p r o p e r tie s .
F or each ru n , th e p ro p e r s p in d le o f th e v isc o m e ter
was s e t i n th e b e n to n ite su sp en sio n and l e f t f o r a minimum
p e rio d o f 18 h o u rs. A tim e clo ck was a ls o employed in
o rd e r to o b ta in th e change o f v is c o s ity as a fu n c tio n of
tim e . The r a t e o f change i n v is c o s ity f o r each su sp en sio n
was h ig h a t f i r s t , and d e c re a se d g ra d u a lly to z e ro . The
tim e e q u ilib riu m , tg , o f ev ery su sp e n sio n was e s ta b lis h e d
by making a g rap h o f tf-Ug v ersu s tim e.
P re p a ra tio n and D e s c rip tio n o f th e A p p aratu s: The
equipm ent u sed in p re p a rin g and h a n d lin g th e m a te r ia l and
p erfo rm in g th e r e q u ir e d s e r ie s o f t e s t s was com prised
e s s e n t i a l l y o f b u c k e ts, m ixer, b ala n ce , ta n k , g la s s tu b in g ,
ru b b e r s to p p e rs , and a tim e r. The main s e t-u p i s shown i n
F ig u re 14.
The d ia m e te r and h e ig h t o f th e c y l in d r i c a l r e s e r
v o ir were 8 | and 18 in c h e s r e s p e c tiv e ly . An opening o f
ab o u t i | in c h e s was made th ro u g h th e b ase o f th e ta n k .
The s t r a i g h t le n g th s o f g la s s tu b in g w ere 2, 5, 8§,
13 and 19 m illim e te rs i n d ia m e te r and one to fo u r f e e t in
le n g th . One end o f each tu b e was sp re a d ev en ly w ith h e a t
i n o rd e r to have a f a i r l y smooth e n tra n c e . E very tu b e was
ru n th ro u g h th e ru b b e r s to p p e r w hich in tu r n c lo s e d th e
*4-
19
Tank
S u sp en sio n
1 1
Rubber S to p p er
G lass Tubing
Cork o r Rubber S topper
Weighed R e c e iv e r
FIGURE 14
Main A pparatus Used fo r th e Experim ent
20
bottom opening o f th e r e s e r v o ir .
The ta n k , w ith th e g la s s tu b in g i n th e bottom , was
su p p o rte d by an ir o n r in g w hich was f a s te n e d to two lo n g
i r o n su p p o rts .
A sim ple a p p a ra tu s so assem bled c o u ld be e a s ily
d ism a n tle d f o r c le a n in g and r e s e t t i n g .
P erform ance o f th e T e s ts : To o b ta in v isc o u s flow ,
i t was found th a t 8 p e rc e n t b e n to n ite su sp e n sio n was b e s t
s u it e d f o r th e a p p a ra tu s u sed . The p ro p e r amount o f ben
t o n i t e powder was added g ra d u a lly to a known q u a n tity o f
w a te r w ith c o n tin u o u s a g i ta t i o n . A fte r a u n ifo rm m ix tu re
was o b ta in e d , th e a g i t a t i o n was d is c o n tin u e d . The s p e c if ic
g r a v ity o f 8 p e rc e n t b e n to n ite su sp e n sio n was c a lc u la te d
to be 1 .0 9 .
The r e s e r v o ir and tu b e in th e bottom w ere th e n
f i l l e d w ith th e f l u i d . A s to p p e r in th e f r e e end o f th e
tu b e p re v e n te d th e m a te r ia l from flo w in g . F in a lly , th e
a p p a ra tu s and th e m a te r ia l were l e f t u n d istu rb e d , a t l e a s t
o v e rn ig h t, p r i o r to u s e .
The flow m easurem ents were c a r r ie d o u t w ith in a
te m p e ra tu re ran g e o f 60° F. to 65° F . F or each ru n , th e
h e ig h t o f h^ o f th e f l u i d in th e ta n k was m easured. By
rem oving th e sto p p e r from th e tu b e, th e su sp en sio n flow ed
th ro u g h i t in to a w eighed r e c e iv e r u n d er g r a v ity h ead . The
r a t e o f flow was m easured by w eighing th e d is c h a rg e over a
21
tim ed i n t e r v a l in o rd e r to avoid any u n c e r ta in ty In h e re n t
i n v o lu m e tric m easurem ents. The volume o f th e f l u i d was
o b ta in e d by knowing th e s p e c if ic g r a v ity and w eight o f th e
m a te r ia l. By knowing th e dim ensions o f th e ta n k and th e
o r ig in a l h e ig h t, h^, o f th e f lu id , th e f i n a l h e ig h t, hg, o f
th e su sp en sio n in th e ta n k was o b ta in e d . U sing t h i s p ro
ced u re i t was p o s s ib le to m easure th e flo w r a t e s as a fu n c
tio n o f su sp e n sio n h e ig h t i n th e ta n k . A fte r th e n e c e ssa ry
d a ta was o b ta in e d , th e tu b e was c u t by one f o o t in o rd e r
to e s ta b li s h th e e f f e c t o f tube le n g th on th e flo w r a t e .
The su sp e n sio n was a g a in poured in to th e tan k and l e f t un
d is tu rb e d f o r th e n ex t ru n .
T his p ro ced u re was fo llo w ed th ro u g h o u t th e e x p e ri
m ent, and th e e f f e c t o f tu b e le n g th s and d ia m e te rs on th e
flo w r a t e was o b ta in e d .
A dvantages and D isad v an tag es o f th e A p p aratu s: Due
to i t s s im p lic ity , th e a p p a ra tu s c o u ld be e a s ily s e t up
and d ism a n tle d f o r r e s e t t i n g . A lso, th e usage o f g r a v ity
head f o r d r iv in g th e b e n to n ite su sp e n sio n th ro u g h th e tu b e s
i s one o f th e ad v an tag es o f th e ex p e rim en ta l p ro ce d u re.
