66
UNCLASSIFIED Ao '4 05 6' AD 140346 DEFENSE DOCUMENTATION CENTER FOR SCIENTIFIC AND TECHNICAL INFORMATION CAMERON STATION. ALEXANDRIA, VIRGINIA UNCLASSIFIED
UNCLASSIFIED
Ao '4 05 6'AD 140346
DEFENSE DOCUMENTATION CENTERFOR
SCIENTIFIC AND TECHNICAL INFORMATION
CAMERON STATION. ALEXANDRIA, VIRGINIA
UNCLASSIFIED
NOTICE: When government or other drawings, speci-fications or other data are used for any purposeother than in connection with a definitely relatedgovernment procurement operation, the U. S.Government thereby incurs no responsibilityj nor anyobligation vhatsoever; and the fact that the Govern-ment may have fozr2ated, furnished, or in any waysupplied the said drawings, specifications, or otherdata is not to be regarded by implication or other-wise as in any manner licensing the holder or anyother person or corporation, or conveying any rightsor permission to manufacture, use or sell anypatented invention that may in any way be relatedthereto.
I
r
TEXACO
EXPERIMENT INCORPORATED
RICHMOND , VIRGINIA A S T A
IMAY 6
0"Ei
IC.
I[EXP 328 14 April 1903
F
KINETICS OF CONDENSATIONFROM THE VAPOR PHASE
Final Report
TM - 1377
Welby G. Courtney
I K TEXACO EXPERIMENT INCORPORATEDRichmond 2, Virginia
Submitted to theDepartment of the Navy, Office of Naval Research
under Contract NOnr-3141(00)
Reproduction in whole or in part is permittedjjfor any purpose of the United States Government
II!I
[U
CONTENTS
SUMMARY 5
INTRODUCTION 6
THEORY 7
Rate of Formation of Solid H20 Particles 7
Steady-state Nucleation from Complex Systems 7
Condensation Kinetics of B20 3 and LiF (Constant Volume) 16
Condensation in Nozzles (Variable Volume) 25
EXPERIMENT 28
Equipment and Technique 28
Results 29
"Memory" Effect 32
Semniquantitative Interpretation 32
Quantitative Interpretation 34
Typical Calculation 48
ACKNOWLEDGMENTS 51
REFERENCES 51
APPENDIX 52
1~
S~-2-
!
FIGURES
Page
1. Rate of Formation of Solid H2 0 Particles by Liquid-dropTheory at -40*C 8
2. Rate of Formation of Solid H2O Particles by Liquid-dropTheory at -60°C 9
3. Rate of Formation of Solid HzO Particles by Liquid-dropTheory at -80°C 10
4. Nucleation from the Complex Li-F-X System 12
5. Nucleation from the Complex Li-F-X System 13
6. Nucleation from the Complex Li-F-X System 14
7. Effect of AkI on Nucleation from Complex Li-F-X System
f at 1000°K 15
"8. Condensation of B 20 3 Liquid at 1000 and 1700°K 18
9. Condensation of B2 0 3 Liquid at 2300°K 19
10. Condensation of LiF Liquid at 1000°K 20
11. Condensation of LiF Liquid at 1521K 21
12. Condensation of LiF Liquid at 2000°K 22
13. Effect of Inert Gas on Rate of Condensation of LiF Liquid at1000K 23
- 14. Summary of 50% Times for Condensation of B2 0 3 and LiF"Liquids 24
S15. Condensation of HzO in Wind Tunnel 26
16. Condensation of B2 0 3 and LiF in Rocket Nozzle 27
"17. Schematic Diagram of Supersaturation during Operation ofCloud Chamber 30
"18. Pressure, Supersaturation, and Temperature during PistonBounce Assuming No Condensation 31
"19. "Memory" Effect in Cloud Chamber 33
20. Semiquantitative Comparison of Theory and Experiment forCondensation of Water with 0.18 atm Inert Gas 35
21. Semiquantitative Comparison of Theory and Experiment forCondensation of Water with 0.26 to 0.31 atm Inert Gas 36Ii -3-
[I
FIGURES (cont'd)
j 22. Semiquantitative Comparison of Theory and Experiment forCondensation of Water with 0. 52 to 0.75 atm Inert Gas 37
23. Semiquantitative Comparison of Theory and Experiment forCondensation of Water with 2. 2 atm Inert Gas 38
S24. Summary of Condensation Comparisons--Effect of Inert Gas 39
25. Heat Conduction from Surfaces into Cloud Chamber 42
26. Summary of Heat Conduction in Cloud Chamber 44
27. Experimental Supersaturation-time and Temperature-timeSCurves 49
28. Condensation of Water from Argon Saturated at 20*C 53
29. Condensation of Water from Argon Saturated at 0°C 54
" 30. Condensation of Water from Argon Saturated at -10°C 55
31. Effect of Argon Pressure on Condensation of Water 56
32. Effect of Argon Pressure on Condensation of Water 57
33. Condensation of Water from Nitrogen Saturated at 20°C 58
34. Condensation of Water from Helium Saturated at 20°C 59
35. Condensation of Water from Helium Saturated at -10°C 60
36. Expansion of Dry Argon Initially at 1 atm 61
i 37. Expansion of Dry Argon Initially at 1/2 and 1/3 atm 62
38. Expansion of Dry Helium and Nitrogen Initially at 1 atm 63
1 -4-
I
SUMMARY
This program is a theoretical and experimental investigation of the kineticsand mechanisms of condensation and particularly of homogeneous nu-cleation from the vapor phase.
Theoretical results are reported for (a) the rate of formation of solidH 20 drops during condensation under constant-volume conditions, (b) therate of steady-state nucleation from a hypothetical complex vapor systemusing Li-F data as a base point and arbitrary rate constants, (c) the rateof condensation in generalized B 20 3 and LiF systems, and (d) the cor-responding rates of condensation in certain B-O-H and Li-F systems in arocket nozzle.
Sem iquantitative comparison of the experimental light -scattering -timecurves obtained in the present cloud chamber with the previously reportedtheoretical curves continues to suggest that the present experimental re-sults can be adequately interpreted by the classical liquid-drop theory ofhomogeneous nucleation together with collision-frequency growth kinetics.This comparison includes the effect of supersaturation and temperature.The experimental rates of condensation are slightly faster with lower con-centration of inert gas (the previously reported opposite conclusion was in-correct). This trend qualitatively agrees with the above theory. Theauthor, now located elsewhere, expects to make theoretical computationsto test this effect of pressure semiquantitatively and these are expected tobe reported later. The mathematical theory required to permit quantitativecomparison between experimental and theoretical rates of condensation isgiven, but the comparison was not made. In view of the incomplete analysis,the raw data from the experimental pressure-time curves obtained duringcondensation in the cloud chamber used in this work are included in theAppendix.
This is the final report in a series of reports generated under contractNOnr-3141(00).
"-5-
I-
INTRODUCTION
The present program is a fundamental investigation of the kinetics andmechanisms of condensation and particularly of homogeneous nucleationfrom the vapor phase. A brief review of the program and accomplish-ments was given in reference 1.
This report is the final in a series of reports generated under contractNOnr-3141(00) and covers the period from about June 1 to August 17, i962.Previous reports are listed as references 1 and 2.
