VISCOSITY OF LIQUID-LIQUID DISPERSIONSIN LAMINAR AND TURBULENT FLOW
John Anthony Cengel
A THESIS
subRitted to
OREGON STATE COLLEGE
in partial fulfillment ofthe requireiients for the
degree of
Master of Science
June, 1960
APPROVED:
Prjessor of Chemical Engineering
In charge of Major
d of Department of Chaical Engineering
Chairman of School Graduate Conunittee
Dean of Graduate School
Date thesis is presented 3pemep' 9//fTyped by Claire Waisted
Redacted for Privacy
Redacted for Privacy
Redacted for Privacy
Redacted for Privacy
ACKNOWLE DGMENTS
The writer is priviledged to make the following
acknowledgments:
To the National Science Foundation for finan
cial support in the form of a research grant.
To Dr. James G. Knudsen, the writer's major pro-
fessor, for suggesting the overall problem, for his
guidance and aid, arid for his inspiring confidence
when it was most needed.
To Mr. Charles Wright, graduate student in the
Chnical Engineering Department, for his invaluable
assistance in obtaining data.
To Mr. Arne Landsberg, graduate student in the
Chemical Engineering Department, for his construction
of the emulsion evaluator, and for his helpful hin
about its operation.
Finally, to the One, because of whom this thesis
was completed, and to whom it is fondly dedicated.
t.
(
* EOI1; 4ICiL &;iJJ.3IO
i;ewtQr.i F1.icauepc2-$: c1tJ
jç : flaytrtozt cf ¶artic1e 3e,
u:
Pipiri yaCtYJL.t(v
4 EI:iL i:5ioi
irL;lr& :'c1 iccesitCapil1ar ..uc V .;coatrP1ctpolerc lMcrt
ChtCJ 1CCapi11r; CftIirtic
iar Flay Vj;coltyr v'11
2 .. ) e. t.s
fzitrar F10 icitio:1crt Zlcw Vjscoiyotc1etic 1icn Vu
i' , . -" '-
-' ,.,-. ' ,,C 4.
CiLIki1IO!q'l _I_ -4-
I.3
I
I
2e
LIST OF FIGURES
Fi9ures Page
1 VISCOUS CHARACTERISTICS OF FLUIDS 8
2 EFFECT 0? FLOW RATE ON VISCOSITY 8
3 VISCOSITY AS A rtJNCTION OF CONCENTRATION 11
4 VISCOSITY AS A FUNCTION OF SHEAR RATE 11
5 SHEAR STRESS AT WALL OF CAPILLARY VERSUSRECIPROCAL SECONDS 19
6 SCHEMATIC FLOW DIAGRAI\i 23
7 DIAGRAM OF TESril SECEIONS 24
8 SUPPLY AI4. MD PUP 26
9 MANOMETER BOARD ARRANGEMENT 29
10 LIGHT AND PHOTOCELL PROBES 33
U WIRING DIAGRAM FOR PHOTOELECTRIC EMUIIONEVALUATOR 36
12 PLOT TO DETERMINE FLOW RATE 51
13 PLOT OF 1/ F VERSUS wfr 53
14 LAMiNAR FLOW VISCOSITIES OF WATER, 5%,20%, AND 35% DISPERSIONS 56
15 LAMINAR FLOW VISCOSITIES OF SOLVENT AND50% DISPERSION 57
16 EFFECT OF REYNOLDS ii3MEER IN PIPING SYSTEM ON MEASURED LAMINAR VISCOSITY WITHCONSTANT iP ACROSS CAPILLARY TIlDE 58
17 SHEAR STRESS AT CAPILLARY WALL VERSUSRECIPROCAL SECONDS 64
18 TURBULENT FLOW VISCOSITIES AS A FUNCTIONOF FLOW RATE 66
19 PLOT OF VARIOUS DISPERSION EATIONS 70
Figure
20 AMOUNT OF LIGHT TRANSMITTED AS A FUNCTION OF MIXIiC I1E
21 EFFECT OF FLOW iATE ON AMOUT OF LIGHTTRANSMITTED
22 DENSITY OF WATER AND SOLVENT VERSUS:1Trtn7,.)I rir'-i
23 VISCOSITY OF SOLVENT A. D WATER VERSUSTEMPERA2URE
Paqe
71
73
39
90
24 PRESSURE GAGE CALILRAflON CURVE 92
L OFFI tJRES (continued)
LIST OF TAB LFS
Table Pacte
1 CAPILLARY TtJEE DIMENSIONS 30
2 NOMINAL AND MEASURED COMPOSITION 40
3 CAPILLARY TUBE INFORMATION 54
4 MANUFACTURER'S SPECIFICATIONS 8?
5 TURBINE PUMP CHARACTERISTICS 91
VISCOSITY OF LIQUID-LIQUID DISPERSIONS
IN LAMINAR AND TURBULENT FLOW
CHAPTER 1
INTROJECTION
Two-phase systems have been known since the beginning
f chemical history. However, the behavior of such systems
in flow has beer under investigation for only a relatively
short portion of that time. This behavior has become in-
creasingly important to the modern chemical engineer in all
inthstries. With the development of liquid-liquid extrac-
tion apparatus, fluidized catalytic chnical reactors, and
other processing equipment, knowledge of the physical prop-erties of two-phase systems is a prime factor.
Considerable study has been given to gas-liquid, gas-
solid, and liquid-solid dispersions. In addition there has
been investigation of combinations of these systems, such
as liquid-liquid-solid dispersions. Yet relatively little
has been accomplished in the region of liquid-liquid flow.The determination of the physical properties of liquid-
liquid dispersions is one of the most necessary contribu-
tions that can be made to chemical engineering theory. The
viscosity of such dispersions is probably the most unique
and important of those properties. From the commercial
standpoint, the viscosity is important, since it plays a
2
major rcie in the design of equipment and since many dis-persions may be marketable only at specific viscosities.nowledge of viscosity has a theoretical value also. The
viscosity, together with hydrodynamic theory, can giveconsiderable information about the structure of dispersionsand clues to their stability.
It was therefore decided to undertake the task of measuring the viscosity of a dispersion of immiscible liquids.Apparatus was designed and built to permit measurement of
both the laminar and turbulent flow viscosities of a pe-troleum solvent in water. Of secondary interest was theinvestigation of the amount of light transmitted throughwater as a function of the interfacial area. This thesispresents the results of this investigation.
CHAPTER 2
THEORETICAL DISCUSSION
The physical properties of fluids are in constant use
in chemical engineering calculations, Probably the most
important of them is the viscosity, or more properly, the
coefficient of viscosity. This is the quantitative meas-
ure of the tendency of a fluid to resist shear.
As a fluid flows, it is deformed by applied external
forces bringing about frictional effects exhibited by the
motion of molecules relative to each other. These effects
are encountered in all real fluids.
The classic example is two parallel plates, analogous
to layers in a fluid, a differential distance dy apart sep-
arated by a fluid. Shear stress must be exerted to keep
one plate moving parallel to the other at a constant rela-tive velocity to the other plate. This force is directlyproportional to the velocity gradient dy/dy. The propor-
tionality factor is removed by introducing the coefficient
of viscosity,p
(1) 7 F =pdvT dy
The coefficient of viscosity is a characteristic physical
property of all real fluids. Its numerical value for any
particular fluid is dependent upon the temperature, pres-
sure, and velocity gradient or rate of shear.
The unit of viscosity in the c.g.s. system is thepoise, 1(dyne) (sec) /sq cm = 1 g/ (sec) (cm), and in
the English system, lb/ (ft) (sec).The viscous force may also be expressed as a rate of
momentum transfer between the fluid layers. The shear
stress is a force per unit area and is equivalent to arate of change of momentum.
Numerous methods have been devised to determine the
viscosity of fluids. Basically all methods make use of
Equation (1), in which a known shear stress is applied tothe fluid and the resultant rate of shear determined.From the two quantities the viscosity may be calculated.
One common method makes use of the capillary tube
viscometer, in which the pressure drop occuring during lain-flow through a capillary tube may be used to calculate
case, i.e.
(2)
where
/u= 7Tr4PO8LV
r radius of capillary tubeti P pressure drop across tubeL length of tubeV volume of measured efflux from tube
ê time to collect ef flux
4
This method of measurement was chosen for the pre
ent work because of the convenience involved in obtaining
a suitable sample for study.
As pointed out in a subsequent section, a class of
fluids known as non-Newtonian exhibit behavior in which
the viscosity is a function of shear stress. Consequert
ly such fluids oftentimes exhibit different viscosities in
laminar from those in turbulent flow. The turbulent flow
viscosity is the viscosity which satisfies the following
equations applied to turbulent flow in a smooth pipe.
3) LPf D and2pU2
(4) 4.0 log (Re if ) -0114
f Fanning friction factor
i P pressure drop due to friction,P = Diameter, ft
)° density, ibm/ft3
U velocity ,ft/sec= conversion constant 32.17 (ibm) (ft)/lbf (sec)
Re Reynolds number
/12
Newtonian Fluid
A Newtonian fluid is one in which the viscosity is
independent of the rate of shear, i.e. is constant in equa-
tion (1) at constant pressure and temperature.
The viscosity of all Newtonian liquids decreases with
an increase in temperature, at constant pressure. The vis-
cosity of gases increases as the temperature increases, at
constant pressure. This behavior is in accordance with the
kinetic theory of gases.
For most liquids the viscosity increases with pressure
at a constant temperature. The viscosity of gases alsoincreases with pressure, contrary to the kinetic theory,whIch states that the viscosity of a gas should be inde-pendent of pressure. The viscosity of the liquid and thatof the gas beco-e ident3.cal at the critical point.
Non.-Newtonian Fluids
A non-Newtonian fluid is one in which the viscosity
is also a function of the rate of shear, in general, non-
Newtonian fluids may be classified by three groups--plastic,peeudoplastic, and dilatant. Referring to Figure 1, it may
be seen that, for a true Newtonian fluid, the shear stressis directly proportional to the rate of shear (curve I).The plastic fluid (curve III) is one which requires a
7
definite stress known as the yield point to start the mater-ial flowing. An ideal plastic flows as a viscous materialaccording to curve lila. Moat plastics exhibit a bend inthe line at x because of a breakdown at the interlockingarrangenent of the molecules. The pseudoplastic fluid
(curve II) exhibits a continuous decrease of viscosity,with an increase in shear rate, approaching a Newtonian
behavior at high shear rates.The dilatant fluid (curve IV) is one whose apparent
viscosity increases continuously with increasing rate ofshear.
Figure 2 8howE how the character of the viscosityaffected by shear rate. It appears that all fluids
would behave as Newtonian fluids at high rates of shear.
)ns
The viscosity of a suspension at very low concentra-
one of the dispersed phases in general are Newtonian inture. However, as the concentration of the dispersed
phase increases, the fluid tends to become non-Newtonian.
Workers in the field of rheology have been classify-ing the non-Newtonian suspensions by the old standards
applicable to a single phase flow, i.e, plastic, pseudo-plastic, or dilatant. Yet it has been repeatedly shownthat the classification into which a suspension falls and
SHEAR STRESS
FIGURE 1. VISCOUS CHARACTERISTICS OF FLUIDS
DILATANT
NE42ONIAN
PS DUD OFL AS TIC
RATE OF SIAR (±LOW)
FIGURE 2EFFECT OF FLOW RATE ON VISCOSITY
8
9
even the numerical values assigned to its rheological prop-
erties is extremely dependent upon the experimental condi-
tions under which the measurements were made. ?or instance,
a particular suspension under different rates of shear can
exhibit plastic, pseudoplastic, and even Newtonian charac-
terietics at a constant temperature and pressure (37, pp.
4344O), Therefore, the viscosity of suspensions is re-
f erred to as an apparent viscosity.
A vast amount of literature exists supporting the con-
clusion that the determination of the viscosity of suspen-sions is a very complex problem. Most of the literaturedeals with gas-liquid, gas-solid, and liquid-solid suspen-
sions or dispersions. Although there is a great deal of in-
tereet in liquid-liquid dispersions in modern chemical engin-
eering1 there has been little accomplished in that direction.
The following discussion concerns suspensions at con-temperature.
The viscosity of suspensions depends upon several fac-3, p. 2S3);
) The volume concentration of the dispersed phaseThe rate of shearThe viscosity of the continuous phaseThe viscosity of the dispersed phaseThe size and shape of the dispersed partic
10
The distribution of the particle
The intorfacial tensions exhibited by the particles.
In general, as the concentration of the dispersed
phase increases, the apparent viscosity increases (Figu
up to maximum value, where inversion takes place. The
point of inversion is very difficult to measure because
the instability of the suspension at that point (22, p. 512;
16, p. 1). The majority of the suspensions also exhibit
a pseudoplastic behavior in turbulent flow, with the vis-cosity steadily declining as the rate of shear increasesuntil a limiting viscosity,,, is approached (Figure 4)
(48, p. 417; 8, p. 84). However, it is not uncotinton for a
particular suspension to show several non-Newtonian charac-
teristics.
Alves (42, p, 108) states that in general non-Newtonian
suspensions behave as Newtonian fluids in the turbulent flow
region. This statient has not been substantiated by other
workers and presumably refers to the limiting region of/b..
Lewis, Squires, and Thompson (29, p. 40) emphasize that
the viscosity of a suspension is independent of particle
size as long as particles are all the same size. If the
particles are polydispersed, i.e. many-sized, another vari-
able is introduced.
Several solutions were given to explain the observed
pstdop1astic behavior. Wilkinson (60, p. 595-600; &: p.
RATE OF SHEAR
FIGUREVISCOSIIY AS A FUNCTION OF SHEAR RATE
11
aS
I0
I
VCLTJ1E FRACTION DISPERSED PHASE,
FIGTJJ 3VISCOSITY AS A FUNCTION OF CONCENTRATION
12
7984) and Robinson (47, p. 549) theorize that the mole-cules or particles are progressively aligned or orientedin the direction of flow. The viscosity will continue todecrease until no more alignment is possible. Hence the
limiting viscosity.Another suggested theory is that the existence of a
ufficient1y thick layer of liquid around discrete parti-cles would account for the viscosity rising with decreasedshear rate (35, p. 574). This explanation is mainly ap-plicable to solids suspended in flowing fluids.
Einstein (11, p. 300 and 12, p. 592) was the firstto consider the problem of two phases. His mathematical
treatment led to the famous wEinsteinN equation
(5) m Pc (1 + k)where
inis the apparent viscosity of the dispersion,is the viscosity of the continuous phase,
0 is the volume fraction of the dispersed phase,k is the "Einstein constant" 2.5,
Einstein assumed a dispersion of uniform rigid spheresins liquid. The spheres were separated by distances much
larger than the partical diameter, random in orientation,non-agglomerating in tendency, and low in concentration.
The equation is actually a limiting law and not consideredapplicable for volume fractions greater than 0.02 for the
dispersed phase (2, p. 59). The value of 2.5 for the "Em-
stein constant" is very much in dispute. Huggins (21, p.
