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Content A RH10L0GICAL STU D Y O F AN A L K Y L AETL
SULFO NATE SLURRY
A Thesis
Presented t o
th e F aculty o f the School of E ngineering
The U n iv ersity o f Southern C a lifo rn ia
In P a r tia l F u lfillm e n t
of the Requirements fo r the Degree
M aster o f S cien ce in Chemical E ngineering
t y
R u sse ll G* McKenzie
January, 1958
UMI Number: EP41758
All rights reserved
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Q .h '58 M IS7
This thesis, written by
...............................................
under the guidance o/fais 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 osf Science la..........
C h C T d c a l^
Date.. Janm JT . 195.8.....
Faculty Committee
o nairm un
C ? .......................................
0 - ~ )? 7 » _
STA T E M E N T OF TH E P R O B L E M
A company w ith headquarters in South G ate, C a lifo r n ia was
engaged in th e manufacture o f commercial and household sy n th e tic
d e te r g en ts. The b a sic su rfa ce a c tiv e in g red ien t o f th e d etergen ts
was an a lk y l a r y l su lfo n a te made by su lfo n a tin g a polypropylene
a lk y lla t e o f benzene w ith 25^ oleum and n e u tr a liz in g w ith sodium
hydroxide. The r e su lta n t slu r r y was f o r t if ie d w ith variou s b u ild e r s,
sp ray-d ried and packaged.
Many problems were encountered in handling la rg e q u a n titie s o f
! th e s u lfo n a te , e s p e c ia lly in pumping and a g it a t in g . The p h y sic a l
i
| p r o p e r tie s o f th e m a teria l w ere v a ria b le and d id not n e c e s s a r ily
I
j have any r e la t io n to th e chem ical a n a ly s is . The flow behavior
! d ev ia ted con sid erab ly from th a t o f a Newtonian f lu id and i t seemed to
i
j depend t o some e x ten t on th e p a st therm al and p h y sic a l h is to r y .
P ast p r a c tic e o f th e company had been to determ ine an apparent
I
j v is c o s it y on each batch o f su lfo n a te s lu r r y in a d d itio n to th e
J regu lar chem ical a n a ly se s. This v is c o s it y was determined by a
i
i B rook field S y n ch ro eleo tric Viscom eter op eratin g a t one speed or one
r a te o f sh ea r. The apparent v is c o s it y o f each batch was compared to
th a t o f oth er batches and used as one phase o f q u a lity c o n tr o l. The
same v is c o s it y was used to p red ict pumping tim e and to s iz e any new
p ip e lin e s .
I The p h y sic a l p ro p erties o f th e s u r fa c e -a c tiv e agent had a very
I
I pronounced e f f e c t on th e spray drying o p era tio n , and p ast use o f th e
apparent v is c o s it y gave no c o r r e la tio n w ith r e s u lt s achieved in p la n t
i i i
o p e r a tio n s. I t proved t o be h ig h ly u n relia b le when used as a d esig n
fa c to r fo r new in s ta lla tio n s *
The use o f the one-speed viscom eter and the apparent v is c o s it y
concept was f in a lly abandoned, and more r e lia n e e put on su b jec tiv e
type t e s t s by experienced p la n t p erso n n el.
In an e f f o r t t o m inimize su b je c tiv e t e s t in g and d ev ise a more
r e lia b le method o f f lu id co n sisten cy t e s t in g , the Research Department
proposed a program o f in v e s tig a tio n w ith the fo llo w in g o b jectiv es*
1* To s e le c t or develop an instrum ent su ita b le fo r determ ining
th e co n sisten cy o f the a lk y l a ry l su lfo n a te in q u estio n .
2 . To p e r fe c t a procedure fo r u sin g the instrum en t,
3 . To determine the c o n sisten cy curves or v is c o s i t i e s o f the
su lfo n a te a t p lan t con cen tration s and tem peratures.
4 . To examine th e e f f e c t s of tem perature from 110 to 160
degrees Fahrenheit (° F .) on th e co n sisten cy curves or v i s
c o s i t i e s .
5 . To c o r r e la te th e r e s u lta n t d a ta .
The In v e stig a tio n was intended to be a prelim inary p art of a
long range attem pt to c o r r e la te the behavior o f the f lu id in spray
drying w ith i t s o r ig in a l p h y sic a l p r o p e r tie s, and fin d a r e lia b le
method fo r batch t o batch co n sisten cy c o n tr o l.
TABLE OF C O ! TENTS
C H A PTER PA G E
I . IHIRODUC T I O N ............................................ 1
R elated L itera tu re and P rior A rt . . . . . . ....................... . 1
F lu id T^pes . . . . . . . . . . . .............................................. 3
Newtonian. ........................... 3
!on -!ew ton ian .... .. . ............................ ..... .. 3
D ila te n t F lu id . . . . . ................... . . . . . . . . . . 4
P seu d op lastic F l u i d ................................................. 4
Bingham P la s t ic F lu id . . . . ................... .. . . . . .. 4
R heopeotic F lu id . . . . . . . . . . . . . . . . . . . 5
Thixotropy . . . . . . . . . . . . . . . . . ................... 5
I I . VISCOM ETER SELECTION............................................... 7
C a p illa ry V iscom eters .................................... . . . . . . . . . . 7
Viscom eters fo r A bsolute Measurements . . . . . . . . . 7
P o is e u ille s * V iscom eter . . . . . . . . . . . . . . 7
Thorpe and Rodgers' Viscom eter • • .. .• . . • • • 7
Coes' Viscom eter . . . . . . . . . . . . 8
V iscom eters fo r R ela tiv e Measurements . . . . . . . . . 8
Ostwald Viscom eter . . . . . . . . . . 8
Redwood Viscom eter ....«•.•••••••... 12
Engler Viscom eter . . . . . . . . . . . . . . . . . 12
R o ta tio n a l Viscom eters ........................................................12
Stormer Viscom eter . . . . . . . . . . . . . . . . . 12
Couette Viscom eter ...................... 12
■ V
CH APTER PA G E
B rook field V iscom eter . . . . . . . . . . . . . . . . 14
H ercules H i-Shear Viscom eter . . . . . . . • 14
MacMiohael Viscom ater . . . . . . ............................... 15
P r e c isio n Interchem ioal Viscom eter . . . . . . . . . . 15
D iscu ssio n of Viscom eter S e le c tio n 15
I I I . PROCEDURE.............................................. . .................................. 22
C a lib ra tio n of the Viscom eter . . . . . . . . . . . . 22
A u x ilia ry Equipment . . . . . . . . . . . 23
C onsistency Curves Method • 25
Curve In te r p r eta tio n . . . . . . . . . . . . . . . . 29
IV . CONSISTENCY CURVES-VARYING TIM E-AT-TEM PERATURE ....................... 33
C onsisten cy Curves a t 110 °F . .............................................. • 33
B asic Shear Diagram ........................... 37
C on sisten cy Curves a t 120 °F« . . . . . . . . . . . . 41
C onsistency Curves a t 130 °F . . . . . . . . . . . . . 42
C onsisten cy Curves a t 140 °F . . . . . . . . . . . . . 54
C onsisten cy Curves a t 150 °F . . . . . . . . . . . . . 54
C onsisten cy Curves a t 160 °F . 59
V. S U M M A R Y O F RESULTS ........................................................................ 72
V I. CONCLUSIONS.........................................................................................................79
BIBLIOGRAPHY...................................................... 81
APPENDIX .............................................................................................. 83
LIST O F TABLES
TA B LE
I* Torsion Wire C onstants .......................
I
II* Time-Temperature Curves a t 110 °F,
I I I . F lu id Behavior Varying Time-at-Temperature
IV . B asic Data a t 110 °F . ...... ... .
| V , Time-Temperature Curves a t 120 °F . . . . .
j V I. F lu id Behavior Varying Time-at-Temperature
i
j V II . Basic Data a t 120 °F ........ ....................... .... . . .
'V III* Time-Temperature T ests a t, 130 °F . • . . .
IX . F lu id Behavior Varying Time-at-Temperature
1 X . B asie Data a t 130 °F . ..........
i
X I. Time-Temperature T ests a t 140 <¥. • . . .
| X I I . B asic Data a t 140 °F . ..........
jX I I I . Time-Temperature T ests a t 150 °F . • . . .
XIV. B asic Data a t 150 ©F..................................................
| XV, F lu id Behavior Varying Time-at-Temperature
XVI. Time-Temperature T ests a t 160 ^F. . . . .
J XVII. F lu id Behavior Varying Time-at-Temparature
X V III. B asic Data a t 160 °P .
C H A P T E R X
INTRODUCTION
The f l u i d in q u estio n appeared t o e x h ib it a r a d ic a l departure
from id e a l Newtonian behavior, on tb s b a sis of p lan t ex p erien ce.
From r e s u lt s obtained w ith a s in g le p o in t v isco m eter, the co n sisten cy
curve appeared n o n -lin ea r and su b ject t o peaks a t c e r ta in tempera
tu r e s . At high tem peratures a j e l l - l i k e c o n d itio n e x is te d where the
water in th e s o lu tio n appeared to be bound t i g h t l y .
Since no reoord o f previous T h eo lo g ica l work on the su b ject f lu id
could be found, and in view of p a st f a ilu r e s w ith the sin g le p o in t
viscom eter and seeming com plexity o f the f lu id , i t was n ecessary to
review the lit e r a tu r e fo r inform ation or su g g estio n s on the fo llo w
in g main p o in ts*
1 . The s e le c t io n o f , or c o n stru ctio n o f a viscom eter su ita b le
I
fo r ev a lu a tin g the a lk y l a ry l su lfo n a te s lu r r y . !
I j
I 2 . Development o f a technique fo r determ ining the c o n sisten cy |
' i
curves a t tem peratures from 110 to 160 degress Fahrenheit I
i
( ° F . ) . J
i . !
| \ r I . R elated L itera tu re and P rior A rt •
< >
The b a sis of th e study of viscom atry s t i l l r e s ts upon the works j
of Newton, P o is e u ille and Wiedeman. Before any ab solu te measurement
of v is c o s it y could be determ ined, soma h yp oth esis was necessary |
i
concerning the magnitude of the fo rce req u ired t o overcome v iscou s
i
r e s is ta n c e .
2
(
»
I Such an h yp oth esis was proposed by Newton ( l ) who con sid ered two
p a r a lle l plan es in a liq u id each o f area (A ), sep arated by a d ista n ce
I
(X ), and moving a t v e lo c i t ie s (V i) and (VJ>) in the d ir e c tio n o f
e ith e r o f the p la n e s. The fo rce (F) req uired to m aintain the d if f e r
ence o f v e lo c it y i s p rop ortion al to the grad ient of v e lo c it y , but as
the v e lo c it y in the liq u id i s changing contin uously the equation may
be w ritten *
v , Adv _ NAdv
T F S
The c o e f f ic ie n t (N) is the c o e f f ic ie n t o f v is c o s it y o f the
liq u id . Experiments have shown ( l ) to be a c h a r a c te r is tie con stan t
fo r each Newtonian f lu id a t a g iv en tem perature.
P o i s e u ille s ’ b a sic work ( l ) on determ ining a law of flo w through
c y lin d r ic a l tu b es made p o s s ib le the deduction o f a b so lu te v a lu es fo r
j
j the v is c o s it y o f a sim ple f l u i d . P o is e u ille d iscovered the fo llo w in g
1 r e la tio n s h ip , u sin g water in f iv e g la ss tu b es:
o _ KAPD4
L“
i
i "W here % * q u an tity discharged in u n it time
| AP « pressure d iffe r e n c e between ends of c a p illa r y
' P * tube diam eter
! L - tube len gth
i X a c o n sta n t, c h a r a c te r is tic o f liq u id
i I t should be n o ted , th a t, had P o is e u ille used b lood , in which
he was in te r e s te d , in ste a d o f w ater he might never have a rriv ed a t
! h is c o n c lu sio n s, sin c e blood i s not a sim ple f lu id .
F lu id Types
| L iquids and suspensions f a l l in to two gen eral ty p e s, ( 2 , 3)
Newtonian and non-Newtonian, w ith th e la t t e r ty p e being d ivid ed in to
sev e r a l c la s s e s . ;
Newtonian* A Newtonian flu id i s ch a ra cterized by a constant j
i
v is c o s it y a t constan t tem perature independent o f th e ra te o f shearj
or in o th er w ords, th e r a te o f shear in th e liq u id i s d ir e c t ly propoi>:
t io n a l to th e shearin g s tr e s s * The curve o f a Newtonian f lu id on a
shear diagram i s a s tr a ig h t lin e beginning a t th e o r ig in . Water i s
a t y p ic a l Newtonian - or sim ple f lu id . ]
Non-Newtonian* For non-Newtonian f lu id s or su sp en sio n s, th e
v is e o s it y i s a v a r ia b le , varying as th e r a te o f sh ea r, th e tim e o f j
I
shear or as some fu n c tio n o f th e p ast h is to r y o f handling o f th e j
flu id * Non-Newtonian f lu id s are g e n e r a lly c la s s if i e d by th e typ e o f
co n sisten cy curve th e y e x h ib it, and are considered to f a l l in to four
general c la s s e s i ( l ) D ila ta n t, (2) P se u d o p la stic, (S) Bingham
P la s t ic , and (4) I h e o p e c tic .
F lu id s which evidence th ix o tr o p ic p ro p erties are not con sid ered j
I
a sep arate c la s s in t h is stud y because o f th e f a c t th a t any o f th e
m entioned four c la s s e s can evidence th ix o tr o p y .