The first section of this present report gives the completed current theo-retical results and includes (a) computer analysis of the rate of steady-state nucleation in a complex Li-F vapor system, (b) computer analysisof the rate of condensation of B 20 3 and LiF liquids, and (c) applicationof these latter condensation rates to rocket nozzlep. The second sectionpresents current but incomplete results of the experimental cloud-chamberwork which investigated the rate of condensation of water vapor. In viewof the incomplete analysis of the experimental results, raw experimentaldata are given in the Appendix.
No further work is anticipated on this contract because of the departureof the principal investigator from Texaco Experiment Incorporated. How-ever, the author plans to carry out brief computer calculations of the effectof inert gas on rate of condensation of water and to continue analysis ofthe experimental data at his new location.* The data presented here arebelieved to be correct, but the interpretation of the results is provisional.
* Present address: Reaction Motors Division, Thiokol Chemical Corpo-ration, Denville, New Jersey.
-6-
,[
THEORY
Rate of Formation of Solid H20 Particles
Figures 1 to 3 show the rate of formation of solid H20 particles by theliquid-drop theory at -40, -60, and -80°C. These results were takenfrom the previously reported computer results (1) .
Lack of time did not permit incorporating the lower limit to the classicalliquid-drop theory, and these figures may use supersaturations for whichthe theoretical g *, the number of molecules in the liquid-drop nucleus, isless than 20.
Steady-state Nucleation from Complex Systems
The previous summary report (pp. 48-61 of reference 1) examined theproblem of the kinetics of nucleation from a complex vapor system and de-rived theoretical equations for complex nucleation kinetics (Equations 99-102 of reference 1).
Computer solution of these equations was done to check the theoreticalformulation of the equations and also hopefully to gain some insight intothe relative importance of the magnitude of the various input data. Sinceno information is available about any of the chemical reaction rates, ex-tensive computer work did not seem warranted.
Specifically, the kinetics of nucleation of LiF(l) from a LiF-(LiF) 2 -(LiF) 3-LiX vapor system was examined at 10000K by solving the referencedequations on a General Precision RPC 4000 Computer at TEL. Here, X isan "inert" atom such that
LiX + F = LiF(v) + X
Input data for (r and p for LiF(l) and the JANAF data for the equilibriumvapor concentrations of monomer, dimer, and trimer were reported previous-ly.
"-7-
0 20 40 60 8016 r
1414 Ss35
12 3025
I0
-J 6
4 -15
2
0
-2 I I I I I I0 I 2 3 4 5 6 7 8
TIME, msec
FIGURE I. RATE OF FORMATION OF SOLID H2 0 PARTICLES BY
LIQUID-DROP THEORY AT -400C
Ss IS SUPERSATURATION WITH RESPECT TO BULK SOLID
cn IS IN PARTICLES/CM3
-8-
IIIJ 14 -,14
"Ssa =0012 , .90
80
10 70
60
c 50
060
4J
42
0
-2 I I0 10 20 30 40 50 6O
TIME, msec
FIGURE 2. RATE OF FORMATION OF SOLID H20 PARTICLES BY
LIQUID-DROP THEORY AT-600C
Ss IS SUPERSATURATION WITH RESPECT TO BULK SOLID
cn IS IN PARTICLES/CM3
"-9-
1 .
TIME, mcc140 90 20 30 40 50 1900
12
10 Ss300
8200
(D6 ISO0-j 160
4 140
1202
010
-230 I2 45 10
TIME, sec
FIGURE 3. RATE OF FORMATION OF SOLID H2O PARTICLES ByLIQUID-DROP THEORY AT -800C
Ss IS SUPERSATURATION WITH RESPECT TO BULK SOLIDCn IS IN PARTICLES /CM 3
-10-
The general mathematical approach was to compute (Rs) g (the approximatevalue of the steady-state homogeneous nucleation rate for the nonequilibratedvapor) for the complex system for successive values of g, where g is thenumber of LiF molecules in the cluster under consideration. The variationin (Rs)g with increasing g was noted, and the steady-state rate of nuclea-tion for the complex system, (Rs)complex, was taken as the value of (Rs)gwhen it did not change significantly with an appreciable increase in g. Therequired computer data were:
Input constants: k = 1.38 x 10-"T = 1000
T = 247.7p = 1.92
Ce = 6.92 x 101Z
C, = 1.1 x 1012
C3 = 1.78 x 1011mi = 4.30 x I0-3
m 2 = 8. 60 x 10-23
m 3 = 12.90 x 10-23
Input parameters: S, S2, S3, Sc, CD, Akr [in presentwork, (ag)I = (ag)z = (ag)3 1]
Input variable: g
Computer output: (Rs) g
where S is the supersaturation of the monomer with respect to condensedphase, S2 and S3 are the supersaturations of the dimer and trimer with respectto the dimer and trimer present at equilibrium, Sa is the supersaturation ofLiX (Equation 90 of reference 1) , S is the complex supersaturation (Equation91 of reference 1), and CD is the concentration of X in equilibrium with bulkLiF (1). (The nomenclature is given in detail in Section IX of reference 1.)
An assortment of input parameters was used, but the influence of specificparameters remains largely uncertain because of interaction between theparameters.
Results are given in Figures 4 to 6 and the effect of Akr* is summarized ing
Figure 7. Dashed lines indicate that g is less than 20 and the liquid-droptheory would not be expected to be applicable. The arrows in the figures
* Akr is the specific rate constant for the reaction of the Pg cluster with D to
form the Pg - 1 cluster, A, and B.
-11-
F
SpI S. lL 4 k qk
1012
3.36 55 2 2 2 2 10'0 IO"s
104 \ \ 36 55 2 2 2 2 10:0 10 'o\N.36 55 2 2 2 2 100 1 0-1
2.83 86 2 2 2 I 1010 IO1'5
10_4 2.38 149 2 2 I I 1010 10-15
I0 8 2.00 292 2 I I I I I s"'2.00292 2 I I I I00O oI5
1020 S g* S S2 S3 S. CO Akor
"4.78 25.4 3.5 I I 3 .5 10IO I
1016
1012 8.96 9.3 3.5 3.5 3.5 3.5 IO 10"o'5
6.55 14.7 3.5 3.5 3.5 10 0o I0"15
IOs \ • '•,78 25.4 3,5 I 1 3.5 10 1O 10"10•.78 25.4 3.5 1 1 3.. 1'o 10-"
Io04 • . g\-•5 50.0 3.5 1 1 1 13-.5 50.0 3.5 I I I I 0"13 .5 50.0 3.5 I I 1I I 0"icr0
0 _ _ I_ _ _ _ 50 10 20 30 40 50
NO. LiF MOLECULES IN CLUSTER, g
FIGURE 4. NUCLEATION FROM THE COMPLEX Li-F-X SYSTEM
S: 2 AND 3.5 TaIO00OK
-12-" -.Z
!i
II
I 0 g s St S3 S. Co Akir
16.7 4.3 5 5 5 5 1010 I100
11.2 6.9 5 5 5 I 10 '°
1016 748 11.9 5 5 I I 1010 1
I0_____ _&__ 107 73 3.5 3.5 5 5 10 '° I0"I51012 9.79 8.2 3.5 3.5 3.5 5 I0I° I0"
l0o 5 23.4 5 I I I I I
1024 , , g* S S2 S3 S. Co Akgf
16.74.3 5 5 5 5 10'0 I• 1020 g*
S...... 1674.3 5 5 5 5 100 10-5
16_4_55_ 1010 10-1016.7 4.3 5 5 5 5 1010 10"'
i012 I I
1020 - S g S S2 S3 S. CO Aki
8.40 10 5 2 2 2 10'0 Ig
1016
01L . -- 8.40 10 5 2 2 2 1I0° I0"'5!I I I I I
0 10 20 30 40 50
NO. LiF MOLECULES IN CLUSTER,g
FIGURE 5. NUCLEATION FROM THE COMPLEX Li-F-X SYSTEM
Su5 T IO00K
-13-
F
IO44 § g* S S2 S3 so Co Akr
1040 20 3.6 20 I I I I01° 101"
loeL 10 8.0 10 I I I 1010 1019I0s/ I I I
SS g* S S2 S3 S o CO A ktr
" i 1044 • ! I I I I _
[ 6 6 .9t 13 20 5 5 5 10'O I019*
-- \66.9 1.3 20 5 5 5 10°0 I0144.7 1.8 20 I 5 5 100 10"9
1040 --- 44.7 1.8 20 5 I 5 1010 10944.7 1.8 20 5 5 I IC'0 1019
29.9 2.5 20 5 I I IC' 0 1019
I03o -g* 20 3.6 20 I I I 1 CIO 101O
66.9 1.3 20 5 5 5 10'° 10'01032 . rTC?.= 14 xUSUAL C2 (=2 Ce)"
II I I I FC 2 =I4KxUSUALC2 (=3Ce) I
0 t0 20 30 40 50 C3 =17xUSUALC 3 (m3 C:
NO. LiF MOLECULES IN CLUSTER, g
FIGURE 6. NUCLEATION FROM THE COMPLEX Li-F-X SYSTEM
SslO AND 20 TzIOOO K
-14-
I.
