Durham E-Theses
Melting ice and cloud electrication
Martin, Peter F.
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Martin, Peter F. (1971)
Melting ice and cloud electrication, Durham theses, Durham University.
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MELTING
ICE AND
CLOUD
ELECTRIFICATION
A t h e s i s presented i n candidature f o r the degree of Doctor
of Philosophy i n the U n i v e r s i t y of Durham
by
Peter F- M a r t i n
BoSc.
o f Grey College
June 1971
\
,13 APR 1972
jBRARl
i.
FOREWORD
Although t h i s t h e s i s i s p r i m a r i l y concerned w i t h the e l e c t r i c a l e f f e c t s
of m e l t i n g ice a chapter on the e l e c t r i f i c a t i o n due t o e v a p o r a t i n g
ice has
been included as t h i s could be r e a d U y s t u d i e d w i t h the apparatus.
The
S . I . system of u n i t s has been used w i t h two exceptions.
c o n c e n t r a t i o n of ions i n s o l u t i o n s are gram molar c o n c e n t r a t i o n s
the e l e c t r i c a l c o n d u c t i v i t y of s o l u t i o n s has been expressed i n
The
and
mho
cm
1
I should l i k e to express my sincere thanks t o a l l those people who
a s s i s t e d me
i n any way d u r i n g the course of my work a t Durham.
.
have
In p a r t i c u l a r
I am g r a t e f u l t o my supervisor Dr. W.C.A» Hutchinson f o r h i s guidance
throughout
the i n v e s t i g a t i o n and t o Professor G.D.
Rochester, F.R.S. f o r
the p r o v i s i o n of research f a c i l i t i e s i n the Physics Department a t Durham.
I would also l i k e t o thank Mr. J. Moralee f o r h i s a s s i s t a n c e d u r i n g the
c o n s t r u c t i o n of the wind t u n n e l and Mr. J. S c o t t f o r the c o n s t r u c t i o n of
the glassware.
I am g r a t e f u l t o the other members of the Atmospheric
Physics group f o r t h e i r h e l p f u l comments and i n p a r t i c u l a r t o Dr. I.M.
Stromberg and Dr. R. Dawson f o r t h e i r advice d u r i n g the e a r l y stages of
the work and Mr. K.M. D a i l y f o r h i s attempts to standardize my
English.
Thanks are also due t o the N a t u r a l Environment Research Council
f o r the p r o v i s i o n of a research
studentship.
F i n a l l y I wish t o thank Mrs.
D. Anson f o r her speed and
efficiency
i n the p r e p a r a t i o n of the t y p e s c r i p t and Mr. J. Normile f o r c a r r y i n g
out the d u p l i c a t i o n of the t h e s i s .
it
13 APR 1972
ABSTRACT.
A v e r t i c a l wind t u n n e l has been c o n s t r u c t e d i n s i d e a cold room t o
simulate the f a l l o f a f r o z e n water drop from the 0°C l e v e l i n a thundercloud.
but
I t was p o s s i b l e t o f r e e l y support an i c e sphere c l e a r o f the sides
the p a r t i c l e crashed e a r l y i n the m e l t i n g process.
The i c e spheres
were f rozen onto a 120 jim diameter p l a t i n u m wire and d u r i n g the f i n a l
stages o f m e l t i n g the p a r t i c l e hung from the w i r e and was f r e e t o
r o t a t e about a l l 3 degrees o f freedom.
The spheres melted on t h i s type
of support produced the same amount o f e l e c t r i f i c a t i o n as those melted on
the
wire loop support used by DRAKE (1968).
The charge on the meltwater was found t o be always p o s i t i v e and t o
be h i g h l y dependent on the f r e e z i n g r a t e , and water drops f r o z e n i n s t i l l
a i r a t between -10 and -15°C produced an order o f magnitude l e s s charging
than drops f r o z e n i n an a i r s t r e a m f l o w i n g a t 11 ms
Examination o f the i c e p a r t i c l e s under a microscope
a t s i m i l a r temperatures.
suggested t h a t t h i s
e f f e c t was due t o a i r escaping from the ice a t low f r e e z i n g r a t e s and
smaller a i r bubbles being formed a t h i g h f r e e z i n g r a t e s .
Evidence
was
found f o r the enhancement o f e l e c t r i f i c a t i o n a t h i g h m e l t i n g r a t e s which
DRAKE a t t r i b u t e d t o the onset o f vigorous convection i n the meltwater.
The e f f e c t o f carbon d i o x i d e on m e l t i n g e l e c t i f i c a t i o n was a l s o discussed.
The e l e c t r i f i c a t i o n due t o m e l t i n g p r e c i p i t a t i o n under i d e a l
-3
c o n d i t i o n s i n a thundercloud was estimated as 4 C km
which can be
_3
compared t o 8 C km
found by SIMPSON and ROBINSON ( l 9 4 l ) .
I t was
suggested t h a t the importance o f m e l t i n g i c e i n thundercloud e l e c t r i f i c a t i o n
cannot be e s t a b l i s h e d u n t i l more i n f o r m a t i o n i s a v a i l a b l e on the nature o f
the
s o l i d p r e c i p i t a t i o n , the environment i n which i t melted and t h e
l o c a t i o n and magnitude o f the lower p o s i t i v e
charge.
CONTENTS
FOREWORD
i
ABSTRACT
ii
CHAPTER I
THE IMPORTANCE OF MELTING ICE IN CLOUD
ELECTRIFICATION
1.1
Introduction
1
1.2
The thunderstorm
1
1.3
The e l e c t r i c charge d i s t r i b u t i o n i n thunderstorms
4
1.4
The lower p o s i t i v e charge
5
1.5
Theories of t h e f o r m a t i o n o f t h e lower p o s i t i v e
charge
7
Laboratory assessment o f the t h e o r i e s of t h e
f o r m a t i o n of the lower p o s i t i v e charge
10
1.6
CHAPTER 2
PREVIOUS STUDIES OF MELTING ICE ELECTRIFICATION
2.1
Experiments With blocks o f i c e
12
2.2
The m e l t i n g o f f r o z e n water drops
12
2.3
The b u b b l e - b u r s t i n g theory of m e l t i n g e l e c t r i f i c a t i o n
13
2.4
Factors i n f l u e n c i n g the charging o f m e l t i n g n a t u r a l
ice p a r t i c l e s .
20
CHAPTER 3
THE DESIGN OF A WIND TUNNEL FOR THE FREE FLIGHT
OF SMALL ICE SPHERES
3.1
The importance o f a f r e e support system
21
3.2
The problem o f turbulence
21
3.3
Laminar f l o w wind t u n n e l s
24
3.4
V e l o c i t y w e l l systems
26
3.5
The design o f t h e support tube
28
CHAPTER 4
THE CONSTRUCTION AND INSTRUMENTATION OF THE WIND .TUNNEL
4.1
The adaption of the c o l d room
32
4.2
The wind t u n n e l
33
4.3
Measurement o f e l e c t r i c charge
35
4.4
The measurement o f temperature and h u m i d i t y
38
4.5
The measurement o f a i r speed
CHAPTER 5
THE PREPARATION OF ARTIFICIAL CLQUDWATER
5*1
The source o f i m p u r i t i e s i n h a i l
42
5.2
Measurement o f i m p u r i t i e s i n c l o u d and r a i n w a t e r
45
5.3
The p r e p a r a t i o n of a r t i f i c i a l cloudwater
CHAPTER 6
L
">
FREE FLIGHT EXPERIMENTS ON MELTING AND EVAPORATING
ICE PARTICLES
6.1
Experimental procedure
50
6.2
The behaviour of the support system
51
6»3
The e l e c t r i f i c a t i o n o f m e l t i n g i c e
53
CHAPTER 7
EXPERIMENTS WITH MELTING ICE SPHERES HANGING.ON
PLATINUM WIRES
7.1
The support of m e l t i n g i c e spheres
55
7.2
The experimental procedure
56
7.3
The i c e p a r t i c l e s
58
7.4
The a n a l y s i s o f t h e m e l t i n g experiments
60
CHAPTER 8
THE EFFECT OF MELTING RATE AND FREEZING TEMPERATURE
ON MELTING ELECTRIFICATION
8.1
M e l t i n g r a t e and the environment
64
8.2
The e f f e c t o f m e l t i n g r a t e on e l e c t r i f i c a t i o n
65
8.3
The e f f e c t of the support
67
8.4
Freezing r a t e and m e l t i n g e l e c t r i f i c a t i o n
68
8.5
A.ir bubbles and m e l t i n g e l e c t r i f i c a t i o n
70
806
Comparison w i t h previous experiments
74
CHAPTER 9
THE EFFECT OF CARBON DIOXIDE ON MELTING ELECTRIFICATION
9.1
Carbon d i o x i d e and l a b o r a t o r y experiments
75
9.2
The importance o f carbon d i o x i d e i n m e l t i n g
electrification
76
9.3
An experiment t o determine the e f f e c t o f atmospheric
carbon d i o x i d e
77
9.4
The absorption o f carbon d i o x i d e by a water drop
79
Carbon d i o x i d e l e v e l s i n p r e v i o u s l a b o r a t o r y
experiments
Conclusion
80
81
9.5
9.6
CHAPTER 10
THE ELECTRICAL EFFECTS OF THE MELTING OF REAL
PRECIPITATION
10.1
The l o c a t i o n o f t h e lower p o s i t i v e
10.2
S o l i d p r e c i p i t a t i o n i n thunderstorms
85
10.3
M e l t i n g i c e and t h e magnitude of t h e lower p o s i t i v e
charge
89
CHAPTER 11
charge
THE ELECTRIFICATION OF EVAPORATING ICE SPHERES
11.1
Previous work
93
11.2
The e l e c t r i f i c a t i o n of i c e p a r t i c l e s evaporating
i n the wind t u n n e l
94
I n t e r p r e t a t i o n of the wind t u n n e l experiment
94
11.3
CHAPTER 12
CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK
12.1
The design o f a wind t u n n e l t o study the e l e c t r i f i c a t i o n
of p r e c i p i t a t i o n
96
12.2
The e l e c t r i f i c a t i o n o f m e l t i n g i c e
97
12.3
The r o l e of m e l t i n g i c e i n cloud
98
APPENDIX 1
Al.l
A1.2
A1.3
A1.4
A1.5
electrification
MELTING ELECTRIFICATION DATA
The e l e c t r i f i c a t i o n o f i c e spheres m e l t i n g on
p l a t i n u m w i r e s - a r t i f i c i a l cloudwater
100
The e l e c t r i f i c a t i o n o f i c e spheres m e l t i n g on
p l a t i n u m w i r e s - deionized water
102.