B ila ta n t F lu id . The c o n sisten cy curve, or a p lo t o f shearin g j
r a te versu s torque o f a d ila ta n t flu id i s not a s tr a ig h t l i n e , but !
concave toward th e fo rce a x is . The curve u s u a lly appears t o s ta r t
from th e o r ig in . A t y p ic a l example is beach sand, in which th e w ater
to sand r a tio i s such th a t th ere i s ju s t enough w ater to f i l l th e
void s when th e la t t e r are a t t h e ir minimum v a lu e . Any ap p lied shear
w i l l grad u ally d ila t e th e v o id s , inducing a s t a t e o f p a r tia l d ryn ess,
4
and the r e sista n c e t o shearin g s tr e s s in crea ses more ra p id ly than i t
would otherw ise* Thus the c o n siste n c y curve is ooneave to th e force
a x is*
P seu d o p la stic F lu id * The co n sisten cy curve of a m a teria l o f
t h is type is not a s tr a ig h t l i n e , but convex to the fo rce a x is* The
curve s ta r ts a t the graph o r ig in and th e v is c o s it y decreases w ith
in crea sin g r a te s of sh ea r. The ra te o f shear is not d ir e c tly propor
t io n a l to the shearin g s tr e s s *
P seu d o p la stic flu id s are g en era lly considered to be composed of
I
long ch ain m olecules which do not a lig n in the d ir e c tio n o f flo w a t
low r a te s of sh ea r. As shear ra te in c r e a s e s, m olecular alignm ent j
in c r e a s e s, and f r ic t io n a l r e s is ta n c e between adjaoent la y e rs d ecrea - (
I
s e s . The r e s u lt is a greater ra te o f shear fo r a given s tr e s s* j
i
Bingham P la s tic F lu id * The c o n sisten cy curve of the s o -c a lle d
id e a l Bingham P la s tic (4 ) i s a s tr a ig h t li n e , o r ig in a tin g a t some
p o in t along the force a x is , the ra te of shear b ein g d ir e c tly propor
t io n a l to th e shearing s tr e s s in ex cess of the y ie ld value* The
in te r c e p t o f the curve on the force a x is is c a lle d the y ie ld v a lu e .
A c tu a lly , the curve is very seldom a p e r fe c tly s tr a ig h t l i n e , J
e s p e c ia lly w ith f lu id s which e x h ib it th ix o tr o p io behavior as w e l l .
Some t y p ic a l examples of t h is type of f lu id are m argarine, cup grease
i
and mayonnaise*
R heopectic F lu id * The apparent v is c o s it y o f a m a teria l o f th is
type in crea ses w ith time a t any con stan t ra te of sh ea r. The c o n s is
ten cy curve shows th a t in most rh eo p ectic sy stem s, th ix o tro p y e x is t s
5
a lso * Soma examples are vanadium pentoxide and gypsum in water*
( T hixotropy. The c o n sisten cy curve of a th ix o tr o p ic m a teria l is
I
1 eonvex toward th e fo rce a x is and o r ig in a te s a t some p o in t alon g the
I fo rce a x is* I f an upcurve and downcurve are run u sin g a r o ta tio n a l
i v isco m eter, the two curves w i l l not co in cid e but w i l l form a loop*
G enerally the fo llo w in g phenomena are observed in t e s t in g a th ix o -
I
(
| tr o p ic m aterial*
1
]
| 1* The breakdown o f th e .structure in crea ses as a fu n ctio n
i
o f in crea sed shear r a te s*
. 2* The stru ctu re reb u ild s upon r e s t .
3* Breakdown in crea ses contin uously w ith con stan t shear ra tes*
Figure I was p lo tte d to illu s t r a t e the shear diagrams o f the
I various typ es o f f l u i d s . The diagram as p lo tte d illu s t r a t e d the
1 synonyms used in d escrib in g th e ordinate and a b sc issa of a shear
diagram*
Shear Rate Shear Rote
6
Newtonian
0 Torque Axis
Pseudo plastic Dilatant
0 Force Ax/s 0 Shear Stress
B ingham Plastic T H in o tr o p ic .
i
c
Q
• * »
2
0 Force Axis
R heopett/c
V
O
-2
J L
3
C
0 Shear S tr e s s
FIGURE 1
FLUID TYPES
I C H A PTER I I
i
I
VISCOM ETER SELECTION
i
Sin oe the tim e o f P o i s e u ille , many typ es o f viscom eters have
; been p e r fe c te d and used, both fo r the study of Newtonian and non-
i
Newtonian F lu id s* A few o f the viscom eters ( l , 8) which have been of
most b a sic importance are d iscu ssed b r ie f ly h ere.
i
I . CAPILLARY VISCOM ETERS
These can be d iv id ed in to two cla sse s*
j 1 . Those fo r measuring ab solu te v is c o s it y d ir e c t ly .
J
(
2 . Those fo r measuring r e la t iv e v is c o s it y by referen ce to
standard liq u id s .
! V iscom eters fo r A bsolute Measurements
P o is e u ille s * V iscom eter, Figure 2 , page 9* The bulb (A) and
c a p illa r y are f i l l e d w ith , and immersed in the liq u id under t e s t ,
j The liq u id in (A) i s forced out through the c a p illa r y and the time
i fo r the le v e l to f a l l from (B) to (B^) is n o ted . The instrum ent is
i
j p r e c is io n made w ith aocurate measurements bein g tak en .
i
' Thorpe and Rodgers1 V iscom eter, Figure S , page 1 0 . The v is c o -
1 mater is f i l l e d and pressure is a p p lied a t (Hg) u n t il the le v e l
stands a t (K2 ) , and ex cess flow s in to ( T i) . The liq u id i s than
!
fo rced through the c a p illa r y by a ir pressure and the time noted fo r
I
! the meniscus to pass from (m i) to (0 2 ) . A d u p lica te reading can be
1
| obtained by rev ersin g the p r o c e ss. The instrum ent i s made o f fin e
, g la ss w ith ground j o i n t s , and w ith maintenance of very sm all t o la r -
I
i anoes*
I
Goes * V iscom eter, Fignra 4 , page 1 1 . This i s supposedly the
most accurate ab solu te viscom eter known fo r t e a ts on w ater.
I L iquid flow s from (G) through (D) t o (E ), the pressu re d i f f e r -
j enoe bein g obtained by a d if f e r e n t ia l mercury manometer (G) in which
| le v e ls are in d ica ted by e l e c t r ic a l c o n ta c ts . A known ra te o f flo w is
!
! produced by in je c tin g mercury in to th e upstream r e se r v o ir from a
! cy lin d er (B) having a p is to n (A) d riven by a geared synchronous
i
i m otor. The ra te of volume displacem ent i s accu rate t o + 0 .0 1 $ .
V iscom eters fo r R ela tiv e Measurements.
' A greater p r e c is io n i s u su a lly obtainable w ith viscom eters
; design ed s p e c if ic a lly fo r r e la t iv e measurements. This is due p a r tly
t o s im p lific a tio n in d esign and p a r tly t o e lim in a tio n o f errors in
dim ension measurements.
R e la tiv e viscom eters use e ith e r an e x te r n a lly a p p lied pressure
or r e ly on th e h y d ro sta tic head o f liq u id in the viscom eter i t s e l f to
induce flo w .
I
( Ostwald V iscom eter, Figure 5 , page 1 3 . This u n it - is charged
I w ith a con stan t volum e, and liq u id is drawn up in to the l e f t limb
j above (A ), then allow ed to le v e l a t (A ). The time o f flo w from (A)
t
! t o (B) i s then measured. C a lib ra tio n w ith a known sim ple f lu id is
n ecessa ry .
Redwood V iscom eter. This u n it c o n s ists o f a standard cup w ith
I an agate j e t mounted in the bottom . The time o f flow by g ra v ity of
FIGURE Z
POISEUILLE V I S C O M E T E R
FIGURE 3
THORPE AND R O D G E R S ' VISCOMETER
11
fix
B
D
C £
f i g u r e : 4
C O E ’ S V I S C O M E T E R
12
a measured volume o f f lu id through the j e t i s used as an a rb itra ry
measure o f kinem atic v i s c o s it y . |
Bngler V iscom eter. This instrum ent is very sim ila r to the
Redwood. The r e su lta n t v is c o s it y i s measured in Bnglar degrees which
i s the time r a tio o f o i l flo w to w ater flo w under the same co n d itio n s.!
R o ta tio n a l Viscom eters
Stormer V iscom eter. In t h is instrum ent (12) a c y lin d r ic a l cup
holds the f lu id and th e sh earin g s tr e s s i s su p p lied by a r o ta tin g bob
or paddle suspended in the liq u id by a s t e e l rod supported by a p re
c is io n b ea rin g . A n o n -stretch oord is wrapped around the upper end
o f the supporting rod , and the la t t e r is r o ta te d by the sim ple means
j
of hanging standard w eights on the co rd . The fo rce o f g ra v ity a c tin g
on th e w eigh ts r o ta te s the rod and sim u ltan eou sly the bob in the
f l u i d . Thus a sh earin g s tr e s s i s ex erted on the f lu id commensurate
w ith the w eight suspended on the cord . i
Couette Viseom atar. This u n it was one o f the e a r li e s t o f the j
r o ta tio n a l ty p e s . Most of the modern r o ta tio n a l viscom eters are modi
f ic a t io n s or improvements of the o r ig in a l Couette u n it.
The instrum ent c o n s ists o f two co n cen tric c y lin d e r s , one in sid e
I
the o th er, w ith the outer c y lin d er having an open top and the inner j
!
cy lin d er being s o l i d . The inner cy lin d er is supported by a to r s io n {
I
w ire fix e d a t the upper end. The outer cy lin d er is r o ta te d a t a j
c e r ta in sp eed , and the torque tra n sm itted to the inner cy lin d er by
the f lu id in between is measured by the d e fle c tio n o f the to r s io n
w ir e .
13
A
B
FIGURE 5
O S T W A L D V ISC O M E TER
14
i
i
B rook field V iscom eter* The B rook field (9 ) is one of the most
popular instrum ents in in d u stry today because o f i t s s im p lic ity of
use* I t was o r ig in a lly a one-speed u n it reading an apparent v i s c o s i
ty but recen t models fu rn ish e ig h t d if fe r e n t sp eed s.
B a sic a lly the u n it c o n s is ts o f a con stant speed motor d rivin g a
I round, bearing-supported sh a ft on the end of which is fix e d a bob,
paddle or d isc* The bob is immersed in the f lu id to be te s te d and
then the motor energized* The r e s i s t ance or drag which th e f lu id
| ex er ts on the bob is measured by a s p ir a l sp rin g o f b eryllium -copp er.
I
The la t t e r is c a lib r a te d to read d ir e c t ly in e e n tip o is e s . Any con-
I
v en ien t beaker serv es as the sample cup*
j
! H ercules B i-Shear V iscom ater* This instrum ent ( l l ) i s compara-
j ■ !
j t iv e ly new to the in d u s tr ia l sc e n e . The u n it operates somewhat on thej
| p r in c ip le o f the B ro o k field but is much more e la b o r a te . The r e s i s
tance which the f lu id e x e r ts on a bob immersed in the f lu id is
i
i
measured and recorded a u to m atically a t a l l r o to r sp eed s.
MaeMichael V iscom eter, Figure 6 , page 1 6 . This instrum ent (10)
1 c o n s is ts o f a bob or plunger suspended from a phosphor-bronze to r s io n
I
I w ire w ith the bob being immersed in the f lu id to be t e s t e d . The flu id
i ^
i s contain ed in a sample cup which is geared to a v a r ia b le speed I
! back-geared m otor. The speed range is from te n to fo r ty rev o lu tio n s
j per m inute. The drag or r e sista n c e o f the f lu id ex erted on the bob
i is measured by the d e fle c tio n or tw is t o f th e to r s io n w ir e . The
speed can be changed by tu rn in g a co n v en ien tly mounted c o n tr o l.
P r e c isio n Interchem ioal V iscom eter. This is probably the most
15
i
iexpensive and ela b orate viscom eter (2 ) a v a ila b le . I t c o n s is ts o f a
r o ta tin g cup con tain in g the m aterial to be measured and a sta tio n a ry
I
|bob immersed in the m a te r ia l. The bob is suspended by a to r s io n
i
spring and la t e r a lly supported a t i t s lower en d . When the cup is
jro ta ted a v isco u s drag is ex erted on the bob and the fo rce i s measur
ed by the d e fle c tio n o f a d ia l s c a le . The p r in c ip le i s id e n t ic a l w ith
th a t o f the MaoMiehael V iscom eter, but the co n stru ctio n is much
b e tte r and the l i s t o f a c c e sso r ie s g r e a te r .
I I . DISCUSSION O F VISCO M ETER SELECTION
I P ast p la n t experience w ith the a lk y l a ry l su lfo n a te f lu id had
;led to the b e lie f th a t i t was not a Newtonian f l u i d , inasmuch as the
!
;on e-p oint method o f measuring v is c o s it y has unpredictable r e s u lts and
the flo w was not n e c e s s a r ily in prop ortion t o the a p p lied fo rce in
imany pumping o p e r a tio n s. Furthermore, the f lu id appeared to pass
I
through a j e l l phase a t e le v a te d tem peratures. T ests w ith the c a p i
lla r y type viscom eters ware u n su cc e ssfu l. The su lfo n a te f lu id would
jnot flo w a t a constant r a te , and even though the com plete u n it was
* kept a t con stan t tem perature, the water in the su lfo n a te s e t t le d and
!
'flow ed through the apparatus lea v in g a more concentrated su lfo n a te
'behind. The c a p illa r y type viscom eter appeared t o have a d d itio n a l
shortcom ings in measuring a non-Newtonian f lu id in th a t the sample
,could n ot be remeasured in a sh o r t period o f tim e. In measuring non-
i
Newtonian f l u i d s , i t is of g rea t importance to in sta n ta n eo u sly measure
'th e e f f e c t o f p a st handling or sh earin g and p lo t a co n sisten cy curve
I
Jof sh earin g rate versus shear s t r e s s . This is not p r a c tic a l w ith the
16
F I G U R E 6
MACMICHAEL VISCOMETER
: 17
I
c a p illa r y viscom eter* The laminar flow o f a non-Hewtonian f lu id in a
tube i s o fte n accompanied by plug flo w . In th e case o f a Bingham
P l a s t i c , th ere e x is t s a s o lid plug o f m a teria l near th e c a p illa r y i
i
a x is reg a rd less o f th e flow v e lo c it y . I t i s n ecessary t o have a i
I
I
f i n i t e len g th o f tube to g e t a measurable shear s t r e s s . However, i f
th e f lu id shows a tim e dependency, as in th e case o f a th ix o tr o p ic
m a te r ia l, i t would be n ecessary t o b u ild a tu be viscom eter w ith a
f i n i t e len g th and a d if f e r e n t ia l tim e elem en t. This i s not p o s s ib le . '
t
! In th e r o ta tio n a l v isco m eter, th e co n fin in g w a lls o f th e in s tr u - 1
i ment move r e la t iv e to a fix e d batch o f f lu id , whereas in th e tube !
I ’
i
| viscom eter th e f lu id flow s r e la t iv e to th e co n fin in g w a lls .