As th e accu racy o f flow r a t e m easurem ents d e c re a se d
w ith in c re a s e o f tube d ia m e te r, i t was n o t p r a c t i c a l to use
la r g e r th a n .700 in c h tu b in g . A lso, a s th e h e ig h t o f th e
su sp e n sio n in th e ta n k d e c re a se d a p p re c ia b ly w ith flow ,
e x a c t c a lc u la tio n o f in s ta n ta n e o u s r a t e o f flo w a t one-
f o o t h e ig h t was n o t p o s s ib le .
CHAPTER X V
THE RESULTS A N D THEIR DISCUSSION
A. C a lc u la tio n
Flow R a te : The in s ta n ta n e o u s flow o f 8 p e rc e n t
b e n to n ite su sp e n sio n u n d er g r a v ity head was c a lc u la te d
w ith th e h e ig h t o f th e m a te ria l in th e tank: c o n s id e re d to
be 12 in c h e s above th e e n tra n o e to th e tu b e . The in s ta n
ta n eo u s r a t e s o f flow p e r m inute, W j_ , were e x tra p o la te d
from g rap h s o f h e ig h t v e rsu s amount o f d is c h a rg e . The
e n tra n c e e f f e c t was n o t c o n s id e re d in th e s e c a lc u la tio n s .
F ig u re 15 shows th e r e s u l t o f th e fo llo w in g
sam ple c a lc u la tio n :
D iam eter o f th e ta n k « 8 | in c h e s
Volume o f th e ta n k p e r fo o t h e ig h t * 0 .5 9 4
c u b ic f e e t
D tu b e » 5 m illim e te r = 0.0164 f e e t
L tu b e - 4 f e e t
D e n sity o f th e su sp en sio n a t 6o° F. =
68 l b s ./ c u b i c fo o t
1 . I n i t i a l h e ig h t o f m a te r ia l in th e r e s e r v o ir b e fo re
d is c h a rg e , h^ * 14.75 in c h e s
W eight o f su sp en sio n d isc h a rg e d in 25 m inutes = 3.15
lb s .

25
D iffe re n c e in h e ig h t o f f l u i d in th e ta n k due to
d is c h a rg e , A h - 1 .4 1 in c h es
C o n sid erin g th e tu b e b ein g in s id e th e ta n k ab o u t 4
in c h , th e n
h i - h£ - 0 .2 5 * 14.50 in c h e s
H eig h t o f m a te r ia l in th e r e s e r v o ir a f t e r d is c h a rg e ,
hg • h i - Ah - 14.50 - 1 .4 1 = 1 3.09 In ch es
2 . hx » 13.09"
Time o f d is c h a rg e » 10 m inutes
W eight d isc h a rg e d * 1 .4 6 9 l b s .
A h - 0.66"
hg = 1 3 .0 9 - 0 .6 6 = 12.43"
3 . h2 » 12.43"
Time o f d is c h a rg e = 10 m inutes
W eight d is c h a rg e d = 1 .4 0 5 l b s .
A h * 0.63"
hg = 1 2 .4 3 - 0 .6 3 « 11.80"
4 . hx ■ 11.80"
Time of d is c h a rg e = 10 m inutes
Weight d isc h a rg e d = 1 .3 1 2 l b s .
A h » 0 .5 8 8 - 0.60"
hg = 1 1 .8 0 - 0 .6 0 = 11.20"
F in a l h e ig h t o f f l u i d in th e tan k « 1 1 .2 0 + 0 .2 5 » 11.45"
26
The g rap h o f av erag e h e ig h ts , —- * + , v e rsu s th e
amount o f su sp e n sio n d isc h a rg e d in 10 m inutes i s g iv en in
F ig u re 15. From t h i s g rap h , th e in s ta n ta n e o u s flow r a t e ,
f o r 12 in c h h e ig h t i s e x tra p o la te d to be 0.140
p o u n d s/m in u te. In o rd e r to e lim in a te e r r o r s , th e amount
d isc h a rg e d in 25 m inutes was not u sed i n making th e g rap h s.
F o llo w in g t h i s p ro ced u re , th e v o lu m e tric r a t e s o f
flow , q, f o r each tu b e d ia m e te r and le n g th were o b ta in e d
and ta b u la te d in T able I .
S hear S tr e s s : The sh e a r s t r e s s a t tu b e w all was
c a lc u la te d by th e fo llo w in g eq u a tio n :
H - L
H ate o f S h ear: The r a te o f sh e a r a t tu b e w a ll i s
g iv en as:
C a lc u la te d r e s u l t s f o r sh e ar s t r e s s and r a t e o f
sh e a r a re g iv e n in T able I I .
