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1964 High Vacuum Distillation. David Bernard Greenberg Louisiana State University and Agricultural & Mechanical College

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GREENBERG, David Bernard, 1928- HIGH VACUUM DISTILLATION.'

Louisiana State University, Ph.D., 1964 Engineering, chemical

University Microfilms, Inc., Ann Arbor, Michigan HIGH VACUUM DISTILLATION

A Dissertation

Submitted to the Graduate Faculty of the Louisiana State University snd Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy

i n

The Department of Chemical Engineering

by' David Bernard Greenberg B.S., Carnegie Institute of Technology, 1952 M.S., The Johns Hopkins University, 1959 August, l$6k ACKNOWLEDGMENT

The author is deeply indebted to Dr. Bernard Pressburg whose

guidance, assistance, and direction were major factors in bringing

this research to fruition. Sincere appreciation is also extended to

Dr. Jesse Coates who took time from his busy schedule to offer council and advice on many of the theoretical aspects encountered during the

course of this work.

The author also wishes to acknowledge gratefully the aid received

from the Ethyl Corporation for lending the modified CMS-5 molecular

s till with-which the experimental work was carried out. Sincere

thanks are especially extended to Mr. Hoyt Cragg, of the Ethyl Corpora­

tion, who gave much technical assistance in setting up and operating

the still. Appreciation is also tendered to Charles Pfizer and Company,

Pittsburgh Chemical Company, Allied Chemical and Dye Corporation, and

Union Carbide and Chemical Company for supplying samples and physical property data which were used in this study. TABLE OF CONTENTS

PAGE

ABSTRACT...... vi i

CHAPTER

I INTRODUCTION ...... 1

II THEORY ...... 6

1. Theoretical Rate of Vaporization ...... 6

2. Significance of the Evaporation Coefficient ...... 10

III EXPERIMENTAL WORK ...... 1 7

1. The Centrifugal Molecular Still ...... 17

2. Modification of the Original S till ...... 24

3. Calibration Procedures and Physical Measurements . . 25

4. Test Materials...... 29

5. Sample. Preparation and Experimental. Procedure .... 32

IV INTERPRETATION OF RESEARCH ...... 35

1. The Mathematical Model ...... 35

2* Method of Solution of the Mathematical Model .... 45

3. Experimental R e s u lts ...... 47

V DISCUSSION OF RESULTS ...... 53

1. General ...... 53

2. Analysis of the Phthalate and Sebacate R uns ...... 58

3. Analysis of the Glycerol Runs ...... 62 CHAPTER PAGE

VI CONCLUSIONS AND RECOMMENDATIONS...... 67

SELECTED BIBLIOGRAPHY...... 70

APPENDIX

A NOMENCLATURE ...... 73

B SKETCH OF COORDINATE SYSTEM . ' ...... 75

C COMPUTER ANALYSIS OF EXPERIMENTALRUNS ...... 76

D NORMALIZED GRAPHS FOR SELECTED RUNS...... 98

AUTOBIOGRAPHY...... 104

i v I

LIST OF TABLES

TABLE PAGE

I Experimental and Estimated Evaporation Coefficients .... 12

II Centrifugal Still - Characteristics and Operating F eatures ...... 23

III Mid-Rotor Flow and Thermal C onditions ...... ' ...... 59

IV Constant Temperature Runs - Glycerol ...... 6 l

V Run No. k - G lycerol ...... 77

VI Run No. 6 - Glycerol...... j8

VII Run No. 9 “ G lycerol ...... 79

VIII Run No. 11 - G lycerol ...... 80

IX Ri|n No. 13 “ G lycerol ...... 81

X Run No. Ik - Glycerol...... 82

XI Run No. 15 - Glycerol ...... 83

XII Run No. 16 - G lycerol ...... 8k

XIII Run No. 18 - G lycerol ...... 8 5

XIV Run No. 19 “ G lycerol ...... 8 6

XV Run No. 20 - G lycerol ...... 87

XVI Run No. 21 - Glycerol ...... 88

XVII Run No. 23 “ G lycerol ...... 89

XVIII Run No. 25 “ Glycerol ...... 90

XIX Run No. 33 "Dibutyl P h th a la te ...... 91

XX Run No. 38 -Dibutyl P h th a la te ...... 92

v TABLE PAGE

XXI Run No. kj - Dibutyl P h th alate ...... 93

XXII Run No. 51 " Dibutyl P h th alate ......

XXIII Run. No. 59 - Dibutyl P h th alate ...... 95

XXIV Run No. 77 - Di (2-Ethylhexyl) Phthalate ...... 96

XXV Run No. 97 ■ Di (2-Ethylhexyl) S ebacate ...... 97 LIST OF FIGURES

FIGURE PAGE

1 Centrifugal Still - Front View ...... 18

2 Bell Jar and Receiver ...... 19

3 Centrifugal Still - Rear View ...... 20

k Diffusion Pump System ...... 21

5 Bell Jar and Calibrated Receiver ...... 22

6 Feed Pump C alibration ...... 30

7 Flow Pattern on Rotor - 50 C entipoises ...... 37

8 Flow Pattern on Rotor - 30 Centipoises • • ...... 38

9 Flow Pattern on Rotor - 20 C entipoises ...... 39

10 Flow Pattern on Rotor - 10 C en tip o ises ...... ^0

11 Experimental Rates - Glycerol • ...... ^8

12 Experimental R ates- Dibutyl Phthalate • • ...... ^

13 Experimental Rates - Dibutyl Sebacate ...... '50

11+ Experimental Rates - Di (2-Ethylhexyl) Phthalate .... 51

15 Experimental Rates - Di (2-Ethylhexyl) Sebacate • • • • • 52

16 Run No. k - Glycerol...... 98

17 Run No. 9 ■ G lycerol ...... 99

18 Run No. Ik - Glycerol ...... 100

19 Run No. 38 - Dibutyl P h th a la te ...... 101

20 Run No. 59 " Di butyl S ebacate ...... 102

21 Run No. 97 " Di (2-Ethylhexyl) Sebacate ...... 103

v i i ABSTRACT

Present knowledge in the field of molecular distillation has ♦ not reached the point where it can be applied to designing commercial s tills without extensive bench and pilot scale development. Analysis of the literature indicates that additional experimental data and improved methods of applying the fundamental laws of transport phenomena to this problem are needed. This research was conducted, therefore, for the purpose of contributing to the experimental and theoretical knowledge in the field.

The centrifugal s ti l l design was chosen for experimental study because there is a minimum of quantitative data published on this type of equipment, and because its unique geometry and operating character­ istics are such as to make it most attractive for future molecular d i s t i 1 lat i on app 1i cat ions.

Mean rates of distillation were measured for five pure liquids over a range of temperatures and feed rates. This experimental work was performed on a modified CMS-5 laboratory s t i l l that had an effective evaporating surface area of 100 sq. cm. The evaporation rates obtained for liquids exhibiting "ideal" liquid.phase behavior agreed quite well with theoretical values predicted on the basis of simple kinetic theory

(Langmuir equation). These liquids were the normal butyl and isooctyl esters of phthalic and sebacic acids. However, in the case of glycerol, an associated liquid, rate measurements were only 35 to 90 per cent

• • • VI i I of the theoretical rates. Although these low values tend to support

the concept of an "evaporation coefficient" as a true molecular property,

there was evidence that surface irregularities could have accounted for all or at least part of the discrepancy insofar as the centrifugal still

i s concerned'.

A mathematical model of the centrifugal still has been derived

which allows Langmuir's vaporization rate equation to reflect the

effect of fluid dynamics and heat transfer as they actually occur in

the s till. This model assumes a thin film of fluid in viscous flow

with a fully developed profile, but negligible normal and tangential

velocity components; it postulates that heat transfer is by conduction

only. Thermal gradients, fi lm thicknesses, and evaporation rates

calculated from this mathematical expression correlate well with

reported literature values as well as with the present data. It is

concluded that the model is capable of quantitatively estimating the

performance of the centrifugal s t i l l and of providing a sound method

which qualitatively predicts the influence of proposed changes in

operating conditions. CHAPTER I

INTRODUCTION

Molecular distillation may be defined as distillation which occurs

from the surface of a film of. liquid under an operating pressure such

that residual gas in the vapor space above the liquid may be considered

to have a negligible effect upon the process. When a low pressure environment and a nearby condensing surface are provided, escaping molecules have a relatively unobstructed path of travel between the evaporating and condensing surfaces. Since the distance separating

these surfaces is of the order of magnitude of the mean free path of

the vaporizing molecules in the residual gas, molecular distillation

has been termed, "short-path", or "unobstructed-path", d istilla tio n . g As Burrows describes this process it can be further catagorized

by comparison with the two more conventional types of d istillatio n :

(a) Distillation by boiling - Vapor is generated throughout the

liquid at a rate which is proportional to the heat flux; the total

pressure acting on the system is the thermodynamic vapor pressure of

the liquid phase.

(b),Evaporative disti.llation - Evaporation which occurs from a

liquid below its boiling point at a rate which is a function of the

surface temperature and of the vapor conditions above the surface

such as occurs in air drying of solids, humidification and similar

processes. (c) Molecular distillation - A form of evaporative distillation in which the rate is governed solely by the absolute rate of molecular escape from the liquid surface: that is, unlike the first two, there is essentially no return of molecules from the gas to the liquid, and the temperature and corresponding escaping rates attained by the liquid are determined by the heat input, and are unaffected by the vapor space conditions. It can also occur at temperatures higher than the boiling point corresponding to the vapor space pressure. Therefore, molecular distillation occurs at the maximum possible rate of vapori­ zation since the vapor molecules reach the condenser unhindered. It differs from ebullient evaporation because neither boiling point nor bubble .formation is a factor, and from evaporative distillation by the fact that it occurs whenever a temperature difference exists between the evaporating and condensing surfaces, and is independent of the vapor phase conditions except that the pressure must be very low.

Thus molecular distillation, because it represents a means of vaporization at low pressures and correspondingly low temperatures, finds utility in the separation and purification of high molecular weight and thermally sensitive materials, the volatilities of which are too low for distillation to occur at practical rates in conventional equip­ ment.

The theory and methods of applying molecular distillation to the separation and purification of various materials have been investigated and reported by many researchers over the past several decades. From po the earliest efforts of Langmuir J who predicted the evaporation rates from metal surfaces under high vacuum, molecular d istillatio n advanced through laboratory studies in which Bronsted and Hevesy purified mercury and Burch obtained liquid fractions from previously undis- tiliable petroleum residues (now known as Apiezon oils). Most of this early work was done on a batch scale in various pot-type, short-path s t i 11s.

The f irs t commercial application of molecular distillation appeared l6 in the early 1930's when Hickman utilized a glass fallin g -film .sti11 for the production of vitamins from fish liver oils. Improvements on this original design continued through the 19^0's; during this period the main emphasis was on spreading the distilland into a thin film and reducing the thermal hazard (high temperature exposure time) for heat sensitive materials. By the late 19^0's two distinct commercial designs had been established. First was the wiped-film still; this evolved as an extension of the original design which used rotating wiper blades to spread the falling distilland into a thin film. The second was based on centrifugal force; this design employs a rapidly rotating cone across which the distilland flows in an ever increasing surface area under the action of the induced high gravitational force.

Today, both s t i l l types are available in sizes ranging from the throughputs of less than one lite r per hour to large scale units which can handle several hundred or more gallons per hour.

Unfortunately, l i t t l e improvement on the basic design of these stills has occurred since the largest units became available about 19^9.

Perhaps the two most important factors responsible for the inertia which occurred in this area are the high capital and operating costs involved with this equipment on the one hand, and the inability of users to predict performance without extensive piloting on the other. This latter fact indicates that basic knowledge of the fundamental mechanisms of heat, mass, and momentum transport underlyfng the phenomena has not been used in describing this process.

However, because the current trends in the chemical and petro­ chemical industries involve more high molecular weight and thermally sensitive materials, renewed interest in this area is taking place. 18 Also, in the new and vital field of water desalinization, Hickman with his vapor compression s t i l l has endeavored to adapt the centrifugal

still design to the production of potable water. Among others, the 7 mathematical analyses of the evaporation coefficient by Burrows' in 15 195^ and by Heideger and Boudart in 1961 as well as the mathematical

treatment of heat transfer accorded Hickman's compression still by

BromleyJ in 1958, are clear evidence that this stagnation is being

overcome. ;

Despite the number of theoretical and experimental research papers 8 T5 published over the years and despite the compendiums available,

little effort has been directed to date toward evaluating quantitatively

the variables which describe high vacuum, molecular distillation.

Therefore, in view of continued interest in this field, it is felt that a renewed attack along experimental and theoretical lines would be of

significant value in aiding in the understanding of molecular distilla-

tion in order that it may take its place among the more conventional multi-phase mass transfer operations.

It was the purpose of this investigation to supplement existing

knowledge in the field by providing a mathematical and experimental

study of the centrifugal molecular still. The centrifugal still was chosen for this work because there are relatively li t t l e published data of a quantitative nature either experimental or mathematical on this design and because it involves new and unique applications of basic

theory..

Specifically, the experimental phase of the study was designed

to obtain mean distillation rate data at several feed rates and tem­ peratures for a variety of pure substances not all of which exhibit

ideal liquid phase behavior. A mathematical model was developed in which the equations of heat and momentum flux were related to such * parameters as film thickness, velocity, evaporation rate and temperatu i gradient, thus providing a basis of interpreting and correlating the experimental results. CHAPTER II

THEORY

1. Theoretical Rate of Vaporization

If a region of liquid surface could be examined on a micro-scale such that the interfacial dynamics were observable, theory suggests that the evaporation process would be found to take place by way of the following interrelated phenomena:

(a) The movement of condensed phase molecules on and beneath the surface, generating a constantly changing surface structure,

(b) The emergence of energetic molecules from the surface into the vapor space; they would leave the surface at all possible angles of escape, that is, in any direction within the enclosing hemisphere.

(c) Collisions among the vapor space molecules that cause many trajectory reversals and momentum exchanges.

(d) Bombardment of the liquid surface by returning molecules; some of those striking the surface remain (i.e. they condense), while others rebound into the vapor.