Because o f th e shortcom ings o f th e c a p illa r y and o r if ic e typ e
j v isco m eters, i t was decided to con cen trate on s e le c t in g a r o ta tio n a l
I
j viscom eter fo r th e in v e s tig a tio n . j
J A survey o f th e lit e r a t u r e showed th a t in alm ost a l l c a se s , th e
i
I
1 c o n sisten cy curves o f non-Newtonian flu id s were determ ined by r o ta -
I
1
! t io n a l viscom eters o f b a s ic a lly th e same ty p e . This was done prim ar-
i l y because th e c o n sisten cy curve o f a mon-Mewtoniam was not lin e a r j
when done w ith a c a p illa r y v iscom eter, but i t was lin e a r when done I
I 1
j w ith a r o ta tio n a l v isco m eter. In th e la t t e r viscom eter th e con dition s :
| were such th a t a l l o f th e f lu id was in laminar flow once th e a p p lied |
*
; torque exceeded th e y ie ld valu e o f th e f lu id . A lso , w ith th e r o ta -
, t io n a l v isco m eter, th e r a te o f shear a p p lied t o th e same sample could
1 '
j be v a ried w ith in th e lim it s o f th e speed range o f th e instrum ent w ith ,
very sm all tim e la g s . Hence, f lu id breakdown, b u ild -up or y ie ld
18
i value could be e a s ily d e te c te d . This was p o ssib le only by in d ir e c t
means w ith other typ es o f v isco m eters.
r o ta tio n a l v isco m eter, the apparent v is c o s it y was determ ined by the
in v erse slop e of a lin e drawn from the o r ig in to a p o in t on the con
s is te n c y cu rve, m u ltip lie d by th e instrum ental c o n sta n ts.
The development o f the flo w equ ation fo r the r o ta tio n a l v is c o
m eter o f the MacMichael type was fu rth ered p rim arily by Reiner and
R iw lin , (2 ) and a p p lied where the torque to which a f lu id urns su b je o t-
1 e d , was s u f f ic ie n t ly large such th a t a l l m a teria l in the sample cup
1 was in laminar flo w . The eq u ation was as fo llo w s :
where W = angular v e lo c it y when a l l m a teria l was in lam inar flo w .
; M » m o b ility or r ec ip r o c a l o f p la s t ic v is c o s it y .
I T = . torque applied*
! h = depth o f immersion o f the bob in the sam ple.
R = radius o f the bob.
| R = radius o f the sample cup.
; f = y ie ld value of the flu id #
th en ftsCTg(T 2 - in te r c e p t of lin e a r curve s e c t io n ) . j
P la s tic v is c o s it y U » ( to r q u e)(S )(K )| where W * 0 , Tg - 0 . |
(BPM) j
X = con stan t of to r s io n w ire supporting the bob*
The B rook field Viscom eter had been used to some e x te n t in p la n t j
On a shear diagram p lo tte d from r e s u lts obtained by use of a
4-rrh \R h2 ! 02
1 1
le t t in g
1 ® I
t e s t s on th e su b ject f l u i d . Both th e s in g le -sp e e d and m u ltispeed
models gave very e r r a tic r e s u lt s . I
t
I
The use o f th e B rook field e n ta ile d changing th e bob to one o f |
another s iz e w h ile r e ta in in g th e same to r s io n w ire fo r each range o f j
v is c o s it y . I t was extrem ely d i f f i c u l t t o keep th e bob assembly from j
i
wobbling a ft e r th e f i r s t few rim s. A fter a s p e c if ic bob had been !
handled on se v e r a l runs a wobble would d evelop . T his undoubtedly
con trib u ted to in a c c u r a c ie s. j
i
i
The B rook field Viscom eter was s p e c if ic a l ly designed to read |
I
!
apparent v i s c o s i t i e s . I t s c a lib r a tio n in h e r e n tly gave a v is c o s it y j
i
which a non-Newtonian f lu id would have i f i t were a Newtonian f l u i d . |
Thus, th e f a c t th a t th e to r s io n sp rin g was a c cu ra tely c a lib r a te d in j
c e n tip o is e s , was o f no valu e in th e study o f non-Newtonian f lu id s .
On th e b a s is o f th e ab ove, th e B rook field Viscom eter was ru led out o f
co ns id e r a tio n .
A model o f th e Stormer V iseosim eter was examined c r i t i c a l l y and
though i t appeared to be a p r e c is io n instrum en t, th er e were se v e r a l
u n sa tisfa c to r y fe a tu r e s . The fa c t th a t a new w eigh t had to be
t
attach ed to th e instrum ent fo r every change in th e r a te o f shear made j
I
th e o p era tio n to o slow fo r studying non-Newtonian f lu id s . In a d d i- j
|
t io n , th e tim e o f descen t o f th e w eight had to be tim ed w ith a sto p - j
I
w atch. Even though a stro b o sco p ic r e v o lu tio n counter was a v a ila b le
as an a c c e sso r y , th e tim in g was s t i l l n e c essa ry . I t was decided th a t
one operator could not p o s s ib ly record a l l th e data and s t i l l
20
m aintain a minimum tima la g between ehanged ra tes of shear*
The P recisio n -In terch em ica l Viscom eter was examined o a r e fu lly
and was deemed id e a l fo r the stu d y . A ll shear or v is c o s it y ranges
eould be stu d ied w ithout changing e ith e r the bob or the sample cup,
and a speed range o f 10 t o 400 rev o lu tio n s per minute was a v a ila b le
by changing the v a ria b le speed c o n tr o l, w ith out stopp ing the in str u
ment* Forty changes in speed could be made in th ree m in u tes. Accu
rate temperature c o n tr o l of the sample cup was an added fe a tu r e .
This viscom eter was not used fo r the in v e s tig a tio n s o le ly because of
high c o s t .
Very l i t t l e inform ation was a v a ila b le on the H ercules H i-Shear
V iscom eter. This viscom eter appeared t o be s a tis fa c to r y excep t fo r
a p ecu lia r sp rin g -lo a d in g fe a tu r e . The p rice o f t h is instrum ent was
a ls o beyond the in v e s tig a tiv e budget.
A model o f the MacMichael Viscom eter was obtained and examined
c r i t i c a l l y . The b a sic op eration of t h is instrum ent was id e n t ic a l
w ith th a t o f the P r e c isio n — Interchem ical Viscom eter although not as
e la b o r a te . The u n it had a speed o o n tro l of from 10 to 40 rev o lu tio n s
per minute and a sample cup w ith b u ilt - i n h e a te r . The bob was s u s
pended from a to r s io n wire of phosphor bronze and the d e fle c tio n of
the w ire was measured by a d ia l sc a le and p o in te r . The instrum ent
had a l l the n ecessary fea tu res fo r the study of a non-Hawtonian
f l u i d , ( 5 , 6) such as a wide range by m erely changing to r s io n w ir e s ,
a v a r ia b le speed whereby shear r a te s could be changed r a p id ly , and
21
sample tem perature c o n tr o l. I t was decided to u se t h is instrum ent
in view ©f th e t e s t perform ance, th e a d a p ta b ility , and th e c o s t .
!
C K & P T E R I I I
PR O C E D U R E
C a lib ra tio n o f th e Tiscom eter
In order to measure th e f lu id p ro p erties in ab so lu te u n its i t
i
m s n ecessa ry to c a lib r a te each to r s io n w ire and th e instrum ent
i t s e l f . The con stan t o f each w ire was determ ined by a ctu a l measure
ment. The viscom eter was assem bled in op eratin g p o s itio n w ith no
sample in th e sample cup. The damping dashpot was f i l l e d w ith 600 W
I
i ,
| o i l and th e clea ra n ce between th e circum ference o f th e assem bly and
th e w a lls o f th e dashpot was decreased t o about 0.002 inches by means I
o f a s o f t brass c o lla r , in order to elim in a te w obbling.
An instrum ent con stan t (Z) was c a lcu la te d t o compare r e s u lt s from
th e viscom eter to p u b lished r e s u lt s on a standard f lu id . T his was th e
! o n ly em perieal constan t u sed , and was determ ined in th e fo llo w in g
j manner j
i
{ A s o lu tio n o f g ly c e r o l in w ater was prepared, and i t s
ex a ct com position determ ined by th e standard pycnometer and
s p e c if ic g r a v ity m ethods. The com position was determ ined
t o be 94.674% g ly c e r o l. This corresponded to a v is c o s it y
o f 419 e e n tip o ise s (c p .) a t 73 degrees Fahrenheit ( ° F .) .
This s o lu tio n was th en run on th e laeM ich ael viscom eter
i and a curve was p lo tte d . The curve in d ica ted a v is c o s it y o f
\
I
| 692 e e n tip o ise s ( c p .) . Thus th e c o rr e ctio n fa c to r (2) fo r
!
th e viscom eter became 419/692 ” © .59. This fa c to r had no
e f f e c t on th e b a sie character or ty p e o f th e cu rv es.
A n o n -stretch cord was wound around th e circum ference o f th e
j in d ic a tin g d ia l and ran out h o r iz o n ta lly p a r a lle l t o th e fa ce o f th e
| I
d ia l . The cord was th en passed ©Ter a p r e c isio n hearing and th en 1
v e r t ic a ll y downward in sp a ce. Standard gram-weights were th en hung
on th e cord and th e d e fle c tio n o f th e d ia l s c a le and to r s io n w ire
n o ted . This was done fo r each s iz e o f to r s io n w ire used and gave a
d ir e c t com parision among th e w ire c o n sta n ts. The l a t t e r were d e s ig - i
nated by th e l e t t e r (X ). I
X s (Wt. in gram s)(9 8 0 )(rad iu s o f d ia l in cm.) r Byiie-Cm. i
(d ia l d e fle c tio n ©l) v 5 ! ) ^ j
i Cm. * cen tim eters j
The d ia l o f th e viscom eter was c ir c u la r and graduated in degrees j
1 MacMichael or (°M) from © to 30© around th e circum ference. Table I
«
I
I
| shows th e r e s u lt s obtained by t h is c a lib r a tio n .
I A u x ilia ry Equipment j
I
In order to keep th e main supply o f su lfo n a te f lu id a t a ■ !
j constan t tem perature and t o bring in d iv id u a l samples to t e s t tem pera- ,
i
t u f e , a double w ater bath w ith tem perature co n tro l had to be fa b r ic s - j
t e d . This was accom plished by rem odelling an o ld Launderometer which j
I was a v a ila b le . The la t t e r c o n siste d o f a double w ater b ath , a j
i .
: r o ta tin g sample a g ita to r and a con stan t tem perature c o n tr o l. The
I
, cen ter sh a ft was removed, new p ip in g was added and th e tem perature •
i
| c o n tro ls checked, w ith th e r e s u lt being a con stan t tem perature bath j
! i
! o f f i f t e e n g a llo n ca p a city w ith a tem perature co n tro l range o f
ambient w ater to 212 degrees Fahrenheit ( ° F .) . The c o n tr o ls h eld a j
TABLE I
TOBSIOMWIRK C O H STA W TS
Wire Wo. Wt. Grams D e fle c tio n °M K Dyne-Cm
26 2 100 101
22 10 75 674
18 30 35 4334
25
I con stan t tem perature o f pirns ©r minus one degree F ah renheit. This
i
bath was used throughout th e in v e s tig a tio n , both fo r b rin ging samples
up t o t e s t tem perature, and fo r sto r in g th e main supply o f su lfo n a te
s lu r r y .
Further work was n ecessary in m aintaining con stan t tem perature
co n tro l o f th e in d iv id u a l sample once i t had been removed from th e
bath and tr a n sfe rr e d to th e viscom eter sample cup fo r t e s t i n g . The
viscom eter cup had an e le c t r ic h ea ter w ire in th e w a lls w ith a s l i p -
i !
ping con tactor to supply power. The slip p in g co n ta cto r was n ecessa ry ;
because o f th e r o ta tio n o f th e cup. There were no p ro v isio n s fo r |
| varying th e power in p u t. Thus, i t was n ecessary to disassem b le th e j
1
j u n it and rew ire th e input c ir c u i t . The power c ir c u it was m od ified t o j
incorporate two power s u p p lie s, one t o th e v a ria b le speed motor and
one to th e h ea tin g elem ent o f th e sample cup. A Powerstat or v a r i-
; i
j a b le v o lta g e reg u la r was incorporated in th e la t t e r c ir c u it so th a t
i
I th e cup h eater output could be varied as d e sir e d .
| i
; C onsisten cy Curves Method j
The MacMichael T iseom eter was s e t up, le v e lle d c a r e fu lly and |
i
fix e d in p la c e . The speed range o f th e viscom eter was d ivid ed in to \
i I
! regu lar in te r v a ls or R evolutions Per Minute (1PM) v a lu es and marked
on a d ia l attach ed to th e speed c o n tr o l knob,
i In running th e a c tu a l c o n sisten cy cu rve, th e sample was measured ;
I
in to th e viscom eter cup, th e bob was in se r te d and th e viscom eter ;
! sta r te d a t i t s low est sp eed . A fte r seven seconds a t th e i n i t i a l speech
th e viscom eter was s e t to th e next speed in te r v a l and th e torque I
I
26
read ing from th e f i r s t speed recorded* A fter f iv e seconds a t the
second speed the torque valu e was recorded and a th ir d speed in te r v a l
begun* The upeurve, or p eriod o f in c r ea sin g sp eed , was con tin u ed ,
w ith the t o t a l time a t each speed being f iv e secon d s.
When the h ig h e st viscom eter speed was a tta in e d , the downcurve,
or p erio d o f d ecreasin g sp eed , was begun, as a co n tin u a tio n of the
upeurve w ith e x a c tly the same tim e and speed in te r v a ls* The t o t a l
time fo r running any co n sisten cy curve was 87 secon d s. The time
in te r v a l between any two torque valu es was f iv e secon d s, w ith the
ex cep tio n o f the f i r s t torque valu e which was read a t seven seconds*
A downcurve was run throughout the in v e s tig a tio n in an attem pt
to determine the e x te n t o f breakdown or build-u p o f f lu id r e sista n c e
due to a p p lied r a te s o f sh ea r. An upeurve by i t s e l f would c l a s s i f y
I
the f lu id but would not determine th ix o tro p y or the degree o f build**
up* '
|
C areful a tte n tio n was g iv en to the time elem ent in a l l t e s t s
because o f i t s extrema importance (?) in d ea lin g w ith th ix o tr o p ie
m a teria ls* When the slu rry was su b jected t o a con stan t sh earin g r a ts
fo r a period o f tim e, con sid erab le breakdown was ev id en ced . Further i
breakdown was found during periods o f in crea sin g shear ra tes a t sm all
time in te r v a ls*
The e f f e c t o f the two methods o f breakdown o f a th ix o tr o p ie
m a teria l was illu s t r a t e d by p lo t t in g Figure 7 , page 28* A c o n s is
ten cy curve run on the xaaterial would approach the lin e (TB) i f no
breakdown occurred. I f the t e s t ware run in zero tim e, breakdown.
