The effect of liquid characteristics upon the breakup of a liquid jet

(1)

THE EFFECT OF LIQUID CHARACTERISTICS UPON THE BREAKUP

OF A LIQUID JET

by

RICHARD ANTHONY CHMURA

Submitted in Partial Fulfillment

of the Requirements for the

Degree of Bachelor of Science

at

the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

August,

1976

Signature

of

Author,

• t ••'

Signature redacted

•• I • • • t e e e f • • I t e • t • t • ♦ t t e e t t t t • t t t t t

Certified

Accepted

Departm~nt of Chemical Engineering,

August 9, 1976

Signature redacted

by· • • • • • •

~ts'G

· · · ·

'"

·~so· · · • •...,... · • • · • · · · • · · •

/J

c?

n

Signature redacted

by •••••

~

.H~~d·of·th;'O;p;.;.t~;~t···

· vMIVfS W.tic::c· I c:-; INSTTU,i: OGY ~ U l

1

994

(2)

Professor

Department of Chemical Engineering

Massachusetts Institute of Technology

Cambridge,

Massachusetts

021)9

August 9, 1976

· Secretary of the Faculty

Massachusetts Institute of Technology

c

· ambridge,

Massachusetts

02139

Dear

Professor

In

accordance with the regulations

of

the Faculty,

I

herewith

submit

a thesis entitled "The Effect of Liquid Characteristics

Upon the

Breakup

of

a Liquid Jet~ in partial fulfillment of

the

requirements for the

degree

of Bachelor of

Science

in

Chemical

Engineering

at the Massa,:-husetts Institute of

Technology.

Respectfully

submitted,_

Signature redacted

V

(3)

dedicated

(4)

ACKNOWLEDGEMENTS

The author would like to 6Ypress his sincere gratitude

to the following people for their contributions to the

execution of this projects

Mr. Stan Mitchell; for supplying apparatus.

Mr. Jack Russell; for help in setting up apparatus.

Mr. Barry Trager; for help in computing the data, and advice

in the method of photography, Mr. Richard Zippel;

for their advice in the method of

and photography.

Mr. David Martin;

Prof. Larry Evans; for the use of his camera.

Mr. Paul Bletzer; for construction of the nozzles.

Very grateful thanks are expressed to Prof. Kenneth A. Smith and Mr. Earl Woltz foritheir invaluable guidance

(5)

ABSTRACT

Breakup of a liquid jet injected into the immiscible

liquid medium water was studied as a function of liquid characteristics such as density, viscosity, and interfacial tension. It was generally determined from photographic evioence that the previous cirrelation set forth by Meister and Scheele relating drop volume to the density, viscosity, and interfacial tension, was valid only for liquids with a viscosity less than 7 centipoise and interfacial tensions

greater than 30 dyne/cm. As interfacial tensions drop below

30 dynes/cm., they account for a very substantial drop in

specific surface area. As the viscosity rises above 7

centipoise, it decreases dramatically as a significant

factor in determining drop volume. Therefore, it was determined that to maximize specific surface areait was most desirable to minimize viscosity and maximize interfacial tension.

It was also determined that previous studies

relating:-specific surface area to flow rate and nozzle diameter were indeed correct.

(6)

Table of Contents

I. Introduction

A. Freeze Water Purification Process

B. Liquid Jets

C. Brief Literature Survey

D. Purpose II. Experimentation A. Apparatus B. Choice of Systems C. Procedure III. Results A. Data B. Discussion C. Error Analysis IV. Conclusions V. Recommendations

Appendix I Tabulation of Data

Appendix II Detailed Experimental Data

Appendix III -Nomenclature

Bibliography

1

4

6

9

10

13

16

18

38

45

47

49

50

68

122

123

(7)

I. INTRODUCTION

A. FREEZE WATER PURIFICATION PROCESS

A freeze water purification process is very much

concerned with the spraying ofnlquid jet into a liquid

medium. The flow diagram of a direct contact refrigeration

process for water purification is on the following page. Direct contact refrigeration is employed- in the crystllizer section (marked by the dotted line) of a

freeze water purification process to produce an ice slurry.