The v a lu e s o f v is c o s ity o b ta in e d a t low r a t e of
sh e a r, u s in g B ro o k fie ld H S y n ch ro -L ee trie" v isc o m eter, a re
n o t a c c u ra te . T his v isc o m e ter g iv e s c o r r e c t v a lu e s o n ly
a f t e r i t has been in o p e ra tio n f o r a few m in u tes. The
1 /se co n d
B. The R e s u lts
E v a lu a tio n and D isc u ssio n
.1
27
TABLE I
RESULTS OP
‘INSTANTANEOUS VOLUM ETRIC RATE OF PLO W
I n s id e Tube L ength o f
D isch arg e
R a tes
R ate o f Plow
C ubic F ee t
D iam eter, In c h e s Tube, P eet Pounds/M inute- P e r Second
0.0788 4
0 .408 x 10“ 3
r- i
i
o
H
3 0 .4 5 4 x 10“ 3 1 .110 x 10“ 7
2 0.529 x 10”3 1 .2 9 5 x 1 0 -7
1§
0 .563 x 10“3 1 .3 8 0 x 10~7
1 2.730 x 10“ 3 6 .6 8 0 x 10“ 7
0.1967 4 0 .140 0.343 x 10“ 4
3 0 .1 4 7 0 .360 x 10“ 4
2 0 .176 0.431 x 10“ 4
1 0 .363 0 .8 9 0 x 10“ 4
0.3345 4 2.345 0 .5 7 4 x 10“ 3
3 2.575 0 .6 3 0 x 10” 3
2 2.785 0.681 x 10” 3
1 4.062 0.995 x 10“ 3
0.5110 4 1 4.50 3 .5 5 0 x 10“ 3
3 1 5.20 3 .7 2 0 x 10“ 3
2 15 .2 0 3 .7 2 0 x 10” 3
1 19.40 4.750 x 10“ 3
28
TABLE I I
\
RESULTS OP CALCULATION FOR
SHEAR STRESS A N D RATE OP SHEAR
I n s id e Tube
D iam eter,
In ch e s
Tube
L ength
F e e t
aF
F e e t
S lu rry
i
AF
L b ./S q .F t.
Tw
L b ./S q .F t
3 .2 . ^
9c**3
. 1/Sec
0.0788
s
4 5 340 0.139 0.1132
3 4 272 0 .149 0.1260
2 3 204 0 .1 6 7 0.1466
i i 2 k
170 0.186 0.1564
1 2
136,
0 .2 2 3 0.7600
0.1967 14 15 1,020 0.299 2.2950
4 5 340 0 .3 4 8 2.4700
3 4 272 0 .3 7 2 2.6000
2 3 204 0 .418 3.1100
1 2 136
0 .5 5 8 6.4100
0.3345 14 15 1 ,020 0 .5 0 8 7.8500
4 5 340 0 .5 8 3 8.4000
3 4 272 0.634 9.2400
2 3 204 0.711 9.9800
1 2
136
0.950 14.6000
0.5110 14 15 1,020 0 .7 7 6 13.8000
4 5 340 0 .9 0 5 14.6000
3 4 272 0 .9 6 7 15.3000
2 3 204 1 .088 15.3000
1 2
136
1 .4 5 0 19.5500
29
g r e a t e s t change in v is c o s ity o ccu rs d u rin g t h i s s h o rt p e r i
od o f tim e; how ever, th e d a ta o b ta in e d g iv e s an in d ic a tio n
o f th e tim e e q u ilib riu m , tjj, and th e v is c o s ity o f th e su s
p e n s io n s . F ig u re 16 shows th e c o n c e n tra tio n e f f e c t o f th e
su sp e n sio n s on e q u ilib riu m tim e. F or 8 p e rc e n t b e n to n ite
i n w ate r, th e tim e r e q u ir e d to re a c h e q u ilib riu m p l a s t i c
v i s c o s ity a t any r a t e o f sh e a r i s found to be 1 0 .3 0
m in u te s.
T able I I I shows th e r e s u l t s o b ta in e d from m easure
m ents made on f i v e , s ix , and seven p e rc e n t su sp e n sio n s. A
g ra p h o f 0 - U E v e rsu s lo g o f tim e gave th e tim e e q u i l i b r i
um f o r each su sp e n sio n .
^ / / S hear Diagram : F ig u re 17 i s th e sh e a r diagram ob
ta in e d from flow measurement r e s u l t s o f 8 p e rc e n t b e n to n ite
su sp e n sio n . The d a ta o b ta in e d u sin g 0.748 in c h d ia m eter
tu b in g were n o t in c lu d e d because of t h e i r in a c c u ra c y .
The c o n s is te n c y cu rv es o f th e th ix o tr o p ic m a te ria l
t e s t e d in te r c e p t th e s t r e s s a x is g iv in g th e y ie ld v alu e of
th e su sp e n sio n . T his v a lu e , as in d ic a te d by th e diagram ,
i s ab o u t 0 .1 3 pounds p e r sq u are f o o t. The c u rv a tu re s a t
th e low er end o f th e c u rv e s a re th e r e s u l t o f t r a n s i t i o n
from p lu g to la m in a r flo w .
The u p p er ends o f th e cu rv es show a s l i g h t cu rv a
t u r e w hich ap p e a rs to be th e t r a n s i t i o n from la m in a r to
tu r b u le n t flo w . The v is c o s ity o f th e su sp e n sio n in th e

31
'TABLE I I I
•RESULTS OF VISOOMETRIC M EASUREM ENTS
1% S uspension 6$ S uspension
5$ S uspension
U - U E U - U E U - U E
Time G entl-? Time C e n ti-
Time C e n tl-
M inutes p o is e s M inutes p o is e s M inutes p o is e s
0 .5 0 520 0 .1 2 312 0 .2 0 84
0 .8 0 460 0 .4 0 180 0 .4 8 64
1.15
416 0 .5 5 160 1 .4 0 32
1 .4 0 352 0 .7 0 140 2 .0 0 24
1 .6 0 320 1 .5 0 88 6 .1 0 00
1.80 280 3 .2 0 24 1 1.20 00
2.10 272 6 .0 0 00
t E = 4. 20 m inutes
2 .7 0 232 8 .8 0 00
3 .0 0 200 1 0 .0 0 00
3 .4 0 168
t E = 5«i00 m inutes
3.90 128
4.60
96
6.30 24
7.40 00
9.90 00
t E « 7 .0 0 m in u tes

33
u p p er re g io n , u sed to c a lc u la te th e a p p a re n t R eynolds num
b e r, in d ic a te d t h a t th e flow i s d e f i n i t e l y v is c o u s . There
f o r e , ex cep t f o r th e lo w er p o r tio n of th e cu rv es w hich
in d ic a te s a t r a n s i t i o n from p lu g to la m in a r flow , th e
sh e a r diagram g iv en in F ig u re 1? i s o n ly f o r la m in a r flow ^
o f th e th ix o tr o p ic su sp e n sio n .
