VISCOSITY OF LIQUID-LIQUID DISPERSIONS
IN LAMINAR AND TURBULENT FLOW
John Anthony Cengel
A THESIS
subRitted to
OREGON STATE COLLEGE
in partial fulfillment of
the requireiients for the
degree of
Master of Science
June, 1960
APPROVED:
Redacted for Privacy
Prjessor of Chemical Engineering
In charge of Major
Redacted for Privacy
d of Department of Chaical Engineering
Redacted for Privacy
Chairman of School Graduate Conunittee
Redacted for Privacy
Dean of Graduate School
Date thesis is presented 3pemep' 9//f
Typed by Claire Waisted
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.
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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 VERSUS
RECIPROCAL 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 EMUIION
EVALUATOR
36
12
PLOT TO DETERMINE FLOW RATE
51
13
PLOT OF 1/
14
LAMiNAR FLOW VISCOSITIES OF WATER, 5%,
20%, AND 35% DISPERSIONS
56
LAMINAR FLOW VISCOSITIES OF SOLVENT AND
50% DISPERSION
57
15
16
F VERSUS wfr
53
EFFECT OF REYNOLDS ii3MEER IN PIPING SYS
TEM ON MEASURED LAMINAR VISCOSITY WITH
17
18
19
CONSTANT iP ACROSS CAPILLARY TIlDE
58
SHEAR STRESS AT CAPILLARY WALL VERSUS
RECIPROCAL SECONDS
64
TURBULENT FLOW VISCOSITIES AS A FUNCTION
OF FLOW RATE
66
PLOT OF VARIOUS DISPERSION EATIONS
70
L
OFFI tJRES (continued)
Figure
20
Paqe
AMOUNT OF LIGHT TRANSMITTED AS A FUNC
TION OF MIXIiC
21
I1E
EFFECT OF FLOW iATE ON AMOUT OF LIGHT
TRANSMITTED
22
23
24
71
73
DENSITY OF WATER AND SOLVENT VERSUS
:1Trtn7,.)I rir'i
39
VISCOSITY OF SOLVENT A. D WATER VERSUS
TEMPERA2URE
90
PRESSURE GAGE CALILRAflON CURVE
92
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
been investigation of combinations of these systems,
as liquid-liquid-solid dispersions.
has
such
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.
standpoint, the
From the commercial
viscosity is important,
since it plays a
2
major rcie in the design of equipment and since many dispersions may be marketable only at specific viscosities.
nowledge of viscosity has a theoretical value also. The
viscosity, together with hydrodynamic theory, can give
considerable information about the structure of dispersions
and clues to their stability.
It was therefore decided to undertake the task of meas
uring 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 petroleum solvent in water. Of secondary interest was the
investigation of the amount of light transmitted through
water as a function of the interfacial area. This thesis
presents 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
frictional effects
forces bringing about
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
arated by a fluid.
Shear stress
distance dy apart sep-
must be exerted to
keep
at a constant relaThis force is directly
one plate moving parallel to the other
tive velocity to the other plate.
proportional to the velocity gradient dy/dy.
tionality factor is
removed by introducing
The propor-
the coefficient
of viscosity,p
(1)
7
TF =pdv
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, pressure, and velocity gradient or rate of shear.
4
The unit of viscosity in the c.g.s. system is the
poise, 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 a
rate 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 to
the 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 lainflow through a capillary tube may be used to calculate
case, i.e.
/u= 7Tr4PO
(2)
8LV
where
L
radius of capillary tube
pressure drop across tube
length of tube
V
volume of measured efflux from tube
ê
time to collect ef flux
r
ti P
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.
LPf
3)
D
and
2pU2
4.0 log (Re
(4)
f
i
P
P
)°
U
Re
if )
Fanning friction factor
pressure drop due to friction,
= Diameter,
density,
-0114
/1
2
ft
ibm/ft3
velocity ,ft/sec
= conversion constant 32.17 (ibm) (ft)/lbf (sec)
Reynolds number
Newtonian Fluid
A Newtonian fluid is one in which the viscosity is
independent of the rate of shear, i.e. is constant in equation (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 also
increases with pressure, contrary to the kinetic theory,
whIch states that the viscosity of a gas should be independent of pressure. The viscosity of the liquid and that
of 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, nonNewtonian 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 stress
is 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 material flowing. An ideal plastic flows as a viscous material
according to curve lila. Moat plastics exhibit a bend in
the line at x because of a breakdown at the interlocking
arrangenent 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 of
shear.
Figure 2 8howE how the character of the viscosity
affected 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 concentraone of the dispersed phases in general are Newtonian in
ture. However, as the concentration of the dispersed
phase increases, the fluid tends to become non-Newtonian.
Workers in the field of rheology have been classifying the non-Newtonian suspensions by the old standards
applicable to a single phase flow, i.e, plastic, pseudoplastic, or dilatant. Yet it has been repeatedly shown
that the classification into which a suspension falls and
8
SHEAR STRESS
FIGURE 1. VISCOUS CHARACTERISTICS OF FLUIDS
DILATANT
NE42ONIAN
PS DUD OFL AS TIC
RATE OF SIAR (±LOW)
FIGURE 2
EFFECT OF FLOW RATE ON VISCOSITY
9
even the numerical values assigned to its rheological properties 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 characterietics 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 conclusion that the determination of the viscosity of suspensions is a very complex problem.
Most of the
literature
deals with gas-liquid, gas-solid, and liquid-solid suspensions or dispersions.
tereet in liquid-liquid
eering1
Although there is a great deal of indispersions in modern chemical engin-
there has been little accomplished in that direction.
The following discussion concerns suspensions at contemperature.
The viscosity of suspensions depends upon several fac-
3, p. 2S3);
) The volume concentration of the dispersed phase
The rate of shear
The viscosity of the continuous phase
The viscosity of the dispersed phase
The 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
flow, with the visdeclining as the rate of shear increases
a pseudoplastic behavior in turbulent
cosity steadily
until 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 characteristics.
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 variable is introduced.
Several solutions were given to explain the observed
pstdop1astic behavior.
Wilkinson (60, p. 595-600; &:
p.
11
aS
I
0
I
VCLTJ1E FRACTION DISPERSED PHASE,
FIGTJJ 3
VISCOSITY AS A FUNCTION OF CONCENTRATION
RATE OF SHEAR
FIGURE
VISCOSIIY AS A FUNCTION OF SHEAR RATE
12
7984) and Robinson (47, p. 549) theorize that the molecules or particles are progressively aligned or oriented
in the direction of flow. The viscosity will continue to
decrease 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 particles would account for the viscosity rising with decreased
shear rate (35, p. 574). This explanation is mainly applicable to solids suspended in flowing fluids.
Einstein (11, p. 300 and 12, p. 592) was the first
to consider the problem of two phases. His mathematical
treatment led to the famous wEinsteinN equation
(5)
m
Pc (1 + k)
where
in
0
k
is the apparent viscosity of the dispersion,
is the viscosity of the continuous phase,
is the volume fraction of the dispersed phase,
is the "Einstein constant" 2.5,
Einstein assumed a dispersion of uniform rigid spheres
ins liquid.
The spheres were separated by distances much
larger than the partical diameter, random in orientation,
concentration.