27
j due s t r i c t l y to Mime a t shear r a te * , would be elim in a te d , but break
down would ooeur due to th e in crea sin g r a te o f sh ea r. Thus, th e
c o n sisten cy curve would approach (TBQ) . S in c e , in any t e s t , a f i n i t e
tim e in te r v a l would be in v o lv ed , th e r e a l curve o f a th ix o tr o p ie
m a teria l would f a l l to th e l e f t o f (TB0 ) , and would approximate (TBj).
I f th e shear r a te were kept a t one le v e l over a p eriod o f tim e,
J th e r e s u ltin g curve would be represen ted by (B© B0 ) .
i
f The downcurves shown were run in th e same manner as th e upcurves
i
| w ith no tim e d ela y a t th e p oin t o f maximum sp eed . I f a tim e la g had
j occurred a t th e (B) le v e l speed, th e downcurves would b eg in a t some
I
i p oin t to th e l e f t o f t h e ir p lo tte d p o s itio n s .
| I t was apparent th e r e fo r e , th a t any co n sisten cy curve o f a
i
th ix o tr o p ie m a teria l would in h eren tly eviden ce breakdown due both to
'tim e as shear r a te ' and 'in cr e a sin g shear r a te * .
S in ce i t was d e sire d t o compare th e co n sisten cy curves o f th e
su lfo n a te s lu r r y a t variou s tem peratures and therm al h is t o r ie s , i t
was n ecessa ry to run curve p o in ts in an id e n t ic a l manner w ith resp ect
to tim e, from t e s t to t e s t .
In th e main phase o f th e in v e s tig a tio n , samples were te s te d in
I
1 s e t s o f s i x , w ith each s e t o f s ix having a d iffe r e n t tem perature.
Each sample w ith in a s e t had a d iffe r e n t tim e a t tem perature.
i
S lu rry in th e main tank was a g ita te d and a s u f f ic ie n t number o f
samples b o ttle d fo r th e t e s t . The h ea tin g bath was brought up to
t e s t tem perature and a l l samples were put in th e bath a t th e same
! tim e. As soon as th e samples had reached th e bath tem perature, one
PPM
28
T
TORQUE. X
F I G U R E 7
T H I X O T R O P I C B R E A K D O W N
29
aample was a r b itr a r ily s e le c te d and a c o n sisten cy t e s t run. The
time was noted a ls o . The balance o f the s ix samples ware run one a t
a time a t 30 minute in t e r v a ls . Thus, the l a s t sample had a tim e -a t-
tsm perature equal to the ela p sed time o f a l l the ru n s, whereas the
f i r s t sample had a tim s-at-tem perature o f very c lo se to z er o . This
procedure was d u p lica ted a t temperature in te r v a ls o f 10 degrees Fah
r en h e it (° F .) from 110 to 160 degrees Fahrenheit (% •) in c lu s iv e .
Curve In te r p r e ta tio n
As a means of ach iev in g a tru er rep resen ta tio n of the f lu id than
th a t afford ed by the apparent v is c o s it y con cep t, the concept of
p la s t io v is c o s it y as developed by Green and Weltmann (2 ) was used fo r
in te r p r e tin g th e cu r v es. This method was based ex a o tly on the R einer
and R iw lin equation mentioned p r e v io u sly .
According to Green and Weltmann, the upeurve o f a th ix o tr o p ie
p la s t ic had an in f in it e number o f downcurves, a l l o f them s tr a ig h t
and a l l in te r c e p tin g the torque a x is a t some y ie ld v a lu e . Thus,
u sing a r o ta tio n a l v isco m eter, th e ir procedure was to run two down
curves and c a lc u la te two p la s t ic v i s c o s i t i e s . Two y ie ld p o in ts were
c a lc u la te d from the downcurve in te r c e p ts on the torque a x i3 . From
th ese four valu es a c o e f f ic ie n t of th ix o tr o p ie breakdown was c a lc u la
ted which was the same fo r both cu r v es. The b a sis o f comparison of
two d if fe r e n t curves was th e breakdown c o e f f ic ie n t , and the v i s c o s i
t i e s , as w e ll as the e n tir e c o n sisten cy cu rve. The prooedure was
illu s t r a t e d by Figure 8 , page 3 2 .
In Figure 7 the upeurve was d esign ated (GC) w ith the top
i
30
viscom eter speed occurring a t (C ). The two downcurves were shown as
(CT), and (BTg). The second downcurve could e q u a lly w e ll have been i
run from p o in t (F) or p o in t ( l ) , as long as th e f i r s t downcurve was
run from th e maximum speed p o in t o f th e t e s t . Green and Weltman !
found th a t, w ith an in crea se in speed from p oin t (B) to p o in t (C ),
th ere occurred a sm all in crea se in y ie ld valu e in te r c e p t o f th e cor
responding downcurve. T his was shown by p o in ts (T j) and (T g ). This
in crea se in in te r c e p t was q u ite sm all even though an in crea se in
I |
1 speed o f 200 rev o lu tio n s per minute (RPM) was used by Green and j
1 ;
j Weltman. In th e p resen t r ep o rt, where th e maximum viscom eter speed j
1 I
! was 42 rev o lu tio n s per minute (KPM), no in c r ea se in y ie ld valu e !
(
j in ter c ep t could be d etected and a l l downeurves in tercep ted th e torque |
| j
’ a x is a t th e same v a lu e . Thus, sin c e th e upeurve o f a th ix o tr o p ie
p la s t ic m a teria l had an in f in it e number o f downeurves a l l in ter c ep
tin g th e torque a x is a t th e same p o in t, i t was n ecessa ry to p lo t on ly j
j th e downcurve from th e point' o f maximum shear o f th e instrum en t. |
I I
i .. 1
J The c o e f f ic ie n t o f th ix o tr o p ie breakdown was c a lc u la te d as j
*
I fo llo w s :
t
j ® * 3(111 ~ P2) M was th e lo s s in sh earin g fo rce per u n it 1
area per u n it In crease in r a te o f sh ear. ]
The above procedure was s p e c if ic a l ly intended to cover th ix o -
; tr o p ic breakdown, where th e downcurve was a s tr a ig h t lin e f a ll in g to
i
j th e l e f t o f th e upeurve. In t h i s in v e s tig a tio n th e concept o f
th ix o tro p y was extended to cover bu ild -u p as w e ll as breakdown.
I Another c o e f f ic ie n t (M^), was introduced as the c o e f f ic ie n t o f
I ■ ■ :
I
31
th ix o tr o p ie build-up* (M & ) was d efin ed as th e gain in sh earin g fo rce
per u n it area* per u n it in crease in rate of shear* and was c a lcu la te d
in th e same manner*
l
/ - I __________________________
0 T Z T
T O R Q U E °M
FIGURE 8
c u r v e A n a l y s i s method
CHAPTER IT
CONSISTENCY CURVES-YARYING TIM B-AT-TEM PERATURE
9
C onsisten cy Carres at 110 Degrees Fahrenheit (°F)
S ix samples were rust a t t h is tem perature w ith Figure 9 being
J
presented h e r e , and th e remaining f iv e bein g l i s t e d in th e appendix.
In Table I I , page 36, th e su b scrip t (A) means th a t th e fig u r e i s
j l i s t e d in th e appendix.
i i
The curve o f Figure 9 w ith a tim e-at-tem p eratu re fa c to r o f j
! approxim ately zero c lo s e ly approached Newtonian b eh avior. The up- !
j curve in d ica ted very s lig h t d ila ta n e y w h ile th e downcurve in d ica ted j
an alm ost n e g lig ib le bu ild -u p in shear induced r e s is ta n c e . The !
, in ter c ep t o f th e downcurve was t o th e l e f t o f th e o r ig in , in d ic a tin g j
! j .
no y ie ld v a lu e . C a lcu la tio n s fo r Figure 9 were made as fo llo w s; ]
f = TC ZK = (G )( 2 .1 ) (10“2) (0 .5 9 )(6 7 4 ) « © dynes/cm2 j
| H, = (2 2 /4 ) ( 9 .5 5 ) ( 1 3 .5 6 ) (1©“3) (© .59)(674) » 4 7 .8 p o ise s i
(1 1 7 1 !
Ig * ( 3 5 /4 )( 9 .6 5 ) ( 1 3 .5 6 ) (I©"8) (0 .5 9 )(6 7 4 ) - 4 7 . 8 p o ise s I
(4S)
M b = ( 2 )(4 7 .8 -4 7 .8 ) • 0 dynes/em2
In (422)
( li^ )
I 1
i In g e n e ra l, th e ’tim e-a t-tem p era tu re’ fa c to r appeared to make
i
(
l i t t l e d iffe r e n c e in th e f lu id behavior a t t h is tem perature. The
p la s t ic v i s c o s i t i e s showed l i t t l e change, as did th e torque intercepts*
i
I t did appear, however, th a t th e longer tim e-at-tem p eratu re p rio r to
viscom eter measurements made th e f lu id le s s fr e e -flo w in g in appear
ance and s l i g h t l y more s t ic k y . The b u ild -u p c o e f f ic ie n t a ls o tended !
34
£
C L
34
3*
30
28
0 z 4 6 8 / O /2 /4 /6 /8 Z a 22 24 26 28 3o 32 34 36 3a
T o R o u e ° m - w i r e z z
FIGURE 1
CONSISTENCY CURVE H O T
35
TABU II
TI1E-TEM EERATURE C U R V E S A T 110 °F .
Figure
Humber
Torque
In tercep t
©1
01
P o ise s
lg
P o ises
M b
Dynes/cm^.
Time
a t
Temp.
Minutes
9 < “4*0 4 7 .8 4 7 .8 0 0
29 - 5 .0 4 9 .6 5 2 .6 - 7 .4 20
30 - 3 .0 4 3 .8
•»•»««»
50
31 - 7 .0 4 9 .5 5 5 .0 -1 3 .6 80
32 - 5 .0 53.5 110
33 - 2 .0 4 2 .4 4 5.5 - 7 .7 140
r _
| 36
I
! TABLE I I I
FLUID BEH A V IO R
VARY IN G TIM E-AT-TEM PERATURE
F lu id Time a t 110 °F . - Minutes
Behavior
P attern 0 20 SO 80 ' 11© 140
S lig h t ly
M la te n t X X XX XXX X
P la s t ic
T hixotropie
B uild-up X X X XX XX
1 T h ixotrop ie
Breakdown X X
i Y ield Value
T ra n sitio n Stage
S tick y
Pourahle X X X X X X
J e lle d
Loose Fluid: , • X X X X X X
S trin g y
Approaches
| Newtonian________________ X X X X X
S lig h t ly Tacky
I
37
t o in crease w ith tim e . A summary of the p ro p erties a t t h is tempera
tu re was l i s t e d in Tables 111 and IV.
Baaio Shear Diagram
For th e MaoMiohael or r o ta tio n a l v isco m eter, the shear s tr e s s <
!
varied w ith r a d iu s, th a t i s , i t v a ried w ith the d istan ce from the i
cen ter o f the sample cup toward th e inner w a ll o f the ©up. Shear
s tr e s s was g en era lly c a lc u la te d a t the w a ll of the bob fo r p resen tin g
b a sic shear diagram s.
The b a sic shear diagram fo r Figure 9 was shown as Figure 10 and
p lo tte d as du/dy versus T fc wherej
du/dy - ra te of shear in ra d ian s/secon d a t bob w a ll
du/dy r 2ftrb (r e v o lu tio n s/se co n d ) * rad ian s/secon d
1 ro - rb
T fc * » shear s tr e s s in d y n es/o s^ , a t bob w a ll
Tb s TK where T w QMacMichael
2 rr r t /h
i
A ll symbols are the same as l i s t e d p r e v io u sly .
Sin ce du/dy a ra te o f sh ea r,
th en jd u dt a T otal displacem ent in d ir e c tio n of flo w
J dy fo r time in te r v a l ( d t . ) .
F igure 11 was p lo tte d showing the displacem ent versu s the tim e
fu n c tio n . The la t t e r was a c tu a lly the tim e a t shear r a t e , and a l l
in te r v a ls were f iv e seconds as mentioned p r e v io u sly . I
A measure o f comparison between th e curves a t various tim e -a t-
temperature in t e r v a ls , should be the work input required t o run the
t e s t .
Thus, a t the bob w a ll, the fo rce would be approxim ately equal to
38
TABLE IT
BASIC D A T A AT 11© °F.
Torgae
°M
I s
R e v ./S ec. du/dy
2
dyaes ./cm ,
Time
t . s e c .
D isp la ce
ment
rad.
du/dy dt
10 0 .2 0 1.38 252 7 9.6 6
13 0.2 3 4 1.62 328 12 8.1 0
15 .317 2 .2 0 378 17 11.00
19 .400 2 .7 7 479 22 13.85
22 .466 3 .2 3 555 27 16.15
25 .534 3 .7 0 630 32 1 8 .5 0
29 .600 4 .1 5 730 37 20.7 5
32 .666 4 .6 2 806 42 23.1 0
35 .700 4 .8 5 882 47 24.25
34 .666 4.62 856 52 23.10
29 .600 4 .1 5 730 57 20.75
27 «534 3 .7 0 680 62 18.50
22 .466 3 .2 3 555 67 16.16
18 .400 2 .7 7 454 72 13.85
13 .317 2 .2 0 328 77 11.00
9 .234 1.62 227 82 8 .1 0
7 .200 1 .3 8 176 87 6 .1 0
i
I
D U /D Y - RADIAHS/SECOND
39
48
4 4
4.4
42
4.0
3 ,8
3.6
3.4
3.2
3.0
Z 8
2 4
24
2.2
2.0
f.8
A6
1.4
1.2
L
too 200 300 400 S O O 600 7 0 0 800 9 0 0
Tb - DYNES /CM*
F I G U R E 10
BASIC SHEAR DIAGRAM 110‘F.
fDU/DY D T - RADIANS ( C U M U L A T I V E )
4Q
330
m
/BO
/so
/to
60 70 80 0 /O
to 30 SO
T I M E - S E C O N D S
F I G U R E U
D I S P L A C E M E N T VERSUS T I M E 1 1 0 ’F
j (2 r^*1 ) (T^). The displacem ent would be ( l s )(tim e )(2 rfc), where th e
j tim e was th e number ©f seconds o f r o ta tio n a t a g iv en speed and
J to rq u e. The work would be th e product o f fo rce and d isp lacem en t,
w ith th e t o t a l , or average work p er t e s t being th e sum o f a l l th e
work done a t th e variou s in t e r v a ls . S in ce th e speed and tim e in t e r
v a ls in a l l t e s t s were id e m tie a l, and th e torque v a ried w ith th e flu id
c o n d itio n , th e work input per t e s t should a lso vary d ir e c t ly as th e
i f lu id c o n d itio n . !