Although this is an oversimplified picture of the vaporization process, it provides qualitative insight into the relative influence of the individual phases. For example, the rate of vaporization would be a maximum if the vapor space were continually swept free of mole- 8 cules as fast as they appeared. Burrows defines the "rate of vapori­ zation" as the absolute rate at which molecules escape from the liquid.

6 ~ Points a and b indicate« that this rate is solely a function of the molecular species and of the energy distribution on the surface. • I This theoretical rate of vaporization has been calculated rigorously 20 2^ from kinetic theory considerations ' based on the assumption that,

(l) at equilibrium, the number of molecules entering and leaving the

liquid phase per unit time are equal, and ( 2) interactions among these molecules are non-existent. The former rate is analogous to the rate of molecular efflux of a Maxwellian stream under isothermal conditions.

Essentially, this development involves the determination of the number of molecules, emitted from a volume element BV in the vapor space, which are directed toward a unit surface Bs of the liquid. By assuming a Maxwellian velocity distribution, as would be true under equilibrium conditions, and allowing for the fact that a distribution of free paths exist, the number of molecules striking a unit area, in unit time is obtained by integrating over all velocity space, and

is given by the expression:

\|f = jj— , molecules/time-area (2- 1)

Here N represents the number density of molecules in the vapor space and v is the mean molecular speed. Equation (2-1) is obviously the absolute rate of condensation or vaporization in the absence of molecular

hindrance effects at the liquid surface. The mass rate of vaporization, w, is obtained by introducing the molecular mass, m, and the density, p, into Eq. (2-1), thus:

( 2 - 2 )

o The "ideal gas" equation of state (2~3a) can be used to eliminate the density and an appropriate expression ( 2~3b) can be substituted for the mean speed:

p = MP/RT , (2-3a)

v =(8RT/*M) 1/2 , (2-3b) thus:

> w = P(M/2*RT ) 1/2 (2-3c) is the absolute rate of vaporization from a liquid surface. Equation

(2~3c) was originally employed byLangmuir2^ in his vapor pressure studies of tungsten filaments. If the thermodynamic vapor pressure P is expressed in mm Hg and the absolute temperature in degrees Kelvin,

Eq* (2"3C) may be written:

w = .0583P(M/T) 1/2 . {2-k)

It is interesting to note that Eq. (2~b), which expresses the theoreti­ cal rate of vaporization, indicates that molecular distillation is a function of the molecular specie and the surface temperature, and hence is a surface phenomena, as was previously postulated.

If the conditions in the vapor above an evaporation surface are such that an appreciable number of molecular collisions occur, the probability is that some of the vaporized molecules will be returned to the liquid; thus the net rate of vaporization will be somewhat less than the value obtained from Eq. (2-^). Furthermore, of those molecules that succeed in escaping from the evaporating surface some will un­ doubtedly be carried out with the vacuum system so that an even lesser number will actually reach the condensing surface. It is also reason­ able to expect that in the process of condensation some re-evaporation will occur so that the net rate of distillation is the actual rate of distillate collection.

In view of this discussion it is apparent that the Langmuir equation provides a limiting value for the rate of molecular distilla­ tion, but that it must be corrected to account for the losses des­ cribed above. Defining an efficiency coefficient as:

a _ _ rate of distillate collection ( 2-5) wg absolute rate of vaporization * the modified Langmuir Eq. (2-4) becomes:

w = .0583aP(M/T) 1/2 . (2-6 )

Thus in summary, the foregoing discussion suggests that there are three rates of evaporation which are of significance in molecular distillation studies: the Langmuir or absolute rate of vaporization as predicted by Eq. (2-4), the net rate of evaporation which reflects the effect of molecular interactions at the evaporating surface, and finally the rate of distillation which is the actual rate of distillate recovery at the condensing surface. From the practical viewpoint, the last of the three rates seems to be primarily a function of design and operation rather than of theory. That is, pumping losses can be minimized by maintaining the condensing surface close and in direct line with the evaporator, while re-evaporation losses from the condenser can be controlled by a judicious choice of operating pressure and condensing temperature. Under these optimum design and operating conditions, the net rate of distillation is essentially equal to the net rate of evaporation and the efficiency coefficient may be re­ defined as:

_ net rate of evaporation ( 0 - 7) absolute rate of vaporization

Thus "a", termed the evaporation coefficient, has alternatively been called the condensation coefficient or the accommodation coefficient. 22 Actually, the latter term was originally used by Knudsen to characterize energy exchanges between vapor and condensed phases; its use in this connection would only cause confusion and, therefore, only the firs t definition will be used in this thesis. A comparison of Eqs. ( 2-5) and ( 2- 7 ) indicates that the efficiency coefficient defined by the former equation and the evaporation coefficient are numerically equiva­ lent quantities only if the net evaporation and distillate recovery rates are identical.

2. Si gni ficance of the Evaporation Coefficient

The physical significance of the evaporation coefficient has been the subject of many theoretical and experimental studies over the past years. In the bulk of this research numerous attempts have been made to evaluate the evaporation coefficient as a real molecular pro­ perty. Although there is some experimental evidence that this may be true, only moderate theoretical progress has been made thus far. Of

interest in this direction, however, are the s ta tistic a l mechanical n Q theories of Polanyi and Wigner and Neumann, the absolute rate theory of Penner,^ and the free angle ratio postulated by Wyllie.^

Polanyi and Wigner, by assuming the surface to be composed of molecules oscillating about their equilibrium positions in an isotropic manner, were able to compute the evaporation probability of a surface molecule as:

f “ l/e"X/kT . (2-8a)

Here X is the energy of surface binding, V is the harmonic frequency of oscillation, and f is the evaporation probability per molecule per second, in this equation it was assumed that any energy fluctuation greater than X leads to evaporation. Because the results from Eq.

(2-8a) generated low probability values, a correction for molecular interactions was made. If a physical model for this calculation is taken to be an array of oscillating point masses, the evaporation probability factor is described by Eq. (2-8b).

f ~ e' X/kT (2-8b)

Subsequent simplification and rearrangement yields a value of the evaporation coefficient:

X/N a = ,,2.2 (2-9) ■m V d where N is Avagadro's number and d is the mean molecular diameter.

A comparison of experimental values with those calculated from

Eq. (2-9) is presented in Table I for various compounds. It can be seen that agreement is generally fair to poor.

The approach used by Neumann was leased on a uniquely determined molecular surface state described, by the Maxwellian energy distribution function f(v), and the spiatial distribution function, p(d), of molecular centers of gravity. By associating a potential energy e(d) with a perturbation d(x,y,z) about the equilibrium point for any molecule, and TABLE I

Experimental and Estimated Evaporation Coefficients

Evaporation _ Coefficient . , Angle Temp. Compound Exp‘l Eq.(2-9) Ratio (°c) Ref.

Benzene 0.90 O.O78 O.85 6 36

Carbon Tetrachloride 1.0 O.79 1.0 0 1, 36

Chloroform 0.16 0.086 0.5*4 2 36 -*4 Dibutyl Phthalate 1.0 O.O52 ~7x l 0 20 2

Diethyl Adi pate O.I77 0.5*4 O.O5 0 33

Di (2-Ethylhexyl) Phthalate 1.0 0.0*42 ~6x l 0 ^ 100 19

Di (2-Ethylhexyl) Sebacate 1.0 0.0*40 ~5x l 0"7 136 19

Ethanol 0.02*4 0.20 0.018 12-15 5

Glycerol 0.05 0.06 0.0*46 19 15

Glycerol 1.0 0.06 0.0*46 18-70 3*4

Methanol 0.0*45 0.30 0.0*48 0 36

Water 0.0*42 O.O33 0.0*4 0 11 ■

Water 0.027 O.O33 0.0*4 *43 11

Water •35-1*0 O.O33 0.0*4 7-50 . 25 by defining the periphery of the sphere of influence in terms of the energy of vaporization as e(dQ) = X, one can express the evaporation probability at the surface as:

00 f = a) J* p(dQ)f(v)dv . (2-10a) o

Upon integration over the entire sphere of attraction this yields

f “ “ '2nm 1/ap’(dJ o > ( 2- 10b) whe re

-X/kT

The integral in Eq. (2-11) represents the volume contribution to the ~ 9 partition function of the condensed phase. Knacke and Stranski have demonstrated that, for ideal behavior in the vapor phase, Eq. t (2— 10b) reduces to Eq. (2-2), which infers that the evaporation co­ efficient approaches unity. They have further indicated that Eq. (2-10b) reduces to Polanyi and Wigner's Eq. ( 2- 8b) for the special case when:

c(d) = 2Jt2V2m d2 , (2-l2a) and

-X/kT

" ”p(d„ ) = rr • (8' ia,) A

As was the case with Polanyi and Wigner's Eq. (2-9), only fa ir agreement between theory and experiment was obtained. 0>T pQ Also of interest are the theoretical developments by Penner '* who considered the problem first from the viewpoint of classical chemical kinetics by treating evaporation as a unimolecular process, and later from the standpoint of non-equilibriurn absolute reaction rates,

in the former case an evaporation rate was defined as:

w = j p/N*^ , mass/time-area . ( 2- 13)

Here p is the mass density of the evaporating substance, N is the molecular density, and the rate constant, j , is described by the © expression:

j e = Be"X/kT . (2-14)

By relating the frequency factor B to the activation energy of the evaporating molecules, based on a free volume model description of

the liquid state, the following equation was obtained for the evapora­

tion rate:

w = ( # ) 1/ a (—eT7o) e 'X/kT . (2-15) K VfN

Good agreement has been reported for the evaporation rates predicted by this equation and by Langmuir's Eq. (2-3c), for several non-polar, 2 0 unassociated liquids such as CCl^, CHCl^* and CgHg. In this analysis

the activated state was described physically in terms of a transition plane in which gas-like molecules moved freely between the condensed and vapor phases.

Based on a more general application of this theory, Penner con­ cluded that the implied assumption of equilibrium between the normal and activated states led to an excessively long energy barrier and thus rejected the equilibrium concept on the basis that the free volume model was inadequate. To account for non-idea1ity in the liquid state, he redefined the rate constant in terms of the partition functions and an accommodation coefficient K.

je = < > f * ' X/kT (2-16)

The complete partition function is given by Q, for the liquid state, and by Q. for the activated state. By substitution of Eq. (2-16) into Eq. (2-13) an

The resulting expression is given below:

w = ™(sZa)WS ■ I*-1?)

It was recognized that Eq. (2-17) had to be modified in order to account for association and steric effects in the liquid phase. The modifying factor for liquids,with hindered rotation was suggested by 21 Kincaid and Eyring to be the ratio of the rotational partition function in the liquid to that in the gas. This ratio has become known as the free angle ratio. Thus Eq. (2-I 7 ) with the introduction of the free angle ratio

W ^ KP(SkT) 1/2 ’ l2- ‘8) Wyllie^ was the first to identify the evaporation coefficient with the free angle ratio. He obtained confirmation for several polar liquids; in other cases, however, agreement is poor as is indicated in Table I.

From the preceeding discussion, it is apparent that, although strong experimental evidence has been reported to substantiate the postulated evaporation coefficient, there is as yet no adequate theory in support of such findings. The statistical mechanical, kinetic, and absolute rate theories that have been thus far advanced still leave unanswered a number, of fundamental questions. Such effects as vapor phase interactions, surface energy distributions, molecular orientation steric, and surface structure considerations, as well,as the range, magnitude, and distribution of surface forces to name just a few, are s t i l l relatively unexplored factors in the present theoretical models. CHAPTER III

EXPERIMENTAL WORK

1. The Centrifugal Molecular Sti11

The centrifugal s t i l l used in the experimental phase of this investigation is a modified version of the CMS-5> manufactured by the Consolidated Vacuum Corporation, Rochester, New York. This still is a laboratory size, self-contained, batch (or semi-continuous) unit with a charge capacity of approximately 1500 cc. It consists of a cone shaped evaporating surface which rotates in a vertical plane, associated feed, distillate, and distilland receivers, and auxiliary vacuum and heating equipment, and their controls. The main portion of the apparatus is suspended beneath a horizontal base plate which sup­ ports the primary drive mechanism and the glass bell jar enclosure.

The base plate also contains the vacuum manifold and a ll other connec­ tions to the enclosed working parts. The bell ja r provides a condensing surface facing the conical rotor and in addition serves as a reservoir for the feed liquid charge. The photographs, Figs. 1, 2, 3> ^ and 5, illustrate the physical setup. Table II provides additional information on the characteristics and operating features of the still. Specific details of the still construction and operation are available in the

CVC instruction and equipment bulletins both of which'are obtainable

17

« Figure 1. Centrifugal S till - Front View Figure 2. Bell Jar and Receiver Figure 3. Centrifugal Still - Rear View Figure k. Diffusion Pump System Figure 5* Bell Jar and Calibrated Receiver TABLE 11

Centrifugal Still - Characteristics and Operating Features

Rotor Aluminum, No. 108 Alloy

Rotor Feed Tube Spun Aluminum

Rotor Gutter 30*t Stainless

Feed Pump Housing Meehanite, Type "G.E."

Feed Pump Gears Steel

Feed Pump Shaft Drill Rod Steel

Rotor Outside Diameter k 1/2 inches

Rotor Center Flat^ 7/8 i nches

Rotor Slant Height 2 i nches

Rotor Face Angle 15°

D isti11ing Area 100 sq.cm. (Effective)

Rotor Speed I65 O-I675 rpm

Rotor Heat Input 500 Watts (Maximum)

Throughput IO-35 cc/min

Charge 100-1500 cc

’fThere is an additional 1/8 inch flat on periphery.

*^The center dimple is 3/8 inch in diameter. ^1 * 8 ^*5 from the manufacturer as well as from other published sources.

2. Modi ficat ion of the Ori qi nal S ti11

In order to adapt the original equipment for the experimental rate studies in this research several design changes were made.