The equation is actually a limiting law and not considered
non-agglomerating in tendency, and low in
applicable for volume fractions greater than 0.02 for the
dispersed phase (2, p. 59). The value of 2.5 for the "Emstein constant" is very much in dispute. Huggins (21, p.
911) says that there is no valid reason to use 2.5, mainly
because there is considerable difficulty in measuring
properties of suspensions at low concentrations. Ting and
lAlebbers (55, p. 116) claim that, for systems of many-sized
particles, voids filled and formed by polydispersed particle5 account for the discrepancy of Einstein's constant.
}iatschek (19, p. 80) derived an equation similar in form
to equation (2), but called "Einstein's constant" 4.5.
Many workers, in an attempt to correlate data, later
expanded Einstein's original equation in the form of a
polynomial,
/ra 1c (1 + k
+a
2 +
b3
+,
where
k is "Einstein's constant," and
a 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 reported 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 & Margaretha (13, p. 276). Others report more extreme values
14
such as 35, Sachs (50, p. 280), and 150, 245, and 340, Roller & Stoddard (48, p. 419-20). The equations that sega
most representative of the preceding group are Kunitz's
(25, p. 716)
/1
=JJ
(1
and Happel's (1,
p.
in
+ 4.50+ l2çb
2
+ 25
1298)
c
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
clude the viscosity of the dispersed phase
to in-
15
ILJ&*
(10)
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/
(
çb1113
id+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, developed 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.
16
1
i-ç=
(13)
Equation (13) was later modified by Sibree (53, p. 35) to
include a volume factor "i" multiplied. by the volume fraction in the denominator. The equation was successful for
stabilized paraffin-water iu1sions.
npirical relationships (49, p.
Roscoe developed two
268
[i4]
2.5)
which describes the characteristic viscosity of a suap
sion 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 applicable to oi1-in.water enulsions.
IUmIic (Ca)
where
"a" is a constant depending upon the system.
Eilers (10, p. 313) presents an epirica1 equation applicable to his work on asphalt suspensions.
(17)
Ii
L
+
L.25
1(ç/o.78)
-2
Miller and Mann (38, p. 719) and Olney and Carison
(41, p. 475) developed a logarithmic expression for immiscible liquids
,L/=,L/ ,LI
Finally Finnigan (17) reports a correlation for petroleum
advent in water.
.,L
(1+2.5
+4.602
Si
Measurement of V
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 that
the measured viscosity will increase with increasing diameter (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.
of diameter the value of the
With each change
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 flow
required to get a reading may result in a breakdown of
some of the globules.
A correlation (8, p. 144; 60, p. 600) has been developed which plots the shear stress at the wall versus
volumetric flow rate terra (Figure 5).
a
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 diameter at a constant length or by increasing the length at
19
k
I
FLOW RATE TJRN, SEC1
FIGURE
5.
SHEAR STRESS AT WALL OF CAPILLARY
VERSUS RECIPROCAL SECONDS
20
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
and
have been made to determine the size
interfacial area of dispersed particles.
Most suc-
cessful investigators have relied upon photographic techniques.
Langloiso and Gullberg (27, p. 360) give a
relationship using light transinittancy.
BAl
(20)
0
is the light incident to suspension,
I
is the light intensity emergent,
A
is the interfacial area per unit volume,
is a specifying constant dependent on the
ratio of refractive indices.
and
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 solutions 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.
the evaluation of the dispersion.
This thesis concerns
A treatment of the heat
transfer experiments may be found in a thesis (62) presented 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 cooling 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 provide 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
THERMOCOUPLE
WELL
(j
2-INCH GATE VALVE
r7ll- INCH GLOBE VALVE
>
WATER
A;
f-HC
HEAT
EXCHANGER
(}1-INCn GATE VALVE
A - ORIFICE
WATER
B - CAPILLARY TUBE
C - TO MANOMETERS
PRESSURE
D - MIXING TANK
GAGE
TO
E - BECKMAN
SEWER
FLEXIBLE
HOSE
THERMOMETER
I'll'
I....'
STIRRER
I, ulIuUUhuIIlI1I
4111111111111 liii
6-FOOT
HEATING COIL
C
C
E2'IULS ION
EVALUATOR
03
PLATFORM
SCALE
T
TAP
TURBINE
PUMP
WATER FLUSH
0
DRAIN
FIGURE 6
SCHEMATIC FLOW DIAGRAM
2
PRESSURE TAPS
COPPER Tw3E
PART A
PRESSURE GAGE
21"
CAP ILLARY
ruBE
NEEDLE
VALVE
1" BRASS PIPE
PLATFORM
AND
38"
WEIGH CUP
TO D.C.
BATTERY
11"
1- UNION
I
II
THBMOCOUPLE WELL
TO GALVANOMETER
III EMULSION EVALUATOR
19"
1
PART B
FIGURE 7. DIAGRAM OF TEST SECTIONS
25
photoelectric emulsion evaluator, a capillary viscoxaeter,
a sight glass, a baffled mixing chamber, a heat exchanger,
a sample tap, three temperature wolls, and appropriate
piezometer taps and valving. There was also a 6-foot horizontal section wrapped with nichrome ribbon for heating.
The scope of the following detailed description will
cover only those parts of the apparatus which directly
apply to the viscosity evaluaticn experiment.
Supply Tank and Pum
The supply tank and pump are the same as used by Finnigan (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., 16
BWG copper pipe, and a section of flexible synthetic rubbor hose. The 2-inch pipe was located between the supply
tank and the pump. The copper line was located between the
two vertical sections of the system, and the flexible hose
s located, at the ef flux point of the system. All other
piping was 1*-inch standard brass.
A 2-inch gate valve (number 1, Figure 6) was installed
11
1-4
27
between the mixing tank and pump to aid in controlling flow
and so that the piping system could be drained independently 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 the
test sectIons. The main system valve (nuither 3, Figure 6
was used to isolate the main system from the supply tank
and was kept wide open during all runs. With this valve
closed, changes could proceed on the test sections without
disturbing the mixing. Finally a 1*-inch globe valve
(number 4, Figure 6) was installed at the ef flux point to
regulate flow and to insure that the aain piping system
renamed full when the apparatus was not in operation.
AU threaded connections were made with the assistance of "Cyl-sea1 high pressure sealant manufactured by
the West Chester Chemical Company and the seats of all unions were sealed with Perxnatex No. 2, manufactured by the
Perinatex Company, Incorporated. It was found that these
sealants were imperious to the liquids used In the experiment.
Unions were used wherever possible for quick disassenbly 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 experimental work on the same system of fluids. His calibration 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 eva
uate 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-foot
distances by drilling l/2-inch diameter holes perpendicular to the pipe wall and brazing short *-inch brass nipples in place. The inside surface was cleaned with emery
cloth to insure an opening free from burrs and flush with
the 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 insure
that the manometer lines were filled with water by poriod
Ic flushing. The 6-foot copper tube was also used (62) in
conjunction with heat transfer coefficient measurements,
Part
(Figure 7) depicts the section used for the
29
FIGTJBE 9
MANO}4ETER BOABD
UNGEMENT
30
laminar viscosity and light transmittancy determinations.
The main flow, indicated by the arrow, was in the vertical
1*-inch brass pipe. Glass capillary tubes of varying
length to diameter ratios were inserted into the main
stream by means of a steel fitting located 21 inches below the entrance and held horizontal by means of a spring
arrangeent. The springs also served to hold polyethylene
gaskets in place. The spring support mechanism was held
in place by a 1-inch pipe cap. The pressure drop across
the capillary tube was measured by a U.S. Gage Company
gage attached directly across from the tubes.