1 C on sisten cy Curves a t 120 Degrees Fahrenheit (G F .)
!
t
| S ix co n sisten cy curves were run a t 120 d egrees Fahrenheit ( ° F .) .
I As b e fo r e , each t e s t was run on a d iffe r e n t sample having a d iffe r e n t j
i
; i
j tim e-a t-tem p era tu re. S in ce th e r e s u lt s were sim ila r l a a l l c a se s ,
on ly one c o n siste n c y ourve, Figure 12, page 4 3 , was shown, w ith th e
balance being appended. The v i s c o s i t i e s and e o e f f ie ie n t s w ere l i s t e d
■ in Table V.
The upeurve o f Figure 12 in d ica ted some d ila ta a c y and a co n si
d erable b u ild -u p . Both item s were h igh er than found a t 110 degrees \
Fahrenheit ( ° F .) . The r a te o f decrease o f torque shown by th e down- j
curve was a ls o g reater th an th a t a t 110 degrees Fahrenheit ( ° F .) . H o
i
' y ie ld value was in d ic a te d . I
!
1 The balance o f th e curves a t 120 degrees Fahrenheit (° F .) j
i i
| follow ed a sim ila r p a tte r n , and th ere appeared t o be no e sta b lish e d
| tren d . The v is c o s i t i e s v a ried somewhat but were not g r e a tly changed
; from th o se a t 110 degrees Fahrenheit ( ° F .) .
| A b a sic shear diagram fo r Figure 12 was co n stru cted , showing
42
torque a t th e hoh w a ll versu s shear r a te , f h is was shown as Figure
13, page 47, w ith th e n ecessa ry data l i s t e d in Table V II, page 4 6 .
C o n sisten cy Curves a t 150 Degrees Fahrenheit (° F .) j
S ix c o n sisten cy curves were run a t 130 degrees Fahrenheit (° F .)
each w ith d iffe r e n t tim e-at-tem p eratu re. Two o f th e cu rv es, Figure
i
14 and 15, pages 48 and 49, were shown, w ith th e r e s t being appended.
The v i s c o s i t i e s and c o e f f ic ie n t s were l i s t e d in Table V III, page SO. j
!
Figures 14,'and 15 showed two sta g e s c a lle d t r a n s it io n s ta g e s ,
th a t appeared t o e x is t a t 130 degrees Fahrenheit ( ° F .) , The sta g e
o f th e tr a n s it io n appeared to be independent o f th e tim e fa c to r . A ll
curves a t t h i s tem perature showed a pronounced y ie ld v a lu e . In th e
t r a n s it io n sta g e th e curve showed both b u ild -u p and breakdown to
in c r ea sin g r a te s o f sh ea r, depending on th e shear range examined.
V is c o s it ie s were lower than a t lower tem p eratures, ten d in g t o
in crea se w ith tim e . A b a sic shear diagram was con stru cted fo r Figure
14 and ta b u la ted as Figure 16, page 5 5 . In a d d itio n th e work input
was c a lc u la te d .
C on sisten cy Curves a t 140 Degrees Fahrenheit ( ° F .)
S ix samples were run a t 140 degrees Fahrenheit (° F .) in th e same !
manner as b e fo r e . A ll curves were appended except fo r Figure 17.
Behavior a t 140 degrees Fahrenheit (° F .) c lo s e ly approached th e
id e a l curve o f a th ix o tr o p ie Bingham P la s t ic as p o stu la ted by
Bingham in h is o r ig in a l w orks. In most eases th e r a te ©f in crea se o f
flow was d ir e c t ly p rop ortion al t o th e r a te o f in crea se o f ap p lied
fo r c e , once th e y ie ld valu e o f th e f lu id was exceeded. At 140 degrees
43
42
40
3 8
36
34
30
I
0 2 4 6 8 to 1 2 /4 /£ /8 H O 22 24 *6 28 30 32 34 36 38
TORQUE °/A - WIRE 22
F I G U R E IZ
C O N SISTENC Y CURVE 120°F.
TABLE Y
THE-THPEMfUH C U E Y BS AT 120 °P .
Figure
lumber
Torque
In tercep t
O M P o ise s
%
P o ises
2
Bynes/em .
Time
at
Minutes
12 -3 4 7 .8 4 9 .0 -3 .9 0
34 -3 51.5 5 4 .0 -6 .2 40
35 -3 6 7 .0 7©
36 — 2 49.6 5 4 .0 -1 0 .9 100
37 -5 6 7 .0 5 5 .0 / 4 .5 13©
38
______ £ 5.,-., .
4 1 .0 5 0 .0 -2 4 .4 160
45
TABU3 VI
FLUID BEH A V IO R
VARYING TUB AT T E M PE R A T U R E
F lu id
Behavior
P a ttern
Time a t IE© °F . b efore t e s t in g - Minutes
40 70 100 ISO 160
D ila te n t X X X
P la s t ic
Build-up X X
Breakdown
Y ield Value
T ra n sitio n Stage
S tic k y
Pourable
J e lle d
Loose F lu id X X
S trin g y X X
Tacky XX
I
i
46
TABLE T il
BASIC D A T A A T 120 9F;
Torque
%
R ev ./S ec.
du/dy
r a d ./
s e e .
d y n es/
Cltfi.
Time
t
s e e .
du /dy-
d t rad.
A v e.-W rF
xlO”3
dynes-cm .
12 .2 0 1.38 302 7 9.66 70.9
14 .234 1.62 353 12 8.10 69.2
16 .317 2.20 402 17 11.00 107.0
2® .400 2 .7 7 504 22 13.85 169.0
23 .466 3.23 580 27 16.15 226.0
25 .534 3.70 630 32 18.50 282.0
27 .600 4 .1 5 680 37 20.75 342.0
32 .666 4.62 805 42 23.10 450.0
37 .700 4 .8 5 932 47 24.25 5 47.0
36 .666 4 .62 906 52 23.10 506.0
33 .600 4 .1 5 830 67 20.75 465.©
30 .534 3.70 755 62 18.50 380.0
26 .466 3.23 655 67 16.15 29 3 .0
20 .400 2.77 504 72 13.85 197.0
16 .317 2 .2 0 402 77 11.00 135.0
11 .234 1.62 277 82 8.10 74.0
9 .2© 1 .3 8 227 87 6.'90 4 4 .5
T o ta l Work 4357.6
du/ d y - RADIANS / s e c o n d
47
S-6
s z
4.0
4.4
4.0
3-4
3.2
Z8
2.4
2.0
A6
!.t U
a L____
0 /O O 200 300 400 500 600 700 800 9oo
rk - d y n e s / c m "
FIGURE 13
bASIC S H E A R D I A G R A M l Z O ’ F.
1000
W dU
42
40
3 0
24
22
20
0 .5 Z S 30 35 40 / S go /o
TORQUE °M ' W IR E 2 Z
%
F IG U R E IN
CONSISTENCY CURVE 130°F
R P t A
49
42
40
38
34
32
30
28
24
O 3 6 9 12 /S /8 2t 24 27 30 33 36 39 42 4S 48 St & 57
T O R Q U E °M - W I R E 2 Z
F IGU RE 15
CONSISTENCY CURVE 130°F
50
TABLE T i l l
TIME-TIMBBMTUHE TESTS A T 1 3 0 ° F .
Figure
lumber
In ter
cep t
01
Y ield
Yalue
Dynes/cm2 .
¥ i
P o ises
%
P o ise s Bynes/cm2 .
Time
At Temp.
Mins.
39 10.5 87.5
* * * * * * * * * * * * * * * * ~ m m . * *
©
40 21 175 21.2 30.6 -2 3 .2 30
41 16 134 31.3 3 6 .8 -1 3 .7 60
14 16 134 3 6 .0 96
42 23 192 33 .1 125
15 15 125 4 0 .5 46.2 -1 7 .2 155
51
TABIE IX
FLUID BE H A V IO R
VARYING TI1E-AT-TEMPBRATUEE
F luid
Behavior
P attern
Time a t IS© °F . b efore t e s t in g - Minutes
0 SO 60 95 125 155
D ila ta n t X X X
P la s tic X X X
Build-up X X X
Breakdown X X X
Y ield Value X X X X X X
T ra n sitio n S tage X X X X
S tic k y X X X X X X
Pourable X X X X X X
J e lle d
Loose F lu id X X X X X X
S trin g y X
Tacky
52
TABLE X
Torque
BASIC D A T A AT L30 F.
%
B e v ./S e c .
du/dy
r a d ./
s e e .
dyn.es/
cm^.
Time
t
s e e .
du/dy
dt rad.
Ave. Work
xlO"3
2
d y n es-cm .
25 .20 1 .38 630 7 9.66 148
25 .234 1.62 630 12 8.10 124
26 .317 2 .2 0 655 14 11.00 174
28 .40 2.77 70S 22 13.85 227
33 .466 3 .23 830 27 16.15 324
41 .534 3 .7 0 1031 32 18.50 462
45 .600 4.15 1135 37 20.75 570
47 .666 4 .6 2 1185 42 23.1 0 664
47 .700 4.85 1185 47 24.25 696
44 .666 4 .6 2 111® 52 2 3.10 622
40 .600 4 .1 5 1010 57 20.75 508
38 .534 3 .7 0 957 62 18.50 429
34 .466 3.23 855 67 16.15 333
32 .40 2.77 805 72 13.85 270
29 .317 2 .2 0 730 77 11.00 194
22 .234 1.62 554 82 8.10 109
19 .2 0 1 .5 8 479 87 6 .9 0 80
T otal Work 5932
du/ d y - r a d i a n s / s e c o n d
53
4 6
4.4
4.0
$6
3 *
2&
2.4
ZO
/■ 6
/ . Z
L ,
0 4oo 5oo 6oo 7oo doo ?oo /ooo Koo /Zoo
Tb - DYNES/CM*
FIGURE U
BASIC SH EA R DIAGRAM 1 3 0 ' F
@ 4
i
i
!Fahrenheit (°F.) no gen eral trend w ith tim e-at-tem parature could be
esta b lish e d *
A b a sie shear diagram was p lo t te d , l i s t e d as Figure 18* page
I 58* and the in p ut work o f th e t e s t ca lcu la ted *
!
| C on sisten cy Curves a t 150 Degrees F ahrenheit (°F »)
j F ive t e s t s were run as b efore a t 150 degrees F ahrenheit (°F*)
I
w ith two o f -the eu rv es, F igures 19 and 2 0 , pages 60 and 6 1 , being
i
included in the main report*
The f lu id a t 150 degrees F ahrenheit (®F.) en tered a com pletely
d iffe r e n t p h ase. From a fr e e -flo w in g f lu id a t 140 degrees Fahrenheit
I -
I ( ° F .) i t changed to a s t ic k y , tacky j e l l of immobile c o n siste n c y .
!
| On c o o lin g , th e m aterial flow ed in long str in g s or as a plug* As
| shown ty Figure 19, the transform ation required se v e r a l m inutes a t
temperature to take p la c e . Figure 20 showed the m a teria l to be w e ll
in to the j e l l sta g e a fte r 100 m inutes a t tem perature.
Except fo r Figure 19, i t was not p o ssib le to determine whether
1
the curves were d ila ta n t or p l a s t i c , although the la t t e r appeared to
I
i be a more true c h a r a c te r isa tio n .
i The y ie ld values and v i s c o s i t i e s were much higher than a t p r e v i
ous tem peratures.
i A b a sic shear diagram was con stru cted fo r Figure 20 and l i s t e d
I
| as Figure 2 1 , page 6 5 . In a d d itio n , the work input was c a lc u la te d .
i
1 C onsistency Curves a t 160 Degrees Fahrenheit (° F .)
Five samples were run a t 160 degrees Fahrenheit (°F«) w ith two
1 b ein g presented in the rep o rt and as F igu res 22 and 2 3 , pages 66 and
R P M
55
42
40
24
22
S 40 IS fo 2 0 35 0
T o r q u e - w i r e 22
FIGURE 17
Consistency c u r v e n o r .
56
TA BLE XI
TIM E-TEM PBH ATUBE TESTS AT 146 °F .
Figure
Humber
In te r
cept
°M
Y ield
Yalue
Lynes/cm^. P o ises
^2
P o ise s
M
Dynes/cm .
Time
At Temp.
Mins,
17 16 84 28.5 2 5 .8 6 .7 0
43 1 6 .5 158 21.2 17.8 8 .4 20
44 11.0 92 2 7 .6 2 3 .3 10.8 40
45 1 6 .0 125 2 3 .6 19 .6 8 .7 @ 0
46
15.5 130 32.2 2 5 .9 2 0 .3 80
47 17.5 146 32.2 2 5 .2 1 7 .4 100
i
i
I
!
i
i
57
TA BLE XII
BASIC BA T A AT 140 °F .
Torque
°M
! s
R e v ./S ee.
du/dy
r a d ./
s e e .
fb /
d yn es/
O ffl .
Time
t
s e c .
du/dy
dt rad.
A ve. Work
xlO
dynee-em .
18 .2 0 1.38 454 7 9.66 106
2© .234 1.62 504 12 8.10 99
22 .317 2 .2 0 555 17 11.00 148
25 .40 2.77 630 22 13.85 212
25 .466 3.23 63© 27 16.15 246
27 .534 3.70 @ 80 32 18.50 305
29 .600 4.15 730 37 20.75 368
3© .666 4.62 755 42 23.10 422
31 .700 4.85 781 47 24.25 460
28 .666 4.62 705 52 23.1© 395
26 .600 4 .1 5 655 57 20.75 330
25 .534 3 .7 0 630 62 18.50 283
23 .466 3.23 §80 67 16.15 226
22 .4 0 2.77 §55 72 13.85 186
20 .317 2 .2 0 504 77 11.00 134
17 .234 1.62 429 82 8 .1 0 84
15 .20 1.38 378 87 6 .9 0 63
T otal Work 4067
DU/DY- R A D I A N S / S E C O N D
58
5 0
4.6
42
3-8
3 .4
2 3
2.4
2.0
U
12
L j < __________________________________________________________________
0 300 400 500 6 0 0 700 8 0 0 fOO / O O O //OO
T h- DYNES/CM*
F I G U R E 1 8
B A S I C S H E A R D I A G R A M 1 4 0 ’F.