(a) A distillate receiver was fabricated from a conical bottom centrifuge tube. The tube, graduated in 0.1 cc intervals through the firs t 10 cc and 1.0 cc intervals up to kO cc, was fitted with clamp type glass vacuum joints, 0-ring sealed top and bottom, with a stop cock in the discharge line. The receiver was attached to the 3_way stop cock on the bell jar condenser at the top and to the feed reservoir at the bottom where a matching connection had been previously welded to the bell jar reservoir. With this arrangement distillate could be either returned directly to the feed reservoir or shunted through the calibrated receiver for rate measurements and then returned to the reservoir. A pressure bleed to the top of the receiver was used to facilitate drainage. The photographs in Figs. 1 and 5 show the distillate receiver attached in place on the bell jar.

(b) The vacuum pumping capacity of the system was increased by

the addition of a second two stage, glass, o il di ffusion-ejector pump, + type GB-25* The two pumps were installed in parallel in the vapor line between the mechanical forepump and the s t i l l . The pump heaters, however, were series connected and operated from a single variable auto-

Vc Instruction Bulletin 35"A, Consolidated Vacuum Corporation, Rochester, New York. t * * Bulletin 3~1, Consolidated Vacuum Corporation. + This pump is identical to the original and was supplied by Consolidated Vacuum Corporation. transformer. This added pumping capability minimized vacuum losses from the numerous glass and tube seals and connectors throughout the system. In order to eliminate contamination of the pump fluid, cold traps were added to the vacuum manifold; one was upstream of the dif­ fusion pumps (between the s t i l l and the pumps) and the other was downstream (between the diffusion pumps and the forepump).

(c) The standard CMS-5 still has no provision for pre-heat treat­ ment of the entering feed. Consequently, in any operation whereby a cold feed is introduced to the evaporator cone some of the heat input must be sensible rather than latent heat. This represents an evapo­ rating capacity loss which is undesirable although not critical from a production standpoint; however, in this study it was importaiit to main­ tain isothermal conditions on the cone surface insofar as was possible.

Therefore, a hot oil heat exchanger was installed on the feed line. The discharge line from the pump, an integral part of the pump shaft, was extended up through the base plate to the preheater and back again to the feed position at the rotor hub. The connections through the base­ plate were steel welded fittin g s and the tubing was aluminum. The heat transfer oil, a silicone fluid,* was circulated by means of a

laboratory air-motor from a thermostatically-controlled bath which was heated by a .5 KW resistance immersion heater. A bimetallic calibrated dial type thermostat was used to control the bath temperature.

3. Calibration Procedures and Physical Measurements

(a) Vacuum measurement: While it would have been desirable to

obtain a measurement of the absolute pressure in the working space

Dow 55O Silicone Fluid

j between the evaporating and condensing surfaces, the location of a pressure sensing device in this region on the present equipment is quite impractical (from a design standpoint). In order to obtain a fair estimate of the working space pressure therefore, two vacuum gauges were used, one upstream and the other downstream of the evaporator.

The upstream gauge, located in the branch line that tapped into the bell jar envelope through the base plate, was the Pi rani (hot-wire) type gauge supplied by the still manufacturer. It is a dual scale instrument having a high sensitivity range that extends to 1.0 micron of mercury absolute pressure. The second gauge, an Alphatron (NCR- •k 515B), was installed in a short line just off the main mainfold about two inches downstream from the baseplate. This instrument is also graduated in 1.0 micron intervals and readable to 0.1 microns in the

1-10 micron range. Since these pressure sensors bracketed the evaporator, an arithmetic average of the two was taken to represent an estimate of the working space pressure.

The gauges were calibrated by comparing their readings simultaneously with a McLeod gauge which is a standard reference vacuum measuring instrument. In this procedure the bell jar was isolated from the system by blanking off the vacuum manifold at the base plate and replacing the downstream cold trap by a special manifold that provided connections for the two gauges and the standard. With the system thus isolated the pumps were capable of producing and maintaining an absolute pressure of about 0.1 micron absolute pressure. A small dry-air bleed was intro­ duced into the system to set the pressure at a desired value. Each

A complete description of vacuum measuring instruments may be obtained from Dushman. See Ref. 13* instrument was adjusted at a pressure setting of 5 microns and tested at 10 and 1 microns, respectively, against the McLeod standard. It was found that both gauges gave reliable readings in this range and rarely was there any noticeable drift although the instruments were checked frequently in the early stages of the experimental work.

(b) Temperature measurement: The measurement and control of the main distilling liquid temperature was a major concern in this experi- * mental study. The s ti l l is normally equipped with a single i ron- constantan thermocouple located in a groove on the rear face of the

rim at the periphery of the cone. The distiH and residue flows across

this probe before entering the stationary gutter surrounding the cone.

Published reports for this type of installation indicated that readings within several degrees of the true film temperature were to be ex­

pected. 3^*35 | n order to calibrate this thermocouple, a test thermocouple was constructed from No. 32, glass wool sheathed iron-constantan wires.

The beaded tip was about .10 mm in diameter. Several rough tests were made at ambient pressures and temperatures up to 139° C using a butyl

phthalate feed. In these primary tests the feed temperature was set

at a chosen value and the probe was moved from point-to-point across

the rotor. In almost all cases the probe temperature reading was

slightly higher than either the feed or residue temperatures by about

one-half degree centegrade or less. The difference between the latter

values never varied by more than 1.0°C. The residue temperature was

estimated to the nearest half degree. The high readings registered by

the test probe were therefore attributed to frictional energy dissipation

effects of the distilland against the probe. It should be mentioned that

the residue probe was properly positioned in its groove according to the procedure described in the CVC Instruction Bulletin No. 35"A, prior to testing.

To ascertain the effect of high evaporation rates on the residue temperature probe the above testing procedure was repeated after first positioning the test probe on the rotor and then pumping the system down to the normal operating pressure. The thermocouple leads were

connected to terminals on the baseplate. It was found that temperature differences between the test probe and the residue probe never exceeded

1.0°C, averaging about 0.6°C. Based on these results it was concluded

that maximum temperature differences between the feed and residue were

1.0°C at the highest evaporation rates and generally lower at modest

feed temperatures. Therefore during any run when the preheater and

rotor heater were adjusted so that the feed and residue thermocouples

agreed to within 0 .1°C the change of the mean film temperature across

the rotor was assumed to be less than 1.0°C.

(c) Feed Pump Calibration: The feed pump, a constant volume,

vane-type, rotary pump operates totally submerged in the bell jar

reservoir well. The hollow drive shaft, which serves as the discharge

line, extends vertically to a rotary shaft seal in the baseplate. It

is coupled to the main shaft by means of gear transmission. The feed

pumping rate is determined by the size of the spur gear in the trans­

mission. The speed of the pump can be changed quite readily by manually

disengaging the spur and worm gears and replacing the former. A

choice of four gears is available-: 80, $ 0 , k0, and 30 teeth.

With the installation of the preheater as described previously

in section 2 (c), the additional fluid frictional losses reduced the

maximum feed rate by a factor of two or three. The pump was calibrated using a series of glycerol-water solutions with viscosities covering the range from 2 to 400 centipoises. The calibration test procedure, performed at ambient conditions, consisted of submerging the pump in a

1 liter beaker of the test mixture, engaging the transmission and recycling the mixture for several minutes until steady flow was obtained.

The soft aluminum tube which fed the rotor was bent slightly and a short length of plastic tubing attached so that the discharged fluid could be directed back to the feed beaker. For each gear the rate of collection of five 50 cc samples was measured and averaged. Reproduci­ b ility of these runs was excellent; a ll measurements were well within

1 % of the mean. The viscosity of each test mixture was checked with a Brookfield, model LVT viscometer before and after the series of

runs. The viscosity varied by about 2~3 9b f°r the more viscous solutions, being generally less viscous after the test. This variation was attri­ buted to energy dissipation as heat due to frictional effects. The arithmetic average of the two readings was taken to be the mean value.

The results of these tests are plotted in Fig. 6 as volume rate vs viscosity for the first three spur gears (30, 40, 50 teeth). The

rates attainable with the 80 teeth gear were so low as to be impractical

for this study. The peculiar shape of these curves is explained by

the theory thatthe decreasing rate at low viscosities is due to low

pump efficiency, but at higher viscosities the volumetric pump efficiency

increases sufficiently to override the frictional losses; hence the

rate increases accordingly at higher values of viscosity.

4. Test Materials

The compounds chosen for study in the experimental phase of this

investigation were: ( 1) glycerol; (2) di-n-butyl phthalate, FIGURE 6 □ c5.

FEED PUMP CALIBRATION

FEED GEAR 1 in-ru

— a Z o \ \ ~ o O FEED GEAR 2

* 111 a I— in- a ; - CO a lU uJ

a in 1------1------1---- 1—I I I I I I------l— i—i in it 10 10D ODD UISCOSJTV, CCENTIP0ISES3 (3) di-'n—butyl sebacate; (4) di ( 2-ethyl hexyl) phthalate; (5 ) di

(2-ethyl hexyl) sebacate. Glycerol was of special interest because its ‘ * viscous oily nature and its non-ideal liquid phase behavior provided a wide range of transport parameters for study. In addition a number of previous investigators have reported experimental evaporation coeffi­ cient measurements (see Table II). The other materials were selected because they have been the subject of earlier molecular distillation studies and therefore offer a basis for comparison between this and previous work in the area. These chemicals were obtained from the following sources:

(a) Glycerol - Fischer Certified Reagent, Fischer Scientific

Company, Fairlawn, New Jersey; purity, 99*4%; vapor pressure data, 15 Heideger and Boudart ; other physical properties: The Merck Index,

7 th ed., (I960), and Handbook of Chemistry and Physics, 40th ed.,

(1958-9).

(b) Di-n-butyl phthalate - Charles Pfizer and Company, Inc.,

Brooklyn, New York; purity, 99*0 % (min.); vapor pressure data,

Werner*; other physical properties: Data Sheet No. 567 , Morflex 140,

Charles Pfizer and Company, Inc., Dibutyl Phthalate Bulletin, Barrett

Division, Allied Chemical and Dye Corporation, and Physical Properties

Synthetic Organic Chemicals, 1964 edition, Union Carbide Corporati’on,

Chemicals Division.-

(c) Di (2-ethyl hexyl) phthalate - Charles Pfizer and Company, Inc.

Brooklyn, New York; purity, 99*0 °/b (min.); vapor pressure data, Werner,

A. C. Werner, "Vapor Pressure of Phthalate Esters," Industrial and Engineering Chemistry, XLIV (1952), 2736-2740. jC Perry, and Weber ; other physical properties: Data Sheet No. 567 ,

Morflex 110, Charles Pfizer and Company, Inc.,"Elastex" 28-P Plasticizer

Bulletin, Plastic and Coal Chemicals Division, Allied Chemical and Dye

Corporation, Phthalic Anhydride, 1961 edition, Plastics Division,

Allied Chemical and Dye Corporation.

(d) Di ( 2-ethyl hexyl) sebacate - Charles Pfizer and Company,

Inc., Brooklyn, New York; purity, 99.0 °A> (min.); vapor pressure data, $ Perry and Weber ; other physical data: Data Sheet No. 556, Morflex

210, Charles Pfizer and Company, Inc.

(e) Di-n-butyl sebacate - Charles Pfizer.and Company, Inc.,

Brooklyn, New York; purity, 99*0 °/o (min.); vapor pressure data,

Perry and Weber ; other physical properties: Data Sheet No. 556 ,

Morflex 2^0, Charles Pfizer and Company, Inc.

5 . Sample Preparation and Experimental Procedure

Because accurate rate measurements were the primary goal of this « experimental investigation, it was important to use high purity materials

Although the samples obtained for study were a ll assayed at 99 °/o

pure or better, it was necessary to pre-process each compound to insure

maximum purity in the starting material. Therefore, each sample was

redistilled prior to making rate measurements. The procedure was to

» charge the still with 1500 cc, and circulate the liquid while pumping

down the system with the forepump and gradually increasing the rotor

heat input. When the liquid no longer bubbled or frothed, the diffusion

pumps were engaged and the heat input was increased until a modest rate

E. S. Perry and J. A. Weber, "Vapor Pressure of Phlegmatic Liquids," Journal of the American Chemical Society, LXXI (19^9)* 3720* of d istilla tio n was obtained* The d istilla te was collected until the rate fell off noticeably, at which time the heat input to the rotor was increased. This process was repeated until approximately 5 00 cc of distillate was collected. About four or five distiHand cycles were required to obtain this quantity of d istilla te . After exchanging distillate receivers the process was again repeated until a ^00 cc heart-cut had been collected. The still was then shut down, drained, washed thoroughly with xylene then with acetone, and dried. After it was reassembled, the system was purged with purified dry nitrogen for several hours. During the latter stages of purging the forepump was run intermittently to insure that the nitrogen was pulled through the entire system. This cleaning procedure was followed routinely every time the s t i l l was opened.

In order to obtain some measure, of quality improvement by the t aforementioned pre-processing technique, samples of the original charge, fore-cut, and heart-cut were qualitatively analyzed by chromato­ graph. ..Since no primary standard was^available, a quantitative assay was not possible, but the chromatographic traces for both the original material and the fore-cut showed several small and a single large peak, whereas in the heart-cut trace only a single uniformly large peak was obtained. These results indicate that the initial distillate cut removed the light ends as well as a portion of the heart material; thus, it was concluded that a very high degree of purity was obtained.

For the experimental rate determinations the initial degassing procedure was analogous to that described above. The 5 00 cc heart-cut was charged, the forepump was used to pump the system down, and the sample was circulated and warmed until completely degassed. When the pressure was reduced below 200 microns of mercury the diffusion pumps were turned on. If there were no gross leaks, an loperating pressure of 1-5 microns was attained within 10 minutes. While the charge was being circulated, the preheater was adjusted until the desired feed temperature was reached. The rotor heater was roughly set during this time, then gradually adjusted until the feed and residue temperature readings agreed. When steady operation was obtained, the distillate was shunted to the calibrated receiver and a measured volume collected.

A cumulative time record was kept of successive 5 cc samples until a total of kO cc had been collected. By so doing it was possible to ascertain roughly whether or not there was a significant drift from the pre-set operating conditions. If any pattern of increasing or de­ creasing times for successive volume intervals was observed the entire run was repeated.

After a satisfactory run was made the sample was returned to the bell jar reservoir and the temperatures were readjusted to new values.