The e l e c t r i f i c a t i o n o f i c e spheres m e l t i n g on
p l a t i n u m loops - f r o z e n i n s t i l l a i r
103
The e l e c t r i f i c a t i o n o f i c e spheres m e l t i n g on
p l a t i n u m loops - frozen i n a i r s t r e a m
104
F o r t r a n program used t o process the m e l t i n g
e l e c t r i f i c a t i o n data
105
APPENDIX 2
THE ABSORPTION AND DESQRPTION OF CARBON DIOXIDE BY WATER
A2.1
A b s o r p t i o n by a s t a t i o n a r y drop
107
A2.2
The d e s o r p t i o n o f a t h i n water l a y e r i n a c o n t a i n e r
108
A2.3
The release of carbon d i o x i d e from a bubble immersed
i n an imsiturdfceid l i q u i d
109
REFERENCES
110
CHAPTER
THE
IMPORTANCE
OF
MELTING
ICE Ity
1
CT.QUD ELECTRIFICATION
1.1. INTRODUCTION
Many t h e o r i e s of the o r i g i n of the e l e c t r i c charges i n thunderclouds
have been based on t h e o r e t i c a l and experimental work on t h e p r o p e r t i e s o f
ice and water.
CHAPMAN ( 1 9 5 3 ) , DRAKE (1968) and IRIBARNE and KLEMES (1970)
have described experiments t o assess the importance o f some o f these c l o u d
e l e c t r i f i c i a t i o n t h e o r i e s by a t t e m p t i n g t o c l o s e l y reproduce
environment
of p r e c i p i t a t i o n .
the n a t u r a l
DRAKE has shown t h a t f r o z e n water drops
produce more e l e c t r i f i c a t i o n on m e l t i n g than would be expected from s t u d i e s
o f blocks o f i c e . The present work attempts tocfevelop t h i s approach t o the
l a b o r a t o r y study of cloud physics by t r y i n g t o estimate the importance o f
m e l t i n g i c e i n convective cloud e l e c t r i f i c a t i o n .
DINGER and GUNN (1946), MAGONO and KIKUCHI (1965), DRAKE (1968) and o t h e r s
have r e p o r t e d f i n d i n g a p o s i t i v e charge o f approximately 1000 pC g * on t h e
meltwater produced from chemically pure i c e . This e l e c t r i f i c a t i o n process i s
of t h e c o r r e c t s i g n , and according t o DRAKE the c o r r e c t magnitude, t o be
responsible f o r the c r e a t i o n o f the lower p o s i t i v e charge which i s o f t e n found
near the 0°C l e v e l i n thunderclouds.
M e l t i n g e l e c t r i f i c a t i o n may a l s o e x p l a i n
why RAMSAY and CHALMERS (1960) and REITER (1965) have found t h a t p r e c i p i t a t i o n
c u r r e n t changes from p o s i t i v e t o negative as steady r a i n t u r n s t o snow.
I
decided t o study the m e l t i n g o f small f r o z e n water d r o p s , t y p i c a l l y 4 mm i n
d i a m e t e r , as they are of a s i z e o f t e n found i n convective c l o u d s .
1.2. THE THUNDERSTORM
1.2.1.
One
The thundercloud as a m e t e o r o l o g i c a l phenomenon
o f the most comprehensive s t u d i e s o f the dynamics o f thunderclouds
y e t undertaken was the American 'Thunderstorm P r o j e c t ' i n t h e l a t e 1940s.
The r e p o r t o f the o b s e r v a t i o n s made i n F l o r i d a as p a r t o f t h i s p r o j e c t
(BYERS and BRAHAM, 1948) has been taken as t h e basis o f a model
(
13 APR 1972
1972
n
Lis,!
J
thunderstorm
UJ
CO
in
4)
(J)
O
S>
\
to
CO
UQ
to
0;
E
.*
(J
00
UJ
N
<3
UJ
0
u
Oo
UJ
0
in
0
to
to
*0
u
CD
4>
2.
ever s i n c e .
By measuring the d i s t r i b u t i o n o f r a i n f a l l and observing radar
echoes BYERS and BRAHAM p i c k e d out c e l l s w i t h i n a thunderstorm system which
were t y p i c a l l y
5 km across and contained an updraught and a downdraught.
These c e l l s were observed t o pass t h r o u g h a w e l l d e f i n e d s e r i e s o f stages
(Fig.
1,1) l a s t i n g a t o t a l o f 30 minutes t o one hour, s t a r t i n g from an
a p p a r e n t l y o r d i n a r y cumulus cloud ( F i g . l a ) .
Due t o a h i g h l e v e l o f v e r t i c a l
i n s t a b i l i t y and a p l e n t i f u l supply o f moisture f l o w i n g i n t o t h e c l o u d , the
growth becomes more r a p i d and more e x t e n s i v e then f o r an o r d i n a r y cumulus.
When t h e downdraught i s s t a r t e d , t h e cloud p'asses i n t o the mature stage
(Fig.
the
l b ) d u r i n g which most o f t h e l i g h t n i n g and p r e c i p i t a t i o n occur.
Finally
downdraught dominates and the cloud e n t e r s the d i s s i p a t i n g o r a n v i l stage
(Fig.
1.1.c).
An i m p o r t a n t f e a t u r e o f t h i s d e s c r i p t i o n o f the thundercloud
i s the r o l e o f the p r e c i p i t a t i o n i n causing the downdraught which then tends
to
l i m i t the l i f e o f t h e c e l l .
1.2.2.
C l a s s i f i c a t i o n o f thunderstorms
Thunderstorms
may be c l a s s i f i e d as heat or a i r mass storms and f r o n t a l
storms, depending on how the i n i t i a l
vigorous updraught was produced.
convergence
necessary t o s t a r t the
Most heatthunderstorms occur i n the t r o p i c s
c\-rC
o v e r l a n d , e s p e c i a l l y over mountains.
F r o n t a l thunderstorms^usually a s s o c i a t e d
w i t h c o l d f r o n t s , and tend t o p e r s i s t f o r several hours as t h e y move w i t h t h e
f r o n t , they are more f r e q u e n t near the coast and can occur over the oceans
o u t s i d e the t r o p i c s ( A d m i r a l t y Weather Manual 1938).
The a c t u a l
size,
s e v e r i t y and l i f e o f t h e storm does not depend on i t s t y p e , but r a t h e r on
the
t o t a l a v a i l a b l e energy, which w i l l be determined by the degree and
v e r t i c a l e x t e n t o f u n s t a b l e a i r and the supply o f moisture from below the
cloud.
S i m i l a r l y the h e i g h t o f c l o u d base wiH be determined by t h e l o c a l
m e t e o r o l o g i c a l v a r i a b l e s e s p e c i a l l y h u m i d i t y and w i l l be much g r e a t e r i n
the
c o o l d r y a i r o f t h e Alps than i n t h e warm moist a i r o f the t r o p i c s .