59
67* The other curves were appended*
As shown by Figure 22 in comparison w ith Figure 2 5 , a d e fin ite
tim e-at-tem p eratu re was necessary before the f lu id com pleted the
transform ation from the p la s t ic s ta te t o th a t a t 160 degrees Fahren
h e it C 0?*)* A t zero tim e, Figure 22 was s t i l l a true Bingham
P la s t ic although p a r tia lly je lle d *
At t h is temperature the f lu id was very tacky and was unpour-
able *
A b a sic shear diagram was con stru cted fo r Figure 23 and l i s t e d
as F igure 2 4 , page 71* The work input was a ls o ca lcu la ted *
60
4 1
4o
38
3 i >
to
8
6 >
4
6
O Z 4 6 e to !Z /4 /& /8 S t O 2Z 2 4 Z8 3o 3? 34 36 38
T O R Q u tr °M - W I R E 18
F I G U R E 11
C O N S IS T E N C Y CURVE 1 5 o T .
R P M
61
to
8
4
*
O J ? 4 t 8 to tx /4 M /& & 34 *6 Z8 30 3* 34 36 38
P O R O U S °M - W I R E 18
f i g u r e : 2 0
CONSISTENCY CURVE 150'F.
62
TABIE X III
TIM E-TEM PERATDK E TESTS A T 150 °F .
Figure
lumber
In te r
cept
om
Y ield
Value
Dynes/cm^.
*1
P o ises
U2
P o ises
M o
D y n es/cm .
Time
At Temp.
Mins.
19 5 268 38.5 3 5 .6 7.15 0
48 30
49 25 1540 71.2 71.2 0 60
50 24 1515 65.2 6 7 .2 - 4 .8 75
20 2 1 .5 1100 7 5 .0 0 100
63
TABLE H T
BASIC DATA AT 150 °F .
Torque
°M R d v./S ec.
du/dy
r a d ./
s e c .
dyags/
c m .
Tim©
t
s e c .
du/dy
dt rad.
At©. Wgrk
x !0 “5
dyaes-cm .
25 .20 1.38 4050 7 9.66 950
25 .234 1.62 4050 12 8 .1 0 795
25 . .317 2 .2 0 4050 17 11.00 1077
26 .40 2.7 7 4210 22 13.85 1415
27 .466 3.23 4370 27 16.15 1710
28 .534 3.7 0 4540 32 18.50 2030
29 .600 4 .1 5 4700 37 20.75 2360
3© .666 4.62 4850 42 23.1© 2720
30 .700 4.85 4850 47 24.25 2850
30 .666 4.62 4850 52 23.10 2720
28 .600 4.1 5 4540 57 20.75 2280
28 .534 3.70 4540 62 18.50 2030
27 .466 3.23 437© 67 16.15 1710
26 .400 2.77 4210 72 13.85 1415
25 .317 2 .2 0 4050 77 11.00 1077
24 .234 1.62 3980 82 8.10 780
23 .20 1.38 3720 87 6.90 625
T otal Work 28,544
TABLE XV
FLUID BE H A V IO R
VARYING TIME-AT -TEM PER ATURE
F lu id
Behavior
P attern
Time at ISO °F . b efo re t e s t in g - Minutes
0 SO 60 75 100
D ila ta n t X X X
P la s tic X X
B uild-up X X X
Break-down X
Y ield Value X X X X X
T ra n sitio n Stage X
S tick y X X X X X
Pourable
J e lle d X X X X X
Loose F luid
S trin g y
X X X X X
' T a c k y X X X X X
DU/DY - k ADI AUS/SECOND
65
A .8
4.4
4.0
U
3.Z
Z8
2.4
20
/.&
/
1 2
o
L
L
3 T O O 3850 4000 4150 4300 4450 4(>00 4150 4100
z
V DYNES /CM*
FIGURE 21
BASIC S H E A R DIAGRAM 150'F.
R P n
66
40
36
3Z
30
0 2 4 6 8 /O /2 J 4 /6 /8 H O 22 Z4 Z6 28 30 32 34 34 38
TORQUE °M - WIRE 18
F I G U R C 2 2
Co n s i s t e n c y c u r v e u o °f.
RPtA
42
40
3 8
%
34
32
3 o
28
28
24
22
20
/8
/8
1 4
/2
fO
8
6
4
2
0 2 4 8 8 fO /Z /4 /6 /& 20 22 24 26 28 30 82 34 $6 38
TORQUE °M - WIRE 18
FIGU RE 23
Co n s i s t e n c y c u r v e u o °f
68
TABU! XVI
T IM E -T E M PE R A T T T R E TESTS A T 160 °F .
Figure
lumber
In te r
cep t
Y ield
Value
D yn es/cm .
*1
F o lses
. ^ 2
P o ise s
M
Bynes/cm^.
Time
At Temp.
M ins.
22 15 804 47.5 41.5 1 4.8
51 19 102© 71.0 71.© © 35
52 22 118©
— — —— — — —
0 65
23 28 150©
1 — mm m mi
l e g . 100
53 26 1400
. . . .
le g . 135
69
TABLE XVII
FLUID BE H A V IO R
VARYIIG TI1.E-AT-TEM PERATURE
F luid
Behavior
P a ttern
Time at 160 °F . b efore t e s t in g - Minutes
0 35 65 100 135
D ila ta n t X X X
P la s tic X X
Build-up X X
Breakdown X
Y ield Value X X X X X
T ra n sitio n Stage X
S tic k y X X X X X
Pourable
J e lle d X X X X X
Loose F lu id X X
S trin g y X X X X X
Tacky X X X X X
7©
TABLE XVIII
BASIC BATA AT IS© °F .
Torque
oh
%
le ? ./S e c .
du/dj
r a d ./
s e c .
d y n es/
cm .
Time
t
s e c .
du/dy
dt rad.
A ve. Work
xlO**
dynes-em.
25 .
to
o
1.38 4050 7 9.66 950
25 .234 1.62 4050 12 8 .1 0 794
25 .317 2 .2 0 4050 17 11.00 1079
25 .40 2 .7 7 4050 22 13.85 1360
25 .466 3 .23 4050 27 16.15 158©
26 .534 3 .7 0 4210 32 18.50 189©
27 .60© 4.15 4360 37 20.75 2200
29 .666 4 .6 2 4700 42 23.10 2630
29 .700 4 .8 5 4700 47 2 4.25 2762
28 .666 4 .6 2 4540 52 23.10 2540
28 .600 4 .1 5 4540 57 20.75 2280
28 .534 3.70 4540 62 18.50 2030
28 .466 3.25 4540 67 16.15 1775
28 .400 2 .7 7 4540 72 13.85 1520
27 .317 2 .2 0 4360 77 11.00 1160
25 .234 1 .6 2 405© 82 8 .1 0 794
25 .2 0 1 .3 8 4050 87 6 .9 0 680
T o ta l Work 28,004
DUlDY- r a d i a n s / s e c o n d
71
4.0
4.4
4.0
3.6
32
28
2.4
2-0
/ .6 >
i 2
D ,
3100 3850 4000 4150 43oo 4450 4 6 oo 4 1 5 0 4100
Th- D Y H E S / C K
FIGURE 2 4
B A S I C S H E A R j D I A G R A M I b O ’F.
CHAPTER T
|
S U M M A R Y O F RESULTS
i
| The a lk y l a r y l su lfo n a te slu r r y was fbund t o be a non-Hewtonian
j f lu id w ith p e c u lia r c h a r a c t e r is tic s . The f lu id sim ulated Newtonian
behavior a t 110 degrees Fahrenheit (° P .) but v a ried through a w ide !
i
i
range o f non-Newtonian c h a r a c te r is tic s as th e tem perature was r a is e d . ]
i At 120 degrees Fahrenheit (°F .) th e f l u i d showed a b u ild -u p in shear I
1 r e s is ta n c e and evin ced d ila ta n t p r o p e r tie s. At 130 degrees Fahren- i
h e it (° F .) a t r a n s itio n range was found w herein behavior sim ulated
p la s t ic or d ila ta n t flow depending on th e shear r a te . The tr a n s it io n
range ended a t approxim ately 134 degrees Fahrenheit ( ° F .) . From 135
t o 148 degrees Fahrenheit (©P.) th e f lu id showed a l l th e p r o p e r tie s ;
o f a Bingham P l a s t i c . At 150 degrees Fahrenheit (°F .) and h ig h er, I
1 - I
another tr a n s it io n range was found in which th e f lu id became a th ic k |
i i
i unpourable j e l l and th ix o tr o p ie breakdown disapp eared. S ev era l m in- i
i
{
; u tes a t tem perature were n ecessary fo r th e m a teria l to en ter t h e j e l l
' i
1 s ta g e . |
™ I
w h ile th e f lu id v is c o s it y decreased from 110 t o 140 degrees 1
i
Fahrenheit (° F .) i t in creased a t h igh er tem p eratures, showing i t s |
i
h ig h e st valu e a t th e j e l l s ta g e . The g r e a te s t changes, however, were !
not in v is c o s it y , but in y ie ld valu e and work required to induce I
I lam inar flo w . From 110 to . 150 degrees Fahrenheit (° F .) th ere was a |
I
tw o -fo ld in crea se in v is c o s it y and a se v e n -fo ld in crea se in work
i
input per t e s t .
J
| Graphs o f th e v a r ia tio n o f fu n ctio n s o f tem perature were p lo tte d
i !
1 75
j
j and ta b u la te d . (F igures 26 through 2 8 ).
I
j I t would appear t h a t , from a p1ant-han dlin g sta n d p o in t, th e
p la s t ic v is c o s it y changes were not as important as th e changes in
y ie ld valu e and p h y sic a l b eh avior.
There appeared to be a c lo s e r e la tio n sh ip between th e rather
p e c u lia r behavior o f th e slu r r y and th e w ater p resen t in th e s lu r r y .
I
At th e j e l l s ta g e , a t h igh er tem p eratures, th e r e appeared t o be no
p h y s ic a lly fr e e w ater in th e m a te r ia l. At t h is sta g e th e slu r r y was
I
I alm ost immovable. On sta n d in g , w ith no a g ita t io n , fr e e w ater would f
i
seep from th e mass and coat th e w a lls o f a co n ta in er. Water would j
i |
a ls o c o lle c t in myriad la y ers w ith in th e mass i t s e l f . The m a teria l
I
t i
j would become le s s immovable and flow as str in g y la y e r s , or as a
j
| s o lid plug lu b rica ted by th e fr e e w a ter. Upon fu rth er a g ita t io n ,
»
I
th e fr e e w ater would disappear and th e mass would again become sem i-
immovable. The same a c tio n occurred a t lower tem peratures to a much
] le s s e r e x te n t.
I
| The a lk y l a ry l su lfo n a te m olecule was describ ed by previous 1
j in v e s tig a to r s as being a h yd rop hile a t one end and a hydrophobe a t '
th e o th e r . I t was p o s s ib le th a t th e se fo rces v a ried w ith both th e
tem perature and th e amount o f shear t o which th e s o lu tio n was su b jec- >
I
, t e d , p a ssin g through a maximum or minimum fo rce a rea . The hydro- j
) i
p h ilic fo r c e could have removed enough fr e e w ater from s o lu tio n such ;
! !
! as to cause a d ila ta n t b eh avior. At another p o in t th e e f f e c t o f 1
I shear and tem perature combined could have been such as to make th e !
i
hydrophobic fo rce dominant, r e le a s in g more fr e e w ater and causing th e
r
74
m a teria l t o e x h ib it th ix o tr o p ic behavior*
The above was considered h ig h ly p o s tu la tiv e , and was beyond the
scope of the in v e s tig a tio n ; however, behavior o f the w ater in the
!
so lu tio n d id appear to have a g r e a t e f f e c t on the behavior o f the
su lfo n a te flu id *
I
W O R K INPUT PERTE5T- DYNE-CMS. X10'
75
42
30
2 2
L J
H o 150 0 130 140
TEMPERATURE T
FIGURE Z S
TEMPERATURE VERSUS AVERAGE TOTAL
W O R K
AVERAGE PLASTIC VISCOSITY- POISES
76
£3
5 7
SI
45
39
33
27
* /
IS
9
L J t
no
120 130 140 /SO
T E M P E R A T U R E °F
/6 0
F I G U R E 2 6
TEMPERATURE VERSUS AVERAGE VISCOSITY
AVERAGE YIELD VALUE- DYNES/CM.
77
1650
1500
1 050
300
/5 0
/60 no 0 /4 0 130
T E M P E R A T U R E "F
F I G U R E 2 7
TEMPERATURE VERSUS YIELD VALUE
COEFFICIENT M - D Y NEs/CM.
78
to
— I
no !4o '50 130
-4
-8
TEMPERATURE °F.
s
FIGURE Z 8
TEMPERATURE VERSUS COEFFICIENT M.
C H APTER VI
COICLFSIOIS
i
A viscom eter b e lie v e d s u ita b le fo r t e s t in g th e a lk y l a r y l s u l- ;
<
fo n a te was s e le c te d and a technique fo r e v a lu a tin g th e f lu id proper- ,
I i
! t i e s was developed. C onsisten cy curves were run on th e f lu id and
analyzed through th e tem perature range o f in t e r e s t .
| The p e c u lia r p ro p erties o f th e j e l l stru ctu re were in v e s tig a te d ;
i
! and v a lu es p lo tte d .
! The fa c t th a t th e su lfo n a te was a non-Hewtonian f lu id was
e s ta b lis h e d . !
i
The p rocess p lan t m anufacturing th e s u lfo n a te , a t one tim e
r e lie d h e a v ily on th e concept o f apparent v is c o s it y . The concept j
j e v e n tu a lly proved inadequate and was abandoned. The reasons fo r t h is J
1 inadequacy w ere illu s t r a t e d , w ith th e b a sic reason bein g th e im p ossi- j
i b i l i t y o f rep resen tin g a non-STewtonian c o n siste n c y curve by one point*;
t
| For purposes o f p lan t q u a lity c o n tr o l, th e in v e s tig a tio n i l l u s -
; tr a te d th e n e c e s s ity o f eaeh batch o f su lfo n a te being rep resen ted by
a com plete co n sisten cy curvej w ith upcurve, downcurve and y ie ld valu e J
i f any, being p lo tte d . With each c o n sisten cy curve, i t would be j
I
n ecessa ry to note th e tem perature, and any unusual d e v ia tio n s in
4 (
therm al or handling h is to r y . |
i
; The in v e s tig a tio n p oin ted out th e f a c t th a t fa e to r s oth er th an
! v is c o s it y were o f a t le a s t equal im portance. The y ie ld v a lu e and th e
|
c o e f f ic ie n t s o f th ix o tr o p ie build-up and breakdown would have a g rea t ,
: e f f e c t in a pumping or m ixing o p era tio n .