The general pattern followed for a^l .samples was to make three or four runs with ascending temperature intervals then repeat the pattern while reducing the temperatures. This series of runs was made at each feed rate starting with the highest. CHAPTER IV

INTERPRETATION OF RESEARCH

1. The Mathematical Model

(a) Fluid dynamics - The mathematical analysis commences with a general description of the flow-phenomena. Liquid is fed through a stationary tube to the inside base of a truncated rotating cone.

Friction between the liquid and the cone wall tends to cause the liquid to attain the same rotational speed as that of the cone. The centrifugal forces set up in the liquid, generated by the rotational motion of the cone, w ill in itiate liquid flow along the walls from the base toward the periphery of the cone. At high rotational speeds, the layer formed against the wall will be very thin.

Therefore, the application of the equations of motion to this fluid dynamical situation is based on the following primary considera­ tions:

(1) The thickness of the fluid film 8, is small in comparison with the cone dimensions.

(2) The flow within the film is entirely viscous.

(3) The flow is assumed to be rotationally symmetric.

In addition, from an evaluation of orders-of-magnitude of the various terms occurring in the equations of motion for viscous flow the following assumptions may be made:

(1) The velocity component in the direction of rotation (the tangential component) is very small when compared with the radial

3 5 component. This implies that the liquid has the same rotational speed as the cone. Thus the path traversedby any liquid particle with respect to the cone surface is straight and radial. Stroboscopic photographs of particle pathlines, shown in Figs. 7 through 10, are visual proof of this.

(2) The velocity component in the normal direction is small with respect to the radial component.

(3) The radial velocity change across the rotor is small com­ pared to its change across the film.

Therefore, by neglecting inertial effects and the normal and tangential velocity components, and assuming a constant sta tic pressure i Vc the jation of motion can be written as :

P a 2 g cos

u = 0, y = 0 at the wall (4-2) = 0 , y = 6 at the free surface .

The particular solution of the differential equation which satis­ fies the given boundary conditions, is

(4-3) U = 2 C1(^ Y " y2)

The volume flow rate at any radius £ is determined by computing

‘the quantity of liquid flowing through the cross section:

The nomenclature is given in Appendix A; a sketch of the coordinate system may be found in Appendix B. Figure 7 . Flow Pattern on Rotor - 50 Centipoises Figure 8. Flow Pattern on Rotor - 30 Centipoises Figure 9* Flow Pattern on Rotor - 20 Centipoises Figure 10. Flow Pattern on Rotor ~ 10 Centipoises 5 Q. = 2it£5u = J 2*£udy . (4-4) o

Substituting for u from Eq. (4-3) and integrating, the mean velocity becomes

u = ~ CjB 2 , (4-5) where, for large values of centrifugal force

p cos

u = sin

In order to obtain an equation relating mass flow and evaporation, the continuity equation is introduced by calculating the mass rate change over a layer of differential length

^ (£p6 u) + £w = o , (4-7) and defining the flow rate per unit perimeter

T = Bp5 . (4-8)

Equation (4-7) becomes

d(« D + - 0 \ , (4-9) V \ where dx has been eliminated by the geometrical\relationship Equatioh (4-8) can be integrated if it is assumed that the surface evaporation rate is constant across the rotor. It may be recalled

that evaporation is defined by the Langmuir Eq. ( 2-6 ) for molecular

distillation and is a function of the surface temperature. By assuming

a mean surface temperature for the film an approximate solution is

obtaine'd, subject to the boundary condition:

£ = i Q, r = To at the feed position , ( 4- 10)

thus,

i r - £ T + — (4 2 - 4 2.) = 0 . (4 - 11) ’ ^o o 2 sin ’o

Defining the following dimensionless parameters:

i* = r/r o (4-12)

Equation (4-11) can be rearranged to yield

I* = \ El - M f 2 - 1)] . (4-13)

In order to obtain 5 as a function of £, Eqs. (4-6) and (4-7) are

substituted into (4-13)J after rearranging one obtains:

8* = (-^)2/3[l - f5w(f2 - 1)] . (4-Ht) A Vc In a similar fashion the elimination of 5 among Eqs. (4-6), (4—Y), and ^ -jV (4-14) gives an expression relating u and £ :

,’c 1 1/3 2/3 U = I1* ) [1 - M f 2 - 1)] , (‘•-15) c

where, in Eqs. (4-13), (4-14), and (4-15) uW = u/u 0 ,

6 * = 5/6 " , (4- 16 ) o

P = 3^/(4A%o3sin ^ p )

(b) Heat transfer - In this analysis it is assumed that heat transfer occurs from the cone wall through the film by conduction, the

flux being exactly that required to supply latent heat for evaporation from the surface film. This assumption appears reasonable for the case whore the feed and mean distilland residue temperatures are stipulated to be equal. Therefore, if radiation loses and convective effects are neglected, the heat flux may be written as,

dq = (*r) 2nf£Tdx . (4-17)

By introducing the latent heat of vaporization into Eq. (4-17)* the evaporation becomes:

(^)dq = (^jr)2rt#VTdx . (4-18)

The rate of mass flow across the cone is

G = 2rt£pu6 . (4-19)

Eliminating u by means of Eq. (4-6), Eq. (4-19) reduces to:

G = C'C'4%3 , (4-20) f s

where

CJ; = q/ v, and = ( 8/ 3) (jt3a>2)sin

. 3®>3 f + 8 s l n V - # £ - . (4-21) f S

Here:

Cg = C^/2rt , and Cf = CjA/k

Equation (4-21) can be simplified by the following transformation

T = , and T* = t / t • (4-22) o

After rearrangement this substitution gives,

+ 2. T. - _ . (4-23) 3 4 3CfCssin«f> ' 3

Equation (4-23) is integrable providing that AT can be expressed as a function of £ (or 5). Recalling from Eq. (4-17) that AT/5 is proportional to q if the heat flux through the film may be assumed constant or if it varies only moderately across the rotor surface, then it is reasonable to write: \

ft-T— =».§_ _ f (£*) AT 5 “''5' > o o or ( 4 - 2 4 )

AT “ 5 = f (£ ) where f(£ ) is a functional relationship, to be determined, which depends on the evaporation. If Eq. (4-2*0 is substituted into Eq. (4-23 )> the resulting equation, rearranged in integral form is, t UT Jd (r W - - fc(3C c °-n--5i) IP'3f <«V* ♦ c , CV25) o J f s for which the boundary condition is:

t* = r* = 1 • ( 4- 26 )

From the previous restriction of a moderate change in the heat flux across the rotor, and the approximate solution of the continuity equation for thecase of constant evaporation rate, Eq.(4-14) may be expressed in terms of a mean or averageevaporation rate:

* * l _ -vp ^ 3 f(5 ) = 5 = (■**) [1 - Pw(4 2 - 1)] . (4-27) t

Furthermore, from Chapter II, the evaporation coefficient can be defined in terms of the ratio of experimentally determined mean evapora­

tion rate to the calculated mean value:

OL = w /w • (4-28) e

Thus, introducing Eqs. (4-27) and (4-28) into Eq. (4-25), integrating and rearranging the result, one obtains as the final expression:

p/O 1/U 8* = <-^) [l - (2*Ul - Cl - - l)]V3}] . PfS9) i e

2. Method of Solution of the Mathematical Model

Equation (4-29) is an expression relating film thickness of the

fluid and evaporation rate as a function of position on the rotor

surface. This expression, along with Eqs.•( 2-6 ) and (4-17) which respectively relate surface temperature to evaporation and film thick­ ness with temperature, represents a system of equations which provide an approximate analysis of the coupled phenomena of fluid dynamics, heat transfer, and surface evaporation for the centrifugal molecular s till.

Since Eq. (4-29) involves an experimentally measured parameter, the mean evaporation rate (w ), the numerical solution of this system of equations applies directly to the actual physical evaporation measurements obtained on the molecular still. The solution technique for any particular experimental run involves a series of initial parameter "guesses" and successive iterations to improve each earlier estimate. The calculations are repeated until convergence is obtained.

In the general computational scheme the evaporation surface is

divided into a series of small equal area segments) then, starting from

the feed position, an evaporation rate, w, can be calculated from

Eq. (2-6 ) for an estimated surface temperature. Using this value and appropriate initial estimates of oc and w, the film thickness is obtained

from Eq. (4-29)* By means of Eq. (4-17), f rom which a AT is evaluated, and the assumption that the bulk mean film temperature is the arith­ metic mean of the surface and the wall temperatures, an improved estimate of tlie surface temperature can be made. This value is used to recal­ culate the. evaporation rate from Eq. ( 2-6 ), as before. The iterations

are continued in this fashion until succeeding values of surface I temperatures and evaporation rates agree. These calculations proceed

for each area element in turn until the edge of the rotor is reached.

A new average evaporation rate, w, calculated from the individual values

is compared with the last estimated value) if agreement is not attained, the entire iteration procedure is repeated, starting with the latest estimated values of a and w. These tedious computations were performed at the IBM 1620 digital computer at the Louisiana State University

Computer Research Center. The computing time per run ranged from

1- 1/2 to 3 hours.

3. Experimental Results

A total of 102 isothermal runs were made on the CMS -5 centrifugal still using five different purified materials. These data are presented in graphical form, Figs. 11-15> plotted as rate vs mean temperature for each compound. Three feed rates were used in each series of runs.

Also, on these graphs, for purposes of comparison, are reported the theoretical evaporation rates, calculated by means of Eq. (2-6 )j this corresponds to an evaporation coefficient of unity.

The results of the computer analysis of these experimental runs are presented in Tables V through XXV in Appendix C. Film thickness, mass flow, velocity, temperature drop, and surface temperature, calcu­ lated as described in section 2, above, are tabulated for each run as a function of rotor position. In addition, for selected runs, graphs of these variables in normalized form have been plotted as a function of a radial position, dimensionless parameter. These graphs are shown in Figs. 16-21, Appendix D.

Defined as the same feed and mean distilland residue temperatures EUHPORflTION, CGMS/SQCM/'SEC] X 100,000 a a a EPRTR, E- C- DEG- TEMPERATURE, ED ER 1 GEAR FEED O ED ER 2 GEAR FEED □ 55JD GLYCEROL ED ER 3 GEAR FEED i 65JQ FIGURE 11 65U EUflPORRTION, CGMS/SQCM/SEC] X 100,000 1 O BOJO “10 JO 0 0 6 INBTL PHTHALATE DI-N-BUTYL EPRTR DG C, DEG- TEMPERATURE ED ER 3 GEAR FEED ^ ED ER 1 GEAR FEED O FE GA 2 GEAR FEED □ IUE 12 FIGURE 90J0 1000 QJQ EURPORHTION, [GMS/SQCM/SECD X 100,000 a a o T0J0 INBTL SEBfiCflTE DI-N-BUTYL EPRTR, E- C- DEG- TEMPERATURE, ED ER 3 GERR FEED ^ ED ER 1 GERR FEED O ED ER 2 GERR FEED □ OO J0 0 9 BOJO IUE 13 FIGURE ioao 0 0 1 1 120LO EUfiPORRTION, CGMS/SQCM/SEC) X 100,000 1000 l 2EHLEY PHTHflLflTE C2-ETHYLHEXYU Dl EPRTR, E- C. DEG- TEMPERATURE, ED ER 3 GEAR FEED ^ ED ER 1 GEAR FEED O ED ER 2 GEAR FEED □ iiao 12110 IUE 14 FIGURE 1300 mao 1500 EUHPORflTION, CGMS/SQCM/SE.C) X 100,000 liao I2EHLEY3 SEBACATE DIC2-ETHYLHEXYL3 EPRTR, E. C, DEG. TEMPERATURE, ED ER 3 GEAR FEED ^ ED ER 1 GEAR FEED O ED ER 2 GEAR FEED □ 1200 1300 IUE 15 FIGURE moo 1500 1600 CHAPTER V

DISCUSSION OF RESULTS

1. General

The computer generated solutions to the simultaneous set of

Eqs. (2-6 ), (4-17), and (4-29) which describe the hydrodynamic§„ajnd heat transfer show performance characteristics of the centrifugal molecular still which are of primary interest and significance.

If our firs t consideration is the liquid flow across the rotor, it is apparent that there is a rapid flattening of the film from cone vertex to periphery) the greatest contour change occurs in the vicinity of the feed point. The degree of change at the rotor rim varies from about seventy to eighty per cent of the initial film thickness and is dependent upon the relative magnitudes of the feed and evaporation rates, but a sixty-five per cent change would be noted with no evaporation due to the increase in periphery length. The shape of the thickness contour depends to some degree on the initial liquid distribution on the rotor (i.e. the feed rate) as pointed out by Emslie, 14 Bonner, ancf Peck who studied the flow of viscous fluids over a rotating disc. They concluded, however, as is postulated here, that centrifugation tends to produce film uniformity as the thickness is reduced.

In the course of their analysis Emslie, et aj. investigated the extent to which reliability of the flow equations is affected if the

5 3 so-called Coriolis effect is neglected. According to their analysis, the Coriolis acceleration (that perpendicular to the radius) is:

aCQR = 2 (2ita>)u . ( 5- 1)

(2rtui) is the angular velocity, and u is the radial velocity, as before.

Similarly the centrifugal acceleration is

aCENT = (2nu))2£ sin P * (5-2)

Here £ ' s the radius and (p is the cone half-angle measured from the axis of rotation. Thus, the condition for neglecting the Coriolis effect requires that

a COR = 2 (2nw) u___<<; j ^ (5“3) aCENT (2nu>)2£ sin

u « (2ito))4 sin (p/2 • (5**0

In Chapter IV it was shown that the radial velocity and film thickness are related by

u = I i sinp][g>y - y2] • (V3)

When the boundary conditions are considered, it follows that the maximum;velocity occurs at the surface (at y = 6 ), thus

um = 2 E(T )f ^ Sin

When this is substituted for u in Eq. (5“*0 and the equation is

rearranged, the result is a dimensionless ratio nc = . ( 5-6 )

This is designated the "C Number" or "Cpriolis Number", and the cri terion is that

Nc « 1 • (5-7 ).