The th ix o tr o p ic c h a r a c t e r i s t i c o f b e n to n ite su s
p e n sio n i s shown by th e f a c t th a t each curve o f th e sh e a r
diagram i s r e p r e s e n ta tiv e o f a c o n s ta n t tu b e le n g th w ith
v a r ia tio n s in d ia m e te rs . The two cu rv es re p re s e n t th e
sh e a r diagram f o r a o n e -fo o t and f o u r - f o o t le n g th o f tu b
in g w ith d ia m e te rs ra n g in g from 0.0788 to 0.511 in c h e s .
S in ce th e p re s s u re h e a d ,' A P, i s c o n s ta n t in each tu b e
le n g th , th e r a t e o f sh e a r and sh e a r s t r e s s in c re a s e a s a
fu n c tio n o f d ia m e te r.
The p l a s t i c v is c o s ity o f th e d isc h a rg e d suspen
s io n co u ld be o b ta in e d from th e v a lu e s o f D, L, p P , q, and
T y o r d i r e c t l y from th e sh e a r diagram .
The dashed l i n e r e p r e s e n ts th e c o n s is te n c y curve
o f 1 4 -f o o t tu b in g . The d a ta f o r draw ing t h i s cu rv e i s
o b ta in e d from F ig u re 18. T his g rap h in d ic a te s th e change
i n flow w ith r e s p e c t to tu b e le n g th a t any s p e c if ic diame
t e r . As th e tu b e d ia m e te r i s known, flow r a t e i s ex tra p o
l a t e d f o r a tu b e le n g th o f 14 f e e t from w hich th e r a t e s o f
s h e a r a r e c a lc u la te d . These v a lu e s a r e l i s t e d in T able I I .
H i m pat.'ja »■■■■■■■■■ i ^ i w n
35
T his p ro c ed u re can be employed f o r o b ta in in g th e c o n s is
te n c y cu rv e f o r any le n g th o f tu b in g .
The d o tte d l i n e s in F ig u re 17 re p r e s e n t th e con
s is te n c y cu rv es o f th e su sp e n sio n a t c o n s ta n t d ia m e te rs.
R ate o f S hear - Time Diagram : S ince th e sh e a r
tim e diagram g iv e s a com plete m a n ife s ta tio n o f r h e o lo g ic a l
b e h a v io r, i t i s ex trem ely im p o rta n t and u s e f u l. F ig u re 19
i s such a diagram a t v a rio u s c o n s ta n t s t r e s s e s . I t i n d i
c a te s t h a t th e l a r g e s t p a r t o f th e d efo rm atio n ta k e s p la c e
a t th e b e g in n in g , im m ed iately a f t e r a p p lic a tio n o f th e
lo a d . A t r a n s i t i o n p e rio d fo llo w s, d u rin g w hich deform a
tio n i s r e ta r d e d . Then th e cu rv es g ra d u a lly approxim ate
s t r a i g h t l i n e s , showing th a t s ta tio n a r y flow i s re ac h e d .
The c a lc u la te d d a ta , g iv en in T able IV, f o r th e re s id e n c e
tim e o f m a te r ia l in th e tu b e s a r e o b ta in e d from th e sh e a r
diagram o f F ig u re 17.
The d efo rm atio n o f th e su sp e n sio n below th e y ie ld
s t r e s s i s so sm all th a t i t co u ld n o t be d e te c te d . A fte r
th e flow i s sto p p ed , an in s ta n ta n e o u s d efo rm atio n ta k e s
p la c e , w hich i s sm a lle r th a n th e in s ta n ta n e o u s d efo rm atio n
a f t e r th e flow i s s t a r t e d . The en su in g t r a n s i t i o n p e rio d ,
fo llo w e d by a slow re c o v e ry , g iv e s th e th ix o tr o p ic b u ild
up w hich in c re a s e s w ith tim e (F ig u re 1 9 ).
L im itin g D iam eter f o r V iscous Flow: For each
le n g th o f tu b in g , L, th e r e co rresp o n d s a d e f i n i t e v a lu e o f

37
AS
TABLE IV
RESULTS OP RESIDENCE TIME
A FUNCTION OP RATE OP SHEAR
S tr e s s L - f t .
A P
L
D
f t .
32. ■ R esidence
Time Sec.
.30 1
136 0.00830 1 .3 2 3 .2
4 85 0.01410 1 .8 3 9 .4 ✓
14 73 0.01645 3 .0 71 .0
.40 1
136 0.01176 2 .8 7 .6
4 85 0.01885 3 .9 1 3 .6
14 73 0.02190 5 .1 31 .3
.5 0 1
136
0.01470 5 .0 3 .4 0
4 85 0.02350 6 .4 6.65
14 73 0.02740 7 .4 17.25
.70 1
136 0.02060 9 .2 1.33
4 85 0.03300 1 1 .0 2.75
14 73 0.03840 12.1 7.53
.9 0 1
136 0.02650 1 3 .4 0.704
4 85 0.04240 1 5 .1 1.560
14 73 0.04930 1 6 .6 4.270
38
A P /L . F ig u re 20 shows th e r e la tio n s h i p betw een L and
a P /L . The y ie ld v a lu e i s g iv en a s:
o r b o a ~ p
Where:
T y ® 0 .1 3 p o u n d s/sq u are f o o t
D0 - th e d ia m e te r o f th e c y l in d r ic a l p lu g
in th e tu b e .