Table 1
Capi lar Tube Dimensions
Tube
Number
A
A-i
C
C-i
C-2
D
E
Length In
Inches
Inside Dia!nete
in inches x 10
Length/Diameter
Ratio
11.95
5.30
11.93
12.02
5.92
12.00
11.93
8.97
1,944
1.944
2.580
3.588
3.588
3.588
4.092
5.076
615
273
462
335
165
334
292
177
The gage was of the stainless Bourdon type tube with
an 8-inch face calibrated in one pound increments between
zero 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
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 except
in the region below 2 pounds per square inch. Therefore
all readings were taken with the gage pressure above that
value,
A 1*-inch needle valve inserted between the main sysiz" 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 by
means of clamps. The volume of liquid caught in the cup
was weighed on a null-point alance manufactured by the
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
Welch Manufacturing Company.
weighing the mercury required to fill the tube. v1easurements of the diameter agreed within ±0.4%. In addition,
one tube was used to measure the viscosity of water to verify the mercury measurement method.
The temperature of the flowing dispersion was measured
by means of a copper-constantan thermocouple situated in a
copper well at the entrance of the test section. The voltage 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 photocell 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 flow
rate and, in turn, to apparent viscosity.
Figure 10 is a detailed drawing of the emulsion evaluator. The light source tube (8) was mounted on the main
piping system (16) by soldering a brass fitting (14) into
a 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 connection. Two light power supply binding posts (1) and
three lamp adjustment screws (4) were fitted into the endpiece. 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.
6
1
2
7
21
8
9
2+
22
25
HALF SIZE
FIGURE 10
LIGHT AND PHOTOCELL PROBES
26
34
The photocell tube was soldered to the main piping
system directly opposite the light source tube by means of
fitting (17), which was inserted into a 1*-inch hole. This
tube was sealed from the system window (20) in the photocell 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 socket
mounted in lucite (21) and was attached to the micarta endpiece (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 set
screw (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 so
that a specified voltage, usually 4.5 volts, could be maintained at the light bulb. To insure that all data were taken under identca1 conditions, the voltage delivered across
the 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 observe 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 could
be 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 dispersion was flowing, it was possible to determine how much
light was transmitted through the dispersion as compared to
the ezaount transmitted through pure water. Sensitivity of
the galvanometer, as it was used, was ±1%.
The electrical system is schematically shown in Figure
The 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 1P4
C2
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 ohm
Helipot
Load resistor (1 megohm)
Coarse adjustment rheostat (5 ohm rheo
Fine adjustment rheostat (10 turn 25 ohm }ie1ipo
Load resistor (50,000 ohms)
R3
R4
R5
R6
HiH
R8
B3
I
S6
R6
/
/!
31/
FIGURE 11
WIRING DIAGRAN
FOR
PHOTOELECTRIC EMULSION EVALUATOR
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 evaluator..
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 constructed 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 determine
the laminar and turbulent viscosities of an unstable
iiqiid-liquid dispersion. The dispersion referred to was
composed of a petroleum solvent, "Shellso].v 360," dispersed in water. Finnigan (17), working on the same sys-
tern, showed that there was a definite limit to the
compositions 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 continuous
phase 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 following runs.
The following pure liquids and dispersions were stud-
ie
1.
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 of
solvent 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 on
the pump. In order to obtain the most rapid mixing possible and to assure a quick turnover of the material in the
system, all valves were initially left wide open and the
tirrer allowed to run at maximum speed. The time necessary to achieve thorough blending of the two liquids depended upon the concentration of the dispersed phase. Mixing time was usually 2 to 3 hours, the higher concentrations
taking the longer time.
The dispersion took on a milk-white appearance characteristic of many liquid-liquid suspensions. It was noted
that, if the stirrer were turned off, a clear layer of solvent immediately became visible at the surface of the sysin the supply tank. This separation indicated instaby of the dispersion. Even with maximum care, the
interface eventually became contaminated with dust and
small pieces of the flexible hose. The contamination acted 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
40
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
Nominal Volume %
Solvent
Measured Volume
1
Solvent, Average
5
4.8
20
19.4
35
34113
50
49.2
At each concentration measurements were made of the
pressure drop across the test sections, orifice pressure
drop, fluid temperature, rate of ef flux from capillary
tube, and light transmittancy. After each series of runs
the liquids were allowed to separate over night. The sdvent was then decanted off and used again in preparing the
ext concentration. The water was discharged to the
eewer.
41
Thrbulent Flow Viscosit Measurement
The measurement of the apparent viscosity of the dispel ion in turbulent flow was accomplished by means of pressure drop determinations over a 6-foot, 7/8-inch O.D., 16
BWG horizontal copper tube. The piezometer lines were
flushed periodically to insure that water was the only
fluid in the tubing. The valve at the discharge point of
the piping system (number 4, Figure 6) was closed, and noflow 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 the
water and solvent runs because of the vertical distance
between orifice piezometer taps.
The discharge valve was then opened to allow flow to
begin, After a period of time to allow for the settling
that had occured in the main piping system, pressure drop
readings were recorded for both the orifice and the test
section. These readings were taken simultaneously with
the laminar flow measurements,
Carbontetrachloride was
used for low flow rates, mercury for high flow rates, and
both fluids for intertu ediate flow rates.
Fluctuations of the manometers were minimized by cbsdown 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 nonhornogeneity 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
of the largest capillary tube. The
end of the capillary tube was positioned so that It would
be at the axis of the 1*-Inch pipe which carried the main
larger than the O.D.
flow. The temperature of the dispersion was allowed to
come 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 definite
ime, measured by a stopwatch. Diring this time the manomtore were read periodically to get an average flow value.
The pressure on the 8-inch pressure gage was noted in order
to 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, if
any.
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
either simultaneously
emulsion evaluator were made
with or immediately after
ments with the capillary tubes,
calibrated to read zero
and water
flowing.
measure-
The evaluator was always
with no light and 100 with light
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 maintained at
the light (Figure 11). The proce&re involved
was as follows:
1.
Set 4.5 volts across the light
ohtind. was value steady a until continued were r.dings
the with chazyo trensittartcy iew
Ihe ixing. of
t roi I recorded
determine to frequently a1vancieter
readings the runs, cf seri each cf heinnirc! the At
apar
tie
l/2C prohos the with iade rins several were there mrt,
l/r3inch probes the with :iade were ohservatior's the of ty
najor- the hi1e rate. flow of ftinction a as changed
transittancy hether erine
Lc rates flow various at
taken were readmnçs .hese water. the thrcuch tranarnitted
light the of percentage a h to calculated were di*persion
the with cThserved readings the water, with lOU to
fron read to calihrated s cjalvanc:oter the 8ince
ro
off, t ±} 1 with çalvanc:eter Read
and on, iQht 1 with alvancicer 1?ead
3
CHAPTER 5
SAMPLE CALCULATIONS
Physical properties of the petroleum solvent and wa
er are discussed in the appendix, as are details of calibrat ion.