In order to test the assumption that the Coriol'is effect may be neglected for typical operating conditions used in this work, consider

Run No. 21-Glycerol, for which a) = 1650 rpm, T = 70°C, p = 1.23 gm/cc,

|i = 50 centipoises, and .012 cm (feed) ^ B ^ .OO 38 cm (rim). Under these conditions a calculation indicates that the Coriolis number varies from approximately .02 to .002 across the rotor. Thus, the assumption is shown to cause little error.

However, application to Run No. 77"Di (2-ethylhexyl) phthalate, for which T = 120°C, V = .0281 cm^/sec, and .0016 cm ^ B ^ .0049 cm, shows that N varies across the rotor, from approximately .15 at the C ' vertex to .016 at the outer edge. The conclusion which may be drawn from this is that for this fluid the Coriolis effect is appreciable in the region around the vertex and should not be ignored. 12 As demonstrated by Dixon, Russell, and Swallow, a liquid at any point on a rotating disc is subject to two main forces, a centri­ fugal force acting in the positive radial direction and a Coriolis * 4 force acting in the plane of rotation and normal to the radius. The resultant of these forces is a function of radius. Thus to a stationary observer, the path described by a fluid particle from center to rim appears to be an equiangular spiral. That is, fluid shear occurs in the tangential directi on whenever the Coriolis acceleration is appreciable and the slip between fluid layers is greatest when the film is thick and the fluid is non-viscous. Visual evidence of this effect for runs such as Number 77 above has been obtained and is presented in the photographs of Figs. 7 through 10. The region of tangential shear about the cone center can be readily discerned in Figs. 7 , 8, and 9 by noting the curved pathlines which emanate from the cone center, then abruptly flatten at some distance further out. However, in Fig. 6 , the liquid was of relatively high viscosityj its pathlines therefore appear flat and straight. These stroboscopic pictures were made using glycerol and water mixtures with viscosities of 50, 30, 20, and 10 centipoises,

respectively.

The gravity force may be considered negligible compared to the centrifugal force,, if the ratio of the former to the latte r is small,

F, GRAV « 1 (5-8) F, CENT

This ratio is named the "6 Number" or "Gravity Number",

- FGRAV pg cos

G FCENT p(2jtu>)2£ sin (p

therefore (5-9)

Ng can be evaluated for this study wi th o = I 65 O rpm,

the gravity force is indeed negligible here.

The mathematical model predicts that there will be a different

surface temperature at various radii corresponding to the change in

film thickness across the rotor. The surface temperature increases across the rotor from vertex to cone periphery. The evaporation rate, calculated using the Langmuir Eq. ( 2-6 ), therefore must also increase

in the direction of increasing radius; the magnitude of the increase

is approximately proportional to the increase in the vapor pressure exerted by the liquid. The molecular still is heated by means of an

electrical resistance element imbedded behind the rotor; this element

is designed to give constant power input per unit area of rotor sur­

face. Thus, in order to reconcile the condition of a varying heat

flux requirement across the rotor with a constant power input per unit

area, it is necessary to assume that heat conduction takes place

laterally within the rotor metal itself. For a spun aluminum rotor

this appears to be a reasonable assumption. g This point has been considered by Burrows who further reasons

that for a given energy rate requirement there is only one rotor

surface temperature which provides the AT across the film required by

the corresponding values of film thickness and thermal conductivity,

for the heat flux that is also fixed by this surface temperature. This

concept is in general agreement with the assumptions made earlier that

the bulk mean temperature is the arithmetic average of the rotor

surface and liquid surface temperatures.

Calculated values of temperature differences through the film vary

from a maximum at the vertex to a minimum at the rotor periphery. The

maximum gradient is approximately twice the minimum in the runs

reported here, thus reflecting the effects of a decreasing film thickness

and small increase in the rate of thermal energy transport through the

f i lm. Representative mean thermal gradient data for several glycerol and dibutyl phthalate runs are presented in Table III. Although a wide variation in the thermal gradient is observed here, over the operating range for glycerol, the data appear remarkably consistent at any given temperature. This is demonstrated for both glycerol and dibutyl phthalate at 70°C over a range of mass flow rates, for which the thermal gradients are relatively unchanging (see Table III). Thermal 31 gradients of the same order of magnitude are reported by Pruger^ who probed the evaporating surface of carbon tetrachloride with a fine thermocouple whose junction had been flattened to a thickness of 0. 0*t mm. • • In his research, Pruger measured a temperature drop of about 3°C within a surface layer of approximately O .3 mm, thus obtaining a gradient of

roughly 100°C/cm.

2. Analysis of the Phthalate and Sebacate Runs

Phthalates and sebacates (especially the isooctyl esters EHP and

EHS) have been the subject of numerous molecular distillation studies /V over the past years, and so provide a basis for comparing the research

reported in this study.

Perhaps the most definitive studies on s t i l l dynamics have been published by Hickman^ and C oli.^ In his work, Hickman obtained film

thickness estimates by means of optical density measurements of dyes

introduced on the spinning rotor. For a rotational speed of about

I65 O rpm, corresponding to the angular velocities in this study, he

/V A materials index has been summarized by Watt (see Ref. 35); P* 335"3^1; covering most of the recent literature. TABLE III

Mid-Rotor Flow and Thermal Conditions

Mean Film Thermal Mass Rate Fi lm Run Temp. Gradient of flow Thickness No. (°c) (°C/cm) (gm/sec) (cm) Compound

9 50 43 • 523 .OO786 Glycerol

14 ■91- 1114 •251 .00033 Glycerol

11 70 238 .447 .00530 Glycerol J V C 16 69 219 • .00538 Glycerol

21 70 239 •350 .00489 Glycerol

33 70 45 •375 .00245 DBP

**7 70 46 .260 .00216 DBP

51 72 55 .183 .00190 DBP reports film thicknesses ranging from approximately 0.06 to 0.01 mm over the rotor from center to edge. Coli, on the other hand, obtained average thicknesses for his funs by dividing the volume feed by the surface of revolution generated by a radial element of the rotor, over equal time intervals. His reported mean values, at roughly the same rotational speed, were about a hundredth of those of Hickman. As

Watt points out, however, this indirect calculation by Coli does not include the effect of variables such as viscosity, density, and sur­ face tension, etc., and therefore is somewhat questionable. Film thicknesses evaluated here from the mathematical model, for the phtha- lates and sebacates, agree quite well with Hickman's data. Several typical mean values are included in Table IV for purposes of comparison

In his study to assess the thermal hazard of this still, Hickman estimated the time the liquids flowing across the rotor were exposed to the high evaporation temperatures. These residence time measure­ ments were made by photographing dye marks introduced with the feed at various rotor positions for known time intervals. Based on Hickman' results, it was reported that average exposure times vary from O.O 5 1 to 0.20 sec over the useful range of operation of the CMS -5 molecular still." Mean radial velocities for the phthalates and sebacates, computed from the mathematical model, varied from about k to 8 cm/sec for the conditions used in this study. If the radial distance from center to edge is approximately 5 cm, the residence time for a typical fluid particle traversing the rotor varies roughly from 0.6 to 0.8 sec.

Bulletin 3-1, August, i 960 , Consolidated Vacuum Corporation, page 5 . TABLE IV

Constant Temperature Runs - Glycerol

Evaporation Rate Mean Fi lm Feed c Run Temp. Rate Alpha = (gm/sq cm/sec)xl0^ No. (gm/sec) w /w w w (°c) e e

4 91 • 544 .879 291-5 331-8

14 91 .412 .642 218.6 340.7

■ 18 90 .414 .560 177-^ 316.6

23 91 •330 •357 124.9 322.5

7 70 .613 .747 53-3 71.3

11 70 .482 • 591 42.4 71.7

16 69 .485 • 590 39-1 66.2

21 70 .386 .498 35-6 71.7 These results, therefore, are about 4-10 times greater than the pre­ viously reported values. There is no satisfactory explanation for this apparent anomaly since Hickman's original data are not available.

The possibility exists, however, that Hickman's measurements were made at greater throughput rates which would easily account for the higher velocities encountered in his case.

The evaporation coefficients that have been obtained for the

sebacates and phthalates in this study agree remarkably well with the

values previously reported (see Table l) by other investigators. The values of the evaporation coefficient for these substances in all

runs for which the calculation was made, ranged from 0.91 to approximately 19 unity. It has been postulated by Hickman and Trevoy that these pure

substances exhibit "ideal" liquid phase behavior and should attain

evaporation coefficients of unity. Similar conclusions have been p reached"by other researchers. The fact that values obtained here are

low in some cases by as much as 6 to 9 per cent might be attributed to

experimental errors in film temperature measurement. As discussed in

Chapter Ilia probable error of one degree in the residue thermo­

couple reading would cause a corresponding 9 per cent error in the

evaporation rate calculated from the Langmuir Eq. ( 2-6 ).

3. Analvsis of the Glycerol Runs

Because of its unique physical and chemical properties, glycerol

has produced most interesting results. Comparison with the phthalate

and sebacate runs discussed above shows that film thicknesses for

glycerol were about twice as large under comparable s t i l l operating

conditions. Although a higher range of feed rates was attained using glycerol (because the feed pump operated at a higher volumetric e f f i­ ciency with the viscous liquid) radial velocities tended to be less than half of those calculated for the previous materials, therefore residence time estimates for glycerol were determined to be roughly twice as great (on the order of a one second exposure across the rotor).

It is interesting to note that this is of the same magnitude as the residence time for the largest commercial molecular s tills that are now in use. All of these differences are attributed to the viscous nature and the corresponding fluid dynamical behavior exhibited by glycerol during molecular distillation.

The evaporation coefficient determinations for glycerol provided the severest test of the mathematical model. In the past glycerol has been the subject of several studies in this area; however, pub­ lished values of evaporation coefficient measurements vary over a 15 twenty-fold range, from about .05 as reported by Heideger and Boudart 19 to unity by Hickman and Trevoy. Much of the previous experimental work on evaporation coefficient determinations has been the subject of criticism for one or more of the following reasons:

(a) Questionable purity of material

(b) Possibility of surface contamination

(c) Geometrical interference problems

(d) Inaccurate evaluation of surface temperature

Of the possible sources of error listed above, the most difficult to overcome from an experimental standpoint has been the evaluation of the surface temperature. For the reason that evaporation is a surface phenomenon involving the most energetic molecules, steep thermal gradients can arise in the surface layers of an evaporating Ol liquid. Therefore unless the surface temperature is accurately known, the experimental rate of evaporation will always be less than the theoretical value by an amount proportional to the degree of surface cooling. This can involve as much as 8 to 10 per cent of the total evaporation per temperature degree as was shown earlier. Undoubtedly, this has been a contributing factor in many of the low evaporation rates reported in the literature, and hence evaporation coefficients as well.

When the mathematical model developed in this work was applied to glycerol, it was found that calculated values of the evaporation coefficient varied from .88 to a low of . 36 , despite the fact that temperature gradients across the film as high as lll4°C/cm were encountered.

In view of the fact that values less than unity have been Obtained here, whereas there have been unity values reported in the literature for glycerol, it is important to examine this research for reasons why there is an apparent lack of agreement between theory and experiment.

(a) Purity - While the actual purity cannot be assessed quanti­ tatively, the starting material was reagent grade and the pre-processing technique of redistilling a heart-cut was carefully executed. If contamination did occur, it must have been from a higher boiling material and therefore could not have occurred from within the still.

The still itself was cleansed with solvents (xylene and acetone), and the diffusion pumps (the pumping fluid was dibutyl phthalate) were separated from the bell jar by a cold trap. It is therefore unlikely

that the purified material became contaminated.

(b) Vapor pressure - There has been some conflict in literature values reported for the vapor pressure of glycerol. The data chosen 15 for this work, ^ however, was thermodynamically sound, and. checked well with most of the latest published‘values.

(c) Residue temperature - This source of error has been discussed

in section 2 above, a thermocouple reading registering 1°C higher than the actual fluid temperature (due to the dissipation of fluid shear as heat) would cause the actual evaporation rate to be lower by roughly 9 per

cent than anticipated.

(d) Hydrodynamical effects on the rotor - The photographs in.

Figs. 7 through 10 show the flow across the rotor. In these pictures

the radial streaks are fluid particle pathlines. As can be seen, the

feed tube, which is directed to the cone center, discharges the feed

liquid in a normal rather than tangential direction with respect to

the rotational plane. The effect of such a feed geometry is to

superimpose an additional radial component upon the centrifically

generated radial velocity. The resulting fluid motion away from the

cone center tends to produce an uneven fluid surface. This condition

is further amplified by feed pump irregularities and surface tension

effects at the feed discharge nozzle, which generate surges in the feed

liquid. The radial streaks that appear in these photographs are

evidence of this phenomena. As a consequence of such behavior larger

temperature differences will be set up at the points of greatest film

thickness thus creating correspondingly cooler surface temperatures.

The net result will be a lower experimental rate of evaporation, thus

reflecting an actual average surface temperature lower than theory

predicts.

Of equal importance is the possibility that the previously described

surface irregularities might promote dry regions on the rotor surface. This would be especially likely near the rotor periphery where the film would be thinnest. Although there is no visual proof of such occurrences, an examination of the constant temperature runs in Table I suggests that a degenerating condition of this nature did exist. From

the data presented it can be seen that both alpha and the measured evaporation rate decrease as the feed rate decreases. On the other

hand, however, the calculated mean evaporation rate remains virtually constant. This la tte r fact indicates that the surface temperature

remains substantially constant in these runs. Since the film thick­

nesses must decrease as the feed rate decreases, theory predicts that

•the heat transfer and the resultant evaporation rate should increase with a decreasing rate of feed. This latter deduction is therefore

in direct conflict with experimental observations as Table IV indicates

The only reasonable explanation for these seemingly anomalous results

at this, time is the fact that portions of the rotor surface must

become dry thus reducing the effective evaporation surface. CHAPTER VI

CONCLUSIONS AND RECOMMENDATIONS

As stated in Chapter I this investigation was not intended as a definitive study of the entire realm of molecular d istillatio n , but * rather as an investigation of the underlying fundamentals, with the objective of developing a qualitative understanding and quantitative description of the very complex nature of this field.