911) says that there is no valid reason to use 2.5, mainlybecause there is considerable difficulty in measuringproperties of suspensions at low concentrations. Ting and
lAlebbers (55, p. 116) claim that, for systems of many-sizedparticles, voids filled and formed by polydispersed parti-cle5 account for the discrepancy of Einstein's constant.}iatschek (19, p. 80) derived an equation similar in formto equation (2), but called "Einstein's constant" 4.5.
Many workers, in an attempt to correlate data, laterexpanded Einstein's original equation in the form of a
polynomial,
/ra 1c (1 + k + a 2 + b3 + ,
where
k is "Einstein's constant," anda and b are constants for a particular suspension.A survey of the literature showed that there was no
defined, accepted value for k. Several experimenters re-
ported values from 1.5 to 18--Orr & Blocker (42, p. 24),Ward & Whitmore (59, p. 286), Hatschek (20, p. 80), Kunitz(25, p. 716), Donnet (7, p. 563), Oliver & Ward (40, p. 397)Thiclauxe & Sachs (9, p. 511), Eveson, W1-dtinore & Ward (15,
p. 105), Eisenschite (14, p. 78) and Eirich, Bunzl & Mar-
garetha (13, p. 276). Others report more extreme values
14
such as 35, Sachs (50, p. 280), and 150, 245, and 340, Rol-ler & Stoddard (48, p. 419-20). The equations that sega
most representative of the preceding group are Kunitz's(25, p. 716)
/1 =JJ (1 + 4.50+ l2çb2
+ 25
and Happel's (1, p. 1298)
where
is an interaction constant ranging from 1.000
to 4.071, while varies from 0.0 to 0.5.
Other experimenters, attetpting to fit their data
the polynomial equation and still keep "Einstein's con-
stant" of 2.5, were Eirich, Bunzi, and Margaretha (13, p.276), Eilers (10, p. 154), Manley and Mason (3, p. 764),Cling and Schachnan (5, p 24) and Vand (57, P. 298). An
example is Vand's equation
I/Im (1 + 2.50+ 73492 +
The values of the "a" constant in the polynomial equa-
tion (6) were in the range from 7.17 to 14.1, while the"b" constant were in the range from 8.78 to 40.
All of the preceding equations were derived without
taking the viscosity of the dispersed phase into account.
Taylor (54, p. 418) modified Einstein's equation to in-
clude the viscosity of the dispersed phase
in c
(10) ILJ&*
where
d is the viscosity of the dispersed phase.
Equation (10) was reported to be applicable for liquid-
liquid systems.
Leviton and Leighton (28, p. 71) obtained an empiri-
cal equation from data on oil-in-water emulsions.
(11) + 0.4,L/ ( çb1113id+c J )
Vermeulen, Williams and Langlois (58, p. 81) present
an equation for liquid-liquid dispersions
(12)
Some workers, deciding that there was no valid rea-son to assume that the Einstein equation was applicable
at higher concentrations of the dispersed phase, devel-
oped more equations desiqred to treat the complexities
of two-phase flow. Hatschek (20, p. 1o4) presented an
empirical equation which successfully predicted the
viscosities of red blood corpuscles.
15
(13)
Equation (13) was later modified by Sibree (53, p. 35) toinclude a volume factor "i" multiplied. by the volume frac-tion in the denominator. The equation was successful forstabilized paraffin-water iu1sions.
Roscoe developed two npirical relationships (49, p.268
[i4] 2.5)
which describes the characteristic viscosity of a suapsion of marty-sized particles, and
/1= ( [1_1.35c] _2.5)
which is applicable to suspensions cf uniform spheres.Richardson (45, p. 32) discusses an equation applic-
able to oi1-in.water enulsions.
IUmIic (Ca)
where
"a" is a constant depending upon the system.Eilers (10, p. 313) presents an epirica1 equation ap-
plicable to his work on asphalt suspensions.
(17)
i-ç= 1
Ii + L.25 -2
L 1(ç/o.78)
16
Miller and Mann (38, p. 719) and Olney and Carison
(41, p. 475) developed a logarithmic expression for immis-
cible liquids
,L/=,L/ ,LIFinally Finnigan (17) reports a correlation for petroleum
advent in water.
.,L (1+2.5 +4.602
Measurement of V Si
When measuring the viscosity of a suspension by means
of a capillary tube, workers have found that the apparent
viscosity depended not only upon the shear rate but also
upon the diameter of the capillary tube. It appears thatthe measured viscosity will increase with increasing diam-eter (15, p. 1074; 33, p. 981). This effect, known as the
sigma effect, has been explained by Vand (57, p. 277), who
assumed that slip takes place between the wall and suspen-
sion, the suspension acting as though there were a layer
of pure fluid adjacent to the wall, De Bruijn (6, p. 220)
atates that the sigma effect is caused by the interaction
of the particles subjected to shear.
Sherman (51, p. 571) shows that the viscosity is a.
function of the shear rate in a particular tube. Lindgren
18
p. 135-6) showed that, with 1.02% bentonite solution
1]. as with the flow of distilled water, the viscosity
ed increased linearily with increasing shear rate
fr a Reynolds number below 500 to one near 3000. In his
riinents Reynolds himself noted this irregularity (44,
p. 84).
Merrill (36, p. 462-5) states that the capillary tube
produces a shear rate varying continuously from zero at the
center to some maximum value at the wall. With each change
of diameter the value of the shear stress on the fluid at
the capillary wall is altered, and thus moves up or down
on the non-Newtonian shear stress-shear rate relations.
Richardson (46, p. 367-73) states that the continuous
shearing action over the comparatively long time of flowrequired to get a reading may result in a breakdown of
some of the globules.
A correlation (8, p. 144; 60, p. 600) has been devel-
oped which plots the shear stress at the wall versus a
volumetric flow rate terra (Figure 5). Assuming that lam-
inar flow exists, that there is no slip at the wall, and
that the rate of shear at a point depends only on shearing
stress at that point and is independent of time, all data
should lie on one line. When one or more of the assump-
tions fail, the figure shows that, by increasing the diam-
eter at a constant length or by increasing the length at
constant diameter, different values of shear stress at the
wall are obtained for a particular flow term. Since vis-
coity depends upon the shear stress, it is evident that
the measured viscosities will depend on tube dimensions.
Narayanaswamy and Watson (39, p. 75), while studying
oil-inwater emulsions, found that entrainment of air was
a factor in erratic measurements of viscosity. The a
sumption was that the air formed very fine bubbles which
lent themselves to a polydispersed system.
Measurement of Particle Size
Many attempts have been made to determine the size
and interfacial area of dispersed particles. Most suc-
cessful investigators have relied upon photographic tech-
niques. Langloiso and Gullberg (27, p. 360) give a
relationship using light transinittancy.
(20)
0
is the light incident to suspension,
I is the light intensity emergent,
A is the interfacial area per unit volume, and
is a specifying constant dependent on the
ratio of refractive indices.
BAl
20
21
The constant B was considered to be independent of the vol-
ue fraction of the dispersed phase.This method may prove erroneous because in dilute solu-
tions scattered light is lost, while in concentrated solu-tions secondary scattering recovers it.
CHAPTER 3
EXPERIMENTAL EQUIPMENT
The apparatus illustrated schematically in Figure 6
was designed to enable investigators to determine both heat
transfer coefficIents and the laminar and turbulent viscos-
ities of liquidliguid dispersions. This thesis concerns
the evaluation of the dispersion. A treatment of the heat
transfer experiments may be found in a thesis (62) pre-
sented at Oregon State College. Figure 7 shows the extent
of the apparatus employed in the viscosity observations.
A stainless steel tank with a jacket for water cool-
ing was used both for containing the test liquids and f or
mixing. A va.riale speed stirrer with propeller blades
was used for agitation.
The dispersion was pumped through the piping system
the respective test sections, where measurements wore
made of the viscosity and heat transfer coefficients. A
by-pass at the pump was used to regulate flow and to pro-
vide additional mixing. The dispersion was returned to
the supply tank through a secondary flow control valve. A
flexIble hose was used at this point so that the flow could
be diverted to a weigh tank for measurement of the flow.
Additional equipment associated with the main piping
system was an orifice meter, a static pressure gage, a
HEATEXCHANGER
FLEXIBLEHOSE
PLATFORMSCALE
STIRRER
WATERWATERA;
f-HCTO
SEWER
03
THERMOCOUPLEWELL
>
PRESSUREGAGE
FIGURE 6SCHEMATIC FLOW DIAGRAM
I'll'I....' I, ulIuUUhuIIlI1I4111111111111 liii
E2'IULS IONEVALUATOR
(j 2-INCH GATE VALVEr7ll- INCH GLOBE VALVE
(}1-INCn GATE VALVEA - ORIFICEB - CAPILLARY TUBEC - TO MANOMETERSD - MIXING TANKE - BECKMAN
THERMOMETER
WATER FLUSH6-FOOT
CHEATING COIL
C
T
TAP
TURBINE 0PUMP DRAIN
PRESSURE TAPS
CAP ILLARYruBE
PLATFORMAND
WEIGH CUP
TO D.C.BATTERY
1- UNION
I THBMOCOUPLE WELLII TO GALVANOMETERIII EMULSION EVALUATOR
PART B
COPPER Tw3E
PART A
PRESSURE GAGE
NEEDLEVALVE
1" BRASS PIPE
FIGURE 7. DIAGRAM OF TEST SECTIONS
21"
19"
1
2
38"
11"
25
photoelectric emulsion evaluator, a capillary viscoxaeter,a sight glass, a baffled mixing chamber, a heat exchanger,
a sample tap, three temperature wolls, and appropriatepiezometer taps and valving. There was also a 6-foot hor-izontal section wrapped with nichrome ribbon for heating.
The scope of the following detailed description willcover only those parts of the apparatus which directlyapply to the viscosity evaluaticn experiment.
Supply Tank and Pum
The supply tank and pump are the same as used by Finn-
igan (17) and are described in detail by him. Figure 8
shows a photograph of this portion of the experimental ap-paratus.
Piping System
The piping system was constructed of nominal 1*-inch
brass pipe, nominal 2-inch brass pipe, 7/8-inch O.D., 16BWG copper pipe, and a section of flexible synthetic rub-bor hose. The 2-inch pipe was located between the supplytank and the pump. The copper line was located between thetwo vertical sections of the system, and the flexible hose
s located, at the ef flux point of the system. All otherpiping was 1*-inch standard brass.
A 2-inch gate valve (number 1, Figure 6) was installed
27
between the mixing tank and pump to aid in controlling flow
and so that the piping system could be drained independent-
ly of the tank. A 1*-inch gate valve was placed between
the pump and by-pass line and between the pump and main
flow system. The by-pass valve (nu.iuber 2, Figure 6) was
used to aid in controlling the amount of flow through thetest sectIons. The main system valve (nuither 3, Figure 6
was used to isolate the main system from the supply tankand was kept wide open during all runs. With this valve
closed, changes could proceed on the test sections withoutdisturbing the mixing. Finally a 1*-inch globe valve(number 4, Figure 6) was installed at the ef flux point toregulate flow and to insure that the aain piping systemrenamed full when the apparatus was not in operation.
AU threaded connections were made with the assist-
ance of "Cyl-sea1 high pressure sealant manufactured by
the West Chester Chemical Company and the seats of all un-
ions were sealed with Perxnatex No. 2, manufactured by the
Perinatex Company, Incorporated. It was found that thesesealants were imperious to the liquids used In the ex-periment.
Unions were used wherever possible for quick dis-assenbly and repair of the equipment. Provision was made
at the low point of the system for drainage. Flow rates
were determined by means of a brass, sharp-edged orifice
28
plate in the vertical section downstream from the pump.
This was constructed by Finnigan (17) for previous exper-
imental work on the same system of fluids. His calibra-tion curve is shown in Figure 12. Flow rates determined
with the orifice meter were within ±41 of measured flows.
Test Section
Figure 7 illustrates the test sections used to evauate the laminar and turbulent viscosities,, Part A was
used to determine the turbulent flow viscosities. This
section was a 6-foot long, 7/8-inch O.D., 16 EWG copper
tube, over which the pressure drop was measured. The
piezometer openings were located at the zero and 6-footdistances by drilling l/2-inch diameter holes perpendic-ular to the pipe wall and brazing short *-inch brass nip-ples in place. The inside surface was cleaned with emerycloth to insure an opening free from burrs and flush withthe inside pipe wall. These taps were connected via --
inch copper tubing to the manometer board (Figure 9).
Both mercury and carbontetrachioride under water were used
to indicate the pressure drop. Care was taken to insurethat the manometer lines were filled with water by poriodIc flushing. The 6-foot copper tube was also used (62) inconjunction with heat transfer coefficient measurements,
Part (Figure 7) depicts the section used for the
30
laminar viscosity and light transmittancy determinations.The main flow, indicated by the arrow, was in the vertical1*-inch brass pipe. Glass capillary tubes of varyinglength to diameter ratios were inserted into the mainstream by means of a steel fitting located 21 inches be-low the entrance and held horizontal by means of a springarrangeent. The springs also served to hold polyethylenegaskets in place. The spring support mechanism was heldin place by a 1-inch pipe cap. The pressure drop acrossthe capillary tube was measured by a U.S. Gage Company
gage attached directly across from the tubes.
Table 1
The gage was of the stainless Bourdon type tube withan 8-inch face calibrated in one pound increments betweenzero and 30 pounds per square Inch static head. Addition-
al calibration points were added to the face of the gage
so that it could be read to t 1/20 pounds per square inch.The calibration was accomplished by checking the gage
TubeNumber
Capi lar Tube Dimensions
Length In Inside Dia!neteInches in inches x 10
Length/DiameterRatio
A 11.95 1,944 615A-i 5.30 1.944 273
11.93 2.580 462C 12.02 3.588 335C-i 5.92 3.588 165C-2 12.00 3.588 334D 11.93 4.092 292E 8.97 5.076 177
31
against a mercury manometer under water pressure. A plot
of the calibration data appears in Appendix .
It was found that the calibration was linear exceptin the region below 2 pounds per square inch. Therefore
all readings were taken with the gage pressure above thatvalue,
A 1*-inch needle valve inserted between the main sys-
iz" and the gage was used for throttling purposes1
The capillary viscometer was provided with a weighing
cup of pyrex glass and a supporting platform adjustable bymeans of clamps. The volume of liquid caught in the cupwas weighed on a null-point alance manufactured by the
Welch Manufacturing Company. The balance had an accuracy
of ±0.5 grams. Time of ef flux of the weighed volume of
dispersion was measured by a stopwatch.
The diameter of each capillary tube was determined by
weighing the mercury required to fill the tube. v1easure-
ments of the diameter agreed within ±0.4%. In addition,one tube was used to measure the viscosity of water to ver-ify the mercury measurement method.
