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.

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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 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

k

I

FLOW RATE TJRN, SEC1

FIGURE 5. SHEAR STRESS AT WALL OF CAPILLARYVERSUS RECIPROCAL SECONDS

19

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

11

1-4

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

FIGTJBE 9

MANO}4ETER BOABD UNGEMENT

29

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.

FIGURE 10

LIGHT AND PHOTOCELL PROBES

2+ 25 26

HALF SIZE

721

6 21 22

8 9

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)

HiHB3 R8

I

R6

S6

//!

31/

FIGURE 11

WIRING DIAGRANFOR

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 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

8 I I I I iiiil I

0.1 1.0J, LB/EC

FIGURE 12PLOT TO DETERMIIE OW PLATE

5].

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.

APPENDICES

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

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i-.

i- '.D

'0

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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

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0000

0000

0000

0000

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0000

0000

oo0'

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0 0

on()

n n

C)

C)

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) 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

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0'0'

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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

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