I t i s known th a t f o r th e sh e a r s t r e s s below th e
y ie ld v a lu e , th e re w ill be no r e l a t i v e m otion betw een ad
ja c e n t p a r t i c l e s and th e m a te r ia l, th e re fo r e , w ill flow
a s a s o li d p lu g . The d ia m e te r of th e tu b in g must be
g r e a t e r th a n D0 f o r v isc o u s flow to be p o s s ib le . At th e
same tim e, D0 depends on th e v alu e o f L. C onsequently,
f o r each le n g th o f tu b in g th e re must be a co rresp o n d in g
d ia m e te r, D0 , a t o r below w hich la m in a r flow can n o t be ac
com plished. The v a lu e s o f D 0 as a fu n o tio n o f L a re g iv en
i n T able V.
F ig u re 21 i s a n o th e r way o f re p r e s e n tin g th e r e
s u l t s . T his f ig u r e i s a g rap h o f re s id e n c e tim e ( th e tim e
n e c e s s a ry f o r th e su sp e n sio n to go th ro u g h th e tu b e)
a g a in s t sh e a r s t r e s s a t th e w a ll. Each l i n e r e p r e s e n ts
t h i s r e la tio n s h i p a t a p a r t i c u l a r r a t e o f sh e a r o r le n g th
o f tu b in g .
*
40
TABLE V
CHANGES OP D0 WITH LENGTH
L ength
F e e t
A P
L
Pounds/C ubic F oot
Do
In ch e s
1 136.0 0.0470
2 102.0 0.06110
3 9 0 .8 0.06880
4 85.0 0.07700
5 8 1 .0 0.07700
10 74.5 0.08380
15 72.5 0.08610
Very Long 6 8 .0 0.09180
i
ilI^ i^ I:IIE [il]In{:IIE iiiIO ![il!?IK i;[Q infill
Iftll
£
V
s
9
L
8
6
z
r
s
9
L
8
6
z
£
r
s
9
L
8
6
I
CHAPTER V
PRACTICAL APPLICATION A N D CONCLUSIONS
A. P r a c t i c a l A p p lic a tio n
In e n g in e e rin g d e sig n c a lc u la tio n s f o r flow o f a
su sp e n sio n in s t r a i g h t p ip e s , many f a c t o r s sh o u ld be tak en
in to c o n s id e ra tio n to a f f e c t f r i c t i o n a l lo s s e s . These
f a c t o r s a r e d ia m e te r and le n g th o f p ip e , v e lo c ity o f flow ,
d e n s ity , y ie ld s t r e s s and p l a s t i c v is c o s ity . In a d d itio n ,
th e e f f e c t o f roughness o f th e p ip e w a ll on f r i c t i o n a l
lo s s e s sh o u ld be c o n sid e re d .
The f r i c t i o n lo s s e s r e s u l t i n g from flow o f any
l i q u i d th ro u g h any p ip e co u ld be p l o t t e d as f v e rsu s
Reynolds number. The e q u a tio n s f o r f and Reynolds number
a r e g iv en a s : A T J _
a . W
and He. Ho. * ^ r e s p e c tiv e ly .
V iscous Flow: F or v isco u s flow , th e p l a s t i c v is
c o s ity o f th e su sp en sio n co u ld be u sed in th e c a lc u la tio n
o f th e Reynolds number. The v a lu e o f p l a s t i c v is c o s ity
c o u ld be g iv en a s : , ____
U = s t r e s s - y ie ld v alu e
r a t e o f sh ear
o r, a s d e riv e d from t h i s experim ent,
.. a., a p n ti* o.i33cni>!
u - ( S T E ^ t 3z~T~ '
43
In th e exp erim en ts perform ed, th e r e la tio n s h i p s
w ere o b ta in e d betw een d ia m e te r, le n g th , v e lo c ity o f flow ,
s h e a r s t r e s s and o th e r v a r ia b le s f o r e ig h t p e rc e n t ben
t o n i t e su sp e n sio n , a ty p ic a l th ix o tr o p ic m a te r ia l. I f th e
flo w p r o p e r tie s a re known, th e p l a s t i c v is c o s ity ( a t any
r a t e o f sh e a r, le n g th , and d iam eter) may be o b ta in e d and
u se d f o r c a lc u la tio n o f th e Reynolds number. S in ce th e
v is c o s ity o f flo w in g m a te r ia ls depends on th e le n g th and
d ia m e te r of tu b in g a s w ell as th e v o lu m e tric r a t e o f flow ,
th e f r i c t i o n f a c t o r c h a rt sh o u ld g iv e s e v e ra l cu rv es
r a t h e r th a n one, in th e c a se o f N ew tonian f l u i d s .
The p ro d u c ts o f many in d u s t r ie s c o n s is t o f m a te ri
a l s h aving th ix o tr o p ic p r o p e r tie s . The method p re s e n te d
c o u ld be u se d f o r th e m easurem ent o f th e p l a s t i c v is c o s ity ,
u n d er d i f f e r e n t c o n d itio n s , and th e y ie ld v alu e o f th e su s
p e n s io n s . S im ila r r e s u l t s co u ld , th e r e f o r e , be employed i n
th e d esig n o f p ip e s iz e s and in com puting th e c a p a c ity o f
equipm ent f o r conveying and pumping t h i s ty p e o f m a te r ia l.
B. C onclusions
The flow p r o p e r tie s o f e ig h t p e rc e n t b e n to n ite su s
p e n sio n (a s an example o f th ix o tr o p ic m a te r ia ls ) u n d er
g r a v ity head, u sin g d i f f e r e n t s iz e s o f g la s s tu b in g , were
I n v e s tig a te d . The r e s u l t s o f t h i s work I n d ic a te d th a t:
1 ) The su sp en sio n had a p r a c t i c a l y ie ld v alu e of
44
ab o u t 0 .1 3 pounds p e r sq u are fo o t, a t w hich i t s e l a s t i c
s tr u c t u r e would b re a k .