Capillary Tube Calibration and the Laminar Flow Viscosity
The bore of the capillary tubes used in the invest
gation of apparent laminar viscosity was a critical factor
in the calculations. Utmost care was taken to get accurate dimensions, since the radius of a. tube was used to the
fourth 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 following equat ions:
V= wt
and
1°
wt
(77)(L)(,,o )(2
47
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.
the calculation for capillary tube E
For example,
wL
was 13.53 g/cc, and L was
was 4.2069 grams,
34 inches, was as follows:
(2k)
4.2069
r
/
\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
,Ia
(23)
(TT)(P)(e)(r)4(p)
(8)(L)(wt
wh
a
P
is the apparent viscosity, cp,
is the
pressure drop across the tube, psi,
e
is the elapsed time of measurement, sec,
L
wt
is the tube length, inches,
is the weight of the dispersion collected, grams,
p
is a conversion factor, 1.043 x
i8
(g)(cp)
(1b) (sec) (in)
4
Data obtained for run 35-27 with tube E, length
11.925 inches and radius 0.0129 inches, was:
weight of efflux, 116.3 grams
i P
10.9 psi
300sec
e
(23a)
Pa _!
416) (10.9) (300) (O.0129)(1.043
(8) (11.925 116.3)
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 lainmar flow, the ReynoldE nuin.ber was calculated for each tube.
(24)
ReT
(D)(u)() = (4)(G)(p)
(7T)(D)(,L/a)
24
where
D
u
p
is the diameter of a capillary tube, inches,
is the velocity of fluid, ft/sec,
is the density, lb/ft3,
a is the apparent viscosity, cp,
G
p
is the mass flow rate, g/sec,
is a conversion factor, 39.37 (in)(sec)(cp/(g).
Again for run 35-27,
49
(24a)
Turbulent Flow Viscos
The pressure drop across the 6-foot copper test section was determined by means of manometers, using carbontotrachioride 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
is a conversion factor, 3C4.8 mm/ft
p
A sample calculation:
(25a)
(843.46_62134)iumHg
304.8
The friction factor was found by using the equation:
f
(26)
(LPf)(g)(D)
(2),P )(u)2(L)
e
(77)2(zPf)(g0)()J
(32) (L) (W)Z
50
is the density of the medium, 1b/ft
is 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)
(26a)
(3.1416)2(99.92) (32.17) (57.6
2)(6) (1.06)2
f
) (0.06 2
= 0.00785
The turbulent flow viscosity was calculated by f it-
g all
the data to Equation (4).
ng 1/ '[
me
versus log
wif,
This was done by plot-
This plot will yield a
straight
when the viscosity is independent of flow rate.
From
o smooth curve drawn through the data, the viscosity at
each flow rate was calculated front the following:
Re
4W
D,JJp7T
1
4.0 log
(4)(W)([7)
(7T)(D)(Jia)(P)
-0.4
where
p is a conversion factor 6.72 x 10
and
is the apparent
viscosity.
lbjft)(sec)(cp)
5].
8
I
0.1
I
I
I
iiiil1.0
I
J, LB/EC
FIGURE 12
PLOT TO DETERMIIE
OW PLATE
52
illustration for the
with
i/f
S% dispersed phase series
equal to 11, WW equal to 0.0821, and W equal
to 0.9022 is:
(28a) 11
4O log
froni which
4) (lO) (0.0821)
-
-0.4
.1416)(0.0621)(6.72) (j'a)
3*534 cp
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.
53
00
o PURE WAITER
PURE SOLVENT
SOLVENT
, 5%
0
400 .,
20% SOLVENT
35% SOLVENT
x 50% SOLVENT
//
/<
13
0
1
000
12H
0.
/0
0
/
0
//
e
0
CC
/
10
0.03
0.10
0.05
LB
'
FIGURE 13. PLOT OF 1/f VERSUS
0 20
/
N
N
N
i'4)
km Posit
2te
ystoz
io fcrat
in
capi1 e
Ct
Su:iarj
1,
try
!eyno1da e
the
Ly
caicilated
wriç
cf
visccitie
to
1CC
te
sh is data
lazy
fv rancleQ niauib.r-
cap the In nuibers Reyxtolds
ar 2) (qtiaticr equaticn isa's
visao6itie The
deteriix c used were
ear
Poie of
3ion3.
shear the of 1xth frctor a
thai cLserired. Lavo , (Ch.atter
after
ec1id with
mis-
i
f]iw
were
dte
3
tuhe the of and
viscosity parent
rate
the
dipersior Uqiid
riieters,
ii
x
cf
t(
:an:,
tuJi
p*.icns.
the for
Cap1iar
os Li Vigci
'7
fl2w AJ1*T,
r
Table 3 (Continued)
351 Dispersion
N
I,
0% Dispersion
N
N
N
N
:6
C-2
0
E
C-2
0
E
C-'
C-2
7
10
17
8
24
19
5
6
3
10
N
0
E
8
Solvent
N
A
IV
Wat e
10
C-2
4
Horizontal
N
N
Horizontal
N
N
Vertical
N
N
N
Horizontal
N
Vertical
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 versus
the calculated Reynolds number in the tube. In addition,
ranges of viscosity measured under turbulent flow conditions 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 viscosity 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
v4/t
FIGURE 1
LA4INAR FLOW VISCOSITIES
OF
WATER, 5%, 20%, AND 35%
3.2
DISPERSIONS
TUBE A
0
o TUBE B
0
2.8
3
TUBE C
TUBE D
SOLVENT
,
HORIZONTAL
, HORIZONTAL
, HORIZONTAL
,
HORIZONTAL
v TUBE E , HORIZONTAL
x 'rUBE A..1, HORIZONTAL
D TUBE B
, IERTICAL
D 'rubE C-2, VERTICAL
TURBULENT FLOW
VISCOSITY RANGE
1.6
20% SOLVENT
WATER
I
0
2
I
I
I
I
I
I
8
10
12
REYNOLDS NUMBER IN 'rUBE X io-2
6
5.8k
U
-
i'W3E A
, HORIZONTAL
, HORIZONTAL
, HORIZONTAL
,
HORIZONTAL
, HORIZONTAL
TUBE C-i, VERTICAL
A TUBE D
, VERTICAL
TUBE B , VERTICAL
EIJ
TIJRLULENT FLOW
VISCOSITY RANGE
I
U
o TUBE
TUBE
4 TUBE
o TUBE
U
D
----"T
5.0
__
£
A
5O
.6 -
A
SOLVENT
B
C
D
E
4,
3
1.2
SOLVENT
0
.
0
0
.
0
Qf4
G
4,
S
S
10
1].
0.8
1
2
3
4a IN CENTIPOISE
6
8
7
REYNOLDS NUMBER IN TUBE X 102
5
FIGURE 15
LAMINAR FLOW VISCOSITIES OF SOLVENT AiD 50
9
DISPERSION
FIGURE 16
EFFECT OF REYNOLDS NUMBER IN PIPING SYSTEM ON MEASURED
LAMINAR VISCOSITY WITH CONSTANT LP ACROSS CAPILLARY TUBE
TUBE D
o TUBE C Cl
Uk3E C
W3E C -
e TUBE A -
35% SOLVENT
35% SOLVENT
5.3 PSI
- 6.2 PSI
5% SOLVENT
5% SOLVENT
- 9.6 PSI
20% SOLVENT -
.1 PSI
3.8 psi
LP WITHIN
C
U
8
10
15
20
REYNOLDS NUMBER IN 1INCH PIPE X
25
35
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 by
the flow rate in the main system, and this factor, therefore, need not be considered in the analysis of the data
represented in Figures 14 and 15.