Shaded
Motion of s t o r m
region
Precipitotion
/HAIL
HA
UPDR AUGHT
Fig.1.2
A steady
state
convective s t o r m
77
(Browning,1964)
- f \
/
ir v e l o c i t y
/
/
/
Mot ion
of-clou d
/
/
•gl. 3
A schematic
view
in w h i c h t h e w i n d
\
of a t h u n d e r s t o r m
shearswith
height
in a n
environment
(Newton.1967 )
3.
1.2.3.
Severe thunderstorms
There i s some evidence t h a t s e v e r e storms? o f t e n producing damaging
h a i l , are a s s o c i a t e d w i t h s i n g l e c e l l s o r super c e l l s , which p e r s i s t f o r
several hours.
A f t e r s t u d y i n g a severe storm a t Wokingham i n 1959,
BROWNING and LUDLAM (1962) d e s c r i b e d the e s s e n t i a l f e a t u r e o f the severe
storm as being the s l o p i n g o f the updraught, e n a b l i n g the p r e c i p i t a t i o n
t o f a l l c l e a r w i t h o u t f o r m i n g a dominating downdraught
described by BYERS and BRAHAM (1948).
as i n the storms
New m o i s t a i r could then be drawn
i n from t h e f r o n t o f the storm as i n F i g . 1.2, e n a b l i n g t h e thunderstorm
t o p e r s i s t and dominate i t s environment.
According t o NEWTON (1967)
severe storms are most l i k e l y t o occur when there are bands o f s t r o n g
winds f l o w i n g i n d i f f e r e n t d i r e c t i o n s .near the upper and lower l e v e l s o f
the cloud ( F i g . 1.3).
I f the storm moves w i t h the v e l o c i t y o f the a i r i n the mid-troposphere,
t h e r e w i l l be a r e l a t i v e movement between the cloud and i t s environment near
both i t s t o p and base.
From an a n a l y s i s o f the f o r c e s i n v o l v e d NEWTON and
NEWTON (1959) suggested t h a t w i t h modest v e r t i c a l motions a storm column
could remain e r e c t w i t h r e l a t i v e h o r i z o n t a l motions between cloud and
environment i n excess of 10 ms ^.
I t i s probable t h a t w h i l e severe storms
are not v e r y common, an a p p r e c i a b l e number o f thunderstorm c e l l s are
i n c l i n e d t o the v e r t i c a l as the r e s u l t o f wind shear.
From the D a i l y
Weather Report and the A e r o l o g i c a l Record i t i s p o s s i b l e t o deduce values
f o r the maximum r e l a t i v e v e l o c i t i e s between cloud and environment when
thunderstorms are i n the r e g i o n o f the upper a i r wind sounding.
1-1- summarizes the r e s u l t s o f t h i s a n a l y s i s f o r the B r i t i s h
d u r i n g p a r t o f the summer o f 1967.
Table
Isles
From these few r e s u l t s i t seems
t h a t an a p p r e c i a b l e f r a c t i o n o f B r i t i s h thunderstorms may have updraughts
s l i g h t l y inclined to the v e r t i c a l .
TABLE l . i
Maxima r e l a t i v e v e l o c i t i e s between cloud and environment
UP t o 10 km f o r summer storms over the B r i t i s h
Relative
velocity
up t o 10 ms
9
from 10 t o 15 ms
1.3
Number o f thunderstorm days
-1
more t h a n 15 ms
Isles
-1
11
-1
5
THE ELECTRICAL CHARGE DISTRIBUTION IN THUNDERSTORMS
The c o n v e n t i o n a l p i c t u r e o f t h e thunderstorm having an upper p o s i t i v e
and a lower n e g a t i v e charge i s supported by t h e work o f SIMPSON and SCRASE
(1937) w i t h an a l t i e l e c t r o g r a p h and MALAN and SCHONLAND (1951) who measured
p o t e n t i a l g r a d i e n t changes due t o l i g h t n i n g f l a s h e s .
p o s i t i v e charge has o f t e n been observed near cloud
A s u b s i d i a r y lower
base-
SIMPSON and
SCRASE i n England, REYNOLDS and NEILL (1955) i n U.S.A. and KUETTNER (1950)
i n t h e Alps suggest t h e n e g a t i v e charge i s l o c a l i s e d a t some temperature
between -8° and -16°C depending on t h e h e i g h t o f t h e cloud base.
However,
measurements i n South A f r i c a by MALAN and SCHONLAND (1951) suggest t h a t the
negative charge i s i n t h e f o r m of a column from the 0°C l e v e l up t o - 40°C.
MALAN ( l 9 5 l ) has p o i n t e d o u t t h a t the South A f r i c a n storms were observed a t
Johannesburg
1.8 km above sea l e v e l and were g e n e r a l l y i s o l a t e d cumulinimbi
as opposed t o t h e E n g l i s h storms which were o f t e n of f r o n t a l o r i g i n and
multicellular.
However, t h e work o f OGAWA and BROOK (1969) has suggested
t h a t the South A f r i c a n r e s u l t s exaggerate the v e r t i c a l e x t e n t of the
negative charge because they were s i n g l e s t a t i o n ' o b s e r v a t i o n s o f e l e c t r i c
f i e l d changes compared t o t h e m u l t i p l e s t a t i o n measurements o f REYNOLDS
and NEILL and the v e r t i c a l dimension probed by t h e a l t i e l e c t r o g r a p h .
5.
TABLE 1 .9
The magnitude and
position
of
ttiemain charge centres i n
thunderclouds
Observer
Positive
charge
SIMPSON and ROBINSON
Negative
height
charge
height
24C
6 km
20C
3 km
GISH and WAIT (1950)
39G
9.5 km
39C
3 km
MALAN (1952)
40C
10 km
40C
5 km
(1940)
T y p i c a l values o f t h e main charges i n thunderclouds are found i n
1
Table 1.2. They are of the same order as those destroyed i n s i n g l e
l i g h t n i n g f l a s h e s a c c o r d i n g t o PIERCE (1955) and WORMELL (1939).
1.4
1.4.1
THE LOWER POSITIVE CHARGE
The evidence f o r a lower p o s i t i v e charge
SIMPSON and SCRASE (1937) found evidence f o r a l o c a l c o n c e n t r a t i o n o f
p o s i t i v e charge i n t h e cloudbase o f some thunderstorms u s u a l l y i n f r o n t
of the main r a i n area.
T h i s lower p o s i t i v e charge has been observed by
several other workers (Table 1.3) i n some b u t not a l l storms.
Because
of t h e nature o f t h e measurements and i t s r e l a t i v e size compared t o t h e
main charge centres a lower p o s i t i v e charge may be present i n most thunderstorms but i s o n l y d e t e c t e d under favourable c o n d i t i o n s .
From the r e s u l t s
of SIMPSON and ROBINSON (1940) and MALAN (1952) i t would appear t h a t the
s u b s i d i a r y charge i s about one q u a r t e r of t h e magnitude of t h e main charges.
T a b l e t s a l s o i n d i c a t e s t h a t t h e v e r t i c a l p o s i t i o n o f t h e charge seems t o
be independent o f temperature but u s u a l l y i t i s l o c a t e d i n t h e l o w e s t
kilometre o f cloud.
7
Return
stroke
Post-return
stroke
> K— L
[
Fig.1.4
Typical
Intermediate
electric field
i Leader i
changes at 5km
( C l a r e n c e and
_
from adishorge to
ground
Malan,1957)
Main l o c a t i o n
of l o w e r p o s i t i v e c h a r g e
Possible location
of p o s i t i v e c h a r g e
Rain sheet
a n d Downdra u ght
Fig.1.5
THE
LOCATION
OF
THE
LOWER
POSITIVE
( W I L L I A M S , 19 5 8 )
CHARGE
6.
TABLE 1.3
The l o c a t i o n of t h e lower p o s i t i v e charge
POSITION
S 0 ( J R C E
REYNOLDS and NEILL (1955)
New Mexico
TEMPERATURE
1 km above cloud base
-3 °C
SIMPSON and ROBINSON ( l 9 4 l ) England
0.5 km
"
"
+8 °C
KUETTNER (1950) Zugspitze
0.5 km
"
»
0 °C
MALAN (1952) Johannesburg
MALAN and SCHONLAND (1951)
MALAN and CLARENCE (1957)*
cloud base
Johannesburg
"
+5 °C
0.5 km below cloud base
+8 °C
0.5 km
+8 °C
"
"
"
Denotes t h a t t h e bottom of t h e charged r e g i o n was l o c a t e d .