The temperature of the flowing dispersion was measuredby means of a copper-constantan thermocouple situated in a
copper well at the entrance of the test section. The volt-age was read from a Leeds and Northrup type K potentiometer.Tuperatures were kept within ±0.4°F. of the desired value.
32
The photoelectric emulsion evaluator was located 38
inches below the capillary tube viscometer and 59 inches
from the entrance to the vertical test section. The eval-
uator, which consisted of a light source tube and a photo-
cell tube, was used to measure the amount of light traits-
tted through the dispersion. This procedure was intended
relate the light transmitted to particle size and flowrate and, in turn, to apparent viscosity.
Figure 10 is a detailed drawing of the emulsion eval-uator. The light source tube (8) was mounted on the main
piping system (16) by soldering a brass fitting (14) intoa 5/8-inch hole. The piping system and the light source
tube were sealed from one another by the glass window (15)
in the stainless steel light directing tube (9). A pack-
ing gland (13) was forced into the stuffing box by the
fitting (12). The light supporting tube (8) was soldered
to piece (10), and this combination was held to (12) by
three brass screws (11). The end of the light supporting
tube was closed by a micarta end-piece (3), held in place
by binding post (2), which also served as a ground con-
nection. Two light power supply binding posts (1) andthree lamp adjustment screws (4) were fitted into the end-piece. The aluminum lamp base (6) and the lucite holder
(5) could be moved along the adjustment screws to give the
proper illumination from the lamp.
34
The photocell tube was soldered to the main pipingsystem directly opposite the light source tube by means offitting (17), which was inserted into a 1*-inch hole. This
tube was sealed from the system window (20) in the photo-
cell supporting tube (24). The packing was held in place
by gland (18), which was forced into the stuffing box by
fitting (19). The photocell was fitted into a socketmounted in lucite (21) and was attached to the micarta end-piece (22). Binding posts (26) supplying the voltage
across the photocell, were also raounted on the end-piece.The entire photocell mounting wag held in place by setscrew (25). Packing for both tubes was constructed from
teflon,The voltage source of the 6-volt, 2-pole light bulb
(7) was a Delco 6-volt lead storage battery. The current
was first -directed into an exterior electrical system sothat a specified voltage, usually 4.5 volts, could be main-tained at the light bulb. To insure that all data were tak-en under identca1 conditions, the voltage delivered acrossthe light bulb was checked before each reading.
i ransrnitted light received by the photocell tube(23) was converted Into a potential, which was measured by
a null-point potentiometer. The galvanometer used to ob-
serve deflection was a Leeds and Northrup instrument, model
number 2430, which is much more sensitive than those found
mary potentiometer systems. The galvanometer was
nal to the potentiometer system.
The face of the galvanometer was calibrated from zero
100 in increments of one so that percent changes couldbe estiivated. When water flowed in the main piping system,
the instrument was set to read zero with the light source
off and 1OC with the light source on. Thus when the dis-
persion was flowing, it was possible to determine how much
light was transmitted through the dispersion as compared tothe ezaount transmitted through pure water. Sensitivity ofthe galvanometer, as it was used, was ±1%.
The electrical system is schematically shown in FigureThe symbols represented are as follows:Bi 90-volt battery (ICA VSO 90)
B2 6-volt lead storage battery (Delco dry charge)B3 4 mercury cells (Mallory ZM-9)
Cl Two sets of contacts for phototube (RCA 1P4C2 Two sets of contacts fcr igrtt (GE No. 82, 6-volt)C3 Galvanorneter connections (Leeds & Northrup 2430a)
Ri Coarse adjustment rheostat (10 turn 20,000 ohmHelipot
R3 Load resistor (1 megohm)
R4 Coarse adjustment rheostat (5 ohm rheoR5 Fine adjustment rheostat (10 turn 25 ohm }ie1ipoR6 Load resistor (50,000 ohms)
R7 Ealancing voltage set potentiometer (10 turn
50,000 ohm Helipo
RB Voltage resistor (10 ohms)
R9 Sensitivity lowering resistor (50,000 ohms)
PlO Sensitivity lowering resistor (1,000 ohms)
P11 Sensitivity lowering resistor (50 ohms)
Si Double pole double throw circuit selector s
52 Single pole double throw push button
53 Single pole double throw cell selector switch
54 Double pole single throw push button
85 Single pole single throw light switch
86 5 position sensitive selector and galvanonteter
switch.
To enable the investigator to view the dispersion as
it flowed through. the system., a sight glass was located 6
inches below the evaluator. Thus if the dispersion tended
to separate, it was easily noticed. Saruples were with-
drawn from a sample cock located 17 inches below the evalu-
ator..
Three unions were used so that each section of the ver
tical pipe could be renoved independently of the others.
The section containing the capillary viscometer was con-
structed so that it could be relocated in the iiain piping
system to give both vertical and horizontal readings of
the laminar viscosity.
CHAPTER 4
EXPERIMENTAL PROCEJRE
ral Discussion
The purpose of this investigation was to determinethe laminar and turbulent viscosities of an unstableiiqiid-liquid dispersion. The dispersion referred to was
composed of a petroleum solvent, "Shellso].v 360," dis-
persed in water. Finnigan (17), working on the same sys-
tern, showed that there was a definite limit to thecompositions suitable for evaluation.
The compositions investigated ranged between zero and
(by volume) solvent dispersed in water, and pure sol-
vent. For the dispersions, the water was a continuousphase and the solvent the dispersed phase. Flow rates
were varied between 1 and 30 gallons per minute.
Physical properties of the solvent as used in all
calculations were those measured by Finnigan (17). The
solvent was recovered after each run and used for follow-ing runs.
The following pure liquids and dispersions were stud-
ie1. Pure water 4. 35% solvent
2. 5% solvent 5. 50% solvent
3. 20% solvent 6. Pure solvent
The supply tank and main piping system were flushed
h solvent several times before any runs were made,When the dispersions were prepared, a calculated weight ofsolvent was added to a previously weighed amount of water
in the supply tank. The total weight was kept near 300
pounds in order to maintain a constant head of fluid onthe pump. In order to obtain the most rapid mixing pos-sible and to assure a quick turnover of the material in thesystem, all valves were initially left wide open and thetirrer allowed to run at maximum speed. The time neces-
sary to achieve thorough blending of the two liquids de-pended upon the concentration of the dispersed phase. Mix-
ing time was usually 2 to 3 hours, the higher concentrationstaking the longer time.
The dispersion took on a milk-white appearance charac-
teristic of many liquid-liquid suspensions. It was notedthat, if the stirrer were turned off, a clear layer of sol-vent immediately became visible at the surface of the sys-
in the supply tank. This separation indicated instab-y of the dispersion. Even with maximum care, the
interface eventually became contaminated with dust and
small pieces of the flexible hose. The contamination act-
ed as a stabilizing agent. However, the dispersion never
reached a point where it could be cona±dered stable.Samples of the dispersion were taken periodically to
insure that proper mixing was occuring and to check the
coiposition. It was found that actual compositions ineas
ured were, in genera slightly lower than the nominal
composition
Table 2
Nominal and Measured Composition
At each concentration measurements were made of the
pressure drop across the test sections, orifice pressuredrop, fluid temperature, rate of ef flux from capillarytube, and light transmittancy. After each series of runsthe liquids were allowed to separate over night. The sd-
vent was then decanted off and used again in preparing the
ext concentration. The water was discharged to the
eewer.
40
Nominal Volume % Measured Volume 1Solvent Solvent, Average
5 4.8
20 19.4
35 34113
50 49.2
Thrbulent Flow Viscosit Measurement
41
The measurement of the apparent viscosity of the dis-pel ion in turbulent flow was accomplished by means of pres-
sure drop determinations over a 6-foot, 7/8-inch O.D., 16BWG horizontal copper tube. The piezometer lines were
flushed periodically to insure that water was the onlyfluid in the tubing. The valve at the discharge point ofthe piping system (number 4, Figure 6) was closed, and no-
flow readings were taken from the manometers. The readings
for the pressure drop manometers were always zero. The
readings for the orifice manometers wore zero only for thewater and solvent runs because of the vertical distancebetween orifice piezometer taps.
The discharge valve was then opened to allow flow tobegin, After a period of time to allow for the settlingthat had occured in the main piping system, pressure dropreadings were recorded for both the orifice and the testsection. These readings were taken simultaneously with
the laminar flow measurements, Carbontetrachloride was
used for low flow rates, mercury for high flow rates, andboth fluids for intertu ediate flow rates.
Fluctuations of the manometers were minimized by cbs-
down on needle valves at the pressure taps and manom-
seal pots. It was observed that the most fluctuation
42
occured at low flow rates, probably indicating nonhornogene-
ity of the dispersion. For very slow flow rates the flop
was measured by means of the weigh tank. Periodic checks
on the flow were also made at higher flow rates.
The temperature was maintained at 70.5°F±0.4°F by
means of the cooling water in the Jacket of the supply
tank.
Capillary Tube Viscometer
To measure viscosity by the capillary tube method, the
tube was inserted into the tube holding section and through
a hole in the vertical pipe wall. The hole was slightly
larger than the O.D. of the largest capillary tube. The
end of the capillary tube was positioned so that It wouldbe at the axis of the 1*-Inch pipe which carried the mainflow. The temperature of the dispersion was allowed tocome to a constant value of 70,5°F ±0.4°F, A tare weight
was taken of the weighing cup before each measurement.
Fluid was allowed to flow into the cup during a definiteime, measured by a stopwatch. Diring this time the manom-
tore were read periodically to get an average flow value.The pressure on the 8-inch pressure gage was noted in orderto obtain the difference between the fluid and the atmos-phere, i.e. across the tube,
43-44
immediately after the run, fluid in the weighing cup
was weighed, Hefore beqinning a new run, the flow rate
and/or the static pressure head was changed. At each con-
centration a series of runs was made with the different
capillary tubes to determine the effect of diameter, ifany.
The majority of the runs were made with the capillary
tubes in a horezontal position. However, because there was
a different value of viscosity measured by each tube (very
noticeable at the high concentrations), the apparatus was
rearranged so that measurements could be made with the
capillary tubes in a vertical position,
Photoelectric Emulsion Evaluator
Measurements with the emulsion evaluator were made
either simultaneously with or immediately after measure-
ments with the capillary tubes, The evaluator was always
calibrated to read zero with no light and 100 with light
and water flowing. After calibration the solvent was
added to make the dispersion.
By manipulation of the various rheostats in the ex
ternal electrical system, a voltage of 4.5 volts was main-
tained at the light (Figure 11). The proce&re involvedwas as follows:
1. Set 4.5 volts across the light
1?ead alvancicer with 1 iQht on, and
3 Read çalvanc:eter with 1 ±} t off, 8ince the cjalvanc:oter s calihrated to read fron
ro to lOU with water, the readings cThserved with the
di*persion were calculated to h a percentage of the light tranarnitted thrcuch the water. .hese readmnçs were taken
at various flow rates Lc erine hether transittancy changed as a ftinction of flow rate. hi1e the najor-
ty of the ohservatior's were :iade with the probes l/r3inch mrt, there were several rins iade with the prohos l/2C
apar At the heinnirc! cf each seri cf runs, the readings
recorded I roi t a1vancieter frequently to determine
iew trensittartcy chazyo with the tie of ixing. Ihe
r.dings were continued until a steady value was ohtind.
CHAPTER 5
SAMPLE CALCULATIONS
Physical properties of the petroleum solvent and wa
er are discussed in the appendix, as are details of cali-brat ion.
Capillary Tube Calibration and the Laminar Flow Viscosity
The bore of the capillary tubes used in the investgation of apparent laminar viscosity was a critical factorin the calculations. Utmost care was taken to get accur-
ate dimensions, since the radius of a. tube was used to thefourth power.
Mercury at room temperature was drawn into the bore
f a capillary tube, which had previously been tared. The
ght and length of the mercury column was found, and the
jus of the tube was calculated by means of the follow-
ing equat ions:
V= wt
and 1°
wt
(77)(L)(,,o )(2
where V is the volume in cubic centimeters,
wt is the weight of mercury, grams,
r is the capillary tube radius, inches,
,P is the density of mercury, g/cc.
For example, the calculation for capillary tube EwL was 4.2069 grams, was 13.53 g/cc, and L was
34 inches, was as follows:
(2k) r/
4.2069
\j (3.14.6)(13.53)(9.34)(2.54)
0.0254 inches
Once the radii of the capillary tubes was established,
it was possible to measure the apparent viscosity of the
dispersion in laminar flow. This was accomplished by use
of the equation derived by Poiseuille
(23) ,Ia (TT)(P)(e)(r)4(p)(8)(L)(wt
wh
ais the apparent viscosity, cp,
P is the pressure drop across the tube, psi,
e is the elapsed time of measurement, sec,L is the tube length, inches,wt is the weight of the dispersion collected, grams,p is a conversion factor, 1.043 x i8 (g)(cp)
47
(1b) (sec) (in)
Data obtained for run 35-27 with tube E, length11.925 inches and radius 0.0129 inches, was:
weight of efflux, 116.3 grams
i P 10.9 psi
e 300sec
(23a) Pa _!
4
2.670 cp
For vertical tube calculations one inch of fluid head was
added to pressures read.To insure that all measurenents were taken under lain-
mar flow, the ReynoldE nuin.ber was calculated for each tube.
(24) ReT (D)(u)() = (4)(G)(p)24 (7T)(D)(,L/a)
where
D is the diameter of a capillary tube, inches,u is the velocity of fluid, ft/sec,
p is the density, lb/ft3,
a is the apparent viscosity, cp,G is the mass flow rate, g/sec,p is a conversion factor, 39.37 (in)(sec)(cp/(g).
Again for run 35-27,
416) (10.9) (300) (O.0129)(1.043(8) (11.925 116.3)
(24a)
Turbulent Flow Viscos
The pressure drop across the 6-foot copper test sec-
tion was determined by means of manometers, using carbon-
totrachioride and mercury under water as the manometer
fids. The pressure drop was measured directly in mliii
meters of manometer fluid, and the readings were changed
pounds per square foot.
(25) J°Hg )H2O
p
iPf the pressure drop due to friction, psf
the millimeters of manometer fluid
p is a conversion factor, 3C4.8 mm/ft
A sample calculation:
(25a) (843.46_62134)iumHg
304.8
The friction factor was found by using the equation:
e
(26) f (LPf)(g)(D)
(2),P )(u)2(L)
(77)2(zPf)(g0)()J
(32) (L) (W)Z
49
is the density of the medium, 1b/ftis the diameter of the test section,is the length of the test section,is the mass flow rate, lb/sec.
For illustration, run 35-27 will be used again.LPf was 99.92 psf and W was 1.06 lb/sec (from Figure 12)
and
= 0.00785
The turbulent flow viscosity was calculated by f it-
g all the data to Equation (4). This was done by plot-
ng 1/ '[ versus log wif, This plot will yield a straightme when the viscosity is independent of flow rate. From
o smooth curve drawn through the data, the viscosity ateach flow rate was calculated front the following:
1 4.0 log
where
Re 4W
D,JJp7T
(7T)(D)(Jia)(P)
p is a conversion factor 6.72 x 10 lbjft)(sec)(cp)
is the apparent viscosity.