Other workers (51, p. 571; 30, p. 135) have observed
that 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 different diameters, resulted in different values, generally
increasing with the diaraeter. This was most evident with
the more concentrated dispersions. This effect, which has
also 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 difference can be observed between tubes B and C. It can be
seen that the viscosity data begin to scatter somewhat
above a tube Reynolds number of 1200, probably because of
incipient turbulence brought about by vibrations in the
flow system. This was also noted with the 20% dispersion.
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,
could be due to agglomeration of
the
This
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 measurements
were impossible with the smaller diameter tubes.
The 35% dispersion showed the first really significant 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.
showed some viscosities, which may
Tube B again
c been the to a
plugging effect.
The effect of capillary tube diameter on the measured
viscosity 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 tube
B.
easurements made on the solvent showed a slight
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
Figure 15.
from the straight line shown in
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 be
the reason for the rise in the calculated viscosity.
Although a slight change in calibration was noted, the
error 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 conclusion that a "settling" effect could give apparently
erroneous results. The settling refers to a two-phase
separation in flow. Therefore, runs were made with the
tubes
,
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 being
obtained in the vertical than in the horizontal positions,
The difference in apparent viscosity, as measured by the
individual tubes, remained proportionately the same distance 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 portions
of the tube, respectively. The measured viscosity would
then 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 slip
at 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 a
measure 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 consta
and the fluid oheys the power law as expressed
wtoniar; when ii' is less
than 1, the fluid is pcoudoplestic; hon n' is greater
When n'
the fi'i±d 1
than 1, the fluid is dilatar
Fiqure 1? i a loç-loq plot of (A.P)(D)/(4)(L) versus (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
t
of data. These irciicate that, under laainar flow cortd
tions, the dispersions are .±ht1 dilatant and the value
of n' is contan for all concentrations of solvent up to
5, These resui.s also verify Figures 14 and 15.
It is siqnificar;t iLt
S experiient verifies the
work of other e eriienterz with solid-liquid dispersions.
While the data here is not sufficient in itself definitely
to conclude this verification, it does sen. apparent that
the equaticns and theories derived for the solid-liquid
dispersion 1old for lqui-liquid dispersions.
6i-
1.0
4__'
'J.
(.I
o
°
0.1
TUBE C-i, 50% DISPERGI0I
L'uBE C-2, 50% DISPERSION
TUBE D,
TUBE B,
35%
5%
DISPIRSION
DISPERSION
1.0
5.0
(8)(V) ,
(7T)(D3)
SEC
FIGURE 17
SHEAR STRESS AT CAPILLARY WALL
VERSUS RECIPROCAL SECOIDS
65
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 calculated from Equation (4).
Figure 18 shows the calculated viscosities as a function of ftow rate for the various dispersion compositions
and pure components. The solid lines represent the values
obtained from the present work; the dashed lines represent
the values obtained by Wright (62) during heat transfer
coefficient 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 for
water, 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 temperature, shown by this line, agrees well with the value of
0.98 centipoises measured by Finnigan (17).
The dispersions reflected a definite dependence upon
10
o CALCULATED
-0M REFERENCE (62)
50% SOLVENT
20% S0LVEIT
SVT
S
5
SOLVENT
WATER
0.0
1.0
2.0
3.0
W, 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.
plastic materials.
This behavior is typical of pseudo-
The majority of suspensions tested by
other workers, although mostly solid-liquid in nature, exhibited 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 explain 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 causing 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 suspensions. This again would lead to the conclusion that
liquid-liquid dispersions do behave in a similar fashion to
solid-liquid dispersions.
upirical equations were developed to describe how the
viscosity changes with concentration of the dispersed phase
68
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 +
2
cz5
+
The results are:
= 1+2.50
(31)
-
10.730
2
+ 60.920
for a flow of 1.5 ibm/s
12
l+2.5qi
($2)
2
+ 46.36ç
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 equation applicable for all flow rates within art average deviation Of
9.5%.
(34)
Equation (34),
in
a form
C
l2.5cb
-
Ii.OiØ
2
+ 52.620
of the Einstein equation, reduces to
it at low concentrations.
:9
Ftgure 19 shows the quantity,/J/J/ plotted versus
the dispersed phase concentration for the equations derived by several workers, It also shows the viscosities
calculated in the present experinent and their relation
to the equations presented. Equation (34) and the equations of Vand and Ioscoe show rdatively good agreeient
with the experimental data, Other equations shc'ti wide
deviations at the higher concentrations.
Photoelectric Emulsion Evaluator
The evaluator was inserted in the vertical 1+-inch
brass pipe perpendicularly to the flow. Two types of
measurements were nade: variation of light transmittance
with time of mixing and variation of light transmitted
with 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-inch
apart.
Figure 20 shows how the percent of light transmitted varied with the length of mixing time for the dispersions. The percent of light transmitted refers to the
amount of light received iDy the photocell probe compared to
the 6mount of light transmitted through clear water. The
70
8
7
A
B
C
D
E
F
c
0
- EIIERS EQUATION
VAliD EQUATION
2 1+2.5Ø_11.0].252.62Ø3
- ROSCOE EQUATION
FINNIGAN EQUATION
- EINSTEIN EQUATION
W 1.5 LBm/SEC
W
2.5 LBm/SEC
W 3.0 LBm/SEC
3
2
1
0,0
0.1
0.2
0.3
VOLUME FRACTION SOLVENT
0.ls
FIGURE 19
PLOT OF VAJIOTJS DISPEBSION EQUATIONS
0.5
100
FIGURE 20
AMOUNT OF LIGHT TRANSMITT) AS
A FUNCTION OF MIXING TINE
80
0
%
60
3% SOLVENT
o
20
SOLVENT
20% SOLVENT
0% SOLVENT
00
0
20
o
+O
0
0
60
80
TINE OF MIXING, SECONDS
100
120
72
percent tranamittancy dropped almost immediately with mixing time to
a constant value,
indicating
formation of the dispersions.
the rapidity of
The dispersions were charac-
terized by an opaque, milk-white appearance,
show the
The data
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,
light tendency for the percent
There seems to be a
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, decreased with increased concentration of the dispersed
phase. 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 independent of concentration,
This conclusion may be inac-
curate, because, as the concentration increases, there is
a secondary scattering of the light lost at lower concentrations.
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 SOLVENT
1/8-INCH SEPARATION
5% SOLVENT
20% SOLVEN', 1/20-INcH SEPARATION
20% SOLVENT, 1/INCH SEPARATION
35% SOLVENT, 1/3-I1IcH SEPARATION
50% SOLVENT, 1/8-INcH SEPARATION
30
H
0
n
no
n
S.
15
I
0.0
1.0
2.0
W,L /3EC
U
FIGURE 21
EFFECT OF PlOW RATE ON AMOUNT OF LIGHT TRANSMITTED
3.0
74
show how the particle size varied. It was expected that
if the particles become smaller, leading to an increase of
interfacial area, the amount of light refracted would increase with the overall result of a drop in amount of light
transmitted. If this phenomena occurred, its effect was
probably too small to be detected by the photoelectric
evaluat
CHJWER 7
CONCLUSIONS
A study has been made of the laminar and turbulent
viscosities of an unstable liquid-liquid dispersion cornpo5ed of a petroleum solvent and water.