1.4.2
The r o l e o f the lower p o s i t i v e charge i n the l i g h t n i n g
discharge
WHIPPLE (1938) suggested t h a t l i g h t n i n g i s not due t o an e x c e p t i o n a l l y
l a r g e p o t e n t i a l d i f f e r e n c e between cloud and ground because i t i s p o s s i b l e t o
have cloud-ground
the c l o u d .
l i g h t n i n g w i t h o u t p o i n t discharge under t h e a c t i v e p a r t of
He a l s o t e n t a t i v e l y suggested t h a t l i g h t n i n g could be i n i t i a t e d
by a b u i l d - u p of p o s i t i v e p o i n t discharge ions i n t h e base o f the c l o u d .
CLARENCE and MALAN (1957) found evidence f o r t h i s process by studying
the e l e c t r o s t a t i c f i e l d changes t h a t occurred before t h e f i r s t s t r o k e i n a
lightning flash.
Fig.1-4 shows t h e i n i t i a l breakdown stage (B) l a s t i n g up
t o 10 ms which i s f o l l o w e d by an I n t e r m e d i a t e stage ( I ) l a s t i n g up t o 400 ms
a f t e r which the leader and t h e r e t u r n stroke s t a r t the l i g h t n i n g
proper.
discharge
A t h o r i z o n t a l d i s t a n c e s up t o 2 km from the discharge t h e B f i e l d
changes were observed t o be negative w h i l e f o r d i s t a n c e s i n excess o f 5 km
they were p o s i t i v e , and between 2 and 5 km t h e f i e l d changes were e q u a l l y
l i k e l y t o be p o s i t i v e o r n e g a t i v e .
initial
CLARENCE and MALAN i n t e r p r e t e d t h i s
breakdown as being due t o a discharge i n t h e cloud between a
p o s i t i v e and a negative r e g i o n where t h e maximum f i e l d a t t h e ground due
to these charges was l o c a t e d a t 2 km and 5 km from t h e discharge.
Using
SIMPSON's (1927) r e s u l t t h a t the maximum f i e l d a t t h e ground a t a
h o r i z o n t a l d i s t a n c e D from the charge passes through a maximum when t h e
7.
charge passes through a maximum when t h e charge i s a t a h e i g h t H
where
H = ^2 D
CLARENCE and MALAN l o c a t e d t h e p o s i t i v e charge a t 1.4 km and the negative
a t 3.6 km. These values agree w e l l w i t h t h e h e i g h t o f t h e cloud base and
the lower r e g i o n o f t h e n e g a t i v e l y charged column found by MALAN and
SCHONLAND ( l 9 5 l ) .
These r e s u l t s s t r o n g l y suggest t h a t t h e lower p o s i t i v e
charge plays an e s s e n t i a l p a r t i n t h e l i g h t n i n g discharge i n a t l e a s t some
thunderstorms.
1.4.3
The l o c a t i o n of t h e lower p o s i t i v e charge
WILLIAMS (1958) has compared t h e data i n Table 1.3 and has drawn up
a model o f a thunderstorm c e l l ( F i g . 1.5) i n which the lower p o s i t i v e charge
i s l o c a t e d i n t h e form o f a p r i s m 1 km wide on t h e boundary between the
updraught and downdraught.
He a l s o suggested t h a t t h e r e i s a r e g i o n o f
p o s i t i v e charge on the r e a r side o f t h e downdraught.
WILLIAMS found evidfeace
f o r t h i s model by a n a l y s i n g t h e experiment o f FETERIS (1952) i n which a dense
network o f ground observers r e p o r t e d the p o s i t i o n and time of occurrence o f
every f l a s h t o ground from a s i n g l e c e l l whose radar echo had a maximum
diameter o f 10 km. Assuming t h a t t h e lower p o s i t i v e charge was i n v o l v e d i n
a l l t h e l i g h t n i n g f l a s h e s WILLIAMS used t h i s a n a l y s i s t o c o n f i r m the
h o r i z o n t a l d i s t r i b u t i o n o f the lower p o s i t i v e charge i n h i s model,
1.5
1.5.1
THEORIES OF THE FORMATION OF THE LOWER POSITIVE CHARGE
Melting p r e c i p i t a t i o n
CHALMERS (1965) suggests t h r e e ways i n which the m e l t i n g o f s o l i d
p r e c i p i t a t i o n may cause t h e charge s e p a r a t i o n necessary t o produce the
lower p o s i t i v e charge.
1) The b u r s t i n g o f a i r bubbles trapped i n t h e i c e
(1.5.3)
2) l a r g e snowflakes o r h a i l may m e l t t o form waterdrops which
are so l a r g e t h a t t h e y break up. (1.5.4)
8,
3) when i c e and water are i n c o n t a c t the water may be p o s i t i v e l y
charged, so any s p l a s h i n g , rubbing o r shaking o f f of water
from t h e s u r f a c e o f a m e l t i n g p a r t i c l e w i l l cause charge
s e p a r a t i o n . (1.5.5)
9
1.5.2
The evidence f o r s o l i d p r e c i p i t a t i o n i n thunderclouds
While i t can probably be s t a t e d t h a t the m a j o r i t y o f thunderstorms i n
temperate c l i m a t e s extend above the 0°C l e v e l and have p r e c i p i t a t i o n i n t h e
ice
phase, t h e r e i s a growing weight o f evidence f o r the e x i s t e n c e o f warm
thunderstorms w i t h no i c e present a t a l l and whose p r e c i p i t a t i o n growth i s
by t h e coalescence of water drops.
FOSTER (1950), LANE-SMITH ( 1 9 6 9 ) , apd
MICHNOWSKI (1963) have r e p o r t e d seeing l i g h t n i n g from clouds whose tops
did
not extend above the 0°C l e v e l .
The A d m i r a l t y Weather Manual
(1938)
s t a t e s t h a t thunderstorms o f t e n occur i n Java w i t h tops below the summits
of nearby mountains which are a l l l e s s than 3 km a l t i t u d e .
t h a t the tops of clouds are v e r y close t o the C°C l e v e l .
the
This i m p l i e s
However i n a l l
thunderclouds where t h e lower p o s i t i v e charge has been found the cloud
extended f o r s e v e r a l k i l o m e t e r s above t h e 0°C l e v e l and i t i s not p o s s i b l e
to say whether t h i s charge i s present i n warm thunderstorms.
1•5•3
The a i r bubble t h e o r y o f the lower p o s i t i v e charge.
The work of DINGER and GUNN (1946), MAC CREADY and PROUDFIT (1965a)
and MAGONO and KIKUCHI (1965) provides s t r o n g evidence t h a t when i c e melts
the
meltwater acquires a p o s i t i v e charge o f the o r d e r o f 300 pC g ^ provided
t h a t a i r bubbles are released from the i c e . DRAKE (1968) found t h a t when
frozen water drops of 1 t o 6 mm i n diameter are melted i n an a i r s t r e a m
vigorous convection may develop i n t h e meltwater and t h e e l e c t r i f i c a t i o n i s
then enhanced by as much as an order o f magnitude.
The p o s i t i v e l y
charged
m e l t i n g h a i l o r snow w i l l f a l l c l e a r o f t h e a i r which has become n e g a t i v e l y
charged so producing a n e t p o s i t i v e charge below t h e 0°C l e v e l .
e s t i m a t e d t h a t t h i s charging process could account f o r a p o s i t i v e
DRAKE
charge
9.
d e n s i t y of 10 G km
, which agrees w e l l w i t h t h e probable value of 8 C km
c a l c u l a t e d by MASON (1957).
There are several o b j e c t i o n s t o t h i s t h e o r y , the most i m p o r t a n t being
t h a t i t i s v e r y s e n s i t i v e t o i o n i c i m p u r i t i e s and i t may be argued t h a t
DRAKE considered water which was more pure than occurs i n n a t u r a l c l o u d s .
I f t h i s c h a r g i n g process can be explained by t h e IRIBARNE and MASON (1967)
theory o f b u b b l e - b u r s t i n g e l e c t r i f i c a t i o n , one would expect the spectrum
of a i r bubble* sizes t h o o t r u o t u r o o f the ioo t o be an important f a c t o r .
F i n a l l y i t i s not known whether v i g o r o u s c o n v e c t i o n would develop i n r e a l
p r e c i p i t a t i o n f a l l i n g through a r e a l
1.5.4.
atmosphere.
The d r o p - s h a t t e r i n g mechanism
I f l a r g e snowflakes o r h a i l s t o n e s melt t o form water drops which are
l a r g e r than about 5 mm i n diameter the r e s u l t a n t raindrops w i l l break up as
they gather speed under g r a v i t y .
SIMPSON (1909) and CHAPMAN (1953) have
found t h a t breaking water drops separate charge , w i t h the drops becoming
p o s i t i v e l y and t h e a i r n e g a t i v e l y charged.