50
(4)(W)([7) -0.4
(26a) f (3.1416)2(99.92) (32.17) (57.6 ) (0.06 22)(6) (1.06)2
illustration for the S% dispersed phase series
with i/f equal to 11, WW equal to 0.0821, and W equal
to 0.9022 is:
(28a) 11 4O log
froni which -
3*534 cp
.1416)(0.0621)(6.72) (j'a)
This correlation was made for a number of points for
1 concenttations, and the values forjUa are plotted
against flow rate, giving the relationship of apparent vis
cosity to shear rate.
52
4) (lO) (0.0821) -0.4
131
12H
10
o PURE WAITERPURE SOLVENT
, 5% SOLVENT20% SOLVENT35% SOLVENT
x 50% SOLVENT
0.0
/
0
000
000 /
400 ., ///<
0 / e0
0/// C C
53
0.03 0.05 0.10 0 20LB'
FIGURE 13. PLOT OF 1/f VERSUS
ystoz 2te
lazy te data is sh in
r '7
AJ1*T, fl2w Vigci Li os
Cap1iar tuJi t( i
for the cf ii f]iw visccitie cf mis-
p*.icns. :an:, x riieters, after wriç with ec1id
Uqiid dipersior (Ch.atter , Lavo cLserired. thai
the parent viscosity 3 a frctor 1xth of the shear
rate and of the tuhe dte 3ion3.
The visao6itie were caicilated Ly ear of Poie
isa's equaticn (qtiaticr 2) ar were used c deteriix the
fcrat io Posit km i'4)
N
N N
Reyxtolds nuibers In the cap try e !eyno1da
niauib.r- rancleQ fv 1CC to 1, Su:iarj Ct e capi1
351 DispersionN
I,
0% DispersionN
N
N
NN
SolventN
IV
Table 3 (Continued)
:6 7C-2 100 17E 8C-2 240 19E 5C-' 6C-2 30 10E 8A
10C-2 4
HorizontalN
N
HorizontalN
N
VerticalN
N
N
HorizontalN
VerticalWat e Nor izont a:
Figures 14 and 15 show results obtained from the
capillary tube measurements. The apparent viscosity of
the pure components and dispersions are plotted versusthe calculated Reynolds number in the tube. In addition,
ranges of viscosity measured under turbulent flow condi-
tions are indicated by vertical bars. These figures do
not take into account any effect produ.ced ky the flow
condItions in the main pipe. Figure 16 shows that flow
conditions in the main pipe have no effect on the viscos-
ity measured by the capillary tubes.Figure 14 shows the results for water and for the
5, 20, and 35! dispersions. Figure 15 shows the results
for pure solvent and the 500 dispersion. Figure 16 shows
laminar flow viscosities, which were measured at constant
3.6
3.2
1.6
3 SOLVENT
v4/t
20% SOLVENT
FIGURE 1LA4INAR FLOW VISCOSITIES
OFWATER, 5%, 20%, AND 35%
DISPERSIONS
TUBE A , HORIZONTALo TUBE B , HORIZONTAL
TUBE C , HORIZONTALTUBE D , HORIZONTAL
v TUBE E , HORIZONTALx 'rUBE A..1, HORIZONTALD TUBE B , IERTICALD 'rubE C-2, VERTICAL
TURBULENT FLOWVISCOSITY RANGE
I I I I I I I
0 2 6 8 10 12REYNOLDS NUMBER IN 'rUBE X io-2
WATER
0
2.8 0
5.8k
5.0
1.2
0.8
U -
IU
U
D
----"T __ A
A £
5O SOLVENT
SOLVENT
i'W3E A , HORIZONTALo TUBE B , HORIZONTALTUBE C , HORIZONTAL
4 TUBE D , HORIZONTALo TUBE E , HORIZONTALTUBE C-i, VERTICAL
A TUBE D , VERTICALTUBE B , VERTICAL
EIJ TIJRLULENT FLOWVISCOSITY RANGE
0 00 0 Qf4 G. . 4, S S
1 2 3 5 6 7 8 9 10 1].REYNOLDS NUMBER IN TUBE X 102
4a IN CENTIPOISEFIGURE 15
LAMINAR FLOW VISCOSITIES OF SOLVENT AiD 50 DISPERSION
.6 - 4,
3
EFFECT OF REYNOLDS NUMBER IN PIPING SYSTEM ON MEASUREDLAMINAR VISCOSITY WITH CONSTANT LP ACROSS CAPILLARY TUBE
C
8
U
FIGURE 16
TUBE D 35% SOLVENT 5.3 PSIo TUBE C - 35% SOLVENT - 6.2 PSICl Uk3E C 20% SOLVENT - .1 PSI
W3E C - 5% SOLVENT 3.8 psie TUBE A - 5% SOLVENT - 9.6 PSI
LP WITHIN
10 15 20 25 35
REYNOLDS NUMBER IN 1INCH PIPE X
59
the Reynolds numboz- in the 1*-inch standard pipe which
carried the main flow. This figure shows that the viscos-itie8 measured by the capillary tubes are not affected bythe flow rate in the main system, and this factor, there-fore, need not be considered in the analysis of the datarepresented in Figures 14 and 15.
Other workers (51, p. 571; 30, p. 135) have observedthat apparent viscosity tended to rise with increasing
flow rate, indicating dilatant behavior. It was also ob-
served that the viscosity, as measured with tubes of dif-
ferent diameters, resulted in different values, generally
increasing with the diaraeter. This was most evident with
the more concentrated dispersions. This effect, which hasalso been noted by previous workers, has been named the
Sigaaeffect (15, p.-1074). Vand (57, p. 277) explains
this phenomenon by assuming slip at the tube wall.Figure 14 shows that, in the experiments with the
5% dispersion, tube A gave viscosities about 7% below those
obtained with tubes B and C. }iowever, no significant dif-ference can be observed between tubes B and C. It can beseen that the viscosity data begin to scatter somewhatabove a tube Reynolds number of 1200, probably because of
incipient turbulence brought about by vibrations in theflow system. This was also noted with the 20% dispersion.
easurements made on the solvent showed a slight
60
Tube A-i measured low viscosities with the 20% dis-.
persion, giving values about 15% below Curve I, which
represents quite well the data for tubes ]3, C, and D.
Data for tube B lie somewhat higher than Curve I, This
could be due to agglomeration of the solvent particles
and a resulting plugging effect, It was observed that dis
charge from tube B was somewhat erratic, indicating the
possible presence of slugs of solvent and water. This
plugging effect may occur within a certain range of diam-
eter and length for each concentration. It was observed
for the higher concentrations that viscosity measurementswere impossible with the smaller diameter tubes.
The 35% dispersion showed the first really signifi-cant change of viscosity with tube diameter, The values
for tube E were 12% above those for tube D, and those for
tube D were 5% higher than those for tube C. Tube B again
showed some viscosities, which may c been the to a
plugging effect.
The effect of capillary tube diameter on the measuredviscosity was also apparent with the 50% dispersion. Tube
E gave results about 10% above tube D, while tube D gave
values 5% above tube C. No results were obtained for tubeB.
61
increase of viscosity with flow rate, as measured with
tubes A and C, while tube E gave a fairly constant value.
At the lower Reynolds numbers deviations in measurements
were about 10%, and at the higher Reynolds numbers the
deviations were about C from the straight line shown in
Figure 15. Since tube A gave consistent results when used
to measure the viscosity of water, the discrepancy was in-
explicable, However, Lindgron (30, p. 135) and Reynolds
(44, p. 84) noted that at times the viscosity of pure wat-er increased linearly with flow rate.
The pressure gage was recalibrated (see Appendix E)
to determine whether an error in pressures read could bethe reason for the rise in the calculated viscosity.Although a slight change in calibration was noted, theerror was not significant in explaining the result.
It was decided that the sigma effect may have been
due to other effects besides slip at the capillary wall,
The fact that the tubes were horizontal led to the con-
clusion that a "settling" effect could give apparently
erroneous results. The settling refers to a two-phaseseparation in flow. Therefore, runs were made with thetubes , C-i, C-2, D and E in a vertical position on the
20 and 50% dispersions. Figure 14 shows no significant
change in data under this condition. However, FIgure 15
shows that there is a definite change in viscosity values
62
for a particular tube, in general, greater values beingobtained in the vertical than in the horizontal positions,The difference in apparent viscosity, as measured by theindividual tubes, remained proportionately the same dis-tance apart. This could be explained by a settling effect.
In horizontal flow, settling would cause layers of solvent
and water to form adjacent to the upper and lower portionsof the tube, respectively. The measured viscosity wouldthen be lower than if no settling had occurred.
These data also indicate that the sigma effect was
not caused by settling, It actually might be du to slipat the wall, as theorized by previous workers (60, p. 600).8ifficient data was not obtained in the present experiment
to corroborate this theory.The laminar flow results on dispersions show a slight
increase in viscosity as flow through the tube increases.This indicates that the dispersion is non-Newtonian a.nd is
slightly djlatant in laminar flow. Metzner and Reed (37,
p. 434) defined a characteristic quantity n', which is ameasure of the deviation of a fluid from Newtonian charac-teristjcs, The quantity n' is defined as follows:
(29)
Wier e
V is the volurftetric flow rate, ft.'/sec.If a plot of lo (D)(P)/(4)(L) versus
log (8)(V)/(Tr)(D)3 is a straic line, n' is constaand the fluid oheys the power law as expressed
When n' the fi'i±d 1 wtoniar; when ii' is lessthan 1, the fluid is pcoudoplestic; hon n' is greaterthan 1, the fluid is dilatar
Fiqure 1? i a loç-loq plot of (A.P)(D)/(4)(L) ver-sus (8)(V)/(7fl(D) for tuh'o !, 5 dispersIon, tu.Le D,
3S dispersion, and tuhes C-i and C-P, 5C dispersion,Lin*s having a elope of 1. [.7 iay he drawn through each tof data. These irciicate that, under laainar flow cortdtions, the dispersions are .±ht1 dilatant and the valueof n' is contan for all concentrations of solvent up to5, These resui.s also verify Figures 14 and 15.
It is siqnificar;t iLt S experiient verifies thework of other e eriienterz with solid-liquid dispersions.While the data here is not sufficient in itself definitelyto conclude this verification, it does sen. apparent thatthe equaticns and theories derived for the solid-liquiddispersion 1old for lqui-liquid dispersions.
1.0
4__' (.I'J.
0.11.0
TUBE C-i, 50% DISPERGI0Io L'uBE C-2, 50% DISPERSION
TUBE D, 35% DISPIRSION° TUBE B, 5% DISPERSION
5.0(8)(V) ,
(7T)(D3) SEC
FIGURE 17SHEAR STRESS AT CAPILLARY WALL
VERSUS RECIPROCAL SECOIDS
6i-
Turbulent Flow Viscosity
The turbulent flow viscosities were measured by means
of pressure drop data over a 6-foot, horizontal, 7/8-inch
O.D. copper tube. The values were calculated by determin-
ing the friction factors in the test section and by substi-
tuting the values into Nikuradse's equation (Equation 4)
for smooth tubes. As explained earlier, all data were
plotted according to Figure 13 and the viscosities cal-
culated from Equation (4).
Figure 18 shows the calculated viscosities as a func-tion of ftow rate for the various dispersion compositionsand pure components. The solid lines represent the valuesobtained from the present work; the dashed lines representthe values obtained by Wright (62) during heat transfercoefficient measurements. For a Newtonian fluid the plot
of 1/ f versus the log W f should have a slope of 4.0 if
Nikuradse's equation holds. In Figure 13 the line forwater, which was calculated from Equation (28), agrees well
with the experimental data for water. The line for pure
solvent is a least squares line with a slope of 4.0. The
viscosity of 1.05 centipoises for solvent at this tempera-ture, shown by this line, agrees well with the value of
0.98 centipoises measured by Finnigan (17).
The dispersions reflected a definite dependence upon
65
10
o CALCULATED-0M REFERENCE (62)
20% S0LVEITS
5 SVT
50% SOLVENT
SOLVENT
WATER
0.0 1.0 2.0 3.0W, LBm/SEC
FIGURE 18. TURBULENT FLOW VI3COSITIES AS A FONCTION OF FLOW RATE
67
flow rate, with the apparent viscosities decreasing with
increasing flow rate. This behavior is typical of pseudo-
plastic materials. The majority of suspensions tested by
other workers, although mostly solid-liquid in nature, ex-
hibited this sam.e pseudoplastic behavior. Finnigan (17)
found that the same system investigated here exhibited
dilatant characteristics under turbulent flow. However,
since Finnigan's measurements were aade with a vertical
test section, a settling effect in horizontal flow may ex-plain the difference.
it is possible that the phases separated, because the
dIpersion flowed horizontally. McDowell and Usher (35,
p. 574) suggest that this type of separation could account
for pseudoplastic behavior. Conglamoration of globules
also tends to decrease the apparent viscosity. Another
theory (60, p. 595) is that the discrete particles tend to
align their major axes to the direction of flow, thus caus-
ing the viscosity to decrease to a limiting value.
The values obtained in this experi3lent then agree with
the majority of observations rtade by other workers on sus-
pensions. This again would lead to the conclusion thatliquid-liquid dispersions do behave in a similar fashion tosolid-liquid dispersions.
upirical equations were developed to describe how the
viscosity changes with concentration of the dispersed phase
at flow rates of 1.5, 2.5, and 3.0 Ibm/sec. These equa-
tiona were derived by a least squares method, assuming
the form of Equation (6)
1+2.50 + cz52
+
The results are:
(31)
for a flow of 1.5 ibm/s
($2)
= 1+2.50 - 10.7302 + 60.920
2 + 46.36çl+2.5qi 12
for a flow rate of 2.5 ibm/sec, and
1+2.5 - 11.20
for a flow rate of 2.5 ibm/sec.
The data for the individual flow rates have an aver-
age deviation from Equation (31) within ±8, from Equation
($2) within 2.5%, and from Equation (33) within 8%. For
convenience these equations were averaged to give one equa-
tion applicable for all flow rates within art average devia-
tion Of 9.5%.
(34)in C
l2.5cb - Ii.OiØ2 + 52.620
Equation (34), a form of the Einstein equation, reduces to
it at low concentrations.
68
Ftgure 19 shows the quantity,/J/J/ plotted versusthe dispersed phase concentration for the equations de-rived by several workers, It also shows the viscositiescalculated in the present experinent and their relationto the equations presented. Equation (34) and the equa-
tions of Vand and Ioscoe show rdatively good agreeientwith the experimental data, Other equations shc'ti wide
deviations at the higher concentrations.
Photoelectric Emulsion Evaluator
The evaluator was inserted in the vertical 1+-inchbrass pipe perpendicularly to the flow. Two types of
measurements were nade: variation of light transmittancewith time of mixing and variation of light transmittedwith flow rate, once the dispersion was formed, The probes
were 1/8-inch apart for the majority of the runs. One set
of data points was obtained, with the probes 1/20-inchapart.