2) The v is c o s ity d ec re ase d w ith in c re a s e in r a t e
o f sh e a r, presum ably because o f th e b re a k in g o f bonds be
tw een c o l lo id a l p a r t i c l e s a t a f a s t e r r a t e th a n th ey co u ld
refo rm . The l i m i t o f t h i s p ro c e ss, however, c o u ld not be
ex p ected to g iv e a v is c o s ity low er th a n t h a t o f th e p u re
l i q u i d .
3) As ex p ected , a t any c o n s ta n t r a t e o f sh e a r,
th e v is c o s ity d e c re a se d a s a fu n c tio n o f tim e, and a f t e r
1 0 .3 m inutes tim e la p s e , th e v is c o s ity rem ained c o n s ta n t.
4) The sh e a r diagram o b ta in e d from th e flow
m easurem ents c o n ta in e d many c o n s is te n c y cu rv es w hich i s an
I n d ic a tio n o f th e th ix o tr o p ic c h a r a c t e r i s t i c s o f th e su s
p e n sio n .
5) The ty p e o f r e s u l t s o b ta in e d co u ld be employed
i n th e d e sig n o f p ip e l i n e s and equipm ent u sed to convey
any th ix o tr o p ic m a te r ia l in la m in a r flo w c o n d itio n s .
6) The flow d a ta m easured by means o f t h i s sim ple
d e v ic e show t h a t th e sh e a r diagram , y ie ld v alu e and o th e r
th ix o tr o p ic p r o p e r tie s can be d eterm in ed . The m ajor lim i
t a t i o n s a re th e a p p lic a tio n o f g r a v ity head, in a c c u ra c y o f
h e ig h t and flow m easurem ents, p a r t i c u l a r l y u s in g tu b in g
l a r g e r th a n 0 .7 0 in c h d ia m e te r.
Recomm endations: I t was le a rn e d th a t th e p l a s t i c
v is c o s ity o f a th ix o tr o p ic su sp en sio n a t a c o n s ta n t r a t e
o f sh e a r, changes w ith tim e. The g rap h o f p l a s t i c v is
c o s ity , U, v e rsu s lo g a rith m o f tim e gave a s t r a i g h t l i n e
w ith th e slo p e B. Also p l a s t i c v is c o s ity i s r e l a t e d to
sh e a r s t r e s s , y ie ld v a lu e , and r a t e o f sh e a r by th e
fo llo w in g e q u a tio n :
U = T - ^
r a t e o f sh ear
S in ce th e o n ly v a r ia b le on th e r i g h t o f t h i s e q u a tio n i s
th e sh ear s t r e s s , th e p l a s t i c v is c o s ity o f th e su sp en sio n
i s p r o p o rtio n a l to T . A graph o f T v e rsu s lo g a rith m o f
tim e , a ls o gave a s t r a i g h t l i n e . The sh e a r diagram ob
ta in e d from p ip e l i n e s tu d ie s In d ic a te d th a t a t a c o n s ta n t
s h e a rin g r a t e , th e h ig h e r th e s t r e s s , th e s h o r te r th e tu b e .
The s t r e s s - l e n g t h and s tr e s s - tim e r e la tio n s h i p s o b ta in e d
from p ip e l i n e d a ta and v isc o m e tric m easurem ents seem to
be s im ila r . The c o n c lu sio n i s reac h ed w ith th e a id o f
F ig u re 21. T his graph shows th e s t r a i g h t l i n e r e l a t i o n
s h ip betw een s t r e s s and lo g of re s id e n c e tim e (w hich de
pends on le n g th ) a t any c o n s ta n t r a t e o f s h e a r. The con
s t a n t slo p e o f th e li n e s seems to be r e la te d , in some ways,
to th e v a lu e o f B ( th e c o e f f ic ie n t o f th ix o tr o p ic b reak
down w ith tim e ). I f t h i s id e a i s sound, th e n th e * slo p e i s
th e c h a r a c t e r i s t i c c o n s ta n t of th e t e s t i n g m a te r ia l.
F ig u re 21 a ls o shows th e d i r e c t r e la tio n s h i p
i
46
betw een s t r e s s and lo g o f re s id e n c e tim e a t c o n s ta n t tu b e
le n g th s . On th e o th e r hand, each s t r a i g h t l i n e i s r e
p r e s e n ta tiv e o f s tr e s s - r e s id e n c e tim e r e la tio n s h i p a t d i f
f e r e n t r a t e s o f s h e a r. The slo p e o f a l l th e s e p a r a l l e l
l i n e s would, th e r e f o r e , seem to be r e l a t e d to th e c o n s ta n t
M , w hieh i s th e c o e f f ic ie n t o f th ix o tr o p ic breakdown w ith
r a t e of sh e a r.
The v a l i d i t y o f th e two c o n c lu sio n s , a lre a d y d is
cu ssed , sh o u ld be proven by f u r th e r re s e a r c h on d i f f e r e n t
th ix o tr o p ic su sp e n sio n s. F ig u re 21, o b ta in e d from lim ite d
e x p e rim en ta l d a ta , on a s in g le m a te r ia l, m erely g iv e s an
in d ic a tio n .
B I B L I O G R A P H Y
BIBLIOGRAPHY
GENERAL INFORMATION
(1) C a ld w ell, D. H ., and B a b b itt, H. E ., "The Flow o f
Muds, S ludges, and S uspensions in C ir c u la r P i p e s ,"
I n d u s t r i a l E n g in eerin g C hem istry. 55. 249-256 (1941).
(2) Green, H enry, I n d u s t r i a l R heology and R h e o lo g ic a l
S tr u c tu r e s . New York: J . W iley, 1949.
(5) Green, H enry, and Weltmann, R uth N ., "A n aly sis o f th e
T h ix o tro p y o f P ig m en t-V eh icle S u s p e n s io n s ," I n d u s t r i
a l E n g in eerin g C hem istry. 15. 201-206 (1 9 4 5 ).