The slurry is supercooled slightly. The temperature difference

between the equilibrium freezing point of the solution in the crystallizer and the actual slurry temperature is the solution

subcooling A Tss which drives the growth and possibly

the nucleation processes.

Refrigerant is injected into the crystallizer through

numerous nozzles in the crystallizer base. Since the density

of the refrigerant will be different than that of water, the

refrig-erant will either rise to the top or sink to the bottom of the

crystallizer where it will be drawn off and/or will evaporate.

During its movement, the refrigerant liquid is in contact with

the warmer ice slurry. The temperature difference between

the evaporation temperature of the refrigerant and the solution is the driving force for evaporation,AT evap'. The sum of

AT and ATevap. is the overall temperature driving force. The heat transfer which takes place between the refrigerant and the slurry is proportional to the temperature difference and the area as follows:

(8)

v A I RA Collo SOLT 17p CRYS TF+LL

K-

IZER URI es 0-p IoV02

s L

- e-EF IC

58f

1(~~JT R~G~R~N

% SftLT W A7/o M oRg COA/C.

CON paccu WAIF S%~ \6 Af.IAG-W ASH en W4,"PR s II/IX y MELTE A

FRESH

w

A -r r--r 5 i

(9)

(3)

QhA(Tslurry

_-

_{Trefrigerant)}

The area dependence is important.

Due to the surface

tension

of the refrigerant, the droplets rise as spheres.

For a

given volume of refrigerant, the

number of droplets

formed is

N=

-(/3)77rd

The overall surface area is

A - N47rr

2

_3v/r

The contact area between the refrigerant and the slurry

increases as the radius of the refigerant

droplets decrease.

The economics of the process is such that if the surface

contact area could be increased, then the

heat transfer

would be more efficient and a savings would result.

In

regard to this fact, it is important that the breakup of the

(10)

B. LIQUID JETS

When a jet of liquid issues from a nozzle into another

liquid: the jet eventually breaks up into drops. For a drop

on a horizontal circular tip, _{withliquid being added, the}

visual changes which occur ax the flbw rate through a nozzle is increased~can be described as follows. At low flow rates

a drop is formed immediately at the tip of the nozzle*

and grows in size until the welight, or buoyancy force

over-comes the interfacial tension and the drops break off, At

increased flow rates, a point is reached where a thin neck of continuous liquid 6xists between the tip of the nozzle

and the point of drop formation; this point is called the

jetting point. As the flow rate is increasedthe let length

increases rapidly. Finally, as the flow rate continues to

increase,the jet begins to become very cloudy at its outer

edge and the drops formed are not very uniform. This point,

which is near the- point of maximum jet length is called the

critical point. At flow rates greater than this, atomization

occurs, where the jet length decreases back to the nozzle

tip _{and a spray of very small bubbles of nonuniform size}

occurs.

In the first _{region, before the jet forms the} _droplets

which form are very large and nonuniform in size. At a point just past the jetting point, the drop size is a b4t

smaller but very unifon" in ths size. The drops continue

to decrease in size while maintaining their uniformity. to

a point just below the critical point. _{This is the point}

(11)

suddenly-appearywhich accounts for the decrease in surface area. As the flow rate increases past the critical point the

rate of appearance of these large drops, and nonuniformity in general increases, which in turn leads to a leveling

off and subsequent dropoff of the surface area.7

The following diagram illn'strates some of these points.

MAX. SURACEI I _ARIA DROP PORMATION II ATOMIZATION CRITICAkL

LIQUID FLOW R1ATE -- ~

(12)

C. BRIEF LITERATURE SURVEY

Liquid jets were first investigated by M. Plateau1 0.

who, in 1873, showed that a cylinder of liquid subject to

surface forces is unstable if its length exceeds its circumference.