F
A S St S3 S. CD
I. 66.9 20 5 5 5 10I0
1040 _
1 035 -
1030 -2. 16.7 5 5 5 5 10I0
1 02011 2 3. 4.78 3.5 I I 3.5 1010
3
l0og - 4. 3.36 2 2 2 2 1010
105 - 41
1 5. 4.78 3.5 1 1 3.5 1
Akqr
FIGURE 7. EFFECT OF Ak r ON NUCLEATION FROM THE COMPLEX
Li-F-X SYSTEM AT IO0OOK
-15-
V
indicate the location of g*. (Rg) g decreased as g increased and usuallyleveled at a steady value, which was taken as (Rs)complex* (A similarvariation occurred in the previously reported computation of nucleationfrom an equilibrated monomer-dimer system and was discussed there.)(Rs) g leveled for a value of g greater than the classical liquid-drop g*and was independent of Akj if Akr was about 10-'° or less. However, thisleveling occurred for a g less than g* when Akr was large (e.g., 1 or 10- ).The latter situation implies that nucleation involves clusters which containfewer molecules than the classical liquid-drop nucleus.
The value of (Rs) complex increased as S increased except that a lowvalue of CD could decrease (Rs) complex despite a higher S (see Figure 7,bottom curve).
A closer examination of the present results might reveal other trends, butthis was not done for the present report.
Condensation Kinetics of B20 3 and LiF (Constant Volume)
The rates of condensation of B 20 3 and LiF liquids were computed by the pre-viously reported modified theory (pp. 65-69 of reference 1) which assumed:
a. Modified liquid-drop nucleation (3) of liquid particlesb. Collision-frequency growth of liquid particlesc. Particle temperature equal to vapor temperatured. Accommodation coefficient of 1
The present brief results are exactly comparable to the previously reportedresults for water condensation. Input data are given in Table I. Inert gaspressure ranged from 2. 6 to 8. 3 atm in most of the present calculations.
Results for B 20 3 are given in Figures 8 and 9 and for LiF in Figures 10 to13. Figure 14 summarizes the times required for 50% of condensatL"n.The effect of inert gas will be noted; for example, with LiF at 2000F, de-creasing the inert gas from 5. 5 to 0. 55 atm decreased the time required for50% condensation about 25%, but a further decrease had only a minor influence.
jI -16-
TABLE I
COMPUTER INPUT DATA FOR BO AND LiF
BlO, a, b LiF a. b
T, "K 1.000 1,700 2.300 1,000 1,521 2,000
aHl 84,500 79,600 75,700 56,550 53,400 50, 260
A 18,500 17,450 16,580 12,400 11,670 11,000
B 29.816 28.989 28.540 28.240 27.680 27.251
Pt 1.55 1.47 1.43 1.92 1.57 1.37
01 73.0 98.0 117 248.0 198.0 149.0
Cc.1 2.070x108 3. 110x100" 9. 330x10"
7 6. 920x10'
1 6. 700x10'6
2. 820x 10'
p,. atm 2.6 4.6 8.3 2.6 4.2 5.5
a MB 2zO3 1.16x 10"n ; mLiF =4.31 x 10-n g
b cz 2.01 x l101 molecules/cm3
Pz - 8.0
P1 30.0
PV 21.9
-17-
I-
4
10000
2
00 10 20 30 40 50
TIME, sec
0 1 2 :3 4 5XlO31.8
u• 1.6 •
4 1.4 17000
S1.2 Pinert "0.046 otm
U) 1.0 1 I I0 1 2 3 4 5
TIME, sec
2.6
2.2
I. 17000
1.4-
Pinert'0.046 atm
1.00 0.4 0.8 1.2 1.6 2.0
TIME, jswc
FIGURE 8. CONDENSATION OF B203 LIQUID AT 1000 AND 1700°K
- 18-
0 0.1 0.2 0.3 0.4 0.51.6 I I I I
1.5
1.4 !
1.3
2F
4 1.2 I I I0 50 100 150 200 250
Ir)n- TIME, msecwa-(/)
0 10 20 30 40 501.4 I
1.3
1.2
I.1 I I I0 I 2 3 4 5xlO3
TIME, sec
FIGURE 9. CONDENSATION OF B2 0 3 LIQUID AT 2300*K
-19-
II
0
460 I 2 3 4 5
TIME, sec
w6
5
SPInert "0.026 atm4 2.6 atm
0 10 20 30 40 50x 103
TIME, sec
FIGURE 10. CONDENSATION OF LIF LIQUID AT 1000"K
-20-
0 10 20 30 40 50x00 3
2.2
1.8
(Si 31.5)
1.4
10
0 0.1 0.2 0.3 0.4 0.5
TIME, sec
A
, 0 I 2 3 4 5C-
3
20 10 20 30 40 50
.. TIME, lssec
FIGURE I1. CONDENSATION OF LiF LIQUID AT 1521 K
-21-
1
0 I 2 3 4 5xI0 4
1.4
1.3
1.2
I.1 I I I
0 0.1 0.2 0.3 0.4 0.5
TIME, sec
10 10 20 30 40 50
U)(n
1 .5
a~l. 1.4"
U)
1.3
1.2 Pinert 0.027&80315 0.270.315 2.7
1.1 atm
1.00 0.1 0.2 0.3 0.5 0.5
TIME, misc
FIGURE 12. CONDENSATION OF LiF LIQUID AT 20000K
!. [ -22-
I
1.4
1.3
5.51.2 - 0.550.05
z
I-I-
9 1.0
!a 0 0.1 0.2 0.3 0.4 0.5TIME, psec
or),,w 1.5!a-
U)
1.4
1.3 5.5 atm
0.551.2 0.055
0.0055
I.1
1.0 -0 10 20 30 40 50
TIME, /see
FIGURE 13. EFFECT OF INERT GAS ON RATE OF CONDENSATION OFLiF LIQUID AT IO000K
-23-
!I
LOG S
0 0.1 0.2 0.3 0.4 0.5 D-66
4
"2
Zt0 B2 03
0 170004 -4C',z 230000
o -6IU I2 3 4
hiI 6 I
0
o 4U, 10000
0
0 LIF
-2
-4
2000o 15210-6 I I I
2 2 4 5
s
FIGURE 14. SUMMARY OF 50 % TIMES FOR CONDENSATION OF
8 2 0 3 AND LIF LIQUIDS
TIME IS IN MICROSECONDS
-24-
I.