( 4 ) Green, Henry, and Weltmann, R uth N ., "The E f f e c t of
T h ix o tro p y on P l a s t i c i t y M easurem ents," J o u rn a l o f
AdpIIed P h y sio s. 15. 414-420 (1944).
(5) G reen, Henry, and Weltmann, R uth N ., "E q u atio n s o f
T h ix o tro p ic Breakdown f o r th e R o ta tio n a l V isco m eter,"
I n d u s t r i a l E n g in ee rin g C h em istry. A nal. E d ., 18.
167-172 (19461:
( 6) H a rriso n , V. G. W., P ro c eed in g s o f th e Second I n t e r
national C ongress on R heology. New York: Academic
P re ss I n c ., 1954.
(7) L apple, C. E ., F lu id and P a r t i c l e M echanics. F i r s t
e d itio n . U n iv e rs ity o f D elaw are: 1954.
( 8 ) Mooney, M., " E x p lic it Form ulas f o r S lip and
F l u i d i t y ," J o u rn a l o f R heology. 2, 210-222 (1951).
(9) P e rry , J o h n H ., Chem ical E n g in e e rs1 Handbook. T h ird
e d itio n . New York: M cGraw-Hill Book C o., 1950.
(10) Roland, E. F ., R heology: Theory and A p p lic a tio n s .
V ol. I , New York: Academic P re s s , 1956.
(11) S c o tt B l a ir , W., An In tro d u c tio n to I n d u s t r i a l
R heology. P h ila d e lp h ia : B lak esto n eT s Son and C o.,
1958.
(12) Weltmann, R uth N ., "Breakdown o f T h ix o tro p ic S tru c
tu r e as F u n ctio n o f T im e," J o u rn a l o f A pplied
P h y sio s. 14, 545-350 (1943).
49
(13) Weltmann, R uth N ., "C o n siste n cy and T em perature o f
O ils and P r in tin g In k s a t High S h earin g S t r e s s , "
I n d u s t r i a l E n g in ee rin g C hem istry. 4 0 . 272-280 (1948).
(14) W ilhelm, R. H ., W roughton, D. M., and L o e ffe l, W . P .,
"Flow o f S u sp en sio n s Through P i p e s ," I n d u s t r i a l
E n g in eerin g C hem istry. 51, 622-629 (1 9 3 9 ).
(15) W inding, C. C ., Braumann, G. P ., and K ran ieh , W . L .,
"Flow P r o p e r tie s o f P s e u d o p la s tie F lu id s - P a r ts I
and I I , " Chem ical E n g in eerin g P ro g re s s . 4 5 . 527- 536,
613-633 (1 9 4 7 ).
A P P E N D I X
51
Series I
V isco m etric M easurem ents
V iscom eter S p e c ific a tio n s :
One speed B ro o k fie ld H S y n e h ro -L e c tric B v isc o m e ter.
S p in d le 500 2M 5M 10M
Read on S c a le 500 500 500 100
F a c to r (M u ltip ly ) 1 4 10 100
5# B e n to n ite S uspension
T e st Run No. 2
S p in d le 2M p u t in su sp en sio n j u s t b e fo re m easure
m ent.
A pparent V is c o s ity Time _ .
S c a le R eading O e n tip o ls e s M inutes u
125 500 0 .2 0 84
120 480 0 .4 8 64
112 448 1 .4 0 32
110 440 2 .0 0 24
104
416 6.1 0 00
104
416 11.20 00
R e s u lts :
1 ) The e q u ilib riu m ap p a re n t v is c o s ity was ob
ta in e d to be 416 c e n tip o is e s .
2) The tim e e q u ilib riu m , tg , found to be 4 .2 0
m in u te s.
52
B e n to n ite S uspension
T e s t Run No. 5
S p in d le 2M was l e f t in th e su sp e n sio n o v e rn ig h t
b e fo re m easurem ents.
S c a le R eading
373
340
335
330
317
301
295
295
295
A pparent V is c o s ity Time
C e n tip o is e s M inutes
1 ,4 9 2 0 .1 2
1 ,3 6 0 0 .4 0
1 ,3 4 0 0 .5 5
1 ,3 2 0 0 .7 0
1 ,2 6 8 1 .5 0
1 ,2 0 4 3 .2 0
1 ,1 8 0 6.00
1 ,1 8 0 8 .8 0
1 ,1 8 0 1 0 .0 0
U - U e
312
180
160
140
88
24
00
00
00
R e s u lts :
1 ) The e q u ilib riu m a p p a re n t v is c o s ity ■ 1 ,180
c e n tip o is e s .
2) The tim e e q u ilib riu m , tj;, = 5 .0 0 m in u tes.
53
7 % B e n to n ite S uspension
T e s t Hun No. 7
S p in d le 2M was employed, and l e f t in th e su sp e n sio n
o v e rn ig h t b e fo re m easurem ents.
A pparent V is c o s ity Time
S c a le R eading O e n tip o ise s M inutes U - IT g
490 1 ,9 6 0 0 .5 0 520
475 1 ,9 0 0 0 .8 0 460
465 1 ,8 5 6 1 .1 5 416
448 1 ,7 9 2 1 .4 0 352
440 1 ,7 6 0 1 .6 0 320
430 1 ,7 2 0 1 .8 0 280
428 1 ,7 1 2 2 .1 0 272
418 1 ,6 7 2 2 .7 0 232
410 1 ,6 4 0 3 .0 0 200
402 1 ,6 0 8 3 .4 0 168
392 1 ,5 6 8 3 .9 0 128
384 1,536 4 .6 0 96
366 1 ,4 6 4 6 .3 0 24
360 1 ,4 4 0 7.40 00
360 1 ,4 4 0 9 .9 0 00
R e s u lts :
1 ) The e q u ilib riu m ap p a re n t v is c o s ity = 1 ,4 4 0
c e n tip o is e s .