Iord Rayleighl8 set forth several postulates concerning wave forms on a jet in a paper delivered to the Royal Society

of London on May 15, 1879. These initial .findings formed

much of ttm basis for further work.

E. Tyler1 0 , in 1933, applied Lord Rayleights Theories to

the prediction of drop size when a fluid jet disintegrates. Tyler's experimental results agreed with the predicted drop

volumes. H.C. Merrington and E.G. Richardson performed

similar experiments and further substantiated Tyler's predictions. These results were presented to the Royal -Society of London

in 1947.

Consequently, this led to work concerning the shape

of the jet undergoing disintegration.

Simon

L. Goren

,

of the University of California at Berkley, derived an.'

expression for the shape of the thread of liquid undergoing

breakup, assuming that the isurface area of the thread

is alwvays a minimum for given constraints.

Most of these earlier studies of the breakup of liquid

jets and subsequent drop formation were concerned with

gas-liquid systems.

These systems have been studied up to the

present and have resulted in studies by Phinney

1, who has

presented us with a report on the influende of the initial

disturbance level on the stability ofaillaminar Viscous

(13)

t- I/ O

Jet, and by- Phinney and Humphries1 5_{, who have completed a}

study on the influence of nozzle- shapes on the stability

of a laminar jet of viscous liquid.

Obviously, the work in this area has been substantial,

but since it relates to gas-liquid systems it is not really

-applicable to the problem at hand which concerns itself with the breakup of a liquid jet in a liquid medium, and subsequent

drop formation. Some of the earliest work, in this field,

though very limited, was done by Christiansen and Hixson3, who in June 1957, presented some very early experimentation

and theory on the breakup of liquid jets in denser liquids.

Probably the most significant work in this field was done by Bernard Meister and George Scheele who.presented

10

us with some significant results. In July 1967 they presented

a generalized solution of the Tomotika stability analysis for a cylindrical jet, in which they analyzed the stability of cylindrical jets in immiscible liquid systems. In

19688, they presented a paper in which they developed

a correlation for predicting the drop volume for injection at low volocities of one Newtonian liquid into a second

stationary immiscible Newtonian liquid in the absence of surface active argents. Their work came to a cumultive head when,

in September, 19699, they presented a theoretical analysis for predicting the size of drops formed from- a laminar

cylindrical jet when one Newtonian liquid is injected through

a nozzle into a second immiscible Newtonian liquid. This

cumulative theoretical work was _{much' more far reaching than}

(14)

(8')

theory in the field.

This major piece of generalized work has led other people

to more specific areas. Kroessor and Middleman5 _{in 1969,}

have done extensive work in the field of the breakup of a jet of a linear viscoelastic fluid. In July of 1971 Lenczyk and

Kiser7 studied the problem of the stability of a vertical jet of non-Newtoniah fluids which had been, for the most part,

2

ignored. Chazal and Ryan have, more recently studied

the formation of organic drops in uater and, although their

testing included many liquids of varying properties, they

were more concerned with non-jetting conditions.

All of these developments were very important and have led us far up the road to understanding the problem at hand.

However, most of the developments were very theoretical, and not yet thoroughly proved to be reliable in practical

applications. This is where the current investigation becomes important. In the current problem, it is vitally important.

as explained earlier, that the surface contact area be

maximized in this contact refrigeration process. This is where

concrete experimental$c.. evidence is needed to present us

with facts which will allow is to develop the most efficient

system and system parameters. This is precisely the

thinking that led to the forerunner to this work, which was completed by Woltz, Carroad, and BenderiB at M.I.T. in January

1970. Their findings gave substantial evidence that specific

surface area of the droplets reached a maximum at some intermediate flow rate and that specific surface area was an inverse function of nozzle diameter.

(15)

D.

PURPOSE

The previous work and, in particular the recent work

of Woltz, Carroad, and Bender have provided

us with some very

useful information, but, in fact, it

is just a start since

much more is needed before an efficient

contact refrigeration

system can be designed.

It is the purpose of this research to extend the

beforementioned studies to the question of how do the liquid

characteristics such as density, viscosity, and interfacial

tension affect the specific surface area of the droplets.