80
The in v e s tig a tio n showed th a t new areas o f e x p lo ra tio n would be
n ecessa ry in order t o com p letely answer th e ’w hys1 o f th e m a teria l
b eh avior. Rigorous s o lu b i lit y and chem ical stu d y o f th e fo r c es a t
work in th e s o lu tio n was in d ic a te d . A thorough m icro sco p ica l stud y
would a ls o be h e lp fu l.
With fu rth er work in t h is d ir e c tio n , i t i s q u ite p o s s ib le th a t
p la n t op eratin g co n d itio n s could be a lte r e d sueh th a t a t le s s power
in p u t, b e tte r m ixing and pumping could be ach iev ed . There seems t o j
be no reason why r e s u lt s in th e p la n t could not be c o r r e la te d w ith
f lu id viseom etry as an a id in p r e d ic tin g f in a l r e s u lt s .
T his in v e s tig a tio n sh o u ld , in th e fu tu r e , be extended t o d eter
mine c o n siste n c y curves o f m ixtures o f b u ild ers and s u lfo n a te s , u sin g j
!
a s im ila r viscom eter capable o f high er shearin g r a t e s . j
BIBLIOGRAPHY
BIBLIOGRAPHICAL ENTRIES
A. B O O K S
1* Barr, Gvy . A Monograph of Vis come t r y , Oxford U n iv ersity P r e ss,
1931.
2 . Green, Henry. In d u str ia l Rheology and R h aological S tr u c tu r e s.
New Yorks John W iley and S on s, I n c ., 1949.
3 . L apple, C. E . F lu id and P a r tlo le M echanics, F ir s t E d itio n .
Newarks U n iv ersity of Delaware P r e ss , 19S4.
4* R ein er, Marcus. Ten L ectures on T h eoretical R heology.
Jerusalem s Sheckter and Fainberg, 1943.
5 . S c o tt B la ir , G. W. Survey of G eneral and A pplied Rheology.
P h ila d elp h ia ! B lak eston 's Son and Company, 1938.
6 . S c o tt B la ir , G. W. Survey o f General and A pplied R heology.
New Yorks Pitman P u b lish in g C orporation, 1944.
7 . Weltmann, R. 1 . Breakdown o f T hixotropic Stru cture as a
F u nction of Time. J . A pplied P h y sic s, 1943.
8 . Weltmann, R. N. In d u str ia l V iscom eters. Interchem ical Review
2 , 1943.
B. PUBLICATIONS O F T H E G O V E R N M E N T ,
L E A R N ED SOCIETIES, A N D O T H E R ORGANIZATIONS
9 . B rook field E ngineering L aboratory. B rook field S yn oh roleotric
V iscom eter. Stoughton, M ass.
1 0 . F ish er S c ie n t if ic Company. MacMichael V iscosim ater I^pe 15-347.
New York.
1 1 . Sm ith, J . W ilson and Paul D. A pp legate. The H ercules H i-Shear
V iscom eter, New Yorks Paper Trade Journal, June, 1948.
1 2. Arthur H. Thomas Co. The Stormer V isco sim a ter. B u lle tin DTJ24-
5M. P h ila d elp h ia s Arthur B. Thomas Company, 1948*
x
A P P E N D IX A
CONSISTENCY C U R V E S
VARYING TIM E-AT-TEM PERATUEE
4 8
4o
38
36
34
32
3o
28
8 6
84
88
80
A 8
/6
(4
/8
/0
8
6 >
4
2
0
86
4 6 8 / 0 / 2 /4 /6 /8 20 22 24 26 28 30 3* 34 34 38
TOFtQ/sf *A1 - WIRE 2 2
FIGURE Z1
CONSISTENCY CURVE 110"F
86
4 2
40
3 8
34
34
32
30
28
2 6
24
22
X
20
/8
Qc
/6
/4
/2
/O
8
%
4
2
O 2 4 6 8 /O /2 /4 /6 /8 20 22 24 26 28 30 32 34 36 38
TO R Q O F °M - WIRE z z
FIGURE 30
CONSISTED Y CUR IIE }1 0 ‘F.
vi d < y
4 2
4 0
38
37
0 2 4 6 8 /O /X /4 /6 ta 2 0 22 24 2 6 28 30 32 34 36 38
T O R Q U f ° M - W I R E ZZ
FIGURE 31
CONSISTENCY CURVE \\0 9F
R P M
88
34
3 3 ?
30
/O
0 Z 4 6 8 /o /X f4 /6 /8 2 0 ZZ 2 4 2 6 2 8 30 3Z 3 4 3 6 3 8
T o r q u e °ro - W I R E 22
FIGURE 32
CONSISTENCY CURVE llO’F
ftP IA
89
28
Z2
go
0 g 4 6 8 /O /Z /4 /6 f8 20 2 4 -2 6 2 8 3 0 3 2 3 * 3 6 3 8
TORQUE °M ~ WIRE 22
FIGURE 33
CONSISTENCY CURVE 110‘F
R P M .
90
32
o o
/O
O 2 4 6 e /O /* /4 /6 / e Ho & 2 4 H6 2 8 3 0 3 2 3 4 3 6 3 9 40
T O R Q u r °M - W I R E .22
F IG U R E 34
CONSISTENCY CURVE 120 °F
91
3 ?
3 0
2 8
3 5 4 0 4 5 5 J 5 2 5 30
0 /O
TORQU£ °M - WIRE 2Z
FIGURE 3 5
CONSISTENCY CURVE 120°F.
P P M .
92
4 Z
40
38
24
6 2 4 6 Q /o /2 M /6 /a 20 22 24 26 20 30 32 34 36 28 40
TORQUE °M - W I R E 22
F I G U R E 3l>
CONSISTENCY CURVE 1Z0°E
42
40
38
%
34
32
30
28
2 b
24
22
20
1 8
/£
14
12
/0
8
6
4
2
O
93
2 4 b 8 /o /g / 4 /6 /8 20 22 2* 26 2 8 3o 32 3* 36 3 8 40
TO RQ U £ 7A- W I R E 22
FIGURE 3 1
CONSISTENCY CURVE 120°F.
RPM.
94
30
/a
5 30 3 5 O /0 40
TORQUE °M - WIRE 2Z
FIGURE 38
CONSISTENCY CURVE 120°F.
RPM
95
4 0
4 o
38
3 6
34
3a
30
08
06
0 4
00
oo
/8
/6
/4
/a
to
8
6
o Z 4 & 8 /o to /4 /4 /S O o oo 04 04 O S 3o 30 34 36 38
TORQUS °M - WIRE 22
FIGURE 31
CONSISTENCY CURVE 130°F.
/? m
96
5 35 40 4 S 0
30 /o
TORQUE °M - WIRE *2
FIG U R E 40
CONSISTENC Y CURVE 13 0 T
97
4 *
5 O /o 2 0
TO R Q U E °M - WIRE 22
F I G U R E 4 ]
CONSISTENCY C U R V E 130°F.
98:
38
3 5 40 4 5 50
5 /S 70 0
T O R Q U E V 7 - W IR E EE
F I G U R E 4 E
CONSISTENCY CURVE 130'F .
RPtA
99
4 2
40
38
36
34
37
30
28
26
24
22
2 0
/8
/6
/4
/X
/ O
8
6
4
2
S to / S 2 0 X S 3 0 3 S 4 0
T O R Q U £ - W I R E 2 2
F I G U R E 4 3
C o n s i s t e n c y c u r v e 1 4 o ° f
uidy
100
4 t
40
34
30
S 3 5 4 0 O / O
TORQUE °M - WIRE 2Z
FIG U R E 4 4
CONSISTENCY CURVE 140°F
42
4 0
38
36
34
3*
30
28
26
24
22
20
/8
/4
12
/O
8
6
4
2
0
101
5 /o / 5 20 2 $ 3 0 3 5 4 O 4 S
TO R O UE 77 - W I R E 2 2
FIG U R E 4 5
CONSISTENCY CURVE l4 o ‘F.
102
40
38
28
35 40 4 5 2 5
0 /O 3 0
TORQUE ° M ~ W I R E 2 2
FIGURE 46
CONSISTENCY CURVE 140°F.
103
4 5 5
40 3 5 3o 0 /5 JO
TOROu£ °M - WIRE ZZ
FIGURE 4 7
CONSISTENCY CURVE 140°F.
4 2
4 0
38
3 f o
34
52
30
28
U
24
22
2 0
/a
Jfo
/4
12
fo
8
fo
4
2
0
104
/
2 * £ 8 / < > /2 H / t /e H O » ** 2* 28 J» 32 3 * 3 t 33
T O R Q U E 7*1 - W I R E 18
F IG U R E 4 8
CONSISTENCY CURVE 150°F.
RPM
105
42
40
38
%
34
32
30
* 8
2 6
2 4
22
2 0
/8
/6
14
/2
/ O
8
6 .
4
2
0 2 4 6 8 10 12 i4 /6 /8 20 22 & 26 28 30 32 3 4 36 3 8
TORQUE °M - WI RE IQ
F IG U R E 41
CONSISTENCY CURVE 150 °F.
4 2
2 4
n
O 2 4 & 8 /O Y2 / 4 /6 / 8 2 0 2 2 2 4 24 2 8 30 3 2 3 4 36 3 8
T O R Q U E °M - W I R E 18
FIGURE 50
t
C O N SIST E N C Y CURVE ISO'F.
RPM
107
40
2 0
3 2 3 6
0 4 8
TORQUE n - W TRE 10
FIGURE S I
CONSISTENCY CURVE M 0 ° F
RPM
108
ze
O X 4 6 8 /O !Z /4 /6 /8 Z O ZZ Z4 26 Z8 30 32 34 36 38
TORQUE °M - W IR E 18
FIGURE 52
CONSISTENCY CURVE U0°F.
4 0
o >
20
I
0 Z 4 i B /o IX 14 H /B ZO XX X 4 X 4 2B 30 3 Z 3 4 3 t 3B
TORQUE °M - w i r e : i s
F I G U R E 5 3
C O N S I S T E N C Y CURVE U O 'F .
APPENDIX B
APPENDIX
FIEXL C ALCULATIO NS
I . INSTRUM ENT FUNCTIONS
Rb 2 rad ios o f the bob*
R0 a rad iu s o f the cup.
h • depth o f immersion o f the bob.
T ■ to rq u e.
R > , a l- 7 /l6 " a 1 .8 3 cm.
2
Rc a 3 .4 9 om.
1 1
s - R b . 2 -. 80 = ~ (3; 4 -^ - (13.56X10"5 ) / «
4 " ft h (4 ji3 .1 4 K l.Z 7 >
C - s (2 .1 X 1 0 * 2 ) /cm3 .
(2 .3 0 3 j lo g ( 5 .4 9 )
( 1 7 8 3 )
I I . IN STR U M EN T C O N ST A N T S
Radius of d ia l « 2 - l/3 2 ” * 5 .1 6 om*
For Wire No. 18
30 gms. « 35°M.
x r g (30) (980) (5*16) , 4334 Dyne - om.
18 (35) °M
For Wire No. 22
10 gms* g 7 5 ^
K 2? r (1 0 )(9 8 0 )(6 * 1 6 ) - 674 Dyne » om*
o m
For Wire No. 26
2 p is . - 100°M
- (2 )(9 8 0 )(5 * 1 6 ) • 101 Dyne m om.
2 6 ------------( 1 0 0 )------- " W.--------
112
I I I . CONSISTENCY C U R V E CALC U LA TIO N S
Figure 9
f « ©
Ut * ( 2 2 /4 ) (9 .5 5 )(1 5 .5 6 )(10“S) (0 .5 9 )(6 7 4 ) « 4 7 .8 p o is e s
(2gy'
% = (3 5 /4 ) ( 9 .5 5 ) ( 1 5 .5 6 ) (10~3) (0 .5 9 )(6 7 4 ) » 4 7 .8 p o ise s
2 ~
S in ce ( 9 .5 5 ) (1 3 .6 6 )(l© “3) (6 7 4 )(.5 9 ) * 5 1 .5
th en 51.5 i s used fo r a b b rev ia tio n .
M b - 0
Figure 29
f « 0
U -, * (2 2 /5 ) (5 1 .5 ) - 4 9 .6 p o ises
(28)
0 9 s (3 8 /5 )(§ 1 .5 ) * 52.6 p o ise s
I i2 )....
% * (2 )(4 9 .6 -5 2 .6 ) = - 7 .4 dynes /cm 2 .
in (4 2 2 )
(28s )
Figure 30
f s 0
01 = ( 3 l / 3 ) (5 1 .5 ) * 4 3 .8 p o ise s
(40)
40 RPM. used because o f ir re g u la r eurve.
Figure 31
f * 0
Uj Z ( 2 0 / 7 )(5 1 .5 ) “ 4 9 .5 p o ise s
J S 0 - <38/7) (5 1 .5 ) * 5 5 .0 p o ise s
(42)
M v « (2) (4 9 .5 -5 5 .0 ) * -1 3 .6 dynes/ora2
ln (4 2 z )
Figure 52
f - 0
f i « (2 4 /5 )(5 1 .5 ) » 53.5 p o ise s
” XW ” ~
% * ( 5 5 /5 )( S I .5) - 4 9 .0
~ (42)
IS « (2 ) (5 3 .5 -4 9 .0 ) ■ 11.2 dynes/cm2 .
In (422)
Figure 53
f s ©
U, * (2 1 /2 )(6 1 .6 ) * 4 2 .4 p o ise s
(28)
Ug * (3 5 /2 )(5 1 .5 ) * 4 5 .4 p o ise s
(4fc)
1 , * (2 ) (4 2 .4 -4 5 .5 ) = -7 .6 5 dyn.es/eia2
------
( I P )
Figure 12
f = 0
W i = (2 3 /3 )(5 1 .5 ) = 4 7 .8 p o ises
(28)
* (3 7 /3 )(5 1 .5 ) * 4 9 .0 p o ise s
K. * ( 2) (4 7 .8 -4 9 .0 ) = - 3 .0 dynes/cm2 .
In (422 )
114
F igu re 54
- f a o
T J t * (2 5 /3 ) (5 1 .5 ) * 5 1 .5 p o ise s
itS)
Up s ( 4 l/3 ) (5 1 .5 ) - 5 4 .0 p o ises
(42)
M u ■ (2 )(5 1 .5 -5 4 .© ) * - 6 .2 dyues/em^.