Figure 20 shows how the percent of light transmit-ted varied with the length of mixing time for the disper-sions. The percent of light transmitted refers to theamount of light received iDy the photocell probe compared to
the 6mount of light transmitted through clear water. The
:9
8
7
3
2
1
A - EIIERS EQUATIONB VAliD EQUATIONC - 2 1+2.5Ø_11.0].252.62Ø3D - ROSCOE EQUATIONE FINNIGAN EQUATIONF - EINSTEIN EQUATION
c W 1.5 LBm/SEC0 W 2.5 LBm/SEC
W 3.0 LBm/SEC
70
0,0 0.1 0.2 0.3 0.ls 0.5VOLUME FRACTION SOLVENT
FIGURE 19PLOT OF VAJIOTJS DISPEBSION EQUATIONS
20 00 0 o 0 0
20 +O 60 80 100 120
TINE OF MIXING, SECONDS
100
FIGURE 20AMOUNT OF LIGHT TRANSMITT) AS
80 A FUNCTION OF MIXING TINE
0 % SOLVENT
60 20% SOLVENT
o3% SOLVENT
0% SOLVENT
72
percent tranamittancy dropped almost immediately with mix-
ing time to a constant value, indicating the rapidity offormation of the dispersions. The dispersions were charac-
terized by an opaque, milk-white appearance, The data
show the apparent consistency of the dispersions at a par-
ticular flow rate.Figure 21 gives the relation of light transmitted to
flow rate past the sensing probes, There seems to be a
light tendency for the percent transmittancy to drop with
flow rate for the 2O7, dispersion at a separation of 1/20-
inch, which is not apparent at the 1/8-inch separation.
However, with accuracy of the evaluator being ±1%, there
is no conclusive proof that this effect is true.The percentage of light transmitted, in general, de-
creased with increased concentration of the dispersedphase. The 35 and 50 dispersions gave approximately the
same values, indicating that there is a point where the
amount of light picked up by the photocell tube is inde-
pendent of concentration, This conclusion may be inac-
curate, because, as the concentration increases, there is
a secondary scattering of the light lost at lower concen-
trations. This light may then be picked up by the photo-
cell tube.
It was hoped that the evaluator would give a definite
trend for the amount of light transmitted with flow rate to
100
35 0 0 0 0
WATER AND SOLVENT5% SOLVENT 1/8-INCH SEPARATION20% SOLVEN', 1/20-INcH SEPARATION20% SOLVENT, 1/INCH SEPARATION35% SOLVENT, 1/3-I1IcH SEPARATION50% SOLVENT, 1/8-INcH SEPARATION
n no n
S.
I
1.0W,L
U /3EC
FIGURE 21EFFECT OF PlOW RATE ON AMOUNT OF LIGHT TRANSMITTED
2.0 3.0
30
H
0
15 0.0
74
show how the particle size varied. It was expected thatif the particles become smaller, leading to an increase ofinterfacial area, the amount of light refracted would in-crease with the overall result of a drop in amount of lighttransmitted. If this phenomena occurred, its effect wasprobably too small to be detected by the photoelectricevaluat
CHJWER 7
CONCLUSIONS
A study has been made of the laminar and turbulentviscosities of an unstable liquid-liquid dispersion corn-po5ed of a petroleum solvent and water.
Iminar flow viscosities, measured by means of a nura-ber of capillary tubes, varied with tube diameter, tubelength, and flow rate. The variation with tube diameter,known as the siama effect, may be caused by slip at thewall, It was shown that it was riot caused by a settlingeffect, This sigma effect was more evident at higher con-centrations, where higher viscosities were measured withtubes of larger diameter. The results are in agreementwith results on solid-liquid nulsions. It is evidentthat the capillary tube method is not suitable for deter-mining dynamic laminar viscosities of these dispersions,
In laminar flow the dispersions behaved in a dilatant
manner, with the viscosity increasing slightly with flow
rate through the capillary.Viscosities measured in turbulent flow indicate that
the dispersions behave in a pseudoplastic manner underthese conditions, with viscosity decreasing to a limiting
value as flow increases. Behavior of this system was found
to be similar to that of many solid-liquid suspensions, and
76
it appears that similar equations are applicable to both.The equation of Vand (Equation 9) and Roscoe (Equa-
tion 14) for predicting the viscosity of suspensions agreereasonably well with the present results. In addition, an"pirical equation which reduces to Einstein's equation at
low concentrations was derived from the data. This may
be used for predicting virosities of the syst studied.
(34) l+2.5çb -ii.oiØ 2 +52.62Ø
Studies with an emulsion evaluator showed that thedispersions formed very rapidly after mixing began. The
percent light transmitted through the dispersion was afunction of concentration up to 3$/ solvent, after whichthe percent transmittancy remained constant, probablybecause of secondary refraction. It was impossible to de-tect any variation of light transmittancy with flow ratepast the light probes.
CHAPTER 8
RECO'1ENDATIONS FOR FURTHER WOIC
The investigation which has been reported in thisthesis has developed the groundwork for furtber study ofliquid-liquid dispersions. Several suggestions for fut-ire experiments are:
1) Determine the effect of length of capillaryo visconieters with constant diameters in the measure-
mont of laminar flow viscosities of the same and other
liquid-liquid dispersions.
Devise a method to measure the viscosity of
similar systems flowing in the transition range betweenlaminar and turbulent flow
Extend the range of turbulent Reynolds numbers
for the present dispersion by employing a larger pumpingsystem.
Use a. photographic technique in conjunction
with the photoelectric emulsion evaluator to measure the
exact size of the dispersion particles.
Determine whether the amount of light transmit-ted through the dispersion related i the time of mixingcan define the concentration of the dispersed phase atsmall increments of the concentration.
Repeat the present work, revising the dispersion
syzten by adding a stai1izinc aç-en to deteriine theeffect of staJiIity on the phica1 propertiea.
78
2. Bec}ir,Ne York
12. EirsteirBeSt In3+: 591-
GiL PT,I 9
A1VeS, Ge . F:ic.>w of flOfl :'..OfliT :;T'siors.Ch:ic: ::or1rig 56:1O7-9. 19+9.
mi1s1ons: theory .rctico,31tih:1d 1957. 3I.2p,
BrouL:hton, C, nd I u1res.in-tcr cusicLs, JournI+2:253-63. 1938,
Br'r, G, G Unit Urticns,6ilo.
Duclaux, J. .0 L.28:i1.i6, 1932,
D, Ellers, II, Yiskositttofrc 1s tor ccr
Zeit schriftE1flStOj!: LS1ore
inc nc.der
. erieder jO1C1911.
Chirig, P, Y. 11. .. Sch- chi,vs.lidity of the ::instein vLscoslaw of sei ticn. Journ Ii6:193a. 1955,
Dc 13r.:Lin, k. .spenslofls rndl6: 220-22. 19+%.
(I zi icit Q ae Ispheres i: - Ch.1+8563_3. 1951,
Dro, T. 13. nd J. W.Vol. I. c- ic ross,19t..
++8p.
or therd Stole's
iYEr $cience
Nature
ic viscosity of oi1ic1 (7; stry
T. Isor
1955.
Ioopes, Jr. dvar.ccs in chc'j.
Journrl Dc Chile 4'ysique
79
cJ.e1u1dimen-(36. 3904.
ZU ojner .r :it ine neueic'nsionen, .in. 1c dcx' rhyik
16. Eveson, G. F., S.C1E5:jc; colloids T'Psittf1, cc;Ls, TISESNo.11 :1L
18. Rappel,Journ1
19. Hatchc.phase1913,
irich, F. ,N. l3unzl cnd ii. rrcth2, KoiloidZejtschrjft 7:276. 1936,
Tlscnsc.i1tz, F, Die Vicott VonIticcit r Tc1sben uno 1 rReuibrutn:. Zeitechrit furChoi.je J15;P:73-9o, 1931,EVSOn , &. F. , . L , Whitmorecoaxie1cv1i(Cr vi sc.rtors and c:;ijT :oo-tube
meters for sospns:.or;s, mture i6:
1951.
The nern1 ieor:;, irnö'y Society
20. Hatschek, I, Die Visc'sit'at vonSuspen sionen. KoiioiJ Zeitscbri
21, Hu1ns, i, L, The v1scosiylonE-oh omn molecules. Jourr :1+2:9i, 1938.
, L. Whjtorj.o ditribu;i.n:
ou viscosity incicty Jiscssions
3. J. J2rc.ssu c' 1 Tsses anc. hoot tsffor i' fo o - tt 1c.E' liuuic incirculc: tubcs, (.:ro'' Stote C11c o, CcrvIlis,Oco t is, c 1 ir , Dcç. 1958.15'- numb. 1ves.
J. Viscosity of susp:nsions of uniform spheres.of App11c hysics 28:12fl92, Nov.,1957.
of vIscosity of two-r.ict1ons 9:8O-92,
onsior. est t.n durchilsehe
erehen-.163-5. 1920.
T.o!1.te soltions of1hysicv1 Chemistry
22. Joshi, S. F. Viscosity of reversjblc? cnuisons,Faradcy Society Tronnctiors. 20:512. 192+.
Knudsen, J, G, ar:cl D. L, itz, r101CHCEt Trensfer, 1F ork .cC:rn-i1].
214. Krieb1.e, J. G. . C. :..tye11, The vi:cosity ofN tcP oj- st c, C d 1te t J i iTeti1e Fosenroh Jourrid 19:253-.258. i.ay 191+9.
80
Use of
1950.
I.
nd576p,
26. }ync., . F. :C efiective vi SCOS.T of H.ms:.orj.sof 3 ' ic I 'tcle, xrofe I , rof 1. eiety(London). ..237:90-116, 1956,
27 Langloise, G rid S. F, Gui1h:r..' 2etc.. Lonof :utcrftc] 1 r in nst -. :ti riis1Ofl. cv1(w of cientiic 1. ts25:360-63, 1951+.
28, Levitori, A. and A. Leighton, Viscosity relatonshipsIi 2s,r s contin ilk ft. Journd of hysic1Chsistrv 1+0:71-80. i)3(.
29. tI. K., L. Squir .::.d . 1, Lo.;on. CoiiiJ1propertiss of ciiy n.icrs, Lrnsctior1s of the
inj.rc r r' r ic] r i rs ll+:38-52.1935.
Irdrcn, F. B. The trnItion cr:css .nd other'Orci Pifl jfl V]5C0L5 iOW, irki fr Fysih 12:1-169.rr7
Knitz , F, .nbtween icos
ourr. 1 .f (:,C.rr.t
31. 1an1ey, H. St. 3. an S. 0.suspensions of rher.s: A1ntcractior eocfLcinrts.ChemIstry 32:763-7. 19
.;sor The v2cosity of'L Le LcLe
( :i: i :rr1 of
32. Mardles, F. , 3, The viscosit of s. ons Inr rnaquc s t iIds, r tctions36:1007-17, 191+0,
81ii1 for the relati
;tt.ons rijd Vc1ue of sioute,y..o1o:y 9:715-25. 1926.
Wbjt3....or The offect andL( . itv ,oui of
102, 1956.
3, 0, ::njth. ynjt o::.tion ofcrk, . c1r...-Fii1, I
3%. NoDovci..1, 0, 1, >r d F, L, Ushr, Viscosity and ridigityir susr.r of fine ps.tic.L: s II on-&ricousSUf; nsions, Roynl 3ociet.- of Lorc.'or: PrccecdingA131: 561+-7, 131,Jerril..., , F, hasis In the vIsc ctry ofnon:Ieutoujn f1nic.s, ISA JoirnE1 2:1+625, 1955,
37, Ietzner, A, B, and J, C, F1c* of non-Neton1.n fiuid-cori' . th 1. .ninr, trans-ition , rd turbu1t-.iII. ro.;:ors, ..eric; nIr'3tiL to of C ic 1 1 ers Journd 1:31+1+O,1955.
iller, . . and C. A, ann. .itrtio of two-phase syst.s of :. .isc!be liçiAcis, ;:ricnInstitue of ChesricrJ...........incers iTWSCtjLfl51+Q:709-.'+5. ic;:
Nara;nasry, B. N, and h, .tscn. Petrol-watera, Journ] of t Ti IsLtute of
8cience 17A(vi):75-81, 1931+,
1+0. ClIver, 1), B. and S. G, ard, Relati.onohlp bet'ieenr.ive visco ty and voLr:i conccrrtion of stai.1esus:enions of s oricol prtcies, rture 171:396-7.1953.
1+i. Cincy, B, B, and 0, , Cn1son. I-o.?r and absorption.1crs; 001'). e Iti I I c ' - s os andfluid propertias, . jcr. in rir.g roress
1+3:1+73_80. l9+7,Orr, C Jr. C, h1ocer, The viscosity ofsi is a ercs, o r- I rf o1loicJ Science1O2'-3, 1955.
1+3.. Pcrry, J. H, CeL.led h.:tineers' T.h.....1co': 3rd. Nd.Ne York, NcQra-Ai1J.
144, Reynolds, 0.35:81+. 1383,
1+5, Riohrc.scn, ;. C, Jber die Vishasitt von Emulsionen,lolloid eitschrift 65:32-7.1+6, Richardson, T. C
8367-..73. 1953.
191+2p,
ournai of Colloidal Science,
147, Robinson, J. B, Studias of Lho 1.isccsity o1 coiloids,I, Tc anor, bus vi:rcosity o1 dilute nr.uns oftric prticbos. L Lccity of ToncoriProcecdi's A170:519-50, 1939.Boiler, 2, s. and C. K, toddard, ViscosIty and riIdityof structur J s o i- a, Journel of hy&ILl C1 iistry1+8:1+10-25, 191+1+,
82
I 1 r. rety ceedings,
Sechs, D.
Sherru:tThe infei;tJ. s: C;nindustry,
52. Sherizn, - ie inflicuce of irtr:on cty of CoiCrc ter-r-(11 S1oDs,Koi:c.;la-zejtschrjft ia :6-n. 1955.
53, Slbreo, J, 0, e vi.eosity of o:uJ.sions, Part 1.Farady Society 26:26-36, 1930,
5tt, Tailor, C. I. The vi:cosit,r of a fluid contirirdrops of nothcr fi 1 Lcciety of I nConProceedings A138:'-i-.. 1932.in(:,, !, P. and . , .. ue..bers, The V1SCOni
SU$pO$iOflS of srheric;1 oth :r idiçripaitc±' In ii rc in0tit to of flF icslEngineers Journal 3:111-16, 1957,Treyi;l, R. E, iu -iin:nsfer (;prtions, New York,NcUraw-niii, l95, 400p,
Vand, V. Viscosity of soitions and nsa.ons, Journalof Physical CherIstry 52:277-99/ l9+,Verre1en, T. , C., , 'Il1ins, nd C 1g1ois.r I 1i,id-1i i s-lj idagita.;ion. Ce.n.jca]. .......: .ncerinLnrcfress 51 :85F-9+F,1955,
lIoscoe, R, The viscosity of susuc:spheres. British Tournoi of AJ.i3267-9. 1952.