More specifically, what I attempt to determine, is which

liquid characteristics directly affect the droplet size

and/or the breakup of the jet and in which way.

If successful

in determining such relationships, it will allow for us to

select the most efficient refrigerat In the contact

refrigeration process.

One other benefit will be that it will

also allow us to judge tre accurucy of u substantial

part of all the theoretical formulation,

wftica

has in the

(16)

II. EXPERIMETATION

A.

APPARATUS

For the most part, the same experimental appa-ratus

used by Woltz, Carroad, and Bender, and as pictured in the

following figure, mrbw:6 used to conduct this experiment.

There were rour ma-ii.. components to the apparatus

used in this experiment, a test liquid reservoir, a flow

system, a water reseryoir, anda_ photographic setup.

The flow systema consisted of *1" copper tubing, and

all the joints were all : made with " brass ferrule rings.

The reservoir wvas. connected to a nitrogen cylinder by

copper tubing, and tnils pressurized Ithe reservoir.

A valve between the pressurized tank and rie nozzle was

the method for adjusting the flow r ates along with the cylinder

regulator valves. The nozzles-:i.dre::> connected directly

to the right angle joint in the water reservoir. This method

of controlling the flow was very _{effective in producing even}

flow rates.

The test licuid reservoir was a five gallon stainless steel tank. Since it vras to be pressurized it ras equipped

with a pressure relief valve and gauge, as a precaution

against over pressurization due to a faulty regulator valve.

Also, since the tank had to be cleaned after each liquid Was

testedit was made with a large opening at the bottom for

easy.entrance. During experimentation this hole ras covered

with a blank flange and gasket.

(17)

UP GoD -IT

WhITr stAciT OoP

I- 4I 4 . o No zz iL GT A-GUF O VT -WA T.1hT -- WA/9TERR TSSK

ITA ix

N -.TROD Y c ottl f*ApRELIEF VLV JC, N 5 GAL. S-. STL TAWI S RVktR R4 CofpE R TL INCr VALVE / / 4-- SC.YLIND P AN-L T

(18)

C~ I./CJ

long by 12 inches deep. A ruler vtat e*. suspended in

This tankto show-bubble size.

The photographic setup was d6finitely the most difficult

to determine. Following the previous works of Woltz, Carroad,

and Bender, a Polaroid camera, model 95B, was first used.

However due to the poor quality

of pictures, the difficult

manner

.of

adjusting the settings, the limitations of the'

camera, and the expense of the film, this method was discarded.

After much research and consultation, it was found that

due to its ease of operation, versatility, and inexpensiveness,,

a Miranda 35mm camera could be used,

if

equipped with a close up lens.

It was mounted on a tripod and focused approximately 12 inches

from the aquarium. Spotlights (200 watt) and a white

background provided the 2;ecessary uniform light and a cable

release was used to prevent any unnecessary movement during

the photography.

The film was Kodak Tri-X and was shot

at ASA 400 with a shutter speed of 1/125 second and

,an

ape.rture

setting : of f8.

This setup was used to obtain 3" x 5'

black and white photographs.

This apparatus was

set up under a fumae hood to avoid

(19)

(I5J

CHOICE OF SYSTEMS

Three basic decisions had to be made in this experiment. First, a choice of nozzle sizes had to be made. Second, a choice of flow rates to be used in the tests had to be made. Third, a group of liquids with a wide enough variation of properties to give the final correlations, needed to be chosen.

The nozzle sizes were chosen by reference to previous works. Once the sizes were establishedthe nozzles were e constricted in the Chemical Engineering Machine Shop.

Nozzle

A

.052 in.

B

_{.035 in.}

C

.025 in.

Once the nozzles were obtained they were attached to the system and tested to see which flow rates were obtainable*

for each nozzle using each different liquid. It was thought

that if all the liquids were compared at the same flow rates, better correlations between the properties could be derived.

Therefore after much testing the following flow rates were chosen.