Condensation in Nozzles (Variable Volume)
The 50%1 times for condensation of B20 3 and LiF may be incorporated intothe previously reported plots (Figures 39 and 40 of reference 1), whichdescribe the condensation conditions obtained in certain wind-tunnel androcket-nozzle cases. The 50% times for case A in the B-0-H systems andfor case B in the Li-F systems are uncertain to perhaps 20% since thepressures of IVinert gas" in the nozzle cases were appreciably differentfrom the pressures used to obtain the 50% times.
Results for HZO (from data given in reference 1) are given in Figure 15 andfor B-O-H and Li-F propellants in Figure 16.
With HzO the 50% time for condensation in the selected cases is about 1000-fold greater than the local residence time, and a problem in condensationmay be anticipated. With B20 3 the 50% times rapidly decrease to becomeless than the local residence times in the two cases, and no problems areanticipated. With LiF no problem is expected for case B, but a conden-sation problem may be expected for case A.
-25-
I.
2..
ujO
105
•L 103
lot
0 i RESIDENCE TIME
0-
to,
,iwJe Io* // / 300I- u 104 / :•
En A, 02 - A/ 'I
W V I*B 250 A
I04 I I 200
" RESIDENCE IF30 A TIME t o00 STEADY-STATE30
LIOUID DROPE •NUCLEATION A
10 OCCURS -.20 A 0-B
"TIME LAG
S 0 I0.1
1.0 o.B 0.6 0.4 0.2 0 1.0 0.8 0.6 0.4 0.2 0
EXPANSION RATIO EXPANSION RATIO
FIGURE 15. CONDENSATION OF H20 IN WIND TUNNEL
INITIAL CONDITIONS
A. N2 + 0.0061 H2 0 (SAT. AT 2730K), I atm, 2980K
B. N2 + 0.0028 H2 0 (SAT. AT 2630K), I atm, 2980K
-26-
1000*
'• 'o. \50% T ME--.•100 - 50 % TIME lo0l
R I C M RESIDENCE TIME
IO l RESIDENCE TIME , 0-I--.--.. A ---
1 C -- A -
1010 1010
•.I T I:/ RSIDENC TIME
10 1000
10 NUCLEATION 0NU0ATIN[ TIME LAO
z j2 O0o E k V 1
. 10RESIDENCE TIME
11- I O -TT
W,
0.1 .0 I I J
S 3000
Li-
FIUR 10. SCEADENS ATIO OF10 N i I OKTNZL
INITIACLONATION"
OCCUR Aa. oo A IF Iý
0. 0.1 LIQUID(BTIEDFRM DRO÷5 II T g~K
ILF-
FiGUR 16. CONDENS SATIO OF60 1N0I I OKTNZLNU A IONITALCNIOS
8-0-N: LSFA. ~~~C C R 3 9 2 6 6 Al
O T I E R M B I , 4 . 1 4 A 9 K . 4 9 K 8 e m I B A N D F O . 4 . 2 4 A 9 KB. 243K 68 lm OSTANEDFROM8gM 43.5 I~O~ AT 98 .33 K6 l OTIE RMU .5NF T28C. 3?5K,68 OlY.IOBTINEDFROM SgI, 45I4~OSATATEK
-. 27-'ý666D.,
Li-
EXPERIMENT
The experimental investigation of the kinetics of condensation of water froma water vapor-inert gas mixture was continued to obtain data to comparewith the theoretical results.
The present experimental results are believed to be meaningful, although
the lack of time did not permit doing several planned variations in the ex-
perimental technique as a check on the present experimental technique.
Interpretation of the results is incomplete. Although the writer plans to
attempt elsewhere a quantitative interpretation of the results, the publi-cation date of subsequent work is uncertain. Therefore, representative
examples of the raw data for pressure during condensation in the presentcloud chamber are given in the Appendix for the consideration of otherworkers.
Equipment and Technique
The equipment and technique generally followed the description in theprevious report (1). However, the results using subatmospheric pressuresin the cloud chamber before expansion were obtained by operating the ther-mostated filter at the usual temperature and then slowly evacuating thechamber to 1/2 or 1/3 atm before expansion. Operation at elevated chamberpressure required replacing the glass parts uf the pretreatment apparatuswith metal parts and using a 3/4-inch plate-glass top on the expansionchamber. A Bourdon-type pressure gauge reading to 1/40 psi was connect-ed to the gas-water inlet line to the chamber. Inert gas was passedthroughthe chamber at slightly above the desired elevated pressure by a throttlingvalve at the exit line on the chamber. The valve on the inert-gas cylinderwas then closed and the throttling exit valve closed when the Bourdon gaugeread the desired pressure. Considerable care was taken to ensure that thechamber pressure never became excessive, for the relieving of a local ex-cess pressure might lead to anomalous condensation in the system. Severalcondensations at unexpectedly low expansion ratios are thought to be due tothis effect.
-28-
I.
The heat-capacity ratio for a mixture of gases A and B is given by
Ymix - 1 (A- I (YB 1)
where ymix is the ratio for the mixture, YA and YB apply to pure Aand pure B, PA and PB are the partial pressures of A and B in the mixture,and P is the total pressure of the mixture. The heat-capacity ratios ofsystems of interest were taken as:
YH2o = 1.330YN2 = 1. 404VAr = 1. 660YHe = 1. 670
and were assumed independent of temperature.
Results
It is most instructive to convert the experimental pressure-time curves tosupersaturation-time curves. Figure 17 schematically shows the super-saturation-time curves obtained in the present cloud chamber when dry andwet inert gas were expanded. The piston rapidly dropped after falling offthe cam, thereby rapidly increasing the supersaturation in the vapor. Afterthe piston hit bottom it bounced twice, thereby abruptly decreasing the super-saturation twice. Heat conduction into the cooled vapor from the "hot" wallthen decreased the supersaturation as time continued to increase. Figure 18shows actual experimental results derived by the adiabatic expansion lawfrom the condensation run presented as Figure 47 in reference 1, and assumingno condensation.
The pressure dependence upon time during piston bounce corresponded ap-proximately to
Pt= 569- 3.5(2- t)' 0 ___t!4
= 564 - 5.6 (4.4 - t) 4 < t S 5.8
-29-
1~
PISTON PISTON HEAT CONDUCTION
DROP BOUNCE
z
4 DRY
-CONDENSATION
wIL
U)
PISTONDROP OFF
SI C0 TIME PISTON HITS BOTTOM
iI
0TIME
FIGURE 17. SCHEMATIC DIAGRAM OF SUPERSATURATION DURINGOPERATION OF CLOUD CHAMBER
3
I"-30-I.