The a c t u a l magnitude o f the charge
depends on t h e s e v e r i t y of t h e s h a t t e r i n g process and according t o CHAPMAN
can v a r y from 0.4 pC g * up t o 1000 pC g
1
where the r e l a t i v e v e l o c i t y of
-1
drop and a i r s t r e a m are as much as 5 ms
. CHAPMAN suggests t h a t i f t h e r e
i s enough m i c r o t u r b u l e n c e i n t h e cloud t o give drops a momentary v e l o c i t y
of 1 ms ^ r e l a t i v e t o t h e i r surroundings then charges of 100 pC per drop
are
possible.
T h i s process could be important i n the t u r b u l e n t i n t e r f a c e
between updraught and downdraught where WILLIAMS (1958) has l o c a t e d the
lower p o s i t i v e charge i n thunderclouds.
A f u r t h e r advantage of t h i s mechanism i s t h a t i t i s l e s s s e n s i t i v e t o
i o n i c i m p u r i t i e s than t h e bubble b u r s t i n g t h e o r y .
MATTHEWS and MASON (1964)
have found t h a t when l a r g e drops are g e n t l y d i s r u p t e d
i n an a i r s t r e a m , the
e l e c t r i f i c a t i o n can be increased by a f a c t o r of a hundred t o 300 pC g ^
4
by a p p l y i n g an e l e c t r i c f i e l d o f the order o f 3 x 10 V m
"1
.
As such
a f i e l d would be expected i n a thundercloud t h i s process should be a c t i v e
to some e x t e n t below the 0°C l e v e l .
Cloud motion
Negatively
charged
colu mn
L o w e r p o s i t ii v e
char ge
\
11
Point discharge
* * .' '
"i
E3
F i g .1.6
T h e point
L i g h t n i n g flash
t o g round
Positive
point d i s c h a r g e
ions
Rai n
discharge
origin
( M A L A N ,1 9 5 2 )
of the l o w e r
positive
charge
10*
1»5*4
The Ice-Water c o n t a c t theory
4
..
Because t h e m o b i l i t y o f protons exceeds t h a t ^ t h e h y d r o x y l ions i n i c e ,
and since f o r both ions t h e c o n c e n t r a t i o n i s h i g h e r i n w a t e r , t h e r e should
be a tendency f o r t h e protons t o pass through t o t h e i c e more e a s i l y than
the h y d r o x y l
i o n s , thus making a t h i n f i l m o f meltwater n e g a t i v e l y charged.
2
TAKAHASHI (1969) found t h i s charge separation t o be about 1500 pC cm" which
f o r a 4 mm i c e sphere corresponds t o 75 pC spread over t h e s u r f a c e .
I f water
i s shed d u r i n g t h e m e l t i n g process the m e l t i n g p a r t i c l e w i l l become
p o s i t i v e l y charged.
This mechanism could be i m p o r t a n t i n the e l e c t r i f i c a t i o n
of m e l t i n g snowflakes, where a i r bubbles escape from a t h i n f i l m of water.
1.5.5. The p o i n t discharge t h e o r y
WILLIAMS (1958) has p o i n t e d o u t t h a t t h e lower p o s i t i v e charge has been
observed t o l i e i n t h e lowest k i l o m e t r e o f cloud and i t s l o c a t i o n does n o t
seem t o be c o r r e l a t e d w i t h temperature.
KUETTNER (1950) and REYNOLDS and
NEILL (1955) l o c a t e d the charge a t o r above the 0°C l e v e l which does not a l l o w
the t h e o r i e s i n v o l v i n g m e l t i n g ice t o be .a s a t i s f a c t o r y e x p l a n a t i o n , although
it
i s not easy t o estimate a c c u r a t e l y t h e temperature
i n s i d e clouds.
MALAN
(1952) has suggested t h a t ions from p o i n t discharge may get caught i n t h e
updraught below t h e thundercloud
attachment
( F i g . 1.6) and become immobilised by
t o cloud p a r t i c l e s i n t h e base o f t h e cloud.
MALAN p o i n t s out
t h a t most o f the l i g h t n i n g f l a s h e s t o ground i n Johannesburg seem t o take
place t o t h e f r o n t o f t h e advancing storm where t h e p o i n t discharge
are being caught i n t h e updraught*
ions
This t h e o r y has o n l y been e x p l a i n e d i n
a q u a l i t a t i v e way but i t could e x p l a i n the anomaly o f t h e absence of an
increase o f f i e l d measured by t h e a l t i - e l e c t r o g r a p h below thunderclouds*
1.6 Laboratory Assessment o f t h e Theories of t h e Formation o f the Lower
P o s i t i v e Charge
Three t h e o r i e s o f the lower p o s i t i v e charge have been o u t l i n e d , which
i n v o l v e t h e e l e c t r i c surface o r bulk p r o p e r t i e s o f i c e and water.
The choice
11.
between these t h e o r i e s does n o t seem t o be determined by v e r i f y i n g these
p a r t i c u l a r p r o p e r t i e s o f t h e water substance, b u t r a t h e r by a t t e m p t i n g
to a s c e r t a i n whether the mechanisms i n which these p r o p e r t i e s are a c t i v e
do i n f a c t occur i n t h e r e g i o n o f t h e lower p o s i t i v e charge. I t was
t h e r e f o r e decided t o t r y and simulate as c l o s e l y as p o s s i b l e the c o n d i t i o n s
present i n t h e thundercloud and a t the same time make the necessary
e l e c t r i c a l measurements t o assess t h e importance o f m e l t i n g i c e i n the lower
r e g i o n s of thunderclouds.
12.
CHAPTER
PREVIOUS
STUDIES
OF
MELTING
2
ICE ELECTRIFICATION
9.1 EXPERIMENTS WITH BLOCKS OF ICE
DINGER and GUNN (1946) melted 2-ml i c e blocks i n a warm a i r s t r e a m and
found t h a t t h e meltwater acquired a p o s i t i v e charge of about 0.4 pC mg ^ i f
the i c e was made from d i s t i l l e d water.
The amount o f charge separated
decreased r a p i d l y i f the m e l t i n g r a t e f e l l below 10 mg s ^ o r carbon
d i o x i d e was d i s s o l v e d i n t h e i c e . Small q u a n t i t i e s o f i o n i c i m p u r i t i e s o f
the o r d e r o f 20 mg 1 * were s u f f i c i e n t t o reduce the charging by a f a c t o r o f
ten.
DINGER and GUNN suggested t h a t t h e charge separation mechanism was
r e l a t e d t o t h e escape o f a i r bubbles trapped i n t h e i c e and p o i n t e d o u t
t h a t the r e d u c t i o n o f charging w i t h increased i m p u r i t y l e v e l s was s i m i l a r
t o t h e behaviour o f t h e charge on a i r bubbles which had been i n v e s t i g a t e d
by McTAGGART (1914) and ALTY (1926).
MATTHEWS and MASON (1963) repeated Dinger and Gunn's experiment b u t
f a i l e d t o f i n d any charging above 0.003 pC mg
I n two l a t e r notes
^MATTHEWS and MASON(l9*4^^DINGER(1964) suggest t h a t t h i s n u l l r e s u l t might
be caused by the presence o f a high c o n c e n t r a t i o n o f carbon d i o x i d e i n t h e
l a b o r a t o r y , due t o the use o f d r y i c e . McCREADY and PROUDFIT (1965) also
repeated t h e Dinger-Gunn experiment and found t h a t the m e l t w a t e r acquired
1
a p o s i t i v e charge o f about 0.02 pC mg" .
ROGERS (1967) melted 15mm
diameter i c e spheres, supported on an air j e t , and found t h a t t h e p a r t i a l l y
melted spheres were n e g a t i v e l y charged i f water had been f l u n g o f f and
p o s i t i v e l y charged o t h e r w i s e .
2.2. THE MELTING OF FROZEN WATER DROPS
DRAKE (1968) c a r r i e d o u t a thorough study o f the e l e c t r i f i c a t i o n
accompanying the m e l t i n g o f f r o z e n water drops over a wide range o f
melting conditions.
The i c e p a r t i c l e s were f r o z e n onto a 1mm loop o f
330 •
o
Many bubbles
•
No bubbles
+
A few bubbles
Charge
PC
120
o o
0°
•
o
o
3o
•
•
L
o
0
*****
© o o<*>
-•—r
-V
*
p
10
Mass of sample
IS
g
Fig.2.1 The e f f e c t o f air bubbles on melting electrification
( A f t e r K!KUCHI/I965a )
-t
Charge
-i
pC mg
3*«
-3
3* |t»
for 4
10
-3
10-1
-I
to
A i r bubble c o n c e n t r a t i o n
v o l u m e / volume
Fig.2.2 The relationship b e t w e e n air bubble concentration
and melting e l e c t r i f i c a t i o n
13.
constantan w i r e amd melted i n a c o n t r o l l e d a i r s t r e a m .
c o n v e c t i o n c u r r e n t s developed
order o f magnitude.