(20)

%; ."r'

Floib* rates (ml/sec.)

Nozzle~A

Nozzle B

Nozzle C

2.17

1.00 .83

4.33

1.42

1.00

6.33

-

2.50

1.33

7.25

3.16

1.63

8.00

4.00

2.08

8.33

4.50

2.50 Our third and final choiceiwas the choice of the liquids

to be used in the experimentation. Some considerations Which

had to be taken into account when choosingihen were that,

Uirst, they had to be safe to work with; second, they had

to

be immiscible in water;

third, they had to be a

liquid at room temperature ; and fourth, they had to vary

significantly in density, viscosity, and interfacial tension

with water.

The safety consideration was taken care of by checking

out each liquid under consideration with manuals and the

M.I.T. Safety Office.

The last three considerations were realized by

searching

through handbooks and previous articles~and finally putting

together a list

which would satisfy all of the requirements.

(21)

used)follows:-~ 4

Systems

A Heptane

B

55%

CC14-

45%

Heptane

C

95%

Benzene-

5%

Acetone

D Chloroform

E

Chlorobenzene

F CC1

4 Density (g/cc)

0.68

0.986 0.870 1.489

1..11

1.59

Iiscosity

centipoise)

00.42

00.488

00.552

06.99

14.8

01.03

Interfacial

tensi&n

(dynes/cm)

51.0

32.0

20.2

32.8

37.4

45.0

Also, it was necessary, since all were clear liquids, that they would have to be dyed to give a cont'ast of color

with water, _{To accomplish this, Calco Oil Red N-1700 which}

was chosen because of its lack of effect on interfacial characteristics, was obtained.

(22)

C. PROCEDURE

The experimental procedure for this research consisted

basically of two parts.

In the first part, for each liquid used the system must

be calibrated. The flow rate can be adjusted via two actions.

One is increasing the pressure of the tank, and the second

is by opening or closing the mechanical valve. The system

was calibrated by first replacing the aquarium with a

1000ml. graduated cylinder. Then by knowing the liquid

level in the cylinder beforehand, the mechanical valve was opened to various incremental levels and the liquid

was allowed to flow for one minute. The change in the

liquid level was then measured to give the flow rate. This

was calibrated for all three nozzles at 2.50 psig,

3.75 psig, and 5.00 psig. Then, after calibrating it

could easily be determined what settings would give the beforementioned desired flow rates for each nozzle.

The second and most important part of the test procedure was as follows:

1. Thoroughly clean the tank and system from previous use.

2. Mix the test liquid with CALCO OIL RED N-1700 until a

dark red color is attained.

3. Pressurize Lne tank to tne desired setting.

4.

Upen the valve until the test liquid is coming out

and all water and air bubbles have been removed from the system.

(23)

5.

Write on the ruler with a grease pencil, what system

and run number you are doing.

6.

Turn on the lights. Upen the valve to the desired

increment. Position the ruler and camera. Take tne

picture. Wait

15

seconds. Take another picture.

7. Uo

to

3

for duplication, or next set of conditions.

This procedure was carried out for every nozzle and

every test liquid used, and resulted in at least two

3"

x

5"

black and white photographs of each set of conditions

(24)

III. RESULTS

A. DATA

The experimental procedure resulted in two photographs

for each set of conditions for each test liquid. Once the

film was developed and the photographs were obtained it

was then necessary to evaluate them.. The photographs

them-selves showed a ruler with a metric scale surrounded by a

large number of droplets. Due to the large number of droplets

it became necessary to count those in a small control volume,

The drops were then counted and classified into six groups;

**4tm, 3mm, 2mm, IauW, 2mm,and *mm radii.**

Once we have counted the droplets we can convert this

to specific surface area, which is the surface area per

unit volume of fluid passed through the nozzle..

Total droplet surface area

'i 7

specific

. 4 3surface area,

Total droplet volume

This reduces to

I'i

However, the radius for surface area is called the effective

radius, and is defined _{Re_} _M

Therefore, specific surface area reduces to

3/Reff

Since all of our

_{measurements are made in mm. it}

will

then be necessary tn multiply by ten to get the specific

surface area in units of cm

2

_/

_cc.