Iminar flow viscosities, measured by means of a nuraber of capillary tubes, varied with tube diameter, tube
length, and flow rate. The variation with tube diameter,
known as the siama effect, may be caused by slip at the
wall, It was shown that it was riot caused by a settling
effect, This sigma effect was more evident at higher concentrations, where higher viscosities were measured with
tubes of larger diameter. The results are in agreement
with results on solid-liquid nulsions. It is evident
that the capillary tube method is not suitable for determining 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 under
these 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 agree
reasonably 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 the
dispersions formed very rapidly after mixing began. The
percent light transmitted through the dispersion was a
function of concentration up to 3$/ solvent, after which
the percent transmittancy remained constant, probably
because of secondary refraction. It was impossible to de-
tect any variation of light transmittancy with flow rate
past the light probes.
CHAPTER 8
RECO'1ENDATIONS FOR FURTHER WOIC
The investigation which has been reported in this
thesis has developed the groundwork for furtber study of
liquid-liquid dispersions. Several suggestions for futire experiments are:
1) Determine the effect of length of capillary
o visconieters with constant diameters in the measuremont 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 between
laminar and turbulent flow
Extend the range of turbulent Reynolds numbers
for the present dispersion by employing a larger pumping
system.
Use a. photographic technique in conjunction
with the photoelectric emulsion evaluator to measure the
exact size of the dispersion particles.
amount of light transmitted through the dispersion related i the time of mixing
can define the concentration of the dispersed phase at
small increments of the concentration.
Repeat the present work, revising the dispersion
Determine whether the
78
syzten by adding a stai1izinc aç-en to deteriine the
effect of staJiIity on the phica1 propertiea.
GiL PT,I
A1VeS, Ge
.
2. Bec}ir,
Ne
:'..OfliT :;T'siors.
56:1O7-9. 19+9.
F:ic.>w of flOfl
::or1rig
Ch:ic:
mi1s1ons:
York
31tih:1d
.rctico,
theory
1957.
nd I
BrouL:hton, C,
3I.2p,
ic viscosity of oi1
u1res.
in-tcr cusicLs,
+2:253-63.
79
9
ic1 (7; stry
JournI
1938,
Unit Urticns,
Br'r, G, G
6ilo.
Chirig, P, Y.
11.
..
1955.
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or
vs.lidity of the ::instein vLscos
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i6:193a. 1955,
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.spenslofls rnd
Nature
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icit Q
zi
(I
spheres i:
1+8563_3.
I
ae
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1951,
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Isor
cJ.e1u1dimen-
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der
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ic ross,19t..
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tofrc 1s
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the
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ojner .r :it
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t t.n durch
ilsehe
J15;P:73-9o,
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80
Use of
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i'
fo
o
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Oco
18.
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I.
ou viscosity in
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C1E5:jc;
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C
Knitz , F,
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btween icos
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xrofe I
eiety
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27
Langloise, G
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ti riis1Ofl.
25:360-63,
r
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in nst
2etc..
-.
cv1(w of
1951+.
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28, Levitori, A. and A. Leighton,
Ii
81
for the relati
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Lon
:
ts
Viscosity relatonships
ilk ft. Journd of hysic1
2s,r s contin
Chsistrv 1+0:71-80. i)3(.
tI. K., L. Squir .::.d . 1, Lo.;on. CoiiiJ1
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itv
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,oui
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3, 0, ::njth. ynjt o::.tion of
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.
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NoDovci..1, 0, 1, >r d F, L, Ushr,
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Viscosity and ridigity
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,
.1crs; 001'). e
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jcr.
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l9+7,
1+3:1+73_80.
Cn1son.
Iti I
I
rture 171:396-7.
I-o.?r and absorption
c
'
s os and
in rir.g
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1+6,
147,
1383,
I
1
r.
T.h.....1co':
3rd. Nd.
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Boiler, 2, s. and C. K, toddard, ViscosIty and
of structur J s o
i- a, Journel of hy&ILl C1
1+8:1+10-25,
191+1+,
riIdity
iistry
lIoscoe, R, The viscosity of
spheres. British Tournoi of
3267-9.
1952.
s of ridgid
susuc:
AJ.i
83
yui Cs
Sechs, D. Journal Do ChirniePhysicue 29:280-6, 1932.
Sherru:t
The inf
ei;tJ. s: C;n
industry,
52. Sherizn,
53,
5tt,
$tudles
In :nter-in-oil o: u1.Loi., I,
co cf Tjs;ersod i:.hase Cu ocuntr; ticn
cc :ity, J ou.rn.u1 Of th Jociety of
on
Thez:±c
:o, 2, 69:571-5. 1950.
ie inflicuce of irtr:
nha o. Vicosj
on
cty of CoiCrc
ter-r-(11
S1oDs,
Koi:c.;la-zejtschrjft ia :6-n. 1955.
Slbreo, J, 0,
e vi.eosity of o:uJ.sions, Part 1.
-
Farady Society
Tailor, C. I.
26:26-36, 1930,
The vi:cosit,r
drops of nothcr fi
Proceedings A138:'-i-.. 1932.
in(:,, !, P.
and
.
,
..
of a fluid contirir
s: a
1 Lcciety of I nCon
ue..bers,
The V1SCOni
oth :r idiçri
SU$pO$iOflS of srheric;1
paitc±'
In ii
rc in0tit to of
Engineers Journal 3:111-16, 1957,
icsl
flF
Treyi;l, R. E, iu -iin:nsfer (;prtions, New York,
NcUraw-niii, l95, 400p,
Vand, V. Viscosity of soitions and
nsa.ons, Journal
of Physical CherIstry 52:277-99/ l9+,
Verre1en, T. , C.,
r
I
,
agita.;ion. Ce.n.jca].
1955,
'Il1ins, nd C
1i,id-1i i
.......:
1g1ois.
s-lj id
.ncerinLnrcfress 51 :85F-9+F,
Ward, S. G, and R. 1.. Jhitnoro, ritish Journal
Applied Physics 1:284-90, 1950,
6o.
flow.
Iud:strial
Non-:;ewtoriian flow,
195I.
Industrial
Iikinson,
. 1.,
Ton-:cwtcnian
33:595-600, 1957.
Cheimist
61.
62,
WIlkinson, W.
Ccn1st
L
31:79_81+,
rigt, C. H,
Pres.L1rc dr
liculd dimersirs
In
c.-!s,
M.S.
120 flU!, len:VE:S,
tui'
Is (ir
(
Ont tra:nsfcr
of
for 1iui
iLi; in a circular tube,
State 0cge, 1957.