Ward, S. G, and R. 1.. Jhitnoro, ritish Journal ofApplied Physics 1:284-90, 1950,Iikinson, . 1., Ton-:cwtcnian flow.
Cheimist 33:595-600, 1957.
61. WIlkinson, W. L Non-:;ewtoriian flow,Ccn1st 31:79_81+, 195I.62, rigt, C. H, Pres.L1rc dr
liculd dimersirs In tui'M.S. c.-!s, Is (ir120 flU!, len:VE:S,
Journal Do ChirniePhysicue 29:280-6, 1932.$tudles In :nter-in-oil o: u1.Loi., I,
co cf Tjs;ersod i:.hase Cu ocuntr; ticn oncc :ity, J ou.rn.u1 Of th Jociety of Thez:±c:o, 2, 69:571-5. 1950.
83s of ridgidyui Cs
nha o. Vicosj
Iud:strial
Industrial
s: a
( Ont tra:nsfcr for 1iuiiLi; in a circular tube,State 0cge, 1957.
6o.
APPENDIX A
NOMENClATURE
It in Letter SymbolsSymbol Meaning Units
A Area ft2A Intorfacial area per unit volume ft1a Constant in viscosity equationsB Ratio of refractive indicesb Constant in viscosity equationsD Diaiueter of tubes or pipe ftF Force lbf
f Fanning friction factorG Mass flow rate g
Sec
Mass velocity lb
(sec)(ft)2g Gravitational acceleration ft
secCcnversion constant, 32.17 (ibm) (ft)
(lbq) (sec)Ii Volume factor
I Light intensity lumens
Coefficient of consistency cp
Einstein constant, 2.5L Length of tubes and test section ftN Volume fraction in mixture
r Capillary tube radius ft
Meaning
t Temperature
u Velocity
V Volume
W Mass flow rate
Greek Letter Smbo1s
Finite differenceTime
,IJ Viscosity
,LJa Apparent viscosity
Continuous phase viscosity
d Dispersed phase viscosity
Limiting viscosity7T Constant, 3.1416
p Density
SiTear force per unit area
Volume fraction of dispersed phase
Interaction constant in viscosityeq.iat ion
Composite Symbols
BWG Birmingham wire gage
gallons per minutein Logarithm (base e)
log Common logarithm (base 10)
O.D. Outside diameter of copper pipe
f
sec
cp
cp
op
op
C
lb
85
Units
ymbol Meaning Un:
Re Reyiolds number
wt Sample weight
Pressure drop across test section
LPf Pressure drop due to fluidfrict ion
Subscripts
g
lbfft2
Apparent
C Continuous phase
Dispersed phase
Force (as in lbf) or friction (as in Pf)
Medium or mass (as in ibm)
o InitialSolvent
Tube wail
Water
Limiting value
86
APPENDIX B
PROPERTIES OF FLUIDS AND INSTRUMENT CALCULATIONS
Solvent and Water
The solvent used was a commercial cleaning solvent
anufactured by the SIteli Oil Company under the name of
"Shelisolv 360." The manufacturer's specifications are
given in Table 4. The fresh solvent, a clear, colorlessiqutd, was used whenever possible. Although recovered
olvertt took on a yellowish tint, probably because of
impurities, it rained clear. Determinations made by
Pinnigan (17) indicated that used solvent viscositydiffered from that of the fresh solvent by less than
Tabi
Flash Tag, O.C, °F 110
Flash Tag, CC., °F 103
Aromatics, Stoddard, 2
Manufacturer's S.ecifications for Shel1solv 360
API Gravity, 60°F 49.1
Specific Gravity, 60/60°F 0.7835
Color, Saybolt 26+
(35)
Table 4 (Continued)
AS Distillation9 °F:Initial Boiling Point 304
Final boiling Point 362
10% Recovered 317
50% Recovered 323
90% Recovered 342
% Recovered 98.5
The solubility of the petroleum in water was quitelow. It is apparent that the solvent-water systern usedin this investigation represents a very immiscible pairof liquids.
The densities of solvent as a function of temperaturewere measured by Finnigan (17) and presented on Fiqure 22.
The density of water at various temperatures, obtainedfrom Perry (43, p. 175), are also included. The viscosityof the solvent at various temperatures was alsc determined
by Finnigan and reported along with the viscosity of water,fend in Perry (p. 374) on Fiqure 23.
The density of immiscible liquids mixed together ±aan additive quality. Therefore, the density was calculatedfrom the mixture law
88
62.+
62 3
62 2
fJ
f9.f
89
WATER
SOLVENT
t I I I L L
60 70
t, O
I ibm/ft3FIGIYRE 22
DENSITY OF WATER AN]) SOLVENT VERSUS TEMPEPLATTJRE
H
9.0
8.o
7.0
6.050
I I I I I I.1
1 L
60 70t, °F-" in lbm/(tt)(sec)
FIGURE 23VISCOSITY OF SOLVENT AD WATER VERSUS TPERATURE
90
where
N5 is the voluue fraction of water and
is the vo1uiie fraction of solvent in the dispersion.
Eqi ipment
The characteristics of tL.e turbine pump as describedby the manufacturer are presen Led j :Ta,10 5.
Table 5
me Pum. Charac
Delivered Flow, gp
10
40
iaterial fTonzeodel Nuzber LJ615
Speed 1750 rpm
42C25011010
Total Head, feet ofWater at 80°F
91
The pressure gage used to determine the pressure drop
across the capillary tubes was calibrated against a mter-
cury open leg uanoneter at the heginnin, and end of the ex-
perlinent. Figure 24 shows the original calibration (heavy
line), and the rocalibration curve (dashed line). The two
calibrations were within 6 at the low pressures and 1% at
the high pressures. Since it is unknown where this devi-
ation in calibration occurred, the old calibration valueswere used in all calculations,
Cl)
r-I
OLD CALIBRATIONNE CALIBRATION
AC2JL PE1JE, PSIFIGTJRE 24
PRESSURE GAGE G LIBAiON CURVE
92
0 8 12 16
APPENDIX C
TABULATED DATA
The run number code Is as follows: The first number
or symbol represents the nominal composition and the second
number represent the run number within the series. Thus,
9
35-L is the fourth run with 35% solvent in water, ect.
OBSERVED DATA
(1) (2) (3) () (5) (6)Run No. t, °F Capillary Capillary Pressure Light
tubePosition
tubeNo.
ga ge, p si Intensity,
5-i 69.9 Horizontal. A - -23 71.0 It A 9.L0
69.7 A 9.755 70.0 A 10.006
7
68.669.3 It
AA
9.9510.05
8 70.3 1 A 10.009 70..5 A 9.9510 70,5 A1112
70.770.7
II
T1
AA
6.758.00
131).
70.570.6
?1
1IAA
8.6510.20
15 '70.6 IT A16 70.9 ft
B 8.201718
1920212223
70.670.670Jj70.670J7Q570.5
I,
II
'I
1!
'IIt
II
BBBBBBTi
8.506.655.005.607.506.25
2fl2526
7r770.6
70.3
I,
If
1I
BB
13
5.556.656.65
27 TI B 6.6528 ?0.6 I' B 6.65
(10) 914Test SectionManometer, mm
142 (Hg)
814 (Cc114)66 "52206 II
14.6367 (Hg)10757 8
7)4 II
7679 II
79 TI
78 "147 (CC114)237214 (Hg)141
5985191231786250
N71 (Cc114)27 (Hg)36 II
53 II
26 '
28 '
27 U
157 ( CC U )1420 "
14J4 (Hg)65 "
148 (Cd14)379 Il
)Q (Hg)
(1)Run No.
(7)We! ghtCapillarytubeefflux, g
(8)Time ofefflux,sec
(9)OrificeManometer, mm
5-i 205.5 720 67 (Hg)2 -3 199.1 720 io14(cCl)14 186.0 660 86 IT
5 189.1 660 69 "6 165.7 660 IT2597 172.3 600 II632.8 1914.14
/ ro7 113 (Hg)9 171.6 600 193 "10 161.7 660 88 '11 1!4J.3 720 128 '12 166.t4 720 127 "
13 181.2 720 TI
it4. 196.14 660 133 "
15 201.3 600 131 II
16 205.8 00 53 (Cc114)17 165.0 2140 31518 129.9 2140 38 (Hg)1920
121.2163.5
300360
I,70It103
21 161.2 270 TI15822 153.5 300 TI3023 139.5 300 It19214 163.2 360 II
1414
25 1143.9 270 'I
135'2627 191.9
300360
I,101IT
7928 193.5 360 IT5'29 175.3 300 It5130 168.5' 360 ItSi31 1514.7 360 'I5132 300 91 (CC114)3333A
266.7263.2
21402140
38 (Hg)55' II
314 263.8 2140I!Si
35' 213.0 2140II
14036 267.5 210 II
37 269.6 2140IT
38 2142.2 2140 198( CC1L)39 265.2 2L0 572 "
140 218.2 2140 67 (Hg)141 257.5 J. 1 214 "
20-12
216. 223.5
2L0300
38 (0c114)1461
3 2614.14 300 66 (Hg
It
IT
1I
I,
(1) (2)29 70.630 70.631 70.632 70.733 70.533A 70.831L 70.b,35 70.836 70.937 70.538 70.'39 70.2140 70.1.141 70.Ii.
20-.170
3 70.714 70.5S 70.76 70.87 70.68 7o.9 70.610 70.611 70.212 70.613 70.5
70.815 70,816 70,61718 70.518A 70.219 70.320 70.L.21 70,522 70.723 70.72t 70.52 70.626 70.727 70.628 70.629 70.730 70.9
70.370.5
31 70.2314 70.J35 70.936 70.9
BBCCC
CCC
CCCC
C
CCCCC
CC
CCC
C
CCDDID
D0ID
A-IA-i
5) (6) 95
7.305.80S)4 : &
L.00
3.20L.90I . .053.503.953 30L ro.1
3.90 21.021.020.5
*-
5.145 --
3.50 21,07.00 -7.65 *9.10 -
8:95 :7.05 -
21.L,6.20 -0
2.j0 -3.00 -225 -2.652.50 -6.05 -
60
5.203.9
6.00
: g
7.356,10
20 -LS678C,
101112131 ).
151617
18A19202122232L252627282930313233
35
U/0i 1L2L3LL
L.61±7
505152-,-)
256. 2278.8261±. 7265.726L.2)5. 8206.5202.2196.923L.. S203 . 3201 1±
2070202.6158.72±1±.1L,I OL/.)219.5159.0193.3177.5289.9208.822. 2
293.7326.3255.1±32.0301.0287.14.160.5171L.5173.7127.5132.7132.14.
176.5196.12 1 . 2303.3281±. 8237.5265.7
21 . 7255.7239.7
2)40 99 (Hg)21±0 111 "300 55300 22 "2140 149i (Cc1L4.)300 501 "300 65 (Hg)51±0 55 (CC1,)L8o 232L.0L 000L0 63 (Hg)1±20 114.2 "
1431± (cc 114.)89 (Hg)
14.30 892L0 291 (ccl214.0 702 ",
21i0 366 "2L0 711 "2L0 506 "21±0 598 "214.0 3952)40 373150 393 "2L0 14.0521±0 391 lI
21±0 595 "180 585180 611. "180 597iSo 586180 591± "14.80 581±80 5931±20 566 "14.60 538 "360 555300 76 (Hg)300 129300 1714.300 208 "214.0 8821±0 122iSo i5L120 192 "120 239 "180 2±8 "130 LjLo (cc1120 312 "105 68 (Hg)90 iLLS U
68 (Hg)75 9
14.1
2014.25 (CC!;,)Li.22147 (Hg)55 (cc114..)225571 "244 (Hg)92 (Hg)381 (CC1L4.)61 (Hg)6126 2( CC 11±)5763214.
583U
114.352 "
3214.
31±7
35631±7LL9O" "1±714.
500 U
1±93LLSO "
::14.80
L85 I?
14.6714.3914.68
(Hg)U
107121±62 "8110011911±238385(CC1,.)
00(Hg)
98 "
(1) (7) (3) (9) (10) 96
* indicates photocell and light 1/20-Inch apart. All other'readings with photocell and light 1/8-Inch apart.6 70.5 Horizontal C 6.30 1.07 70.6 'F
C 5.)4.O iB.o89
70.370.3 F!
CC
7.055.35
17.518.0
10
1170.14
70Ji
1,
tlCF)
6.65L.90
18.518.512 70.5 'F
F) 5.90 18.513 70.6 F'
F) 6.55 1.01!4. 70.6 'F
F) 5.75 i8.o15 70.)4 'I
O 5.1.51617
70.LL70.2.
F,
'F0o
7.356.10
18.5lu.O
18 70.5 IFF) 6.25 iO.o
1920
70.570.5
F,
'FF)
05.355.00
18.518.0
21 70.8 F?
B 10.70 iB.o2223
70.970.9
F,
F'BB
11.2512.25
18.02L. 70.9 'F
B 12.852526
70.970.9
F,
PT
BB
11.5512.20
2728
70.870.6
F,
'FBF)
11.107.L5
2930
70J70JL
F,
'F
(1) (2 (3) (L) (5) (6
37 70.b F' A-i 9.253839
70.L70.9
F,
VerticalA-i 5.85
6.00 26.0*70.6 B 7.35 25. 5*
!Ll 70.5 PrB 0.70 25.0*L2 70.3 F!B 10.05 25.5*
)43tJ
70.570.6
'F
,,BC-2
11.103.95
25. 5*26.0*
L.6LL7
70.L70.370.3
F'
Fr
C-2C-2C-2
5.957.709.90
25.5*
L8L9
70.370.6
F,
'FC-2F)
12.502.60
25.0*25.5*
5051
70.870.8
F,
FrF)
3.80 26,0*25. 5*
525'3
70.670.5
F,
Ft
p ,.0010.05
25.5*25.0*
35-1 70J C 5.75 18.52 70.Lt
70.LF,
F1
C
C6.557.35
-16.5
570. L70.5
'F
I,C
C6.707.35
17.518.0
(1) (7) (9) (10)
35-1 217.8 300 398 (CC 365 (CC1)23
2.9 .276.5
300300
H
t166616 3
H627251.9
S 27L.8300300
UL2353 (Hg)
I,390L5 (Hg)
6 23L!.8 300 H66 'I537 200.3 300 Hci VI61e 261.5 300 'I91 'V739 196,7 300 H39 H71101112
2!8.1227.9278.7
300202L.0
H
tt
U
TV73I,L6IT5Li.