270
S265
a. 260
I-
2551
2f
6
U) 40..a
U)
z 570E
a:tj 560U)
U) vI 550 I I I I II. -2 0 2 4 6 8
TIME, msec
FIGURE 18. PRESSURE, SUPERSATURATION, AND TEMPERATURE DURING
PISTON BOUNCE ASSUMING NO CONDENSATION
CONDENSATION RUN SAME AS FIGURE 47 IN REFERENCE I.
ZERO ON TIME SCALE INDICATES PISTON STRIKING BOTTOM
-31-
I.
Figure 18 thus presents the situation (S and T) for condensation in thatrun. Although the nominal supersaturation in the system was 7.7, thevapor initially was in a very time-dependent system and at first onlyspent 1 msec above a supersaturation of 7.
From a condensation viewpoint, therefore, the vapor is in a state whichvaries with time (a) abruptly during the first 5 or so msec because ofpiston motion and bounce and (b) mpoderately during the remaining timebecause of heat conduction. In view of the time-dependent situation and
particularly of the error in supersaturation in the present work, the* quantitative usefulness of the present results is perhaps doubtful However,
the experimental errors in the present work are believed to be about thesmallest absolute errors obtainable in a cloud chamber without going toexceedingly expensive equipment. Although this absolute error is still aburdensome relative error from the viewpoint of supersaturation, it is of
* interest to analyze the present results to determine the general usefulnessof an expansion chamber for condensation experiments.
"Memory" Effect
r As noted previously, a memory effect was encountered with "used" gas,where wet gas was purposefully overexpanded to give a dense visible mist
and then recompressed, held recompressed for several minutes, and thenagain expanded. The intensity of the scattered light was reduced to thebackground level in about 1 sec or less after recompression, suggestingthat the particles in the mist had evaporated.
Typical results showing the effect of hold time after recompression aregiven in Figure 19. The amount of scattered light after the re-expansionseemingly should depend primarily upon the expansion ratio of the re-expansion, i. e., upon the amount of water which condensed during the re-expansion. Since this ratio was held constant in Figure 19, the observedvariation in the maximum scattering is perhaps due to a difference in thesize distribution of the particles appearing after the second expansion.
I Semiquantitative Interpretation
As noted previously (1), upper envelopes to the scattering-time curvesobtained with fresh vapor were drawn and the times required to achieve50% of the maximum scattering intensity were noted. The initial super-
Ssaturation and temperature (i. e., after expansion but before condensation)
f I-32-
PREVIOUS EXPANSION RECOMPRESSED
RATIO To,OK S, HO. TIME, min
L I. I.i I .I,/,, I(DRY)
(NONE)
1.356 239.6 37
1.356 239.6 37 2
1.553 219.4 250 2
S1.553 219.4 250 5
1.553 219.4 250 10
FIGURE 19. "MEMORY" EFFECT IN CLOUD CHAMBER
INITIAL CONDITIONS SUBSEQUENT EXPANSION
THERMOSTAT TEMPERATURE, 19.0C EXPANSION RATIO, 1.158
CHAMBER TEMPERATURE, 19.0-C SUPERSATURATION, 3.53CHAMBER PRESSURE, 761 mm Hg TEMPERATURE, 265.5-C
1- -33-
,[
of each run were then plotted with the 50% time noted. Results are givenin Figures 20 to 23, where the actual pressures in the chamber after ex-pansion were 0.18, 0.25-0.26, 0.51-0.75, and 2. 2 atm* respectively, withthe lower value in each case applying to the lower temperature in the par-ticular figure. Superimposed on these figures are the theoretical valuesfor the 50% time when the partial pressure of the inert gas was 0. 526 atm(400 mm Hg).
The approximate supersaturations required at a certain temperature to give50% condensation in, say, 10 msec can be extracted from the above figures
and plotted against the actual partial pressure of inert gas in the condensingsystem. Figure 24 is such a plot and shows the experimental effect of thepartial pressure of the argon in the system on the rate of condensation astaken from the above scattering curves. The theoretical values for 0. 526atm are included.
Figure 24 therefore summarizes the present experimental and theoreticalresults. The close agreement between theory and experiment is satisfyingbut is undoubtedly largely coincidental. ** The experimental value at 2. 2 atmis somewhat lower than expected, but the high-pressure data were measuredin haste at the end of the contract and therefore may be incorrect. Additionaltheoretical condensation curves with other partial pressures of argon will becalculated to check this apparent agreement between theory and the semi-quantitative interpretation of the present light-scattering experiments.
Quantitative Interpretation
Quantitative interpretation of the experimental pressure-time curves re-quires conversion of the pressure-time curve to a supersaturation-timecurve via a theoretical calculation of the corresponding temperature-timecurve.
Calculation of this temperature during condensation requires taking intoaccount (a) heat conduction into the chamber from the walls and (b) thenonisentropic nature of the condensation.
The nominal chamber pressures before expansion were 0.33,0.5, 1.0,
and 3 atm, respectively.
* The experimental points used to draw the experimental lines in Figure24 were taken by crude visual inspection from Figures 20 to 23 butwere taken before the theoretical point was known.
-34-
80
70 EXPERIMENTAL THEORETICAL 50% CONDENSATION IN50 % TIME, msec I msec
60 41 2-3 4-7 NONE 5 msec
50 4 A 4 10 msec
100 msec
40
30
2 20
w0.
* 10
8 -
6
1 ~4
3 I 3I 8 i I, I 4 I 4AI 4 4 4 103/T
270 263 256 250 244 238 233 227 222 217 213 T, "K
Y FIGURE 20. SEMIQUANTITATIVE COMPARISON OF THEORY ANDEXPERIMENT FOR CONDENSATION OF WATER WITH 0.18 ATM
F INERT GAS
1* -35-
Ssoi80 I I ' I ' I ' I ' I ' I ' I I I ' I
70 EXPERIMENTAL THEORETICAL 50% CONDENSATION IN
50 % TIME, msec I msec
60 • 2-3 4-7 <7 NONE 5 msec.50 -- W V • •time y I0 mue¢ -100 mse.
40
30
°044
I-mirU,w
10
7
56
4
3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 103/T270 263 256 250 244 238 233 227 222 217 213 T, OK
SFIGURE 21. SEMIQUANTITATIVE COMPARISON OF THEORY ANDEXPERIMENT FOR CONDENSATION OF WATER WITH 0.26 TO
0.31 ATM INERT GAS
-36-
I,
70 EXPERIMENTAL THEORETICAL 50% CONDENSATION IN50% TIME, msoc I msec
60 4 12-3 4-7 >7 NONE Scr 5 m -ec
50 Ar A A &time 10 msec
N2 0 0 a a 100 msec
He 0 0 0 *time 0 -40 - A i •
30
30
2 20 -e a °
tow
20 0*
,o Q"o ,10
7 02
6
5
43.7 38 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 IO/T270 263 256 250 244 238 233 227 222 217 213 T, OK
FIGURE 22. SEMIQUANTITATIVE COMPARISON OF THEORY AND
EXPERIMENT FOR CONDENSATION OF WATER WITH 0.52 TO
0.75 ATM INERT GAS
-37-
Ii
70 EXPERIMENTAL THEORETICAL 50% CONDENSATION IN
50 % TIME, msec I msec
60 2-3 4-7 NONE 5 msec
"4 A 4 10 msec50-4- o100 msec
40
30-
0S20
V-
a.