APPENDICES
APPENDIX A
NOMENClATURE
It in Letter Symbols
Meaning
Symbol
Units
A
Area
ft2
A
ft1
D
Intorfacial area per unit volume
Constant in viscosity equations
Ratio of refractive indices
Constant in viscosity equations
Diaiueter of tubes or pipe
F
Force
lbf
f
Fanning friction factor
G
Mass flow rate
g
Sec
Mass velocity
lb
a
B
b
ft
(sec)(ft)2
g
Gravitational acceleration
ft
Ccnversion constant, 32.17
sec
(ibm) (ft)
(lbq) (sec)
Ii
Volume factor
I
L
Light intensity
Coefficient of consistency
Einstein constant, 2.5
Length of tubes and test section
N
Volume fraction in mixture
r
Capillary tube radius
lumens
cp
ft
ft
85
Units
Meaning
t
Temperature
u
Velocity
V
Volume
W
Mass flow rate
Greek Letter Smbo1s
Finite difference
,IJ
,LJa
d
7T
p
Time
sec
Viscosity
Apparent viscosity
Continuous phase viscosity
Dispersed phase viscosity
Limiting viscosity
Constant, 3.1416
cp
cp
op
op
C
lb
Density
SiTear force per unit area
f
Volume fraction of dispersed phase
Interaction constant in viscosity
eq.iat ion
Composite Symbols
BWG
Birmingham wire gage
in
gallons per minute
Logarithm (base e)
log
Common logarithm (base 10)
O.D.
Outside diameter of copper pipe
86
ymbol
Meaning
Un:
Re
Reyiolds number
wt
Sample weight
g
Pressure drop across test section
lbf
ft2
LPf
Pressure drop due to fluid
frict ion
Subscripts
Apparent
C
Continuous phase
Dispersed phase
Force (as in lbf) or friction (as in
Medium or mass (as in ibm)
o
Initial
Solvent
Tube wail
Water
Limiting value
Pf)
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, colorless
iqutd, 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 viscosity
differed from that of the fresh solvent by less than
Tabi
Manufacturer's S.ecifications for Shel1solv 360
API Gravity, 60°F
Specific Gravity, 60/60°F
49.1
Color, Saybolt
26+
Flash Tag, O.C, °F
Flash Tag, CC., °F
110
Aromatics, Stoddard,
2
0.7835
103
88
Table 4 (Continued)
AS
Distillation9 °F:
Initial Boiling Point
Final boiling Point
304
10% Recovered
317
50% Recovered
323
90% Recovered
342
% Recovered
362
98.5
The solubility of the petroleum in water was quite
low. It is apparent that the solvent-water systern used
in this investigation represents a very immiscible pair
of liquids.
The densities of solvent as a function of temperature
were measured by Finnigan (17) and presented on Fiqure 22.
The density of water at various temperatures, obtained
from Perry (43, p. 175), are also included. The viscosity
of 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 ±a
an additive quality. Therefore, the density was calculated
from the mixture law
(35)
89
62.+
WATER
62 3
62 2
fJ
f9.f
SOLVENT
t
I
I
I
L
70
60
t,
I
L
O
ibm/ft3
FIGIYRE 22
DENSITY OF WATER AN]) SOLVENT VERSUS TEMPEPLATTJRE
90
9.0
8.o
H
7.0
6.0
I
I
I
I
50
I
60
I
t, °F
.1
1
L
70
-" in lbm/(tt)(sec)
FIGURE 23
VISCOSITY OF SOLVENT AD WATER VERSUS TPERATURE
91
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 described
by the manufacturer are presen Led j :Ta,10 5.
Table 5
me Pum. Charac
iaterial
odel Nuzber
Speed
fTonze
LJ615
1750 rpm
Delivered Flow, gp
Total Head, feet of
Water at 80°F
10
42C
250
110
10
40
The pressure gage used to determine the pressure drop
across the capillary tubes was calibrated against a mtercury open leg uanoneter at the heginnin, and end of the experlinent.
Figure 24 shows the original calibration (heavy
line), and the rocalibration curve (dashed line).
calibrations
were within 6
the high pressures.
The two
at the low pressures and 1% at
Since it is unknown where this devi-
ation in calibration occurred, the old calibration values
were used in all calculations,
92
OLD CALIBRATION
NE
CALIBRATION
r-I
Cl)
0
8
12
16
AC2JL PE1JE, PSI
FIGTJRE 24
PRESSURE GAGE G LIBAiON
CURVE
9
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,
35-L is the fourth run with 35% solvent in water, ect.
OBSERVED DATA
(1)
Run No.
5-i
2
3
5
6
7
8
9
10
(2)
t,
°F
69.9
71.0
69.7
70.0
68.6
69.3
Pressure
tube
tube
ga ge, p si
Position
No.
Horizontal.
It
It
70.3
1
70..5
15
'70.6
16
17
70.9
70.6
ft
18
19
70.6
II
70Jj
70.6
'I
20
21
22
23
2fl
25
26
70J
7Q5
70.5
7r7
70.6
70.3
27
28
-
A
9.L0
II
T1
?1
1I
IT
I,
1!
'I
It
10.00
A
10.00
A
9.95
A
A
A
A
A
6.75
8.00
8.65
10.20
8.20
B
B
B
B
B
B
8.50
6.65
5.00
5.60
7.50
6.25
II
Ti
B
B
1I
13
I'
10.05
B
I,
If
9.75
9.95
A
A
A
A
TI
?0.6
A
A
13
1).
12
(5)
Capillary
70,5
70.7
70.7
70.5
70.6
11
()
(3)
Capillary
B
B
5.55
6.65
6.65
6.65
6.65
(6)
Light
Intensity,
-
(1)
Run No.
We! ght
(8)
(9)
Time of Orifice
tube
sec
(7)
Capillary efflux, Manometer, mm
efflux, g
5-i
2
3
14
5
6
7
8
9
10
11
12
13
it4.
205.5
199.1
186.0
189.1
165.7
172.3
1914.14
171.6
161.7
1!4J.3
166.t4
181.2
196.14
23
201.3
205.8
165.0
129.9
121.2
163.5
161.2
153.5
139.5
214
163.2
15
16
17
18
19
20
21
22
25
26
1143.9
27
28
191.9
193.5
29
175.3
30
31
32
33
33A
314
35'
36
37
38
39
140
141
20-1
2
3
(10)
168.5'
1514.7
266.7
263.2
263.8
213.0
267.5
269.6
2142.2
67 (Hg)
142 (Hg)
720
660
86
io14(cCl)
IT
814 (Cc114)
69
"
259
IT
660
660
600
/ r
o7
600
660
720
720
720
660
600
00
2140
2140
300
360
270
300
300
360
270
300
360
II
632.
113 (Hg)
57
"
II
133
"
76
79
79
TI
131
TI
II
53 (Cc114)
315
38 (Hg)
70
103
158
30
19
I,
It
TI
TI
It
II
1414
135'
101
79
5'
'I
I,
IT
55'
2L0
216. 2
2L0
2614.14
300
300
2140
J.
14.63
'
2140
2140
2140
2140
II
67 (Hg)
107
91 (CC114)
210
"
"
360
300
360
360
300
2140
2140
66
52
206
193
88
128
127
'
8
II
7)4
78
"
147 (CC114)
237
214
(Hg)
141
59
85
19
12
31
78
62
50
IT
It
51
It
IT
51
'I
Si
It
38 (Hg)
Si
140
II
I!
II
II
IT
198( CC1L)
572
67
1 214
"
(Hg)
"
38 (0c114)
1461
66
(Hg
914
Manometer, mm
720
265.2
218.2
257.5
23.5
Test Section
1I
N
I,
71 (Cc114)
27 (Hg)
II
36
53
26
28
27
II
'
'
U
157 ( CC U )
1420
14J4
65
"
(Hg)
"
148 (Cd14)
379 Il
)Q (Hg)
(1)
29
30
31
32
33
33A
(2)
70.6
70.6
70.6
70.7
70.5
70.8
5)
31L
70.b,
35
36
37
38
39
70.8
70.9
70.5
70.'