(25)

Appendix I shows us our results in tabulated form while .

Appendix II gives us the drop distribution breakdown of

each individual photograph.

The following figures graphically demonstrate our results

by plotting the specific surfacf nrea of each liquid versus

(26)

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q. / r

It was also felt that since this study might be used to predict results of other systems of the same or similar liquids, the results should be plotted non-dimensionally.

Therefore, using my experimental data, the graphs were

made for each liquid system, plotting

a)vs.

and

using as a parameter. There

(-V)

specific surface area (C C)

GIN nozzle diameter F

(ATC-velocity through nozzle 5

/7

(

t/^ kinematic viscosityJ

interfacial tenslion: (d^ C

density of dispersed phase

These graphs, if used for these liquids or similar liquids,

(45)

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(49)

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(50)

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(51)

B._ -DISCUSSION

When analysing this data; it becomes very clear--that

certa'.n previous studies have been verified. First of all we can plainly see that for each nozzle size, the specific

surface area reaches a maximum at some flow rate.

Interest-ingly enough, these maxima, in most cases, are abruptly reached, which is the same phenomena witnessed by Woltz, Carroad, and Bender.1 8 _{A probable explanation for this,}

at least in these experiments, was that since the flow rates

to be tested _{were chosen beforehand to cover a wide variety}

of rates, it was not possible to observe the flows of each

individual system, _{and nozzle size, and thus test} _{flow rates} which are closer to the point of maximum area. Had I done so,

it is quite possible that we might-have noticed that the maximum area point, was attained at a much more gradual

pace than accounted for here,

It _{is also quite noticeable from this data that.. the}

nozzle size does _{indeed have a great deal of}_{effect on}_the specific surface area. In fact, this data confirms beyond doubt, the previous findings that _{as the nozzle size} _goes

down the specific surface area increases.

One last _{observation which can be noticed by just looking}

at the graphical results, is that strangely enough all of

the _{systems seem to reach their maximum area point at the}

same flow rates. _{This can be explained by the fact that,} again, only one flow rate in each approximate area was tested. _{Therefore, it is not impossible that each reached}

(52)

(37)

unreasonable to assume, that each reached its maxima in the

same general areas of flow rates. Thus, since I only tested

one flow rate in each general area all of the systems seem

to reach their maxima at the same flow rates, when in fact, this was probably not the case.

So far I have just discussed the results in relation to previous findings. Now I would like to get down to the point at hand. When examining the graphical evidence, it is very evident that there is a definite grouping of liquids you can

make with respect to the specific surface area of the drops

which they break up into. System C (Benzene-Acetone),

consist-ently breaks into the larger droplets. Eystem-D,. (Chloroform)

although its _{droplets are smaller than those of system C,}

has has droplets which are still larger th% the other

liquids. Systems A (heptane), B (CCl4-heptane), E

(Chloro-benzene), and F (CC14) _{produce droplets which seem to be}

in the same general size ranges, although E and F do show a slight tendency to produce smaller droplets.

Comparing these observations with the list of liquid

properties on the preceding (pages, it is not readily

notice-able which properties, and to what extent and in which direction) affect the specific surface area, Therefore, since there is

no one property which dominates the surface area phenomena, there is a good possibility it is some relationship,of some or all of the properties which is the determining factor.

To gain some insight into this problemlet us review some of the findings of Meister and Scheele9 _{who set forth an}

(53)

L7 V

equation predicting drop size-using previously formulated

stability theory. 1 0 The part of the eqdation which concerns

us . is the fact that the drop size is inversely proportional to (ka)max which is the dimensionless wave number of

the dominant symmetrical wave.~ This relationship was also evident in a similar, but less exact equation set forth by Schiffler.9

To continue our study we should note that (ka)max can be easily evaluated, using the stability theory set forth by Meister and Scheele.1 0

First, a correlating parameter is formulated.