13 22W U VT58114
15267.5260.5 2LQ
I,L3Uhh
H69'I
L; .0
1617
261.0265.7
180210
58H
71i
I.,
if6229).7 20 U76 It63
19 256,0 2L.0 U70 'I592021
232.5161.9
2h0L8o
U73U
H65ftL2
22 156.0 L20 7 IT20232
175.8161.7
L 20360
I,
ULaIT38U37
25 120.9 300 HL2 TV3926 123.5 :300 ULJ 'V
27 116.3 300 UL2 -'C, U
28 352.5 21W 'I VT
2930
297.6333,0
i6o180
U137'1153
I,101TV111
31 333,9 130 U TI11332 369.9 172 'I12133 332.0 150 U187 'I1293L 359.1 150 H203 TI1 L035 297.9 120 H83 'I653637
367.0297.8
12090
H102ft113
Vt78Q 'V
38 332.7 90 'I125 ft9339 263J 90 ft98 VT75
2L6.3 90 H89 'I70195.8 90 U73 Vt5922.5 120 H
61L H52
50-i2
177.1209.L.
300303
325 (CC 1 L)ftL.56
L38 (cclL)57° 9
3 189.9 300 If686 815191.8 300 63 (Hg) 66 (Hg)
56
207.5232.9
300300
I,102It132
9LUS
7 201.9 2L0 'IiW 1228 199.5 2Lo H162 129
N r
\.) N
N N
N N
NO
J 0'
N 0
\O O
j-3
0'.
N
1111
11 I
IttItil
lIN
f\)
$-P
-I.-
i-.
i- '.D
'0
Oa'
J1--
-'i r
\i .-
0N
0 I-.
I- I.
-..
I.-I-
I-a
II-
S p
.__
p.I.-
.- I-
..f.
I.- I-
I-cx
CT
cO O
CJc
J\J1
0 J
\.fl\j
LJ1
Y 0
0
- -J
-J
-J -
J -J
--J
-J-J
- -
-J-I
-J
-J -
J-J
-J
- -J
-J
- -J
-J -
J-J
--J
-J -
-J -
- -
-J -
--J
-J-J
- -
-00
0000
0000
0000
OO
Q 0
0000
0000
0000
0000
00Q
O00
0000
0000
oo0'
NN
0 0
on()
n n
C)
C)
C)
0 C
) 00
C)
C C
)C
l Cl C
l Cl C
l Cl C
l Cl :
::3 0
0 0
--
- I-
.-.
I-.
-I-
- I-
.C
)0'O
".0J
rp-
Q..Q
co-i
CD
O*
YC
:--
- -
o'.o
(0X
)'O-J
0'0'
JThJ
- 0
O.
..
..
..
.I
IS
0')
G'J
J 0
N'D
0000
'-N
O c
'.DO
0 Q
iiO'0
O-J
0'f\
) N
-Jf-
-J 0
CD
0'0'
- C
Ofl
fO\J
Q 0
0T
JO\J
LO
0 0
O\j-
O\j-
O 0
x ro
O 0
\.Q 0
rr \J
0 0
0\jy
O-\
y
.0j.)
')L
i '\ji
.'-0
'O(J
\ .n:
:- L
J N
1111
1111
11 I
I
i 001) (7) (8) (9) (10)
9101112131L
151617
210.9228.2260.7265.L282.8125.7l)L9.9177.7198.8
2)402)4.0
255214.0
2L0300300300300
176193207224.2L0
836L666LL
(Hg) 1 L815616517217786677066
(Hg)ft
ft
ft
ft
t1
ft
ft
ft
1819202122232)4.
25262728
21)4.2196.2222. 5250.52145.7265.0238.9257.7238.9260.7222.9
300214.02)40
2)4.0210210180180150150120
633):.6096
135i)4.8158177108215228
"
'H
661.16)4
951251.321)4.1
1531651714.
179
H
ftifft
ft
ft
itft
ft
ft
ft
2930
29!L.523)4.6
180120
7589
It 7789
H
ft
31 298.8 120 iii tt 106 ft
32333)4.
36373839
14.1
LL
266.7291.7169 . L,
239 L198.0261.L259.2232.2252.8261.61)4.0.5172.5167.5200.1
9090
2)4.02L01801801501201201202)40214.0160iSo
1331)4.7
85123135181215214.6
2'7l2831171)4.5191229
"
"H
12313686
1161281581812014.
218231113133165192
It
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
itft
ft
L6
218.9201.722L.0
180150150
253280311 "
2062282)48
H
ft
ft
L.9 1L0.5 180 102 102 Ii
505152
235.62714.61L7.)4
i8o150180
168214.0
106
' 15120010 L
H
ftft
535)4.
55
197.5218.82L8.5
180iSo150
1L1188212
131163179
'7
ft
ft
5657.5859
232.2259.14221.8103.9
12012090
180
250285326122
202233259117
'Iifft
ft
101(1) (2) (3) (L) ( 6 )
39 71.0 Horizontal D 16.55L10 71.0 0Li 70.9 0 18.85t2 70.5 C-2 8.10IL3 70.5 C-2 9.95
70.LL ft C-2 12.8515 70.6 C-2 15.35I6 70.6 C-2 16.8017 70.7 H C-2 18.35L8 70.7 'I C-2 20.251t9 70.3 V8rtical 0 6.7050 70. 0 11.0051 70 . 1 15 5552 70.3 ft 0 6.8553 70.3 0 9.20
70. 3 ID 12. 2555 70.. ft 0 13.8556 7o.L ft 16.3557 70.6 0 13.3058 70.7 0 20.9059 70.8 C-2 7.8560 70.8 C-2 9.LLO61 70.9 C-2 11.6062 70.8 c-i 5.7063 70.6 C-i 6.756L 70.5 C-i 7.9065 70.6 " C--i 9.1066 70.7 ft C-i 9.7567 70.3 " C-i 10.9568 70.7 " 3.7069 70.5 L.L:.070 70.L. 6.1571 70.L E72 70.L " 9.2073 70. 3 " E 10. L07L. 70.Li. E 12.1575 70. 5 :E 1. 30
S-I 70.3 Vertical A 7.55 1002 70.3 A 6.35 1003 70 . A . 25 -
70.5 A 3.LLO 1005 70.6 " A 10.656 70.7 A 11.35 1007 70.7 A 13.30 -8 70.8 A 15.90 1009 70.9 I' A 18,55 -10 71.0 Horizontal A 12.00 10011 70.9 A 1i.77 -12 70.b. A 17.05 *13 70.3 A 8.90
1.02
S-i 71.9 (Hg) 26 (Hg)2 82.7 LLSO 51 I' 3L 'I
3 iih.31oL..9
5 131.3
L8 0L8oL8o
70
1 iL
Vt
'Ift
LLL.r
68
I,
II
Vt
6 139.7 LLL) 160 I? 90 'I
7 161.0 1480 260 'V ILl 'I
8 165.59 i6h.810 106.9
. 20360360
308359155
I''V
it
16218792
'Itt
'I
11 171.112 11.7.7
t8o360
190166
Vt
ft106 VI
U
13 1OL.9 L 80 83 'I 'I
1 LL 75. 2 flSc VtL. 1
'V
15 106.3 L0 l i1; 'V 71 II
16 1 23. 1 2J0 '76I' 50 Vt
17 1LO.0 2L02)L0
70205
I,
'V
'V
'I
29 90.820 115.3
2i0300
105103
'V
'V656L
'Ift
21 135.522 157.3 300
8769
(Hg)ft
565.6
(Hg)'I
2.3 i3L.8 371? 56 I'
2L 90.5.25 136.2
3001 20 28 ft 22
TV
Vt
26 113.0 120 It 30 It
30
27 92.028 109.929 150.5
120
)20
52151119
I',,
I,I'
38353972
I,
'I'I'I
3231 180.8
106.5L. 20LLBO
91139 ft
5831
'I'I
33 9 L. 6 600 I 'I I,
1) (7) (8) (9) (10)
6061 156.6
iSo180
155179
(Hg)ft
133156
(Hg)TI
62 lLtl.963 171.56t.. 202.265 229.566 206.2
180180180180150
911061231)41168
Vt
ft
ft
TV
ft
92205119132151
,'itI'fT
I1
67 230.3 150 165 VT
151I'
68 1L3.1 1 20 61 'V 66 It
69 170.270 21L3.2
120120
71 'tIT
7697
'Ift
71 2)i0.3 90 1It 120 'I
72 270.2 90 1'I I )I I'
73 30.3 90 I ft 1L5 I'
7L1.. 31L9,S 90 190 'I 165 I'
75 )i0l.3 90 223 'V 195 Vt
(3) () (5)
Horizontal A 6.35'I B
B 7.1.0U B
S6789101?12131i.15
.067.
70.770 7
I, BI, B
U BU BH C-2U 0-2U C-2U 0-2
706.607,65
.90
17.70
(6)103
A t .-tl.j.
A 6. L,O
A 9.5 100A 7,6E 100A 7,G5 100A 7.75 100
0.75 100A ..0J 100A 9.25 100A 6.95 100A 0.05 100A 9.05 100A 615 200A .9O 200A 9.60 100A ..20 100A 6,13 100
(1) (2)
s-lL 70.315 70.316 70.t.17 70.216 70.i19 70.20 70.321 70.b.22 70,32? 70.2)i.
?n.25 70.26 7..,.727 70..:28 70.,29 7t,730 70.L.31 70.?.32 70.233 70.0
W-1 72...'2 71..3 71
H JO
H
H
H
U
H
U
H
H
'IH
H
20-A
35-A
50-A
(11)L"ixing time, iiin
0.02.05.08.0
10.015.022.027.030.060.095.0
120.0160.0195.0
0.00.52.5
10.022.527.037.050.071.0
0.01.03.06.0
10.012.0
39.0L.8.o63.079.0
0.01.03.06.5
12.016.025.026.30.0141 .0147.057.06L.0
Light Intensity,%100.038.0
35.0:t!. 036.5
:g
36.036.037.0.35.03.531H S
100.033.022.021.522.022.022.022.021,0
100.029.022.01( .51 L). 513.5i3.513.518.518.513.513.5
100.0314.021.020.020.020.020.019.519.515.518.518.518.0
---
L.-)
j)J
) LJ
r., r
Ri r
i ri r
ir'i
ri
- '-i
- -
- -
'-. -
' )-
'-0 C
Y-.
3 C
Y-'j
1---
'-'-'
r)-
0 -
O O
)-.3
O\r
U)
r\)
0 C
3C
u c
t-a
s-ç-
Z i-
'J1
0:
.'-'
I-'
I- C
) C
) -
e--
- 0
'-'-
i--
I-' -
: 00
fj I-
a F
-'00
s-
i-. -
'*
..
.ru
I-00
000:
I::'
.,.
.4
.0
pp
II
.p
S-.
0I
4p
5
cY'\J
-r:-
-cr
'\n R
i 'Jj
JiO
ji
-C O
-jt)
F-
C)
CY
' 0 0
OJ
C)
Y'O
- 0"
U,) J"
'p
C)
F-)
n a"
- c'
cc'
0-' 0
-' C
Y' O
' 0-'
0-'
r\si
\J-
r\i
¼n\
ni O
-'-U
\i- -
-3
o'-a
-.
p.
Ip
pp
pp
p.
.p
00
Ip
con
0U
i0
Ui
Ri R
i 0i
U)
IC
)C
D 0
-R
i Ri U
i Ui
Ui U
i0
0\5
l> I-'
Ui
- co
O0
coO
QJU
QjU
) cc
::ucc
oUlo
Ui
0
Ri I
DR
iID
IDR
)'R
ir(
UiU
)fJ
F-'
ID f\
) f\i
$---
..) ID
-J
CY
0-' 0
-' (Y
'-'O
ID'-j
rr'J
Lfl
gi--
r o-
'-rL
IP
C)
c
'O -
ID R
i 00
(iID
0Q
U,
T0
C)
C)
C)
Ui
C)
I'-'
F-'
'I-
.' F
- I-
'F
-'F
-' F
-' F
- I-
' -F
-'F
-F
-F
-'-
1F
-'I-
' *1
I-I-
' I-'
I-'
Ip
p.
pp
.p
pp
p5
4p
4p
p5
SI
Pp
pp
p0
I'-'.
IDID
ID ID
-ID
ID ID
ID ID
IDID
0000
00
0-U
--a
CO
CD
I\.)
C 'f
\)O
\0U
i Oj-'
O-'.
O'.O
'0 Q
J ru
-'r\
J-c-
r\)
F-'
0-0 '-0
I-' C
).
'1
I-' F
-'F
-' F
-'F
-' I-
' F-'
- I-
'C
)D
ii.)
()F
-.C
Q\ji
c-0U
- fO
0-)
O--
j-
CT
'\ LD
1(Y
'.-
j-'
I-'S
.-'
0'1
's-tC'J C
)Oc;) ::G
N-czt
DcU
L(0!ON
-N-(0.:-
)-Q -9
frO'Lc\o cJifC
jO
t\C)S
\N
c-(0 --i ('JC
).-4 tc\ cr\) 'J c'-D
) -4o.(0 (0N-o(O
(0'-D z-'
N-U
'(O N
c'O .-
O N
N-'-C
) N-C
O-' C
- N- y'-D
Lf\.-tJU
\-.O ±
(0-L)-O
)-f\1f\ 0"D aa N
- a' rC
)0
C) U
\'0 -'0czJ-Lc\ N
-C) N
--4-9 0-4 1-41--4
1-4.--4
--4
-4 c(3s
CO
(3s CY
-'- C) -.(0'O
'-C) N
-'-C 0 N
N-
(J(0 .z 1.flcQ C
zN-C
\J N---.4
'-4 N N
-'--tf\-4 (0'.O
a'-:N-0 N
-4 N-(0 N
NN
'4) '-0 N'-O
(0 N-N
-t-N- -N
-N-N
-N-'O
N-'0--O
N-N
-N-O
'.cOcO
(0 a-CO
O-C
YC
O)-(0S
't'-0--D
N-N
-N-'O
C-.::) ,---.Q
..
SS
.S
SS
*0
SS
SS
SS
SS
SS
0-I .-4
-4-I -4 r-4
-4 ..-4.-4
,-4 ,-4 ,-4 ,-4 -4 .-4 ,-.4 .-4 .-44 0-i
4 .-.94
..4 o4 .._9 .9,.4 ,_.4 ,.4 ..4 ,9
4..4 _.4
4.-1 .-4
-1.-1 -I -4 .-4 .-i C
\.J ,-
o)-r\N-oo
(\J cr)a'a' Lr\ -0 C
- C-)J\ N
'.0\ N
C) C
O C
C) N
-)-c\CO
--0 '-0 0 --i '-C) (0 .d --' 0 0 C
O 0 0
0 - 0 C)
'- 0 CX
) 0 _d -1 '.o N r'(0 C
\J.