70.2
C
C
C
140
70.1.
70.Ii.
C
C
141
20-.1
70
3
14
S
6
7
8
9
10
11
12
13
15
16
70.7
70.5
70.7
70.8
70.6
7o.
70.6
70.6
70.2
70.6
70.5
70.8
70,8
70,6
C
C
C
C
19
70.3
20
21
C
C
C
C
22
23
2t
2
26
27
28
29
30
31
314
35
36
70.9
70.3
70.5
70.2
70.J
70.9
70.9
3.20
L.90
I . .05
3.50
3.95
3L 30r
o.1
3.90
-
5.145
-
3.50
7.00
7.65
9.10
21,0
-
2.j0
3.00
225
-
5.20
3.9
ID
6.00
0
A-I
A-i
*
-
6.20
60
ID
-
:
C
D
-
8:95
7.05
2.65
2.50
6.05
C
C
D
D
21.0
21.0
20.5
*
0
70.L.
70,5
70.7
70.7
70.5
70.6
70.7
70.6
70.6
70.7
L.00
C
70.5
70.2
S
)4 : &
C
17
18
18A
7.30
5.80
B
B
C
C
C
C
C
C
(6) 95
:
g
7.35
6,10
-
21.L,
-
-
(1)
(7)
20 -L
256. 2
2)40
278.8
99
S
21±0
111
(Hg)
"
261±. 7
300
300
55
22
"
2140
149i
501
6
7
8
C,
10
11
12
13
1 ).
15
265.7
26L.
2)5. 8
206.5
202.2
(3)
300
300
51±0
196.9
L8o
23L.. S
203 . 3
201 1±
L.0L
L0
1±20
(10)
(9)
(Cc1L4.)
"
(Hg)
(CC1,)
158.7
14.30
18A
89
89
2±1±.
2L0
291 (ccl
214.0
702
366
",
711
506
"
598
395
"
214.0
2)40
373
150
2L0
393
20
21
22
23
2L
25
26
27
28
29
30
31
32
33
35
219.5
159.0
193.3
177.5
289.9
208.8
22. 2
293.7
326.3
255.1±
32.0
301.0
287.14.
160.5
171L.5
U
173.7
127.5
132.7
21i0
2L0
2L0
21±0
21±0
21±0
180
180
180
14.05
20
14.25
(Hg)
55 (cc114..)
92
576
3214.
583
U
114.
"
356
31±7
LL9O" "
1±714.
597
500
1±93
"
14.80
::
"
"
"
L85
2
214.0
88
62
21±0
122
81
100
119
1
.2
303.3
L.6
281±. 8
iSo
1±7
237.5
265.7
120
120
180
130
120
105
50
51
52
-,-)
21 . 7
255.7
239.7
90
(Hg)
(Hg)
U
129
107
1714.
208
i5L
192
239
2±8
"
"
"
"
LjLo (cc1
312
"
68
(Hg)
iLLS
I?
14.67
14.39
14.68
LL
L2
76
U
LLSO
176.5
196.1
i1
555
"
31±7
L3
132.14.
"
(Hg)
(Hg)
3214.
"
611.
58
593
566
538
244
352
"
591±
225
571
360
300
300
300
300
/0
(CC!;,)
Li.22
"
595
585
180
14.60
"
lI
586
1±80
1±20
(Hg)
391
iSo
14.80
14.1
381 (CC1L4.)
61
(Hg)
61
26 2( CC 11±)
1431± (cc 114.)
19
9
147
2070
I1L,
OL/.)
(Hg)
65
55
232
000
(Hg)
63
114.2
"
16
17
202.6
68
75
U
121±
"
11±2
38
385(CC1,.)
00
(Hg)
98
"
96
(1)
37
38
39
(2
(3)
70.b
70.L
F,
tJ
L.6
70.L
70.3
L2
)43
LL7
L8
L9
50
51
52
5'3
35-1
2
5
A-i
A-i
F'
70.9 Vertical
70.6
70.5
70.3
70.5
,,
70.6
!Ll
(L)
B
B
Pr
F!
B
'F
C-2
C-2
C-2
C-2
F'
70.3
70.3
70.6
Fr
F,
C-2
'F
F)
70.8
70.8
F,
Fr
F,
p
Ft
70J
26.0*
11.10
25. 5*
F,
70. L
'F
F1
I,
C
C
C
C
25. 5*
10.05
25.0*
25.5*
3.95
26.0*
25.5*
5.95
7.70
9.90
12.50
2.60
3.80
25.0*
25.5*
26,0*
,.00
25.5*
25.0*
10.05
C
70.Lt
70.L
(6
9.25
5.85
6.00
7.35
0.70
F)
70.6
70.5
70.5
B
(5)
5.75
25. 5*
18.5
6.55
-
6.70
7.35
16.5
17.5
18.0
7.35
* indicates photocell and light 1/20-Inch apart. All other'
readings with photocell and light 1/8-Inch apart.
6
70.5 Horizontal
7
70.6
8
9
70.3
70.3
10
11
70.14
12
13
1!4.
70Ji
70.5
70.6
70.6
'F
F!
1,
tl
'F
F'
'F
15
16
70.)4
'I
70.LL
F,
17
18
19
70.2.
20
21
22
23
2L.
25
26
27
28
29
30
70.5
70.5
70.5
70.8
70.9
70.9
70.9
70.9
70.9
70.8
70.6
70J
70JL
'F
C
C
C
C
C
F)
F)
F)
F)
O
0
o
IF
F)
F,
F)
'F
0
F?
B
F,
F'
'F
F,
PT
F,
B
B
B
B
B
B
'F
F)
F,
'F
6.30
5.)4.O
7.05
5.35
6.65
L.90
5.90
6.55
5.75
5.1.5
7.35
6.10
6.25
5.35
5.00
10.70
11.25
12.25
12.85
11.55
12.20
11.10
7.L5
1.0
iB.o
17.5
18.0
18.5
18.5
18.5
1.0
i8.o
18.5
lu.O
iO.o
18.5
18.0
iB.o
18.0
(1)
35-1
(7)
217.8
2
2.9 .
3
276.5
251.9
27L.8
S
6
7
e
9
10
11
12
13
114
15
16
17
19
20
21
22
23
2
25
26
27
28
29
30
31
32
33
3L
35
36
37
38
39
23L!.8
200.3
261.5
196,7
2!8.1
227.9
278.7
267.5
260.5
261.0
265.7
29).7
256,0
232.5
161.9
156.0
175.8
161.7
120.9
123.5
116.3
352.5
297.6
333,0
333,9
369.9
332.0
359.1
297.9
367.0
297.8
332.7
263J
2L6.3
195.8
22.5
50-i
2
3
5
6
7
8
177.1
209.L.
189.9
191.8
207.5
232.9
201.9
199.5
(9)
300
300
300
300
300
300
300
300
300
300
(10)
398 (CC
H
666
L23
t1
U
53 (Hg)
H
66
ci
H
'I
91
H
39
H
20
tt
2L.0
U
22W
U
I,
L3
2LQ
hh
180
210
58
20
2L.0
2h0
71i
76
70
73
L8o
L20
U
H
U
U
U
L2
:300
LJ
U
300
L2
U
137
153
U
187
150
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