10
7 -,
6
5 1" / "
413.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 103/T
270 263 256 250 244 238 233 227 222 217 213 T,.K
FIGURE 23. SEMIQUANTITATIVE COMPARISON OF THEORY AND
EXPERIMENT FOR CONDENSATION OF WATER WITH 2.2 ATM
INERT GAS
-38-
1)
225K
2050
20
0 15 THEORYEXPERIMENT
W 10S"" 250o:K"
(0.. I0 - ... ,,,, - .,. .. ,.- --
5
0 I I I I0 0.5 1.0 1.5 2.0 2.5
ARGON PRESSURE, atm
FIGURE 24. SUMMARY OF CONDENSATION COMPARISONS-EFFECT
OF INERT GAS
-39-
Heat Conduction into Chamber. Immediately after expansion the surfaces ofthe chamber walls, piezoelectric gauge, etc. are at a temperature appre-ciably above the temperature of the expanded gas. Heat therefore tends tobe conducted into the gas layer adjacent to these hot surfaces. This gaslayer tends to expand, thereby compressing the remaining bulk gas.
If this compression of the bulk gas is adiabatic and is assumed to be reversi-ble (thus is assumed to be isentropic), the pressure and temperature of thebulk gas at time t are respectively given by heat-conduction theory as
Pt - Po = kltl/z = 1. 14 -y PA (T' - TO) ht/2 (1)
Tt- To ktl/2 = 1.14 (y- 1) A (T' To) ht/Z
However, the volume change may be calculated without using the assumptionof reversibility to give
Vt - Vo = k3tVz= -1. 14A (T' - T htl/z (2)To
and finally, again assuming isentropy,
Pt - Po = k2 t 1._'t/2 (3)y - 1 To
where
A = area of hot surfaces after expansion (area of expanded2chamber + auxiliary equipment in chamber), cm
c = specific heat of gas, cal/g
h = (thermal diffusivity) '/2 = (K/cp) V'
K = thermal conductivity of gas, cal/cm-sec-*K
P' = pressure before expansion, mm Hg
Po = pressure immediately after expansion is completed,mm Hg
Pt = pressure at time t after expansion is completed, mm Hg
-40-
V = temperature before expansion, OK
Tt, To = temperature at t = t and t = 0 after expansion, *K
t = time, sec
Vo = volume of chamber immediately after expansion, cm 3
Vt = "compressed" volume of chamber at time t after ex-pansion is completed, cmn3
y = heat-capacity ratio
p = density of gas, g/cm3
Thus, Pt and Tt should vary as t1/2 according to heat-conduction theory.
We are not acquainted with any experimental verification of this theory.Hazen (4) observed experimentally that the pressure in his cloud chambervaried essentially linearly with time when expansion times were about 100msec or greater. He assumed a temperature equation of the type
Tt = Bt + Ct1/2
and arrived at the final pressure equation
P' - Po = 0.008 (e)1/2
where e is the time involved in the expansion process. This equation agreedsatisfactory with his measurements of the pressure after expansion when theexpansion ratio was 1. 125.
In the present work, for example, dry argon at 1-atm pressure was expandedwith ratios up to 1. 5 and with expansion times of 5 to 10 msec. Since theinitial pressure after expansion can be adequately predicted by assumingadiabatic expansion (1), our approach therefore is necessarily different fromHazen's approach.
The experimental pressure-time curves in the present dry-expansion workwere measured and converted to pressure-time curves (1). Figure 25 plotsthe results as pressure versus t"', with the point at zero time calculated as-suming adiabatic expansion. Experimental error in pressure is *5 mm. Re-suits could be adequately interpreted by the Pt - t1 /? law. Plots of Pt versusBt + Ctl/Z showed appreciable curvature, and Hazen's approach was discarded.The slopes of the straight lines in Figure 25 are equal to kj.
-41 -
600,
550
EE 50
w
U)
~-450C
400
3501 1 10 0.1 0.2 0.3 0.4
TIME, tl, secl
FIGURE 25. HEAT CONDUCTION FROM SURFACES INTO CLOUDCHAMBER
A a C D
INITIAL T,-K 293.3 293.3 293.8 296.0P, mm Hg 760.8 767.0 760.2 761.0
EXPANSION RATIO 1.158 1.220 1.379 1.510FINAL T,-K 266.1 259.5 237.6 225.6
P, mm H9 591.4 551.3 446.3 384.0
-42-
Figure 26 plots the experimental values of k/l/P versus T' and also the ex-perimental values of k 2 (calculated from Equations 1 and 3) versus expansionratio. The theoretical variation of k z is included in Figure 26. This wascalculated from Equation 3 using k = 3. 8 x 10-i , c = 0. 12, computed valuesof p assuming the ideal gas law, and the appropriate values for y, A, and V.Figure 26 thus shows that the experimental heat conduction was somewhatgreater than theory, but both the experimental and theoretical values of k.2are somewhat uncertain. The experimental values of k 2 are used in laterapproximate calculations in this report.
Nonisentropic Nature of Condensation. Condensation inevitably is nonisentropicbecause of irreversibility. The temperature variation in a simple constant-volume, nonisentropic system can readily be calculated (viz., p. 66 ofreference 1). However, the present cloud chamber, while nominally a con-stant-volume system, is actually a variable-volume system due to pistonbounce and heat conduction. The effect on temperature of the time-dependentvariation in volume must therefore be taken into account. Since the volumevariation is not isentropic, the usual adiabatic calculation cannot be made.
The problem is to convert the experimental pressure at a time t to the super-saturation of the water vapor remaining in the chamber at this time. Theproblem can be resolved into (a) converting the experimental pressure to thenumber of moles of uncondensed water in the closed system, n, and the cor-responding temperature and (b) converting n and T to supersaturation. Theresulting supersaturation-time curve may then be compared to the theoreticalsupersaturation-time curve computed for the same initial supersaturation andtemperature.
This calculation can be separated into a simple approximate approach, whichneglects piston bounce and assumes heat conduction is isentropic, and alaborious exact approach, which incorporates piston bounce and makes noassumption about entropy.
1. Approximate Approach. The pressure in the chamber at any time t, Pt,is given by the ideal gas law as
Pt = (7 60) (0. 0820 5) n Tt (4)
where Pt is the pressure in mm, n is the total number of moles of gas inthe system, Tt is temperature in *K, and Vt is the chamber volume inliters. For a water vapor-ice-argon mixture at constant volume, the
-43-
I|
0.6
0.4
0.2
0220 240 260 280 300
TEMPERATURE BEFORE EXPANSIONT1 , 'K
60 I I I
0
o 0••*• 40 -EXPERIME T "
0 U 20 -THEORY
01.0 1.2 1.4 1.6 1.8
EXPANSION RATIO
FIGURE 26. SUMMARY OF HEAT CONDUCTION IN CLOUD CHAMBER.
-44-
previous report (1) noted that
AHs ns oTt = To + fznz + Pvn + Isns
(5)To+ H no -nSTo+ AHs Pznz+Ps -no (p. - Pv)]n
where Tt and To are the temperatures at t t and t = 0, AHs is the heat ofcondensation of vapor to form solid, Pi is the constant-volume heat capacityof the i-th species, ni is the number of moles of the i-th species, and n andno are the number of moles of the condensable vapor at t = t and t = 0. Aliquid condensed phase merely requires replacing the subscript s by 1.