DRAKE found t h a t , when
i n the m e l t w a t e r , the charging increased by an
He also found t h a t carbon d i o x i d e o n l y i n h i b i t e d charging
i f t h e r e was no convection i n t h e meltwater and t h a t h i g h c o n c e n t r a t i o n s A
carbon d i o x i d e increased the c h a r g i n g .
The a c t u a l amount o f charging
depended on the r a t e o f heat f l o w t o the m e l t i n g i c e and on t h e f r e e z i n g
temperature and p u r i t y o f the water.
i m p u r i t y ions of l e s s than 2 mg 1
For water w i t h a c o n c e n t r a t i o n o f
the charge separated l a y t y p i c a l l y
between 1 and 2 pC mg ^.
DRAKE found a good q u a l i t a t i v e argeement w i t h the amount o f e l e c t r i f i c a t i o n
p r e d i c t e d by the a p p l i c a t i o n o f the IRIBARNE and MASON (1967) bubble
e l e c t r i f i c a t i o n experiments
melting i c e .
bursting
to the escape o f trapped a i r bubbles from the
However, the enhancement o f e l e c t r i f i c a t i o n w i t h h i g h
c o n c e n t r a t i o n s o f carbon d i o x i d e d i d not f i t t h i s t h e o r y .
2.3. THE BUBBLE-BURSTING THEORY OF MELTING ELECTRIFICATION
2.3.1
The evidence
f o r an a i r bubble
mechanism.
KIKUCHI (1965a) showed t h a t blocks o f i c e made from d e i o n i z e d water d i d
not become charged on m e l t i n g unless some a i r bubbles were present i n the i c e
( F i g . 2.1).
The l e v e l o f charging was t y p i c a l l y two orders of magnitude les<=
than t h a t found by DRAKE ( 1 9 6 8 ) , probably because o f the d i f f e r e n t m e l t i n g
conditions.
KIKUCHI also found t h a t the h i g h e r t h e c o n c e n t r a t i o n o f a i r
bubbles trapped i n t h e i c e , the g r e a t e r the charging ( F i g . 2.2).
I f large
a i r bubbles o f about 1 mm diameter were p r e s e n t , the charging was reduced,
suggesting t h a t t h e spectrum o f bubble s i z e s was also i m p o r t a n t .
Although
KIKUCHI estimated t h e mean charge on an a i r bubble t o be 3 x 10
pC, t h i s
cannot be d i r e c t l y compared w i t h t h e r e s u l t o f the experiment o f IRIBARNE
and MASON (1967) who s t u d i e d bubbles l a r g e r than 160 Jim compared t o the
average diameter of 50 jim i n the i c e samples.
This value f o r t h e charge
Al R
/
/
/
7
/
/ /
/ / / /
/
/ / / / /
'//
///ft
©0x-0©x;x-000 X-QQ0
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f
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U n c o v e r e d ion
it
©
©
.2.3
Water dipole
Hydroxy! ion
P r o t on
r
Impurity
cation
X
Impurity
anion
Schematic i l l u s t r a t i o n of t h e double layer
( After Alty,1926)
14.
on an a i r bubble i s not i n c o n s i s t e n t w i t h the IRIBARNE and MASON experiments
i f one assumes the main i o n i c i m p u r i t y t o be atmospheric carbon d i o x i d e
d i s s o l v e d i n the i c e .
2*3.2. The E l e c t r i c a l double l a y e r a t an a i r - w a t e r i n t e r f a c e .
The s e p a r a t i o n o f charge when a i r bubbles b u r s t a t a water surface and
when water drops splash o r s h a t t e r may be e x p l a i n e d by t h e r u p t u r e o f an
e l e c t r i c a l double l a y e r o f p o s i t i v e and negative charges a t t h e a i r - w a t e r
interface.
The e x i s t e n c e o f such a double l a y e r was f i r s t suggested by
HELMHOLTZ (1879)> and i t s presence confirmed by t h e work o f McTAGGART (1914)
and ALTY ( 1 9 2 6 ) , who s t u d i e d the motion o f a i r bubbles i n an e l e c t r i c
field.
By s t u d y i n g the way i n which t h e negative charge on a i r bubbles i n pure water
v a r i e d w i t h bubble s i z e and p u r i t y o f the w a t e r , ALTY developed a t h e o r y
d e s c r i b i n g the form o f the charges which made up t h e double l a y e r ( F i g . 2.3).
ALTY said t h a t the p o l a r water molecules were o r i e n t a t e d i n a p r e f e r r e d
d i r e c t i o n a t t h e a i r - w a t e r i n t e r f a c e , w i t h the p o s i t i v e end o f the d i p o l e s
pointing into the l i q u i d .
These surface molecules e l e c t r o s t a t i c a l l y a t t r a c t e d
negative ions and o t h e r water molecules. I n very pure water w i t h a t y p i c a l
-4
--J - ]
c o n d u c t i v i t y o f 10 ohm m
i m p u r i t y ions w i l l be present i n c o n c e n t r a t i o n s
7
8
of 1 i n 10 and i o n i z e d water molecules i n 1 i n 10 . Most o f the surface
water d i p o l e s w i l l become covered w i t h a s t r i n g o f water molecules bonded
t o them by hydrogen bonds.
ALTY showed t h a t t h e i m p u r i t y n e g a t i v e ions were
7
8
a t t r a c t e d t o t h e surface i n c o n c e n t r a t i o n s of about 1 i n 10 t o 10 . This
l a y e r o f n e g a t i v e ions then a t t r a c t e d i m p u r i t y p o s i t i v e i o n s and protons
which formed a d i f f u s e space charge and which were more r e a d i l y removed
by molecular c o l l i s i o n s and a i r escaping from t h e bubble.
The a i r bubbles
i n ALTY's experiment were n e g a t i v e l y charge because 10% of the n e g a t i v e
ions were not covered by p o s i t i v e ions ( F i g . 2.3).
CHALMERS and PASQUILL (1937) measured the p o t e n t i a l d i f f e r e n c e across
a w a t e r - a i r i n t e r f a c e and found t h a t t h i s c o u l d be e x p l a i n e d by 1 i n 25
of t h e water d i p o l e s being o r i e n t a t e d p e r p e n d i c u l a r t o the s u r f a c e .
They
Bubble film
—
Film drops
Jet
Jet
T h e bursting of a 1 5 mm a i r
( After Woodcock
drops
bubble
et al. 1 9 5 3 )
.15.
suggested t h a t i n r e a l i t y the water molecules are not a l l o r i e n t a t e d i n the
same d i r e c t i o n as ALTY has suggested but on average tend t o produce the
e f f e c t observed.
2.3.3. The mechanism o f bubble b u r s t i n g
The b u r s t i n g o f a i r bubbles a t a water s u r f a c e haa been s t u d i e d w i t h a
h i g h speed cine camera by WOODCOCK e t a l
(1953). who obtained a s e r i e s o f
photographs s i m i l a r t o F i g . 2.4. WOODCOCK found t h a t the b u r s t i n g process
was s i m i l a r f o r bubbles w i t h diameters ranging from 0.2 t o 2 mm.
I n stage
1 the bubble reaches t h e surface and then forms a r a i s e d cap o r f i l m
2).
(stage
This f i l m b u r s t s and may e j e c t a l a r g e number o f small d r o p l e t s c a l l e d
f i l m drops (stage 3 ) . A small j e t forms a t the base o f the depression and
grows r a p i d l y as t h e r a i s e d l i p subsides (stage 4)»
The j e t becomes
unstable and on r e a c h i n g i t s maximum h e i g h t e j e c t s t y p i c a l l y f i v e drops c a l l e d
j e t drops (stage 5 ) .
The t o t a l time taken from stages 1 t o 5 was o f the o r d e r
of 2 ms. The diameter o f the j e t drops were found t o increase w i t h bubble
size from 10 ^m f o r a 100 |im bubble t o lOQjtn f o r a 1mm diameter bubble.
The* time taken f o r the f i l m d r o p l e t s t o form i s g e n e r a l l y a few
microseconds and MASON (1954) using a microatscope slide technique has measured
the
diameters t o range from 0.4 t o 1.0 urn.
DAY (1964) and BLANCHARD (1963)
demonstrated t h a t t h e number o f f i l m drops produced f e l l o f f r a p i d l y from
100 f o r a 2 mm diameter bubble t o 10 f o r a 1mm bubble and l e s s than 1 f o r a
300
Jim bubble.
BLANCHARD (1963) estimated the charge c a r r i e d by a f i l m
drop t o be 3 e l e c t r o n charges per d r o p l e t from a b u r s t i n g bubble i n seawater
3
which i s a f a c t o r o f 10 l e s s than t h e charge c a r r i e d by a j e t drop from a
s i m i l a r bubble.