(rP'D,

=interfacial tension

viscosity of continuous and dispersed phases density of continuous and dispersed phases

D9_A.

₌

_{nozzle diameter}

Next the value of'Xis determined. Then the following

method is used to determine (ka)ma. Using the values of ANo

and and the- following figure we can obtain a value of ka

--. - .-- ... ...

0.2

0.3-

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Then by calculating$and knowing# we can use the following

graph to abtain a value ofCo .

-0.024 0.016 N" C -0.016 - - - - - -- - - - - -2. 5.0 --0.032 --- ----0.048- ---0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 P P

VWhere

(ka)max =+ CO

we can solve for (ka)max.

From this method we can see that the value of $will

have the most effect on the final answer, only if the value

of Miis

below

50. If a. is below

,50,then

to get maximum

surface area (smaller drop volume) conditions, the value of

should be between .2 and

.5.

If No is above 50 then-is not

a very important factors, and Witself is the major factor.

In

both the above cases the value of tis a very minor value,

although at lower values of

N

,

a low value off

will

'

decrease drop volume slightly.

In general however, for this

method the viscosity of the dispersed phase is the major

determining factor since it

is the major term in the calculation

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viscosity reading will resnilt in a lower value of (ka)mi as will an extremely low viscosity, although to not the same degree as a high value.

I now used this method to determine (ka)max, for my six. systems.

/

0.43

0.51

0.575 .7.30

15.41

1.1

1.47

1.01

1.15 .67

.90

.67

.670

.584

.40

.08

.043

.53

(ka)max

.612

.61

.59

.458

.391

.592

1/(ka)max

1.63

1.64 1.69

2.18

2.56

1.69

*NOTE;, These calculations were made for nozzle C

(

D,= .025"=.06350m).

From these values it is plane to see that these results

do not entirely agree with the ones obtained experimentally.

However, we should note that certain similarities do exist..

Firstly, in both cases, systems A and B are quite similar

in terms of drop size,

**Also, syste* D shows a definite trend**

in both cases of larger drop volume. The most glowing difference

is the fact that) while experimentally system C". showed the

largest drop volume of all, when evaluated by this criterion

it should show that its drop

volume is comparable to systems

A, B, E, andF. Also, experimentally the drop volume of system

E was comparable to system F) while according to Meisterts theory,

the drop volume of system E-should be the greatest. The slightly higF

System

A

B

C

D

E

F

(56)

%. F .0,

value of system F could easily be explained by experimental

error.

When noting these differences it is interesting to note that Schiffler9 _{who also had the drop volume inversely}

proportional to (ka)maxi had a snap off constant, B, in the numerator, to give us Vf a B/(ka)max. B is a functi ion

of interfacial tension, decreasing from 6.0 for an

interfacial tension of

1.8 dynes/cm. to 1.7 for

an:

interfacial

tension of 40 dynes/cm. Therefore, we have the general result that drop volume increases with a decrease in

inter-facial tension. AlthoughA.Ieister and Scheele also have this general relationship apparent in their findings, it is

clear that it plays a much more important role in Schiffler's t'heory. If we insert this fact into our results we could

have an explanation for the larger drop volume of system C.. Even though its viscosity is. not high, and by the methodr

of Meister and Scheele its drop volume is grouped with the other system, it seems quite obvious that its low interfacial tension accounts for the higher drop volume. This is consistent with Schiffler's observations.

As far as the differences involving system E, it becomes clear that its high viscosity accounts for its predicted large droplet size by the method of Meister and Scheele.

How-ever, from our experimentationit is clear that its high

interfacial tension is the major factor in accounting for its smaller droplet size, and that its high viscosity value is.

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17 7J

Therefore, we can see that at high viscosity values7 the

form-ulation of Meister and Scheele does not apply.