At a first approximation the temperature increase in the bulk phase due toheat conduction (Equation 1) may be taken as an additive correction toEquation 5. This is only an approximation since Equation I presumes isen-tropic heat conduction so that the adiabatic PVT laws can be used and sincethe available volume in the chamber actually is decreasing because of theheat conduction from the hot walls. However, this approximation gives thepressure at time t as (condensed phase = liquid):
Pt = (760) (0.08205) (n. + n).V
ITo + &HI [zno'n-'n + K ] / 6+ Plno - (Pl - Pv Kt/zl
The technique for analyzing the experimental pressure-time curve for con-densation is as follows:
1. For a particular condensation run, the volume of the expandedchamber, K2 , and other parameters are incorporated into Equation 6.
2. A voltage and time are measured for a point on the Polaroid photo-graph or a magnified version.
3. The abolute pressure corresponding to this voltage is calculated byEquation 135 in reference 1.
-45-
4. The moles of gas, n, are calculated by Equation 6 by successiveapproximation (Equation 6 converts to a quadratic in n, but thisapproach is cumbersome).
5. The partial pressure of H 2O vapor at this time t is calculatedfrom n, V, and the corresponding T (the bracketed term inEquation 6) by the ideal gas law.
6. The vapor pressure of bulk liquid water, Pe, at this T is cal-culated by Equation 120 in reference 1.
7. Finally, the supersaturation at this time t is given by
S = P/Pe
This procedure is done for a succession of voltage points measured fromthe experimental curve. An experimental supersaturation-time curve isconstructed and may be compared to the theoretical S-t curve computedfor the initial S and T in the cloud chamber.
2. Exact Approach. Since condensation is nonisentropic, the vapor tem-
perature during piston bounce and heat conduction is not truly given byan adiabatic type of calculation. This true vapor temperature can becalculated as below.
The energy equation for a reacting gas mixture containing i species is
(5)
dH = VdP = Z (AHf) idni + T, ni PidT
where H is the enthalpy of the mixture, (AHf) i is the heat of formation,ni is the number of moles of the i-th species, Pi is the heat capacity atconstant pressure of the i-th species, and T is the temperature. Forthe present water vapor-liquid water-argon mixture, the energy equationis
VdP = (AHf) 1 dnl + (AHf) vdn+ (AHf) z dnz + (Pznz + Pinl + P'n) dT (7)
Since n, no - n and dnz = 0, Equation 7 becomes
VdP = [(AHf) v - (AHf) ldn + [ .Pnz + P3n 0 + (P' - Pl) n]dT (8a)
-46-
1i
VdP - AHldn + [ Pznz +PI'n 0 - (13 - P)n]dT (8b)
Dividing by the coefficient of the dT term, integrating from t = 0 to t t,
and rearranging gives
Tt = To + AHIl( n + n' P
.innO -no'
+pP = Pt VdP
+ = Fz -+ Pino - (Pi )n
(9)
TtTPA'I (,nz + pnp-(Pj - P')n)Tt = To + (• -, -. 5 ln, -(P3' - f1) Pznz + P'n 0
+ t VdPJ P nz + Pino i - P')n
/P= P0
The above equation is to be compared with Equation 5.
Now, for a given expansion ratio and also for a given cloud chamber, V is
a function of t due to piston bounce and heat conduction. Since the volumechange due to heat conduction is negligible during the time involved in pistonbounce, these two effects may be separated, or
V = V(t) = volume at time t
= q(piston bounce) + r(heat conduction)
These functions q and r can be calculated from experimental curves of Pversus t obtained during expansion of dry argon. The function q typicallywould be the Pt versus t equation noted at the beginning of this section.The function r would be the t1/2 equation in Equation 2.
Therefore, Equation 9 becomes
AHI 'P.nz + PIng + (P' - P1) nTt :T P + 9 in Pnz + P'no
"-47-
A'
+, (q + r)dP (10)S = o znz + Pins + (P' - Pj) n
and finally,
Rt (z+ )T AH1In tPZnz + Pinp + (P'- Pj) nt P - Phin Pnz + pY'no
(II)+ t(q + r) dPt
0 Pznz + Pino + (p - Pj)n
Equation 11 may be compared with Equation 6 for the approximate case.
All parameters in Equation 11 are known except the values for n whichsatisfy the experimental values of Pt. If the integral in Equation 11 is con-verted to intervals, Equation 11 may be solved for n during each successivetime interval by successive approximations. Each value of n is then con-verted to S by the technique noted previously.
Typical Calculation
No exact calculations have been made as yet. Results of the approximatecalculation of the supersaturation-time curve for the condensation runpresented as Figure 47 in reference 1 are given here. The conditions im-mediately after expansion are (corrected from Figure 47):
S1 = 7.70
Chamber temperature = 259. 5*K (after expansion)
7' Chamber pressure = 553.7 mm (after expansion)
The pressure immediately before and during piston bounce during the dry ex-pansion and the corresponding supersaturation and temperature were givenin Figure 18 assuming no condensation. The value of kz for an expansionratio of 1.220 was taken from Figure 23.
The resulting supersaturation-time and temperature-time curves after thepiston bounce were then calculated as noted earlier and are given in Figure 27.
f -48-
I
2801
Li 270
a.260
w
20 5 10 15 20 25 30 35 4
-49
For comparison, the upper envelope to the scattering-time curve was
measured, normalized to the supersaturation at zero time and infinity,
and superimposed on the above plot. The agreement between the super-
saturation and scattering curves is better than might be expected.
Theoretical curves are currently being calculated by the author.
-50-
ACKNOWLEDGMENTS
The generalized steady-state nucleation problem was programmed by Mrs.
Margaret Sullivan and run on the General Precision Computer RPC 4000at TEL.
The experimental work was done by Kent Renalds.
REFERENCES
(1) W. G. Courtney, "Kinetics of Condensation from the Vapor Phase,"Texaco Experiment Incorporated TM-1340, 15 July 1962.
(2) W. G. Courtney and W. J. Clark, "Kinetics of Condensation from theVapor Phase," Texaco Experiment Incorporated TM-1250, 15 July1961.
(3) W. G. Courtney, J. Chem. Phys., 35, 2249 (1961).
(4) W. E. Hazen, Rev. Sci. Instr., 13, 247 (1942).
(5) B. Lewis, R. N. Pease, and H. S. Taylor, Combustion Processes,p. 33, Princeton, Princeton University Press, 1956.
-51 -
APPENDIX
Some representative samples of the experimental pressure-time curvesobtained during condensation in the cloud chamber are given in Figures28 through 38.
-52-
I.