2) tE = 7 .0 0 m in u tes.
54
Series II
Flow M easurem ents
Tube D iam eter * 0.0788 in c h e s
Tube L ength H eig h t o f F lu id D isch arg e Time
F e e t In th e Tank, In ch es Grams M inutes
a.
12£ 74.40 10.00
1 12| 65.70 53.00
l i
12* 11.00 43.00
2 12* 1 2 .3 0 51.30
5
12* 13.00 63.00
4 12* 18.00 87.00
N ote: S in ce th e h e ig h t o f f l u i d in th e ta n k does n o t
change a p p re c ia b ly w ith th e d is c h a rg e , i t i s
assum ed to be c o n s ta n t.
55
S e r ie s I I I
Flow M easurem ents
Tube D iam eter = ■ 0.1967 in c h e s
Tube L ength
F eet
D iffe re n c e in H eight
o f F lu id in th e Tank
Due to D isch arg e,
a h, in c h e s
1.6250
1.0200
0.8680
0.7000
D isch arg e
Pounds
3.312
2.281
1.938
1 .562
Time
M inutes
9 .0 0
7 .0 0
7 .0 0
7.00
H eig h t o f su sp e n sio n in th e ta n k in c h e s:
O rig in a l h e ig h t, hx - 13.675
F in a l h e ig h t, hg = 9 .162
I n te r p o la te d in s ta n ta n e o u s flow a t one fo o t
h e ig h t, = 0 .363 lb ./m in .
0.7400
0.6700
0.6150
1 .6 5 6
1 .500
1.375
10.00
10.00
10.00
hx « 11.735
h2 = 9 .7 1 0
W 7 = 0 .1 7 6 lb ./m in .
0.7150
0.7000
0.6850
0.6300
0.5880
1 .594
1.562
1.531
1.406
1.312
10.00
1 0 .0 0
10.00
10.00
1 0 .0 0
14.26
10.93
0 .1 4 7 lb ./m in .
56
Series III
Flow M easurem ents ( co n 1t . )
D iffe re n c e in H eig h t
o f F lu id in th e Tank
Tuhe L ength Due to D isch arg e, D ischarge
F e e t Ah, in c h e s Pounds
4 1.4100 3.150
0.6600 1.469
0.6300 1.405
0.5880 1.312
hx » 14.75
hg » 11.45
s 0.140 lb./min.
Time
M inutes
25.00
10.00
10.00
10.00
57
Tube Diameter *
Tube L ength
F e e t N
1
2
3
S e r ie s IV
Flow M easurements
G.3345 in c h e s
Ah, in c h e s
1,5400
1.3050
1.1200
2.7600
2.4200
2.0300
hl =
2.4000
2.0900
1.8650
1 .5 1 0
1 .4 5 4
1.360
1.275
D isch arg e
Pounds
3.4375
2.9060
2.5000
11.15
7.185
4.0625 lb ./m in
6.1560
5.4060
4.5310
15.75
8 .5 4
2 .7 8 5 lb ./m in .
5.3750
4.6875
4.1875
14 .2 5
7.895
2.575 lb ./m in .
3.375
3 .250
3.030
2 .8 4 4
15.875
1 0 .0 2 6
2.345 lb ./m in .
Time
M inutes
1.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
1 .3 0
1 .3 0
1 .3 0
1 .3 0
!
58
Series V
Flow M easurem ents
Tube Diameter * 0.5110 inches
Tube L ength D isch arg e Time
F e e t A h , in c h e s Pounds M inutes
1 4 .5 5 1 0 .1 0 0 .5 0
3 .8 5 8 .6 0 0 .5 0
2 .6 9 6 .0 0 0 .5 0
2 .1 3 4 .7 5 0 .5 0
h± = 16.06
hg s 2 .6 1
W A - 1 9 .4 lb ./m in .
3 .6 5
3 .3 0
2.91
8 .1 5
7 .3 5
6 .5 0
1 6.75
6 .6 4
1 5 .2 0 lb ./m in .
0.50
0 .5 0
0 .5 0
2 .8 7
2 .9 1
2.55
2 .1 3
2.845
4.480
1.700
*1
*2
%
h -j_ -
h2 =
W , =
6 .4 0 0 .5 0
6 .5 0 0 .5 0
5 .7 0 0 .5 0
4 .7 5 0 .5 0
11.75
1 .0 4
1 5 .2 0 lb ./m in .
6 .3 5 0 .5 0
1 0 .0 0 0.92
5 .0 0 0 .6 6
10.625
1 .3 5 0
1 4 .5 lb ./m in .
59
S e rie s VI
Flow M easurem ents
Tube Diameter - 0.748 inches
Tube L ength D isch arg e Time
F e e t Ah, in c h e s Pounds M inutes
1 3 .4 8 0 8 .0 0 0 .1 2
2.860 6.60 0.12
2.540 5 .9 0 0 .1 2
hx = 15.375
hg - 6.045
Wi - 6 0 .8 lb ./m in .
3.135
2 .9 1 0
2.690
2.240
h l *
ho =
7 .0 0
6 .5 0
6.00
5 .0 0
16.125
4.675
0.10
0.10
0.10
0.10
6.279
3.135
2.780
2.620
h2 =
ho =
14.00
7.00
6.20
5.85
17.125
2 .070
0.2 4
0.10
0.10
0.10
.^sfvercitv — —

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Creator Mehrali, Mehdi (author)

Core Title An experimental investigation of thixotropy and flow of thixotropic suspensions through tubes

Degree Master of Science

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, chemical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Rebert, Charles J. (committee chair), Chilingar, George V. (committee member), Lockhart, Frank J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c20-309219

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