By studying these previous facts and by looking back at

our experimental evidence, it seems fairly clear that the

main factor in determining drop size is the interfacial tension. It is especially apparent that the interfacial tension

factor is much more of a factor atlow values. The viscosity value is also a major controlling factor,with the lowest drop volume coming at values between .1 -and 1.0 centipoise.

How.-ever, as the viscosity rises above

7

centipoise, it ceases

to play a major role in determining drop size. The density

factor i'

_{also seems to affect droplet size slightly,}

with a low value of

f

_{decreasing droplet size slightly,}

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YL -5 ]

C. ERROR ANALYSIS

Although the experimental procedure was carried out

carefully, there remain several distinct possibilities

for error.

Interpreting the photographs was the main source of

error. _{In the photographs where a large number of droplets}

existed and a controlled volume was used to count the drops,

there was _{probably a slight deviation of droplet size from}

the entire sample. _{There was also the possibility of an error}

in counting the droplets, although this was very carefully

done. _{Probably the biggest problem in interpreting the}

photographs was in determining into which size group in

which they belonged. _{This was especially apparent in the}

case of small droplets, because the smallest division on the ruler was lmmgand therefore educated guesses were frequently used., However, I do believe I was

consistent-in my ;judgements.

Another possibility for error was _{the controlling of the}

flow rate. _{Since a mecharicdl valve was used,} _{it was}

probably not possible to duplicate flow conditions each time

a situation was tested.

Another _{possibility for error which was not mentioned}

earlier is _{the fact that wid-ely. varied flow rates were tested.}

Therefore it could be possible thatAsystem was showed to peak at a certain flow rate, when in fact, it might have

peaked at a flow rate which was _{a little} _{greater or lesser}

(59)

LY'J

-a la-rge error if one wanted to compare the systems which seemed

fairly close in droplet size sucf as systems A and B.

however, _{in this}study, _{general trends were} _{desired, and I} believe this was _{ac very small error factor} _{in this regard.}

The last poisibility for error in my results was with the question of reproducibility of the data. Since,

when calculating the specific surface area, the average

effective radius was takenf'rotr the two photographs taken of each situation, there was a possibility that a great

deal of uncertainty could result if the two _{values from}

which the average value vas calculated, were very different.

However, it is felt _{that a very good reproducibility A}

was achieved, and that almost all pairs of values were

(60)

IV CONCLUSIONS

1. The previous studies which showed that a maximum surface

Sarea

point was reached at some flow rate, and the fact

that

specific surface area does increase with a decrease

in nozzle size have been substantiated.,

2. The droplet volume correlation set forth by Scheele and

Meister proved to be applicalle at interfacial tensions

of greater t#an 30 dynes/cm and with a viscosity ratio

of less than 7.3.

3.

In general, a decreasing of interfacial tension will increase droplet size,.. However, while at intermediate to high interfacial tensions (r > 30 dynes/cm) it is

not the dominant factor -. while at low interfacial tensions,

it is indeed the dominant factor and will increase

droplet size, regardless of other proerties.. Thus, the formulation of Meister and Scheele is not applicable.

4.

In general, a high viscosity will increase droplet size. However, at high values of

A-ji(>

7), it is apparent that

the viscosity does not have as significant :an effect as

itcontinues to rise. Thus, in this instance also, it is apparent that the formulation of Scheele and Meister does not apply.

From the preceding conclusions, it is apparent that

when investigating for a refrigerant to use in a contact reL Trigeration process, it would indeed be most efficient, in

(61)

(9X)j

scheme.

One should avoid the low interfacial tension and high

viscosity systems.

Once in these general areas, one should

strive to maximize the relationships set forth by Meister and

Scheele, which generally state that one should try to maximize

interfacial tension while trying to keep the viscosity

ratio

(i)

between

0.1

and

1.0 .

The density ratio,

although a much smaller factor, could be used to decrease

(62)

t77J

YT-RECMIENDATIONS

. _{The effects of a vertically placed nozzle as compared}

to a horizontally placed nozzle in the system should

be studied.

.2. _{The effects of centrifugal force on droplet size should} be studied by using a rotating nozzle in the system.