Specifically, the present study has taken two steps toward this goal. First, it has provided previously unavailable and badly needed experimental data on the performance of the centrifugal molecular s till, under a wide range of operating conditions, using pure materials with a wide range of physical and chemical properties. Secondly, a mathematical model of the transport behavior of the fluid in a centri­ fugal molecular still has been developed, which, despite its limitations gives good agreement between predicted and observed-sti 11 performance.

Many questions were raised during the course of this work. These reflect .the stage of development of the field, and provide points-of- departure for further researches in the area. The following points are those most worthy of mention:

(a) The results of this workshow that the existence of an evaporation coefficient less than unity is primarily a dependent upon the liquid used. Evaporation coefficients for "ideal" liquids such as the phthalate and sebacate esters studied were found to be unity, -

6 7 within the range of experimental error. Similar evaluations with glycerol, however, have yielded evaporation coefficients which ranged from O.36 to 0.89 approximately. * _ ■ *

This may be due to its non-ideal associated nature, or to its unique physical properties. Various reasons have been suggested as to why the measured rate of evaporation decreased with decreasing film thicknesses while surface temperatures remained constant. No one of these can be accepted universally. Based on limited evidence, it appears likely that surface irregularities on the flowing fluid and surface tension effects may be responsible for this apparent anomaly.

It is necessary therefore that further study be carried out in this area, using more refined apparatus and methods.

(b) The mathematical model has been used to predict film thick­ ness and thermal gradients across the film which are consistent with values previously reported in the literature. It does not account for tangential acceleration effects and is based on the assumption of a fully developed velocity profile. Both of these factors can lead to errors, especially in the vicinity of the vertex. The Coriolis Number developed in the previous chapter has been suggested as a useful criterion or correlating device, but added data are needed to verify this. However, the Qoriolis effect was small in many of these experi­ ments.

In summary, therefore, it is recommended that the present research be extended to include the following items:

(a) A specifically designed and a more precise investigation of the fluid dynamics and heat transfer effects on the centrifugal still geometry. (b) An extended experimental study of evaporation coefficients with additional 1iquids, especially those exhibiting non-ideal liquid phase behavior.

(c) A theoretical and experimental study of the separations attainable with binary systems.

(d) A thorough investigation of the surface structure of liquids as a means of evaluating the evaporation coefficient. Special emphasis should be placed on association effects, the concept of a labile transition zone between liquid and vapor, the concept of active and passive surface sites, and finally, the effect of molecular shape on the escaping tendency. SELECTED BIBLIOGRAPHY

1. Alty, T., "The Maximum Rate of Evaporation of Water," Philosophica1 Magazine. XV (1933)> 82.

2. Birks, J. and Bradley, R. S., "The Rate of Evaporation of Droplets," Proceedings of the Royal Society (London), Series A, CXCVIII . (19^9), 226 .

3* Bromley, L. A., "Prediction of Performance Characteristics of Hickman-Badger Centrifugal Boiler Still." Industrial and Engineering Chemistrv. L (1958), 233-236 .

k. Bronsted, J. N. and von Hevesy, G., "The Separation of the Isotopes of Mercury," Nature. CVI (1920), Ikk.

•• •« Bucka, H., "Uber den Kondensationskoeffizienten von Athylalkohol • und ein Verfahren zur Bestimmung von Kondensationskoeffizienten," Z. Phvsik. Chem. . CXCV (1950), 260 -269 .-

6 . Burch, C. R., "Oils, Greases, and Vacua," Nature. CXXII (1928), 729*

7* Burrows, G., "Some Aspects of Molecular D istillation," Transactions of the Insti tution of Chemical Engineers (London), XXXII (195*0; 23"3^*

8. •______. Molecular Distillation. Oxford: Oxford University ■ Press, i960 .

9* Chalmers, B. and King, R., Progress in Metal Physics, VI. London: Pergamon Press Ltd., 1956, pp. 210-213. > . 10. Coli, J. C. Jr., "The Design, Construction, and Operation of a Centrifugal Molecular Still," Doctoral Dissertation Series, Publication 533*+> University Microfilms, Ann Arbor, Michigan, 1953-

11. Delaney, L. J., Houston, R. W., and Eagleton, L. C., "The Rate of Vaporization of Water and Ice," Chemical Engi neeri ng Science, xix (196*0, 105.

12. Dixon, B. E., Russell, A. A. W., and Swallow, J. E. L., "Liquid Films Formed by Means of Rotating Discs," British Journal of Applied Physics, III (1952), 3.

70 13* Dushman, S., Scientific Foundations of Vacuum Technique, New York: John Wiley and Sons, (19627.

14. Emslie, A. G., Bonner, F. T., and Peck, L. G., "Flow of a Viscous Liquid on a Rotating Disc," Journa1 of Applied Physics. XXIX (1958), 858-862 .

15* Heideger, W. J. and Boudart, M., "interfacial Resistance to Evaporation," Chemical Engineering Science," XVII ( 1962), 1- 10.

16. Hickman, K. C. D., "Identification of Vitamins by Molecular D istillation," Nature, CXXXVI11 (1936), 881.

17 . ______. "High-Vacuum Short-Path D istillation—A Review," Chemical Reviews, XXXIV (1944), 51-106.

18. ______. "Vapor Compression S till," Industrial and Engineering Chemistry, XLI (1957), 786 .

19. ______and Trevoy, D. J ., "Studies in High Vacuum Evaporation," Industrial and Engineering Chemistry, XLIV (1952), 1882.

20. Kennard, E. H., Kinetic Theory of Gases. New York: McGraw-Hill and Company, 1938, pp. 68 - 7 I.

21. Kincaid, J. F. and Eyring, H., "Free Volumes and Free Angle Ratios of Molecules in Liquids," Journal of Chemical Physics, VI (1938), 620 .

22. Knudsen, M., "Die Gesetze der Molekularstromung und Innern Reibungstromund der Gases Durch Rohren," Annales de Physique, i XVIII (1909), 75-

23* Langmuir, I., "The Characteristics of Tungsten Filaments as a Function of Temperature," Physical Review, VII (1916), 302.

24. Loeb, L. B., The Kinetic Theory of Gases. Third Ed. New York: Dover Publications, Inc., 19^1, pp. 104-112.

25* Nabavian, K. and Bromley, L. A., "Condensation Coefficient of Water," Chemical Engineering Science, XVIII (1953), 65 1 •

26 . Neumann, K., "Bemerkungen zur Theorie der Verdampfungsgeschwindigkeit, Z. Physik. Chem. . CXCVI (1950), 16.

27* Penner, S. S., "The Maximum Possible Rate of Evaporation of Liquids," Journal of Physical Chemistry, LI I (1948), 367 *

28. , "Melting and Evaporation as Rate Processes," Journa1 of Physical Chemistry, LI I (1948), 949* 29* • "On the Kinetics of Evaporation," Journal of Physical Chemistry, LVI (1952), 475-479*

• • 30. Polanyi, M. and Wigner, E., “Uber die Interferenz von Eigenschwingungen als Ursache von Energieschwankungen und Chemischer Umsetzungen," Z. Physi k. Chem. , CXXXIX (1928), 439-452.

31. Pruger, W., “Die Verdampfungsgeschwindikeit der Flussigkeiten," h Physik. LXV (1940), 202.

32. Schrage, R. W., A Theoretical Study of Interphase Hass Transfer. New York: Columbia University Press, 1953*

33* Sherwood, T. K. and Cooke, N. E., “Mass Transfer at Low Pressures," American Institute of Chemical Engineers Journal. Ill (1957), 37-42.

34. Trevoy, D. J., “Rate of Evaporation of Glycerol in High Vacuum," Industrial and Engi neeri nq Chemi stry, XLV (1953)* 2366 - 2369.

35* Watt, P. R., Molecular S tills . New York: Reinhold Publishing Company, 1963. -

36 . Wyllie, G. and Wills, H. H., “Evaporation and the Surface Structure of Liquids," Proceedings of the Royal Society (London), Series A, CXCVII (1949), 383-395- APPENDIX A

NOMENCLATURE gravitational acceleration gravitational constant p/V

8/ 3 (jAo2)sin

-(§) cos

3^/(^Jt2co%o3sin

V kinematic viscosity

Z = + x sin

p density ^ b r £5 , a transformation variable

( J O = angular speed of cone, rpm

AT = Ts - Tw, film temperature drop

Subscripts and Superscripts

= mean value

s = pertains to surface

w = pertains to wall

o = initial value

* = normalized, dimensionless variable APPENDIX B

SKETCH OF COORDINATE SYSTEM

0 -

90°-

75 APPENDIX C

COMPUTER ANALYSIS OF EXPERIMENTAL RUNS

76 TABLE V

GLYCEROL

RUN NO. 4 MEAN TEMPERATURE = 91.00 DEG.C. ALPHA = .8786 MEAN EVAPORATION = .0033179 GM/SOCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 I.000000 1.000000 1.000000 0.000000 1.868289 .647153 .946043 .782454 6.285962 2.445610 .529685 .888851 .686157 5.453473 2.910587 .460992 .829931 .618540 4.889693 3.310894 .412571 .769820 .563565 4.464517 3.667769 .374878 .708722 .515446 4.123272 3.992873 .343608 .646790 .471426 3.830880 4.293430 .316422 .583995 .429870 3.576975 4.574281 .291895 .520387 .389741 3.342414 4.838858 .268977 .455654 .350087 3.134465 5.089701 .246919 .389989 .310316 2.918863

RADIAL FILM MASS LINEAR SUR-FACE POS’IT ION THICKNESS FLOW RATE VELOCITY TEMPERATUI (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.

1.111100 .010016 .544000 6.392498 91.000000 2.075856 .006482 .514647 5.001842 87.852895 2.717318 .005305 .483535 4.386260 88.271609 3.233953 .004617 .451482 3.954017 88.553627 3.678735 .004132 .418782 3.602592 88.765467 4.075258 .003754 .385544 3.294989 88.937615 4.436481 .003441 .351854 3.013593 89.082411 4.770430 .003169 .317693 2.747949 89.210944 5.082483 .002923 .283090 2.491423 89.326235 5.376456 .002694 .247876 2.237931 89.437738 5.655167 .002473 .212154 1.983695 89.540001 TABLE VI

GLYCEROL

RUN NO. 6 MEAN TEMPERATURE = 49.00 DEG.C. ALPHA = .5091 MEAN EVAPORATION = .0001171 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658846 .998256 .810985 .536390 2.445610 .550258 .996494 .740492 . .441011 2.910587 .489682 .994730 .697927 .393167 3.310894 .449104 .992964 .667791 .360978 3.667769 .419229 .991195 .644622 .337544 3.992873 .395916 .989424 .625883 .319081 4.293430 .376991 .987652 .610193 .304023 4.574281 .361182 .985882 .596727 .290963 4.838858 .347684 .984110 .584944 .280420 5.089701 .335963 .982336 .574481 .271176

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .020682 .666000 3.711335 49.000000 2.075856 .013626 .664838 3.009840 48.731804 2.717318 .011380 .663665 2.748217 48.776877 3.233953 .010128 .662490 2.590241 48.800481 3.678735 .009288 .661314 2.478397 48.815158 4.075258 .008670 .660136 2.392410 48.827611 4.436481 .008188 .658956 2.322862 48.837611 4.770430 .007797 .657776 2.264634 48.845721 5.082483 .007470 .656597 2.214654 48.850373 5.376456 .007191 .655417 2.170925 48.855377 5.655167 •.006948 .654236 2.132093 48.860201 TABLE VII

GLYCEROL

RUN NO. 9 MEAN TEMPERATURE•= 50.00 DEG.C. ALPHA = .5439 MEAN EVAPORATION = .0001287 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

I.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658699 .997588 .810624 .534866 2.445610 .550011 .995153 .739828 .439565 2.910587 .489351 .992714 .696983 .391782 3.310894 .448698 .990272 .666583 .359622 3.667769 .418753 .987826 .643160 .336195 3.992873 .395376 .985377 .624175 .317731 4.293430 .376389 .982927 .608246 .302667 4.574281 .360521 .980480 .594545 .289600 4.838858 .346967 .978029 .582532 .279040 5.089701 .335191 .975577 .571843 . .269778

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1. 111100 .018779 .529000 3.248783 50.000000 2.075856 .012369 .527724 2.633541 49.732566 2.717318 .010328 .526436 2.403541 49.777598 3.233953 .009189 .525145 2.264348 49.801172 3.678735 .008426 .523854 2.165585 49.815835 4.075258 .007863 .522560 2.089490 49.828282 4.436481 .007424 .521264 2.027810 49.838281 4.770430 .007068 -519968 1.976060 49.846394 5.082483 .006770 .518673 1.931548 49.851048 5.376456 .006515 .517377 1.892522 49.856057 5.655167 .006294 .516080 1.857794 49.860887 TABLE VI11

GLYCEROL

RUN NO. 11 MEAN TEMPERATURE = 70.00 DEG.C. ALPHA = .5910 MEAN EVAPORATION = .0007165 GM/SQCM/SEC

RADIAL FILM MASS LINEAR F ILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .656071 .985691 .804166 1.941065 2.445610 .545531 .971033 .727825 1.646543 2.910587 .483283 .956241 .679805 1.472015 3.310894 .441188 .941373 .644455 1.350733 3.667769 .409893 .926437 .616230 1.260631 3.992873 .385231 .911455 .592554 1.188404 4.293430 .365012 .896459 .572030 1.127146 4.574281 .347946 .881417 .553792 1.077691 4.838858 .333222 .866344 .537294 1.034220 5.089701 .320300 .851247 .522163 .995746

RADIAL FILM MASS . LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

I.111100 .012930 .482000 4.341013 70.000000 2.075856 .008483 .475103 3.490897 69.029467 2.717318 .007054 .468038 3.159498 69.174175 3.233953 .006249 .460908 2.951046 69.260989 3.678735 .005704 .453741 2.797588 69.320063 4.075258 .005300 .446542 2.675065 69.366509 4.436481 .004981 .439321 2.572288 69.403554 4.770430 .004719 .432093 2.483190 69.431605 5.082483 .004499 .424843 2.404018 69.457110 5.376456 .004308 .417578 2.332404 69.479599 5.655167 .004141 .410301 2.266717 69.499449 TABLE IX