Sa
SS
SS
IS
II
II
*S
SS
S5
5I
05
IS
II
SS
SI
II
SI
çv\J v)C) C
C) C
U N
N N
tco1s\ C\J'.Q
N C
--N-0'-)-f\01s\0 C
\J(0 N-N
-CO
CO
N N
N N
N N
N N
N N
0-c\-tQC
O N
-C'JC
Oa'a'
-i C\J N
CO
N -i .-
'--i N.- N
CO
-IR
IR
Ii
f--i-$
-4-.9
-4'--4 '-1
-4-4
-4-1
'--1-4
-4 -4 CO
'-0 Cl' C
) N '0 (\ z-:j -I
-4
j-RI 0--N
-CU
'-0 N--f\I--sC
OC
X) R
I 0-.Q cy-a'tc\N
-.Q --ia'. N
o 0'Nr' a'N
-lroj-.--4a)CO
N---4 N
coO C
NO
(0l'N
---1 (7ç5'.lf\ N-C
ON
CO
Ct) a'N
--'-D (00 Q
)S\Q'.) a--C
) O-..tQ
C -I '--C
C) N
--i 0(0 N---- C
) -01OcO
tNcO
'0zjN 0
SS
05
00
05
SS
SS
IS
I.
I(0'C
J ULC
\-0 N-N
-N----0 -.0 N
--Q'.0 )-f\(----O
D N
-N-N
-s-U N
-N-N
-N-N
-r-N-'.O
-0 N-N
-'-Us-0 N
-N-'.0 N
-N--'0U
c0U\tO
tc\tr\N-
4'0-0 CO
N -1 (Q
a'0 JCtflJ\c0Q
0.zcOc0-
::c-i-s-D --4y'-C
cO--.D
-'0 N-s-O
s-C N
-'.O N
-s-Os!) N
N N
-(0'-f) N-R
i N-N
--N-c
CU
)s\a'CO
a'C-L
OU
fl 0-vO a--.00O
t-'D C
--C--C
-GC
i0:C
L)C
..:::cco_-
-i -'mu-
C) C
sJU'-i
SS
IS
IS
II
S*
SS
IS
SS
SS
SS
SI
SI
00
SS
IS
C) 0 '-
'' 0
C) C
)C
)0 C
) '- -4C)
-1 -4 0 0 C C
C) 0
C)C
) 0 C) 0 0 0 0 0 0 C
) C) 00 0
C) '--i
.-i N C
U .-i f-i N
CU
N
0N
-CO
CO
a'C)
CU
N-
N-C
O a'0
Na'
-4-
'--I 04 N N
N ('4 C
U ('4 C
U C
('si (0(0 o oC
O (0(0 C
o o
rk)
)
i__S
I.,S
I'._S
l-'
f\) N
) N
) N
) N
)'
'-.0
I-p-
'i_
-'-
I'-I-
I- l-
F-
I-' I
-l-
IS I-
Sf\j
Ui
0'G
O--
.) 0
JiU
i '-
i_-'-
0 C
ji'-0
'.0
'-0 '-
1) '.
C)
o4::-
U.)
I-. 0
-O-j:
:-N
) O
Ui-'
3 C
T'U
lS
55
5
Ji. (
.00
031:
--r:
-r\.)
'.0
Cr'
0 '.O
x--)
p,j
U' 0
Ir-
'D 0
ct o
D4.
0-U
i o-p
j '-
'.0 c
oN)
i--' r
N.)
\ii.
CoC
t\JU
.) C
T'
r'.-
ç0
a-'
'.0 '.
0-,)
ico
-i -
0
'-i-'
'-° U
U.
--'
ri-u
ru
ti\,
r'ru
r'N
) N
.) ft
,) N
) N
.) N
.) N
) f-
u N
) N
) ru
ru
ru r
uS
SS
S*
0S
S5
0S
SS
SS
-55
SS
-.S
S5
i__S
'4-0
'0'.f
-Ui '
- i-
000
0-0
'---,
,]--
cc'-0
OJC
O'.L
) C
o'.0
a'.C
) ct
c:c:
.-J
0'-.
)--.
)---
)--.
)---
.]-.J
0--.
cY-
Ui (
r'.-
C)
0'-)
Ui
0-)
Cr
-oco
r -'-
0pj
r'j-
-'-04
:r 0
-
I--S
\.0'
- 0)
Q 0
-0
0)-.
) '.0
Q C
j-.] -
0' 0
'r U
iU
i4t
nn.
'.-.
3 N
) U
i.0
-.)
U)
U' -
4 -
Ji.\J
.0-)
I-' (
LI-
'.0 N
) '-.
L)i-
i-' 0
" -
U'
'- 0
Ui 0
-) \-
fl '-.
0 '-0
\.n
'.1)
i_-s
s-
"J1,
p-i
(3' C
D i_
-' -
0) 0
"
U' \
)
N 4::-
0 C
D-.
)0
'.0 j-
i
p-S
I-. I
-j\4
Ui..
C-.
t--U
' it-
U'
-.C
TU
i_.
.j 4-
U' '
-C)
) O
'-O"J
i.---
-) C
) N
)-f.4
t0-.
]Ui-.
.]Ui C
ra'
o-0'
n.i-
'-0 c
o'.0
U-i.
---.
0 o
'-o C
r' '-
rU
'. C
ri(fi.
C)
(ii. 0
-
0U
i
'.__'
J '_
_) U
i U.)
U.)
Ui U
i Ui U
i ) j\
) 1\
) r'J
1.)
P3
-. -
-. I
-l-
P-s
'-0
CD
-.)
(3'
iiN
., D
-uiJ
WJl
I-.
'- 0
'-0 C
t-.)
0"
U.&
-Ui P
3 '-
0 '-.
0 C
t-)
0"Y
ijUi N
)o-
.ii4
-Ui r
'-
0U
i f\)
0
000
k- I-
jI.
I- N
) N
) N
) N
)-
*-I-
.ê-
i-..
I-. I
- i-
I-I-
t--
- I-
- -
- 00
0000
SS
SS
SS
0S
SS
SS
SS
SS
00
05
55
55
55
55
55
.S
S*
o)_-
3 0'
'.1)
I-.
P31
.Ct-
) 'N
) N
)0'
0 C
D-.
) 00
0000
0çr
Ui.ç
r-U
i rj 0
4:U
i r'j
nfU
i '--
-.3
LO-4
---.
)C
D-)
'- C
DO
04'
.O 0
0'.0
-4"N
)I-
U)-
-)'.O
P3U
i'D C
ON
)\fl
D"4
:-' N
4:'-'
---3
N)
CD
-) 0
OU
i 0'--
-'.0
Ui'-
ji
I-.
--3
-3
0'-
CT
'- 0'
- (3
' 0'-.
) 0"
CT
- C
T'-
CT
' (3"
(3-
CT
'-,)
CD
Co
Co
CO
-) -
3 --
.3-)
0'-)
-3
-3 -
3---
.) -
.3 -
4--)
-3 -
3 0"
--.]
-3 (
.0--
] -3
-3U
i. (3
'--.,)
'-C
)S
SS
SS
SS
SS
SS
S*
*S
Se
SS
SS
\) O
)L)
f-u
0'0-
)\f(
--,]
Ct'-
00
'-N)U
-CO
(3-'C
oL.,
-0-
3 cc
U.l\
5j(.
0o'-c
oo '-
-'-i 0
4r'j
CD
c)D
rJ--
i cy'
-co-
-I-
' '-0
f-u
CtU
i-J i
'--S
c.0
CD
CtN
)-ui
.rlr
co0j
io"c
yN)
00pj
.Ui O
Ui '
- C
D--
--3
0C
OO
"'- 0
C
N N
cy(\JN
-±o"-4
a-'-c\o
o3QJo
CO
cCi .0
cvcOj-trO
(jaD: c-.-i NIlf\ C
) S\N
-0 - coP
N ')0 o ç) c ') 0
-0
N-C
'C) O
-) N
- U' N
-NO
c)N
c-co co
D o _-
o N- 0
N C
\J C\J (\J C
\J.-
Ckj
- N (\J (\J cc0c0c0c
c\c0)f\1-4 N N
ccj- N C
U cj-- c-C
U N
co
.ztD .-i N
-N- N
('r\)fU
\cQ N
-C O
O O
'C0 'C
N-r\zJ-c\J 'C
U\') N
N (J'1J\Q
(\'C) C
O '00 r-c -
.S
SS
SS
SS
.
-.-
-N
CotO
OL
) C'J'C
a) C '-i 0
N-'C
Co0 JC
o- N- .'C
c0\J Ncy.-i
cOcO
cZ) 0 O
J'OC
o cy'j'J --d-c(ycO 0 N
-'-D.
..
..
..
..
.a
..
a.
.CJ
..
a.
.a
a.
..
..
.a
a*
.a
-DC
o CO
a C 0 - N
N lt0ttc
o' cy 0
-.- JO
N-C
o cC) '-0 N
-CO
0(0 (0N
-c3 C) N
cozkro a-' N N
-CO
0'_-4
4'_
-'-
._-I '_'_.4
._44 5-4
-4.-
-
- (0(0 N-'Lf"--C
O O
CC
) -zt N-cO
CO
zj-u Nç-
i1c\')'C
CU
cOC
O '-0 - Q
-1rcoO
co N-C
O '-0 C
U .-
:d-cO -zhj-
c0.0N
NC
oC C
;"0l(\N N
NS
\CN
-'_i N-N
-U'co--a C
;C0 N
--d--N
-CU
N N
-ZO
J CX
\c- N O
'N-(O
C\JC
)S
0S
SS
.a
..
SS
SS
SS
SS
Sa
SS
SS
SS
SS
SC
cN
-'C N
-N-'C
D'C
0G'G
0Q cC
)) N-N
-N-N
-N-'C
cOC
oCO
cococ0a;)c) N-N
-N-N
-N-030D
N-N
-N-N
-'CG
D N
-N-aO
cC)
N-
--4
CT
'0 -00 N
-00N'C
CO
'C1JN
NiN
CU
0C - C
N-C
O o-'-O
-- -4-olr\OJ
N-(3(0
00-' 'C C
UC
O1sU
-C\JC
o'C(X
)CO
0-44 N
(0_thzf N N
N N
o-'NccO
y-ç--i CU
cOc-j-'C
cO C
Y-N
-CO
s-4 Cj-If)N
-C;'-i (0-0'C
N-t\Q
'DC
O -
aa
aa
aS
S-.
.a
aa
a*
aa
aa
aa
a.
aa
a,
a.
a.
,.
0 'N
rozt'u\'C N
-CO
0" 0 N 0-tf\'C
N-a) C
o C) - N
(0-Rr'C
N-C
Oa" 0 '-i C
UN
-C;)
0tf --O
N-C
O O
-4-'
.--
.-N
CU
0-1 CU
N 0-i ("J C
U C
U N
coro
co
C
(\j....Qr---C
)cJ\-O
C)
r>-O
ON
CO
N- C
) 0 N- () '-0 C
i N- N
C)
coL
c\.cOC
)C
) C) 'C
)N
N C
l N C
)cCcC
.z-N C
lC
1X\C
)C) N
-
cOC
O O
N-4N
N--4O
0-4Cij----Z
-N.N
-.--4C
' C' 0 (' N
- N-C
O C
O C
O N
-C
' C' G
0)oO
N .-i O
cc'-j -..C
.Q-C
)Q N
Cltc'C
\IC) C
)C! cO
NN
N-C
) N--
C' 0 0 000 0 0 0 C
) 0000'-4 - --i - -i - - '-i -i -i
N '--i - 0 0
04
40
40
00
00
00
00
00
00
V0
00
00
4*
00-
0
0'-4 -4
-1 .-44 ,-4 ,-4
-4 .-4 .-4 ..-4 --4 '-4 '-4 '-4 ,4 '--4-4 -4 -4
-4 '-4-
,,
-4
'00''SO
C)
s-I'-4
CiC
O-C
OC
)C
0009C) O
CO
CO
'0N-- N
-'O t--'--
CoC
)-C)
N-'0C
C) 00
oc'C
'S\- Ci
CJf
C)
.0
00
00
04
00
00
0S
00
00-
00
00
00
4S
00
00
04 C
)O
f\N-C
Z) 0 '1) N
-N-C
) C'Q
'dC)C
oC) o'-o C
iN
N-a' N
-N-N
C) iC
locJo '--C) C
'N-') 0L N
N- N
.-cJ-J
-,-
--i
-4-
'-'iC
i C)cO
-UN
-N-cQ
J C\(\U
\
0 '0:tko N
O C
OO
C'-ai) N
-1f\cO-C
OtC
'LCN
-N N
C) N
-N-
00-
00
0S
0*
00
4N
-N- E
-N-C
oCO
N-o3C
OoD
CO
cC N
-C'
OC
OcC
- N-N
-N-
00 CiztC
)c"O
C\I-O
C'cfD
-S-D
lr\a)C
)CJ -lO
CocO
:) C)
olrcoo C'cO
N-4 O
-CO
NC
OS
\N-N
-NN
-C
OO
)N
-Co
N\N
-0) 0--C)
oN '0cO
c))C
)N
coN cooN
-C'
o.
00
04
00
40
00
00
40
00
50
40
S0
45
00
SS
00
00
00
00
04
C\J C
) Cl N
'-'--i C
ii V
44 .-
('i --i
'-'-i N
C') C
\i0 -4
4.
N C
')C
J ,- .-.-i
.-.-4 o-4
-I-t
--I C
) 0 -I'
-4
N-C
oC
)s\)r\U'\-c) '-0
U\C
) N-a) a' o - C
U oir
-C) '-0 C
O '0 '-0 N
- N- N
- C- N
- N-
C) 0 _-
N-C
) )J' N-C
) 'C) C
) C) c
)'
C 0 N
- Ci '-4 C
i C) o c -
:DLC
\N-N
-0j C'----4 N
-C) O
tCzr N
-CO
'-C)'-O
'-0a'C
O C
--4
'-40-4
CC
C C
)J Q'-4 N
-CO
C'
CN
-C\lU
tcc) c0Lr\N-C
)o'0N-.-1 -0 -'-o
tc\Co t----c co y- r-'-o 1c\ C
U a' 0 '-C
) '-i (0 N-C
) C)tC
lC0 a'
'D - --i
j N-C
)0
0*
00
50
04
4S
40
0I
05
45
0
CO
l.C)0:±
-LCLr\C
) LC1C
ILN
-C) 1f\)S
)f\
Ci
N-C
11)
C)
O .1 C
i-ic-o N
-oJ cy- 0 04 C') '0zJf\C
O N
-CL) a'
110(1) (2) (3) (4J (5) (6)
S-30 1.60 5.39 48.8 1.05 90931 1.41 5.59 43.0 1.09 106032 1.72 5.25 52,5 1.02 56633 1.51 5.42 46.1 1.00 411
1 72.8 0.94 8542 71.8 0.96 6623 71.3 0.96 6584 68,3 1.00 6375 68.5 1.00 792
68,0 1.00 6347 67.8 1.01 7208 67.8 1.01 5379 67.9 1.01 705
10 70.7 0.97 78211 70.8 0.97 54912 70.7 0.97 75013 70.7 0.97 81014 70.7 0.97 67815 70.7 0.97 487
Top Related