IF
BEFORE AFTEREXPANSION EXPANSION EXPANSION
T*,'C T',*C P', mm RATIO To, *K S,
19.3 20.3 760.8 1.211 259.6 7.6
, 19.3 20.3 760.8 1.224 257.2 9.1
19.3 20.3 760.8 1.224 257.2 9.1
V 19.3 20.3 760.8 1.237 255.7 9.9
FIGURE 28. CONDENSATION OF WATER FROM ARGON SATURATED AT 20°C
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTERT' CHAMBER TEMPERATURE EXPANSION
P1 CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a5 msec
VERTICAL- PRESSURE, I unit - I volt (SEE TEXT)
SCATTERING, I unit .5 volts (ARBITRARY)
-53-
V
BEFORE AFTEREXPANSION EXPANSIONEXPANSION
T*,*C T',*C P',mm RATIO To,.K St
r0 20.0 760.2 1.382 237.1 12.7
0 20.2 760.2 1.382 237.2 12.5
0 20.5 760.2 1.382 237.5 12.2
(HORIZONTAL SCALE: I UNIT 10 msec)
O 20.8 760.2 1.395 235.6 14.6
S0 20.5 760.2 .395 235.6 14.6
0 20.5 760.2 1.395 235.6 14.6
FIGURE 29. CONDENSATION OF WATER FROM ARGON SATURATED AT 0OC
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTERT' CHAMBER TEMPERATURE EXPANSION
PI CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit 5 msec
VERTICAL - PRESSURE, I unit a volt (SEE TEXT)
SCATTERING, I unit 5 volts (ARBITRARY)
-54-
BEFORE AFTEREXPANSION EXPANSION
TtC T',c P1',m RATIO ToK S_
".- 8.0 23.0 759.1 1.500 226.7 18.0
-s
-8.2 23.1 759.1 1.500 226.7 17.7
-10.0 23.0 759.1 1.513 225.4 17.5
l I A'' IT I.l
S[T.1 Ll I F. -10.2 23.0 759.1 1.526 225.4 17.3
FIGURE 30. CONDENSATION OF WATER FROM ARGON SATURATED AT-10C
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTERT' CHAMBER TEMPERATURE EXPANSION
pI CHAMBER PRESSURE
SCALE: HORIZONTAL- I unit r 5 msec
VERTICAL- PRESSURE, I unit a 2 volts (SEE TEXT)
SCATTERING, I unit 5 volts (ARBITRARY)
-55-
BEFORE AFTEREXPANSION EXPANSION EXPANSION
T*,*C T','C P',mm RATIO To,*K SoLa| I I ± r-
A. 18.1 22.5 382 1.278 252.1 6.18
SB. 18.1 22.5 382 1.291 250.5 6.92
K1,1=11.hbI"1I~ C. 18.1 22.5 382 1.291 250.5 6.92j .A -[--!;,
FIGURE 31. EFFECT OF ARGON PRESSURE ON CONDENSATIONOF WATER
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTERT' CHAMBER TEMPERATURE EXPANSION
P' CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit : 5 msec
VERTICAL - PRESSURE, I unit : 0.5 volt (A), 1.0 volt (B,C)SCATTERING, I unit 2 5 volts (ARBITRARY)
-56-
i
BEFORE AFTEREXPANSION EXPANSION EXPANSION
T*0,C T',_C P1,mm RATIO To, OK S1
I ! A. 24.0 18.0 225 1.357 243.9 7.01
B. 24.0 18.0 225 1.357 243.9 701
Lýý T -r I-
{ ; C 24.0 18.0 225 1.357 243.9 7.01SI. I U• U U '
FIGURE 32. EFFECT OF ARGON PRESSURE ON CONDENSATIONOF WATER
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTER
T1 CHAMBER TEMPERATURE EXPANSION
P1 CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a 5 msec
VERTICAL - PRESSURE, I unit a 0.5 volt (AB), 1.0 volt (C)
SCATTERING, I unit . 5 volts (ARBITRARY)
-57-
Ii
I
BEFORE AFTEREXPANSION EXPANSION EXPANSION
T*,*C T',°C P',mm RATIO To,OK S1
... . ..... :22.2 25.3 767 1.434 258.3 8.35
22.0 24.7 767 1.448 25&5 9.26
22.0 24.7 767 1.448 256.5 9.26
FIGURE 33. CONDENSATION OF WATER FROM NITROGEN SATURATEDAT 200C
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTERT' CHAMBER TEMPERATURE EXPANSION
PI CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a 5 msec
VERTICAL PRESSURE, I unit a I volt (SEE TEXT)
SCATTERING, I unit a 5 volts (ARBITRARY)
-58-
BEFORE AFTEREXPANSION EXPANSION EXPANSION
T*-,C T',*C P',mm RATIO To, K S1
""-A V. . 18.0 21.3 765.4 1.239 255.9 9.2
""" 18.0 23.5 763.5 1.257 255.4 9.60
18.o 23.5 763.5 1.265 254.3 10.1
IflI4..O18.0 18.0 7654 1.226 254.8 10.3
H 4.i 18.0 21.3 765.4 1.252 254.1 10.5
FIGURE 34. CONDENSATION OF WATER FROM HELIUM SATURATED AT 200C
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTER
T' CHAMBER TEMPERATURE EXPANSION
Pi CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a 5 msec
VERTICAL - PRESSURE, I unit x I volt (SEE TEXT)SCATTERING, I unit a 5 volts (ARBITRARY)
-59-
BEFORE AFTEREXPANSION EXPANSION EXPANSION
T*,C T',*C P',mm RATIO To, K Si
-10.0 19.0 768.5 1.526 220.1 30.9
-100 19.0 769.5 1.526 220.1 30.9II!EEEIIMIFIGURE 35. CONDENSATION OF WATER FROM HELIUM SATURATED AT - IO0C
T* SATURATOR TEMPERATURE To INITIAL TEMPERATURE AFTER
T1 CHAMBER TEMPERATURE EXPANSION
P' CHAMBER PRESSURE
SCALE: HORIZONTAL- I unit a 5 msec
VERTICAL - PRESSURE, I unit 2 volts (SEE TEXT)
SCATTERING, I unit= 5 volts (ARBITRARY)
-60-
V..
BEFOREEXPANSION EXPANSION
T',*C P',mm RATIO
19.3 760.8 1.092
S19.3 760.8 1.158(TIME: I UNIT= 20 msec)
I\ t i i: ~
I .jbj r i•iiiliI4:l } 19.3 760.8 1.237
19.3 760.8 1.356
W .19.3 760.8 1.553- - - (PRESSURE: I UNIT= 2 volts)
FIGURE 36. EXPANSION OF DRY ARGON INITIALLY AT I ATM
T' CHAMBER TEMPERATURE P1 CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a 5 miecVERTICAL - PRESSURE, I unit a I volt (SEE TEXT)
SCATTERING, I unit • 5 volts (ARBITRARY)
-61-
1*
BEFOREEXPANSION EXPANSION
T',*C P',mm RATIO
FI ffl -A. 22.1 382 1.278
B. 23.0 386 1.491
•j JHC. 25.1 18.3 1.357
FIGURE 37. EXPANSION OF DRY ARGON INITIALLY AT 1/2 AND 1/3 ATM
T1 CHAMBER TEMPERATURE P1 CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a 5 msec
VERTICAL- PRESSURE, I unit z 0.5 volt (A,C), I volt (B)SCATTERING, I unit a 5 volts (ARBITRARY)
-6z-
[
BEFOREEXPANSION EXPA .IN
GAS T',*C P',mm RA";iO
He 23.1 7663.5 1.2 ;5
He 19.0 768.5 1.5!6(PRESSURE: I UNIT= 2 volt;)
Me -2.7 767 1.434
FIGURE 38. EXF'ANSION OF DRY HELIUM AND NITROGEN INITIALLY
AT I ATM
T' CHAMBER TEMPERATURE P' CHAMBER PRESSURE
SCALE: HORIZONTAL - I unit a 5 mseC
VERTICAL - PRESSURE, I unit a I volt (SEE TEXT)
SCATTERING, I unit 5 volts (AReITRARY)
-63-
,Ii