GLYCEROL

RUN NO. 13 MEAN TEMPERATURE = 84.00 DEG.C. ALPHA = .5264 MEAN EVAPORATION = .0020586 GM/SQCM/SEC

RAOIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .649550 .956593 .788261 4. 136941 2.445610 .534103 .911277 .697650 3.551240 2.910587 .467402 .865035 .635861 3.171311 3.310894 .421040 .818203 .586938 2.893170 3.667769 .385531 .770875 .545157 2.677262 3.992873 .356630 .723148 .507835 2.497407 4.293430 .332092 .675126 .473502 2.339943 4.574281 .310557 .626719 .441171 2.205795 4.838858 .291162 .577954 .410218 2.083280 5.089701 .273302 .528829 .380171 1.969952

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .010162 .437000 5.044563 84.000000 2.075856 .006601 .418031 3.976433 81.927861 2.717318 .005427 .398228 3.519343 82.221790 3.233953 .004750 .378020 3.207642 .82.411431 3.678735 .004278 .357555 2.960847 82.546681 4.075258 .003918 .336872 2.750082 82.658699 4.436481 .003624 .316015 2.561809 82.749772 4.770430 .003374 .295030 2.388612 82.825418 5.082483 .003156 .273876 2.225518 82.893959 5.376456 .002959 .252566 2.069371 82.956266 5.655167 .002777 .231098 1.917800 83.013657 TABLE X

GLYCEROL

RUN NO. 14 MEAN TEMPERATURE = 91.00 DEG.C. ALPHA = .6417 MEAN EVAPORATION = .0034069 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 I . 000000 1.000000 1.000000 0.000000 1.868289 .642893 .927482 .772186 5.784386 2.445610 .522016 .850800 .666432 4.966499 2.910587 .449978 .771858 .589338 4.407321 3.310894 .398042 .691322 .524572 3.977382 3.667769 .356472 .609373 .466074 3.624481 3.992873 .320748 .526097 .410786 3.314038 4.293430 .288246 .441470 .356724 3.026558 4.574281 .256971 .355059 .302060 2.755039 4.838858 .224854 .266190 .244651 2.479302 5.089701 .188307 .172975 .180478 2.177848

RADIAL FILM 1 MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .009115 .412000 5.320031 91.000000 2.075856 .005860 .382122 4. 108058 88.105801 2.717318 .004758 .350529 3.545441 88.514684 3.233953 .004101 .318005 3.135301 88.794185 3.678735 .003628 .284824 2.790741 89.007743 4.075258 .003249 .251061 2.479528 89.186137 4.436481 .002923 .216752 2.185395 89.342253 4.770430 .002627 .181885 1.897786 89.483728 5.082483 .002342 .146284 1.606969 89.620687 5.376456 .002049 .109670 L. 301552 89.759057 5.655167 .001716 .071265 .960151 89.909315 TABLE XI

GLYCEROL .

RUN NO. 15 MEAN TEMPERATURE = 48.00 DEG.C. ALPHA = .5699 MEAN EVAPORATION = .0001068 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FI LM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658800 .998043 .810870 .468759 2.445610 .550180 .996070 .740282 .383149 2.910587 .489578 .994093 .697629 .341708 3.310894 .448976 .992115 .667410 .313566 3.667769 .419079 .990133 .644162 .293116 3.992873 .395746 .988150 .625345 .277027 4.293430 .376802 .986169 .609582 .263526 4.574281 .360974 .984185 .596042 .252747 4.838858 .347459 .982200 .584187 .243471 5.089701 .335721 .980214 .573653 .235369

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .019712 .542000 3.166722 48.000000 2.075856 .012986 .540939 2.567803 47.765620 2.717318 .010845 .539870 2.344270 47.803480 3.233953 .009650 .538798 2.209198 47.826261 3.678735 .008850 .537726 2.113503 47.839293 4.075258 .008261 .536652 2.039882 47.850213 4.436481- .007801 .535577 1.980296 47.858947 4.770430 .007427 .534503 1.930380 47.863803 5.082483 .007115 .533428 1.887500 47.868961 5.376456 .006849 .532352 1.849960 47.873866 5.655167 .006617 .531276 1.816602 47.878339 ' TABLE XII

GLYCEROL

RUN NO. 16 MEAN TEMPERATURE = 69.00 DEG.C. ALPHA = .5900 MEAN EVAPORATION = .0006618 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP {DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .656325 .986837 .804789 1.822747 2.4456 10 .545968 .973367 .728991 1.544375 2.910587 .483879 .959783 .681483 1.380449 3.310894 .441930 .946133 .646626 1.266845 3.667769 .410774 .932425 .618883 1. 182572 3.992873 .386246 .918678 .595680 1. 115127 4.293430 .366156 .904919 .575623 1.058025 4.574281 .349218 .891121 .557849 1.011952 4.838858 .334621 .877296 .541813 .971513 5.089701 .321823 .863450 .527141 .935770

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .013106 .485000 4.308045 69.000000 2.075856 .008602 .478616 3.467069 68.088626 2.717318 .007155 .472083 3.140526 68.225312 . 3.233953 .006341 .465495 2.935861 68.306837 3.678735 .005792 .458874 2.785694 68.362129 4.075258 .005383 .452226 2.666176 68.405595 4.436481 .005062 .445558 2.566220 68.440215 4.770430 .004798 .438885 2.479811 68.466297 5.082483 .004576 .432193 2.403239 68.490055 5.376456 .004385 .425488 2.334157 68.510994 5.655167 .004217 .418773 2.270951 68.529454 TABLE XI I I

GLYCEROL

RUN NO. 18 MEAN TEMPERATURE = 90.00 DEG.C. ALPHA = .5602 MEAN EVAPORATION = .0031663 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .643989 .932233 .774821 5.527551 2.445610 .524035 .860711 .671597 4.747273 2.910587 .452936 .787179 .597111 4.218463 3.310894 .402019 .712249 .535105 3.815395 3.667769 .361609 .636094 .479601 3.487999 3.992873 .327265 .558818 .427646 3.203212 4.293430 .296492 .480450 .377425 2.943009 4.574281 .267539 .400689 .327414 2.702827 4.838858 .238882 .319181 .276128 2.466192 5.089701 .208579 .235070 .221428 2.222098

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .009260 .414000 5.259893 90.000000 2.075856 .005963 .385944 4.075479 87.234019 2.717318 .004852 .356334 3.532531 87.624209 3.233953 .004194 .325892 3. 140742 87.888490 3.678735 .003722 .294871 2.814599 88.088538 4.075258 .003348 .263343 2.522652 88.254226 4.436481 .003030 .231350 2.249377 88.397568 4.770430 .002745 .198906 1.985217 88.525302 5.082483 .002477 .165885 1.722165 88.646711 5.376456 .002212 .132141 1.452404 88.765741 5.655167 .001931 .097319 1.164692 88.888007 TABLE XIV

GLYCEROL

RUN NO. 19 MEAN TEMPERATURE = 49.00 DEG.C. ALPHA = .5795 MEAN EVAPORATION = .0001174 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658628 .997264 .810448 .465777 2.445610 .549892 .994505 .739507 .380472 2.910587 .489191 .991741 .696528 .339219 3.310894 .448502 .988974 .666001 .311198 3.667769 .418524 .986204 .642456 .290821 3.992873 .395115 .983431 .623353 .274782 4.293430 .376100 .980661 .607310 .261322 4.574281 .360203 .977887 .593496 .250563 4.838858 .346622 .975112 .581373 .241300 5.089701 .334819 .972335 .570575 .233206

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.) ’ \ 1.111100 .017820 .426000 2.755204 49.000000 2.075856 .011737 .424834 2.232951 48.767111 2.717318 .009799 .423659 2.037493 48.804830 3.233953 .008717 .422481 1.919077 48.827513 3.678735 .007992 .421303 1.834969 48.840489 4.075258 .007458 . .420122 1.770099 48.851367 4.436481 .007041 .418941 1.717465 48.860072 4.770430 .006702 .417761 1.673265 48.864913 5.082483 .006419 .416580 1.635204 48.870057 5.376456 .006177 .415397 1.601803 48.874953 TABLE XV

GLYCEROL

RUN NO. 20 MEAN TEMPERATURE = 60.00 DEG.C. ALPHA = .5410 MEAN EVAPORATION = .0003149 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) .(DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .657559 .992417 .807820 .968104 2.445610 .548083 .984727 .734651 .808686 2.910587 .486756 .977005 .689611 .721168 3.310894 .445501 .969257 .657119 .662250 3.667769 .414999 .961494 .631679 .618115 3.992873 .391097 .953728 .610737 .582713 4.293430 .371608 .945947 .592893 .554731 4.574281 .355257 .938158 .577310 .530935 4.838858 .341236 .930361 .563447 .510412 5.089701 .329005 .922560 .550933 .492459

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATUI (CM), (CM) (GMS/SEC) (CM/SEC) (DEG.C. « 1.Ill 100 .014268 .407000 3.305761 60.000000 2.075856 .009382 .403914 2.670462 59.515947 2.717318 .007820 .400784 2.428583 59.591681 3.233953 .006945 .397641 2.279690 59.634599 3.678735 .006356 .394487 2.172279 59.665594. 4.075258 .005921 .391328 2.088183 59.688634 4.436481 .005580 .388167 2.018952 59.704609 4.770430 .005302 .385000 1.959964 59.719099 5.082483 .005068 .381830 1.908452 59.731586 5.376456 .004868 .378657 1.862623 59.742338 5.655167 .004694 .375482 1.821254 59.751700 TABLE XVI

GLYCEROL

RUN NO. 21 MEAN TEMPERATURE = 70.00 DEG.C. ALPHA = .4977 MEAN EVAPORATION = .0007171 GM/SOCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .655259 .982037 .802177 1.810883 2.445610 .544146 .963658 .724135 1.531486 2.910587 .481402 .945121 .674525 1.366553 3.310894 .438851 .926492 .637645 . 1.251881 3.667769 .407123 .907782 .607930 1.166503 3.992873 .382043 .889015 .582788 1.09 7926 4.293430 .361416 .870230 .560817 1.039652 4.574281 .343948 .851388 .541141 .992418 4.838858 .328826 .832506 .523211 .950793 5.089701 .315505 .813591 .506648 .913844

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) {CM/SFC) (DEG.C.)

1. 111IOO .012007 .386000 3.743558 70.000000 2.075856 .007868 .379066 3.003000 69.094558 2.717318 .006534 .371972 2.710842 69.231724 3.233953 .005780 .364816 2.525124 69.313735 3.678735 .005269 .357626 2.387064 69.369521 4.075258 .004888 .350403 2.275822 69.413543 4.43648 L .004587 .343159 2.181702 69.448737 4.770430 .004339 .335908 2.099452 69.475321 5.082483 .004130 .328635 2.025794 69.499653 5.376456 .003948 .321347 1.958673 69.521189 5.655167 .003788 .314046 1.896668 69.540260 TABLE XVI I

GLYCEROL

RUN NO. 23 MEAN TEMPERATURE = 91.00 DEG.C. ALPHA = .3566 MEAN EVAPORATION = .0032248 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1 .000000 1.000000 1.000000 0.000000 1.868289 .638403 .908183 .761437 5.409761 2•445610 .513756 .811048 .645508 4.605743 2.910587 .437789 .710814 .557841 4.049886 3.310894 .381388 .608126 .481593 3.614520 3.667769 .334362 .502872 .410050 3.248045 3.992873 .291423 .394589 .339105 2.912393 4.293430 .248193 .281826 .264476 2.582973 4.574281 .196920 .159779 .177380 2.218108 4.838858 .138086 .061650 .092266 1.250579 5.089701 .160547 .107201 .131190 -.681773

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATUI (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.

1.111100 .008465 .330000 4.588373 91.000000 2.075856 .005404 .299700 3.493760 88.292749 2.717318 .004348 .267645 2.961833 88.694704 3.233953 .003705 .234568 2.559583 88.972318 3.678735 .003228 .200681 2.209731 89.187893 4.075258 .002830 .165947 1.881466 89.373269 4.436481 .002466 .130214 1.555942 89.542123 4.770430 .002100 .093002 1.213514 89.707199 5.082483 .001666' .052727 .813888 89.888903 5.376456 .001168 .020344 .423352 90.378093 5.655167 .001359 .035376 .601950 91.340886 TABLE XVI I I

GLYCEROL

RUN NO. 25 MEAN TEMPERATURE = 60.00 DEG.C. ALPHA = .5650 MEAN EVAPORATION = .0003146 GM/SOCM/SEC

RADIAL FILM MASS LINEAR FI LM POSITION THICKNESS FLOW RATE VELOCITY . TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .657559 .992417 .807820 .968105 2.445610 .548083 .984727 .734651 .808689 2.910587 .486756 .977005 .689611 .721172 3.310894 .445501 .969257 .657119 .662254 3.667769 .414999 .961493 .631679 .6 ia i2 0 3.992873 .391096 .953728 .610737 .582720 4.293430 .371608 .945947 .592893 .554737 4.574281 .355257 .938157 .577310 .530943 4.838858 .341236 .930361 .563447 .510420 5.089701 ..329005 .922559 .550933 .492468

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE ( CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .014268 .407000 3.305761 60.000000 2.075856 .009382 .403914 2.670462 59.515947 2.717318 .007820 .400784 2.428583 59.591680 3.233953 .006945 .397641 2.279690 59.634597 3.678735 .006356 .394487 2.172279 59.665591 4.075258 .005921 .391328 2.088182 59.688631 4.436481 .005580 .388167 2.018952 59.704606 4.770430 .005302 .385000 1.959963 59.719096 5.082483 .005068 .381830 1.908451 59.731582 5.376456 004868 .378657 1.86262 3 59.742334 5.655167 .004694 .375481 1.821253 59.751695 TABLE XIX