I t can t h e r e f o r e be assumed t h a t the maincharge t r a n s f e r
mechanism a s s o c i a t e d w i t h a i r bubbles r e l e a s e d i n t h e m e l t i n g o f small
p r e c i p i t a t i o n p a r t i c l e s w i l l be r e l a t e d t o the e j e c t i o n o f j e t drops.
2.3.4. Charge s e p a r a t i o n accompanying the b u r s t i n g of bubbles.
BLANCHARD (1963) and IRIBARNE and MASON (1967) have found t h a t t h e
d r o p l e t s e j e c t e d from b u r s t i n g bubbles are g e n e r a l l y n e g a t i v e l y charged
f o r water w i t h i o n i c i m p u r i t y c o n c e n t r a t i o n s less than 1 0 ~
4
N and
9
i n Molar
g A = Thickness of double loyer
Negat ive charge
density
pC mm
10
Molar
B
i
O-OOl
0'0»
o
0-1
d - D i s t a n c e from w a t e r surface
Fig.2.5
Net c h a r g e
f»m
density between the s u r f a c e and a depth d
?7/A
Negat ive charge
F-f J
Posit ive ch ar§e
-r
Fig.2.6a. Formation of a negatively charged jet — P ure w a t e r
7> ^ ;
Flg.2.6b. Formation of a neutral j e t — Less pure
water
16.
p o s i t i v e l y charged f o r l e s s pure water,
IRIBARNE and MASON e x p l a i n e d
these
r e s u l t s q u a l i t a t i v e l y by s t u d y i n g the behaviour o f the double l a y e r d u r i n g
the f o r m a t i o n of the j e t drops*
IRIBARNE and MASQN p o s t u l a t e d t h a t the j e t was composed o f the water
nearest the surface of t h e a i r bubble, which had s l i d down the edge of t h e
depression t o form a j e t a t t h e centre ( F i g . 2.4)-
From photographs o f the
f o r m a t i o n o f these j e t s , taken by WOODCOCK e t a l (1953) and NEWITT e t a l
( 1 9 5 4 ) , they estimated t h a t the volume of the j e t was about 1% of the volume
of
the bubble.
They were then able t o c a l c u l a t e the depth d of the surface
l a y e r which was needed t o make t h e j e t o f a bubble o f r a d i u s R. (Equation
2.1).
I f the surface l a y e r down t o a d e p t h d i s m a i n l y the negative h a l f o f the d •
double l a y e r then the j e t w i l l be n e g a t i v e l y charged (Fig- 2.6A).
However?
should d be g r e a t e r than the t h i c k n e s s of the complete double l a y e r then the
j e t w i l l be n e u t r a l ( F i g . 2.6B)-
So the t h i c k n e s s o f the double l a y e r w i l l
govern the charge s e p a r a t i o n due t o bubble b u r s t i n g and the way t h i s charging
v a r i e s w i t h bubble s i z e .
2.3.5.
The e f f e c t o f i m p u r i t i e s on the t h i c k n e s s of the double l a y e r -
By c o n s i d e r i n g t h e r a t e o f removal of the ions o f t h e double l a y e r from
the e l e c t r o s t a t i c a t t r a c t i o n o f the surface water d i p o l e s * GOUY (1910)
deduced an expression f o r the i n t e g r a t e d charge d e n s i t y Q- over the d i s t a n c e
from t h e s u r f a c e t o a depth x (Equation 2.2)«T = (a D7C•* exp( 4 -P<^ x)
where
a and £
2.2
are constants c o n t a i n i n g the gas constant and the
p e r m i t t i v i t y o f a f r e e spaceD i s the d i e l e c t r i c constant o f water
T i s the a b s o l u t e
temperature
c i s t h e gram molar c o n c e n t r a t i o n o f i o n i c i m p u r i t y .
10
Molar
\
CHARGE:
pc
8x10
Molar
\
/
5x10
Moor
/
I
20
40
io
too
0
BUBBLE
Fig.2.7
DIAMETER
H- m
C h a r g e s e p a r a t e d by t h e
Iribarne
and
b u r s t i n g o t bubbles
Mason—theory
3
00
17.
I n f i g - 2.5 o* i s p l o t t e d as a f u n c t i o n o f x f o r two c o n c e n t r a t i o n s o f
i m p u r i t y , 10 M corresponding t o extremely pure d e i o n i z e d water and 10 M
corresponding t o a t y p i c a l cloud water c o n c e n t r a t i o n o f 6 mgl o f sodium
c h l o r i d e . The t h i c k n e s s o f the double l a y e r i s t h e d i s t a n c e from the water
surface a t which cr , the i n t e g r a t e d charge d e n s i t y below t h e s u r f a c e f a l l s
t o zero. I t can be seen from f i g . 2.5 t h a t a f a c t o r of 100 increase i n t h e
i o n i c i m p u r i t y c o n c e n t r a t i o n causes a f a c t o r of 10 decrease i n t h e t h i c k n e s s
of the double l a y e r . From equation 2 . 1 t h e t h i c k n e s s of t h e s u r f a c e l a y e r
d which forms the j e t o f a 200 Jim diameter bubble i s 0.3 \xm and IRIBARNE
and MASON observed t h a t bubbles o f t h i s diameter e j e c t j e t drops o f t o t a l
charge -3 x 1 0 ~ pC f o r 1 0 ~ M s o l u t i o n s and + 3 x 1 0 ~ pC f o r 10** M.
These observations agree q u a l i t a t i v e l y w'.th t h e above t h e o r y .
1
5
2
2.3.6
5
4
4
The dependence o f the charge separated by b u r s t i n g bubbles on the water
p u r i t y and bubble r a d i u s .
By combining equations 2.1 and 2.2, IRIBARNE and MASON deduced a
r e l a t i o n s h i p between t h e t o t a l charge on t h e j e t drops (Q) and t h e water
p u r i t y and bubble r a d i u s , ( e q u a t i o n 2»3)»
Q = 2.9 x 1 0
9
2
R C^" exp (-£ - 1.1 x 1 0
7
c£ R) .... 2.3
where Q i s measured i n pC.
Figure 2.7 i s a graph
of t h i s equation? from which i t i s c l e a r t h a t
f o r any i m p u r i t y c o n c e n t r a t i o n t h e r e should be a bubble diameter a t which
the charge separated i s a maximum.
These maxima should a l s o tend t o occur
a t s m a l l e r bubble diameters as the water becomes l e s s pure.
IRIBARNE and
MASON found good agreement w i t h t h i s t h e o r y down t o 200 urn, t h e s m a l l e s t
bubbles t h a t they s t u d i e d . A p o s s i b l e cause f o r t h e breakdown o f equation
2.3 f o r b , t a l e s o f l e s s than TOO^i-p diameter may be t h a t the volume o f
the j e t may n o t be 1% of the volume of t h e bubble.
This behaviour o f
very small bubbles may be very i m p o r t a n t i n e x p l a i n i n g t h e e l e c t r i f i c a t i o n
of m e l t i n g i c e as i c e samples o f t e n c o n t a i n many bubbles s m a l l e r than
50 \i m.
18.
2.3.7 The r e v e r s a l o f t h e s i g n o f ch-.rae pppa,T-at.ipn w i t h very impure water.
I f t h e j e t i s made up o f both components of the double l a y e r t h e n
according t o the above t h e o r y the j e t drops should be uncharged.
However,
IRIBARNE and MASON have suggested a mode o f charge s e p a r a t i o n which w i l l
e x p l a i n t h e i r own and BLANCHARD's (1963) o b s e r v a t i o n s t h a t w i t h h i g h l e v e l s
of
i m p u r i t y the j e t drops are p o s i t i v e l y charged w i t h t y p i c a l l y 3 x 10 pC
separated per bubble.
As t h e j e t breaks up necks w i l l form between the
b u l g e s , which e v e n t u a l l y form the d r o p s .
Water w i l l tend t o f l o w o u t o f
these necks i n t o the drops which are then e j e c t e d .
Now the p o s i t i v e space
charge o f t h e double l a y e r w i l l tend t o be d i s t r i b u t e d along the v e r t i c a l
a x i s o f t h e j e t and so w i l l tend t o move out o f the necks f a s t e r than t h e
negative p a r t o f the double l a y e r which i s r e s t r i c t e d by t h e surface.
IRIBARNE and MASON a p p l i e d the theory o f t h e f l o w o f water i n a c a p i l l a r y
tube t o t h e o u t f l o w of p o s i t i v e charge from the neck and o b t a i n e d an upper
value f o r the charge s e p a r a t i o n o f 3 x 10
pC, which agrees w e l l w i t h t h e i r
observations.
2.3.8
The release o f a i r bubbles by m e l t i n g i c e •
When a water drop i s f r o z e n v i r t u a l l y a l l the d i s s o l v e d a i r i s r e l e a s e d
as bubbles which are then trapped i n t h e i c e . On m e l t i n g these bubbles are
l i b e r a t e d from the i c e and are p a r t l y absorbed by the meltwater before
b u r s t i n g a t t h e water surface.