In U 2 2)
(2p )
Figure 35
Too ir re g u la r to c a lc u la te r e lia b ly .
Figure 36
f a 0
Wl ■ ( 2 § /2 )(5 1 .5 ) = 4 9 .6 p o ise s
(28)
U9 - (4 2 /2 )(5 1 .5 ) = 5 4 .0 p o ise s
(421-----
M u * (2 )(4 9 .6 -5 4 .© ) * -1 0 .9 dynes/cm^,
la (42^)
(28^)
Figure 37
f • ©
T N ■ (2 6 /5 )(5 1 .5 ) - 5 7 .0 p o ise s
i i —■
Up = ( 4 0 / 5 )(5 1 .5 ) * 6 5 .2 p o ise s
(42)
^b * ( 2 )( 5 7 .0 -5 5 .2 ) * 4 .5 dynes/cm^,
la (422)
(IP)
115
F igu re 38
f * (3 ) (2 .1 )(1 0 * 2)(0 .5 9 )(6 7 4 ) • 25 dynes/cm2 .
Since ( 2 .l)(l0 -2 )(0 .5 9 )(6 7 4 ) 3 8,34
th en f * (3 ) (8 .3 4 ) « 25
Ul » (2 5 -3 )(5 1 ,5 ) « 4 0 ,5 p o ise s
(28)
U p s (44— 3 )(5 1 ,5 ) 3 50,3 p o ise s
(42!
* (2 ) (4 0 .5 — 5 0 .3 ) ® «34.4 d y a es/es^ .
^ l a ( 4 £ )
(282 )
Figure 14
f « (1 6 )(8 .3 4 ) « 134 dynes/ora?.
Ug a (4 7 * 1 6 )(5 1 .5 ) * 36 p o ises
(42)
Figure 15
f s (1 5 )(8 .3 4 ) - 125 dynes/om2 .
Ui s ( 5 7 -1 5 )(5 1 .5 ) « 40*5 p o ise s
(28)
Ug » ( 5 0 -1 5 )(5 1 .5 ) s 46.2 p o ise s
(39)
» (2)(4 0 * 5 -4 6 .2 ) « -17*2 dynes/cm2 .
la (392 )
(282)
Figure 39
f a (1 0 * 5 )(8 .3 4 ) * 87.5 d yn es/ea2 .
F igu re 40
f * (2 1 )(8 .3 4 ) • 175 d y n .e s /e m 2 ,
U, = (3 2 .5 -2 1 )(5 1 .5 ) - 21.2 p o ise s
1 ^ -----------
% • (4 6 -2 1 )(5 1 .5 ) = 3©.6 p o ise s
T42)
• ( 2 )( 2 1 .2 -5 0 .6 ) * -2 3 .2 dynes/cm2 .
In ( 422)
(282)
Figure 41
f = (1 6 )(8 .3 4 ) » 134 dynes/cm2 .
© 1 ■ (3 3 -1 6 )(5 1 .5 ) • 3 1 .3 p o ise s
1 M
1 ? s (4 6 -1 6 )(§ 1 .5 ) = 3 6 .8 p o ise s
(I£J—
% s (3 1 .3 -3 6 .8 ) * -1 3 .7 dyn.es/om2,
in (422)
(282)
Figure 42
f * (2 3 )(8 .3 4 ) * 192 dymes/em^.
8 (5 0 -2 3 )(5 1 .5 ) = 33.1 p o ise s
1 4 2 )
Figure 17
f s (10) (8 .3 4 ) * 83.4 dyn.es/eHi2.
1 . = (2 5 .5 -1 0 )(§ 1 .5 ) * 28.5 p o ise s
1 — m —
U2 = (3 1 -1 0 )(5 1 .5 ) » 2 5 .8 p o ise s
(42)
1 * (2 )(2 8 .5 -2 5 .5 ) « 6.66 dynes/em2 .
—
la
F igure 43
f = (1 6 .5 )(8 .3 4 ) - 158 dynes/cm2 .
I
I U -i = (2 8 -1 6 .5 ) (5 1 .5 ) * 21,2 p o ise s
j (28)
i
j V9 = (3 1 -1 6 .5 )(5 1 .5 ) - 1 7 .8 p o ise s
1 (4§)
M = (2 )( 2 1 .2 -1 7 .8 ) m 8 .4 dynes/cm2 .
; In (42*)
* (282)
Figure 44
j f = (1 1 .0 )(8 .3 4 ) - 92 dynes/cm2 .
! T3i * (26-11) (5 1 .5 ) « 2 7 .6 p o ise s
! — m —
| % = (3 0 -1 1 .0 )(5 1 .5 ) - 2 3 .3 p o ise s
, ^
| M a ( 2 )(2 7 .6 — 2 3 .3 ) ■ 10.6 dynes/em2 .
I In (422)
(282)
1 Figure 45
! f = (1 5 )(8 .3 4 ) a 125 dynes/cm2 .
0 , a (2 7 .5 -1 5 )(5 1 .5 ) a 23 p o ise s
| (18)
!
I 6 5. - (3 1 * 1 5 )(5 1 .5 ) • 19.6 p o ise s
i ( 4 S ) '
M * ( 2 )(2 3 -1 9 .6 ) = 8 .7 dynes/cm2 .
| la (422)
(iS * )
i Figure 46
i , ?
f * (1 6 .5 )(8 .3 4 ) » 15© dynes/cm .
1
I . . . .
« (3 5 -1 5 )(5 1 .5 ) - 3 2 .5 p o ise s
I t t i )
I
j U 2 “ (3 5 -1 5 .5 )(5 1 .5 ) s 2 3 .9 p o ise s
1 M = (2 )( 3 2 .2 -2 3 .9 ) s 2 0 .3 dynes/cm2 ,
la (422 )
(282)
Figure 47
1 f • ( 1 7 . 5 )( 8 .3 4 ) * 146 dynes/cm2 .
U. « (3 5 -1 7 .5 )(5 1 .5 ) » 32.2 p o ise s
— m —
Up - (3 8 -1 7 .5 5 (5 1 .5 ) * 2 5 .2 p o ise s
M * ( 2 )(3 2 .2 -2 5 .2 ) » 1 7 .4 dynes/cm2 .
In (422 )
! ( i P )
Figure 19
| f * (5 )(2 .1 )(1 0 -2 )(0 .8 9 )(4 3 3 4 ) • 268 dynes/em2
; S in ce (2 .1 )(1 0 -2 )(0 .5 9 )(4 5 3 4 ) ■ 5 3 .5
, th en f * (5 )(5 3 .5 ) ■ 268 dynes/cm2 .
I U, s ( 8 .2 5 - 5 ) ( 9 .5 5 ) ( 1 3 .5 6 ) (1®~2) (4 3 3 4 )(0 .5 9 ) *
; ---------------------------------------------------
S in ce ( 9 .5 5 ) (1 3 .5 6 )( l 0 ”S) (4 3 3 4 )(0 .5 9 ) - 332
th en U, s (8 .2 5 -5 )(3 3 2 ) ■ 3 8 .5 p o ise s
I ^
I
| U 2 “ (9 .5 -5 )(3 3 2 ) » 35.6 p o ise s
(4 l)
I M ■ (2 )( 3 8 .5 -3 5 .6 ) ■ 7.15 dynes/cm2 ,
i (422)
(282)
Hot c a lc u la te d due t o curve I r r e g u la r itie s
j Figure 49
j f - (25) (5 3 .5 ) ■ 1340 dynes/cm2 .
! ¥ , ■ (3 0 -2 4 )(3 3 2 ) * 11.2 p o ise s
~ m —
1
0 2 - (33— 24) (332) = 71.2 p o ises
(42)
Figure 50
f - (24) (5 3 .5 ) - 1315 dynes/cm2 .
5 - , = (3 0 -2 4 .5 ) (332) * 65.2 p o ise s
(28)
U 2 s ( 3 3 -2 4 .5 )(3 3 2 ) * 67.2 p o ise s
T i l )
M * , = (2) (6 5 .2 -6 7 .2 ) * - 4 .9 dynes/cra2 .
1„ (42^)
(282)
Figure 20
f ■ (2 0 .5 )(5 3 .5 ) a 1100 dynes/cm^.
% ■ (3 0 -2 0 .5 )(3 3 2 ) * 7 5 .0 p o ise s
"— m r ~
Figure 22
f * ( l 5 ) (5 3 .5 ) ■ 804 dynes/em2 .
0! * (1 9 -1 5 )(3 3 2 ) - 47.5 p o ise s
(28)
Ug • (2 0 -1 5 )(3 3 2 ) * 4 1 .5 p o ises
til) .
M s (2) (4 7 .5 -4 1 .5 ) • 1 4 .8 cyues/eia2 .
(282)
f = (1 9 )(5 3 .5 ) ■ 1020 dynes/cm2
U9 - (2 8 -1 9 )(3 3 2 ) = 7 1 .0 p o ises
(42)
T Jj » 7 1 .0 p o ise s
I s ©
Figure 52
f * (2 2 )(5 3 .5 ) * 1180 dynes/cm2
M * 0
Figure 23
f * (2 8 )(5 3 .5 ) » 1500 dynes/cra.2
M * Seg&tiv©
Figure 55
f = (26) (5 3 .5 ) * 1400 dyaee/cia2
M » N egative
121
CGNSISTEICY C U R V E D A T A
FIG U R E 9 FIG U R E 29 FIG U R E 30 FIGURE 31
R P M UP SOW UP DOW UP DOW UP BOW
12 10 7 10 7 13 8 10 9
14 13 9 10 9 13 9 12 10
19 l i 13 13 15 17 11 13 14
24 19 18 17 18 19 17 16 17
28 22 22 2© 24 22 20 17 23
32 25 27 27 27 24 24 25 28
36 29 29 29 31 27 27 29 32
40 32 34 33 36 30 33 32 36
42 35 38 34 38
FIG U R E 32 FIG U R E 33 PIGU11 12 FIG U R E 34
12 13 9 11 9 12 9 15 10
14 15 11 12 11 14 11 17 12
19 17 13 16 15 16 16 20 16
24 20 18 19 19 20 20 21 20
28 24 22 21 22 23 26 25 26
32 25 26 24 25 25 30 27 30
36 30 30 27 30 27 33 30 35
40 33 34 32 34 32 36 35 39
42 35 35 37 41
FIG URE 35 FIG U R E 36 FIG U R E
37 FIGURE 38
12 14 13 16 12 17 12 17 14
14 17 17 17 IS 17 13 18 17
19 21 23 19 19 20 18 20 22
24 24 29 22 25 24 21 22 26
28 27 35 25 31 26 26 24 30
32 30 38 29 35 28 30 31 35
36 36 40 33 39 30 35 35 38
40 38 42 38 42 35 39 39 43
42 45 42 4® 44
1 2 2
FIG URE 14 FIG U R E 39 FIG URE 40 FIG U R E 41
R P M O F D G R V UP D O W N BP D O W N UP D O W N
12 25 19 14 15 17 19 21 18
14 25 22 15 16 19 23 22 22
19 26 29 16 19 24 30 24 29
24 28 32 2© 22 27 34 30 33
28 33 34 21 22 30 38 31 37
32 41 38 25 25 36 40 35 38
36 45 40 31 27 4© 42 41 40
40 47 44 31 28 45 44 44 44
42 47 32 46 46
FIGURE 42 FIG URE 15 FIG U R E 17 FIG URE 43
12 30 28 30 23 18 15 17 18
14 30 30 30 26 2© 17 20 19
19 32 35 31 33 22 20 23 23
24 34 37 34 38 25 22 24 25
28 39 40 37 42 25 23 27 28
32 47 43 43 46 27 25 29 27
36 49 45 48 48 29 26 30 29
40 50 46 51 50 30 28 31 30
42 50 53 31 31
FIG U R E 44 FIGURE 45 FIG U R E 46 FIG U R E 47
12 21 15 22 17 25 18 29 20
14 21 16 24 19 28 20 31 22
19 23 19 25 22 30 23 32 24
24 24 21 27 23 32 25 34 26
28 26 23 27 24 33 26 35 27
32 27 25 29 26 34 28 36 29
36 28 26 29 27 34 28 36 31
4© 30 27 30 28 35 31 38 34
42 31 31 34 38
123
FIG URE 19 FIG URE 20 I H
n
48 FIG URE 49
R P M UP DOW UP ] D O W UP DOW U P DOW
12 7 6 26 23 19 27 27 27
14 . 7
s i
25 24 20 27 27 28
19 8 7 25 25 22 28 28 29
24 8
7 i
26 26 22 29 29 30
23 8 8 27 27 2 3 | 30 30 31
32 9 § 28 28 25 30 31 32
36 9
si.
29 28 27 30 31 32
40 9 9 30 30 28 30 32 32
42
s > 4
30 29 33
FIG URE §0 FIG U R E 22 FIG U R E 23 FIGURE 51
12 27 26 17 16 25 25 23 22
14 27 27 18 16 25 25 23 22
19 28 28 18 17 25 27 24 24
24 28 29 19 18 25 28 24 24
28 29 30 19 18 25 28 25 25
32
30
31 19 19 26 28 26 25
36 31 32 19 19 27 28 26 26
40 32 32 20 19 29 28 27 27
42 33 21 29 28
FIG URE 52, FIG URE 53
12 23 19 23 23
14 22 20 23 23
19 22 21 23 24
24 22 21 23 25
28 22 22 24 26
32 22 22 25 26
36 23 23 25 26
40 24 24 26 26
42 25 27
124
M ISC ELLAN EO US OBSERVATIONS |
------------- j
I
i
During th e p relim in ary runs i t was noted th a t th e viscom eter j
had a pronounced wobble in th e su spension assem bly during t e s t i n g . j
j
This was elim in a ted by in s e r tin g a s o f t b rass c o lla r in th e cen ter
bracing poin t* The c o lla r had 0.002 in ch es clearan ce between i t s e l f
and th e assem bly and was kept lu b rica ted w ith o i l . On a fu tu re
instrum ent t h is c o lla r should be rep laced w ith a p r e c is io n b ea rin g .
The speed range o f th e instrum ent was not w ide enough. A fu tu re
instrum ent should have a range from 0 t o 200 rpm.
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