DI-N-BUTYL PHTHALATE

RUN NO. 33 MEAN TEMPERATURE = 7 0 .0 0 DEG.C. ALPHA = .9488 MEAN EVAPORATION = .0001882 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658155 .995115 .809283 .191554 2.445610 .549098 .990204 .737373 . 147635 2.910587 .488129 .985296 .693507 .131160 3.310894 .447199 .980383 .662138 .120266 3.667769 .417000 .975469 .637786 .112195 3.992873 .393383 .970556 .617900 .105803 4.293430 .374170 .965641 .601094 .100687 .4.574281 .358083 .960724 .586531 .096392 4.838858 .344319 .955806 .573674 .092709 5.089701 .332339 .950887 .562154 .089499

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .005884 .384000 9. 160004 70.000000 2.075856 .003872 .382124 7.413042 69.904222 2.717318 .003231 .380238 6.754341 69.924867 3.233953 .002872 .378353 6.352528 69.932086 3.678735 .002631 .376467 6.065193 69.937976 4.075258 .002453 .374580 5.842124 69.942469 4.436481 .002314 .372693 5.659974 69.944819 4.770430 .002201 .370806 5.506025 69.947278 5.082483 .002107 .368918 5.372635 • 69.949582 5.376456 .002026 .367029 5.254863 69.951654 5.655167 .001955 .365140 5.149334 69.953491 TABLE XX

DI-N-BUTYL PHTHALATE

RUN NO. 38 MEAN TEMPERATURE = 6 8 .0 0 DEG.C. ALPHA = .9160 MEAN EVAPORATION = .0001558 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658336 .995939 .809730 .165553 2.445610 .549404 .991859 .738194 .125673 2.910587 .488539 .987781 .694672 .111708 3.310894 .447703 .983700 .663631 .102437 3.667769 .417590 .979618 .639593 .095581 3.992873 .394055 .975537 .620012 .090164 4.293430 .374919 .971454 ,603503 .085824 4.574281 .358907 .967369 .589233 .082183 4.838858 .345214 .963284 .576663 .079064 5.089701 .333304 .959199 .565425 .076348

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURI (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .006041 .383000 8.889391 68.000000 2.075856 .003977 .381444 7.198013 67.917223 2.717318 .003319 .379882 6.562103 67.934733 3.233953 .002951 .378320 6.175219 67.941839 3.678735 .002704 .376757 5.899277 67.947088 4.075258 .002522 .375193 5.685594 67.950965 4.436481 .002380 .373630 5.511535 67.952967 4.770430 .002265 .372066 5. 364781. , 67.955057 5.082483 .002168 .370502 5.237926 6 7.95,7013 5.376456 .002085 .368938 5.126183 67.958770 5.655167 .002013 .367373 5.026285 67.960326 TABLE XXI

DI-N-BUTYL PHTHALATE

RUN NO. 47 MEAN TEMPERATURE = 7 0 .0 0 DEG.C. ALPHA = .9 9 2 4 MEAN EVAPORATION = .00018 85 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .657687 .992994 .808133 .171075 2.445610 .548311 .985954 .735261 .130190 2.910587 .48 7073 .978916 .690510 .115610 3.310894 .445902 .971874 .658301 .105909 3.667769 .415478 .964829 .633139 .098719 3.992873 .391651 .957786 .612468 .093026 4.293430 .372235 .950741 .594894 .088455 4.574281 .355954 .943693 .579579 .084613 4.838858 .342002 .936643 .565981 .081314 5.089701 .329839 .929593 .553729 .078435

RADIAL FILM ■ MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURI (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.>

1.111100 .005193 .268000 7.242499 70.000000 2.075856 .003416 .266122 5.852905 69.914462 2.717318 .002847 .264235 5.325133 69.932415 3.233953 .002529 .262349 5.001021 69.939799 3.678735 .002316 .260462 4.767748 69.945278 4.075258 .002157 .258574 4.585515 69.949338 4.436481 .002034 .256686 4.435805 69.951440 4.770430 .001933 .254798 4.308523 69.953638 5.082483 .001848 .252909 4.197603 69.955698 5.376456 .001776 .251020 4.099117 69.957552 5.655167 .001713 .249130 4.010386 69.959197 TABLE XXII

DI-N-BUTYL PHTHALATE

RUN NO. 51 MEAN TEMPERATURE = 7 2 .0 0 DEG.C. ALPHA = •9412 MEAN EVAPORATION = .00022 70 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .656660 .988350 .805612 .181057 2.445610 .546579 .976641 .730624 .138412 - 2.910587 .484744 .964939 .683921 .122673 3.310894 .443032 •.953228 .649854 .112208 3.667769 .412104 .941512 .622897 .104421 3.992873 .387798 .929799 .600478 .098229 4.293430 .367923 .'918081 .581191 .093241 4.574281 .351197 .906359 .564190 .089034 4.838858 .336811 .894634 .548928 .085407 5.089701 .324222 .882906 .535031 .082230

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.>

1.111100 .004600 .194000 5.924904 72.000000 2.075856 .003021 .191740 4.773174 71.909471 2.717318 .002514 .189468 4.328881 71.929512 3.233953 .002230 .187198 4.052172 71.936424 3.678735 .002038 .184926 3.850326 71.942076 4.075258 .001896 .182653 3.690608 71.946404 4.436481 .001784 .180381 3.557780 71.948675 4.770430 .001692 .178107 3.443505 71.951063 5.082483 .001615 .175833 3.342776 71.953310 5.376456 .001549 .173559 3.252350 71.955339 5.655167 .001491 .171283 3.170008 71.957147 TABLE XXI11

DI-N-BUTYL SEBACATE

RUN NO. 59 MEAN TEMPERATURE = 110.00 DEG.C. ALPHA = .9369 MEAN EVAPORATION = .0015681 GM/SQCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP {DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .648876 .953616 .786625 .939921 2•445610 .533189 .906606 .695264 .772703 2.910587 .466386 .859406 .633099 .678619 3.310894 .419982 .812055 .583994 .613050 3.667769 .384482 .764599 .542194 .562486 3.992873 .355630 .717078 .504989 .520983 4.293430 .331160 .669457 .470847 .486152 4.574281 .309735 .621756 .438839 .455468 4.838858 .290493 .573977 .408334 .427866 5.089701 .272834 .526118 .378871 .402534

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .004519 .331000 11.403289 110.000000 2.075856 .002932 .315647 8.970113 109.530030 ,2.717318 .002409 .300086 7.928302 109.611610 3.233953 .002107 .284463 7.219420 109.658310 3.678735 .001898 .268790 6.659458 109.691870 4.075258 .001737 .253082 6.182802 109.717590 4.436481 .001607 .237352 5.758542 109.737460 4.770430 .001496 .221590 5.369212 109.755160 5.082483 .001399 .205801 5.004214 109.770760 5.376456 .001312 .189986 4.656352 109.784760 5.655167 .001233 .174145 4.320378 109.797570 TABLE XXIV

01 { 2-ETHYLHEXYL) PHTHALATE

RUN NO. 77 MEAN TEMPERATURE = 120 .00 OEG.C. ALPHA = 1.0000 MEAN EVAPORATION = .0003502 GM/SOCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C.)

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .656922 .989532 .806253 .244154 2.445610 .547026 .979037 .731818 .203835 2.910587 .485344 .968525 .685615 .181135 3.310894 .44.3771 .958010 .652026 . 165679 3.667769 .412974 .947487 .625530 .154292 3.992873 .38879 i .936960 .603558 .145316 4.293430 .369035 .926430 .5.84709 .137971 4.574281 .352426 .915905 .568145 .131699 4.838858 .338153 .905375 .553313 .126430 5.089701 .325677 .894841 .539841 . 121808

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .004899 .333000 10.135377 120.000000 2.075856 .003218 .329514 8.171687 119.879730 2.717318 .002680 .326019 7.417260 119.895860 3.233953 .002378 .322519 6.948970 119.907810 3.678735 .002174 .319017 6.608531 119.914900 4.075258 .002023 .315513 6.339986 119.920940 4.436481 .001904 .312007 6.117288 119.925810 4.770430 .001808 .308501 5.92625-5 119.929770 5.082483 .001726 .304996 5.758368 119.932010 5.376456 .001656 .301490 5.608043 119.934450 5.655167 .001595 .297982 5.471500 119.936830 TABLE XXV

0 1 (2-ETHYLHEXYL) SEBACATE

RUN NO. 97 MEAN TEMPERATURE = 1 2 0 .0 0 DEG.C. ALPHA = .9457 MEAN EVAPORATION = .00008 63 GM/SOCM/SEC

RADIAL FILM MASS LINEAR FILM POSITION THICKNESS FLOW RATE VELOCITY TEMP. DROP (DMSNLSS) (DMSNLSS) (DMSNLSS) (DMSNLSS) (DEG.C. )

1.000000 1.000000 1.000000 1.000000 0.000000 1.868289 .658655 .997388 .810515 .076900 2.445610 .549940 .994768 .739637 .050776 2.910587 .489258 .992150 .696719 .045122 3.310894 .448586 .989532 .666251 .041385 3.667769 .418624 .986913 .642764 .038629 3.992873 .395231 .984294 .623717 .036475 4.293430 .376229 .981676 .607730 .034701 4.574281 .360346 .979055 .593969 .033271 4.838858 .346779 .976437 .581900 .031989 5.089701 .334989 .973816 .571155 .030937

RADIAL FILM MASS LINEAR SURFACE POSITION THICKNESS FLOW RATE VELOCITY TEMPERATURE (CM) (CM) (GMS/SEC) (CM/SEC) (DEG.C.)

1.111100 .004710 .331000 11.146383 120.000000 2.075856 .003102 .330135 9.034320 119.961540 2.717318 .002590 .329268 8.244280 119.972990 3.233953 .002304 .328401 7.765906 119.975220 3.678735 .002113 .327535 7.426293 119.977270 4.075258 .001971 .326668 7.164500 119.978980 4.436481 .001861 .325801 6.952195 119.980380 4.770430 .001772 .324934 6.773991 119.980380 5.082483 .001697 .324067 6.620609 119.981880 5.376456 .001633 .323200 6.486085 119.981880 5.655167 .001577 .322333 6.366312 119.983210 I. D*, G*, U*, T*, CDMSNLSS3 o co — to — to ru — O □ O * TEMPERATURET* DROP LINEARU*. UELOCITY G*„ MRSS FLOU RATE UK N O R M A L I Z EGR D A P HFO SSE R L E C T ERU D N S FILM THICKNESS 2J0 AIL OIIN CDMSNLSSD POSITION, RADIAL A P P E N DD I X FIGURE

3,0 RUN 4 NO. EN TEMPERATUREPERN DEC. C. 31.0 = 16 5.0 5.0 D*, G*, U*, T*, CDMSNLSS] iq— ru ru — 1.0 * FILM D*. THICKNESS □ G*. MA5S FLOUO RATE T*„ TEMPERATURE O DROP VK LINEAR UELJOCITY AIL OIIN CDMSNLSS] POSITION, RADIAL FIGURE 3J0 RUN NO. 9 MEAN TEMPERATURE DBG. 50.0 = C. 17 .0 5 6.0 D*, G*, U*, T*, CDMSNLSS] 03 ru — a— ID — « — 1.0 D*, FILM THICKNESS □ O O O T*„ TEMPERATURE U*, LINEAR DROP UELOCITY UK MASS FLOW RATE 2JD RIl PSTO, CDMSNLSS] POSITION, RRDIflL FIGURE 18 3J0 U N. 14-RUN NO. MERN TEMPERATURE 91.0 DEG. = C. .0 5 6.0 D*, G*, U*, T*, CDMSNLSSD - o t 3— ru ru — « 1,0 Dx, FILM THICKNESS □ Ux, LINEAR UELOCITY^ O O x TEMPERATURETx, DROP Gx, MASS FLOW RATE o A A PSITIO, CDMSNLSS] POSRAD I IAL T I ON, FIGURE 19 % MEAN TEMPERATURE RUN DEC. 68.0 NO. C. 38 - 5.0 6.0 6.0 20 MIAN TEMPERATURE = 110. DEG. C. 59 DEG. = 110. NO. RUN TEMPERATURE MIAN 3J0 5.0 figure RflDlflL PO SITIO N CDMSNLSS3 2D Tx, TEMPERRTURE DROP Tx, TEMPERRTURE O O O Gx, MASS FLOW RATE RATE O FLOW MASS Gx, * U*, LINEAR UELOCITY *UELOCITY LINEAR U*, .□ Ox, FILM THICKNESS .□ THICKNESS FILM Ox, 1.0 ru— a— oo- CSS1N9WQ3 '*1 y*fi y*0 y*Q D*, G*, U*, T*, CDMSNLSSD 3 0 a ia- - r : o ru — m - 1U A A O □ O O UK UK UK TK TEMPERATURE LINEAR DROP VELOCITY MASS FLOLJ RATE FILM THICKNESS 2J0 AIL OIIN CDMSNLSS] POSITION, RADIAL FIGURE 21 10 MEAN TEMPERATURE RUN NO. 91 120. = DEG. C. 5.0 AUTOBIOGRAPHY

The author was born in Norfolk, Virginia, on November 2, 1928.

He received his secondary education in Baltimore, Maryland, however, and graduated from the Baltimore Polytechnic Institute in 19^7* He attended the Carnegie Institute of Technology in Pittsburgh,

Pennsylvania, and received the degree of B.S. in Chemical Engineering

in 1952. After six years of industrial experience with the Radio

Corporation of America, National Distillers Product Corporation, and

Food Machinery and Chemical Corporation, he returned to graduate

school and in 1959 earned the degree of M.S. in Chemical Engineering

at the Johns Hopkins University. Mr. Greenberg was appointed to the.

Engineering Faculty of the United States Naval Academy as an assistant

professof in 1958. He has also served on active duty with the United

States Navy and presently maintains a reserve commission. In 19&1 he

joined the Chemical Engineering Faculty of the Louisiana State University

and enrolled in graduate school simultaneously. He is presently

a candidate for the-degree of Doctor of Philosophy in Chemical

Engineering at that same institution.

1 0 lf EXAMINATION AND THESIS REPORT

Candidate: David Bernard Greenberg

Major Field: Chem ical E n gin eerin g

Title of Thesis: High Vacuum D i s t i l l a t i o n

Approved:

Major Professor and Chai

Dean of the Graduate School

EXAMINING COMMITTEE:

Date of Examination:

J u ly 27 r 1964