Because the s o l u b i l i t y o f a i r i n water
r a p i d l y decreases w i t h f a l l i n g temperature, a high p r o p o r t i o n of t h e bubbles
w i l l reach the water surface and b u r s t .
The amount o f a i r which would be
released by the m e l t i n g o f a 4 mm diameter water drop f r o z e n a t - 10°C
3
would be about 0.45 mm • The i c e p a r t i c l e s melted by DRAKE (1968) and
the
author contained a i r bubbles ranging from 10 ^m up t o 400 ^m d i a m e t e r ,
9
however DRAKE d i d not f i n d any n o t i c e a b l e c o r r e l a t i o n between bubble
spectrum and the degree o f charging on m e l t i n g .
He e x p l a i n e d t h i s by
p o i n t i n g o u t t h a t t h e a i r bubble s t r u c t u r e changed d u r i n g t h e m e l t i n g
process as some bubbles coalesced
and o t h e r s d i s s o l v e d .
Ex p e n m e n t
-9—& T h e o r y
+
10
Charge
i—r
10 S"o too
zoo
k-oo
Diameter
Fig. 2 . 8
Hm
The c h a r g e s e p a r a t e d by t h e bursting of bubbles
-4
in a 3 * 5 x 1 0
Molar
solution
I r i b a r n e and Mason
(1967)
19.
2.3,9
n
f
n
The a p p l i c a t i o n of the bubble ^ r f i ^ . P H t K I T - m e l t i n g i c e
electrification.
DRAKE found t h a t the way i n which the charge separated by m e l t i n g i c e
v a r i e d w i t h the .concentration o f i o n i c i m p u r i t i e s agreed w i t h t h e IRIBARNE
4
and MASON Ibubble b u r s t i n g t h e o r y f o r concentrations l e s s than 10
Mo The
l e s s pure the water, the s m a l l e r the charge gained by the m e l t w a t e r .
However the t h e o r y p r e d i c t e d t h a t the m e l t w a t e r should become n e g a t i v e l y
<
-4 ~
charged f o r i m p u r i t y c o n c e n t r a t i o n s g r e a t e r than 10
M„
DRAKE d i d not
find this.
I t i s suggested by the author t h a t the reason why DRAKE f a i l e d t o
f i n d a r e v e r s a l i n the s i g n of charge separated
was t h a t a t h i g h i m p u r i t y
c o n c e n t r a t i o n s the charging o f small a i r bubbles i s more important than
t h a t o f the l a r g e r bubbles.
Figure 2.8 shows the v a r i a t i o n i n the charge
c a r r i e d by the e j e c t e d drops as a f u n c t i o n o f bubble diameter f o r water
4
of p u r i t y 3.5 x 1 0 ~ M. Below 100 |im diameter
the IRIBARNE and MASON t h e o r y
p r e d i c t s t h a t the drops e j e c t e d w i l l be negative,so i n the m e l t i n g o f i c e
the meltwater would be p o s i t i v e l y charged.
F u r t h e r j the negative charge c a r r i e d by the drops from a 20 jim
diameter bubble should be an order o f magnitude g r e a t e r than the p o s i t i v e
charges from a 300^ bubble.
So even the meltwater
from i c e o f g r e a t e r than
10 ^ c o n c e n t r a t i o n of ions may be p o s i t i v e l y c h a r g e d
bubbles smaller than 50 jim.
9
i f t h e r e are enough
The range o f a i r bubble diameters
i n the samples
melted by DRAKE was 10 t o 400 |*m.
Another possible disagreement between experiment and t h e o r y was the
enhancement of e l e c t r i f i c a t i o n which was found by DRAKE f o r i c e w i t h high
c o n c e n t r a t i o n s of carbon d i o x i d e .
According
t o t h e double l a y e r t h e o r y the
carbon d i o x i d e should have i n h i b i t e d e l e c t r i f i c a t i o n *
I t w i l l be suggested
l a t e r i n t h i s t h e s i s t h a t the carbon d i o x i d e probably had escaped from the
a i r bubbles before they b u r s t a t the s u r f a c e o f the
meltwater.
20.
2.3.10 MgHpnrj ] r
P
e l e c t r i f i c a t i o n ^nd the s.pgs±£um_o_£
bubble s i z e s .
The range o f a i r bubble diameters trapped i n the i c e samples of DRAKE
and KIKUCHI (1965) was l O ^ m t o 400 ^m. From both t h e t h e o r y and experiments
of
IRIBARNE and MASON i t would be expected t h a t t h e charge separated by
bubbles i n d i f f e r e n t p a r t s o f the bubble diameter spectrum would vary
considerably w i t h the concentration of i m p u r i t i e s .
The spectrum p r o b a b l y
depends on the r a t e o f f r e e z i n g of the o r i g i n a l water and the size o f t h e
water drops.
Water drops f r o z e n i n an a i r stream w i l l f r e e z e much f a s t e r
than i n s t i l l a i r .
The s i z e d i s t r i b u t i o n o f a i r bubbles i n s o l i d p r e c i p i t a t i o n
w i l l be h i g h l y i n f l u e n c e d by the c o n d i t i o n s under which the i c e p a r t i c l e s grow
and w i l l be d i f f e r e n t f o r opaque and c l e a r h a i l .
the
F i n a l l y , the way i n which
i c e m e l t s may a f f e c t t h e s i z e o f the a i r bubbles a c t u a l l y b u r s t i n g a t t h e
s u r f a c e , as the r a t e s a t which they d i s s o l v e o r coalesce may be a l t e r e d .
2.4 FACTORS INFLUENCING THE CHARGING OF MELTING
NATURAL ICE PARTICLES
L a b o r a t o r y s t u d i e s o f m e l t i n g i c e and bubble b u r s t i n g e l e c t r i f i c a t i o n
have r e v e a l e d s e v e r a l p r o p e r t i e s t h a t w i l l decide the amount o f c h a r g i n g
produced i n t h e r e a l atmosphere by the m e l t i n g o f n a t u r a l p r e c i p i t a t i o n
particles.
I f one i s t o p r e d i c t t h e amount o f e l e c t r i f i c a t i o n
produced
by t h i s process, not o n l y must t h e i r e f f e c t on m e l t i n g i c e e l e c t r i f i c a t i o n
be known, b u t t h e e x t e n t t o which c o n d i t i o n s i n clouds w i l l encourage
appreciable e l e c t r i f i c a t i o n must also be d i s c o v e r e d .
The p r i n c i p l e f a c t o r s i n f l u e n c i n g m e l t i n g i c e e l e c t r i c i c a t i o n are
then
1) P u r i t y o f t h e water
2) M e l t i n g r a t e
3 ) A i r bubble s i z e spectrum
4) C r y s t a l s t r u c t u r e of t h e p a r t i c l e
5) The way i n which t h e m e l t i n g takes place
e.g. does c o n v e c t i o n occur i n t h e meltwater?
21.
CHAPTER
3
THE DESIGN OF A WIND TUNNEL. FOR THE FREE FLIGHT
OF SMALL ICE SPHERES.
3.1. THE IMPORTANCE OF A FREE SUPPORT SYSTEM
Some o f t h e v a r i a b l e s which i n f l u e n c e the amount o f charging occurring
when i c e melts were l i s t e d i n s e c t i o n 2.4.
I f an attempt i s t o be made t o
draw conclusions about t h e e l e c t r i f i c a t i o n o f m e l t i n g s o l i d p r e c i p i t a t i o n from
a l a b o r a t o r y experiment, probably the most important p r o p e r t y t h a t must be
r e a l i s t i c a l l y reproduced
i s t h e a i r f l o w around the p a r t i c l e .
This a i r f l o w w i l l
not o n l y i n f l u e n c e the development of convection i n t h e m e l t w a t e r , b u t a l s o t h e
m e l t i n g process.
I n t h e experiment o f DRAKE (1968), the i c e p a r t i c l e s were
suspended from a loop of w i r e 1 mm i n diameter and so could be supported when
the a i r f l o w was g r e a t l y d i f f e r e n t from t h e i r t e r m i n a l v e l o c i t y .
Also the
p a r t i c l e s were not f r e e t o r o t a t e and i f they had been f r e e , t h e onset o f
convection i n t h e meltwater might not have occurred u n t i l much h i g h e r
temperatures o r a i r f l o w r a t e s .
Furthermore, i f
#
the p a r t i c l e s could be
supported f r e e l y i n an a i r s t r e a m , then the e f f e c t o f the e l e c t r i c a l c o n t a c t
between t h e support and t h e i c e p a r t i c l e could be assessed.
I t was t h e r e f o r e
decided t o t r y t o develop a method o f h o l d i n g an i c e p a r t i c l e i n a v e r t i c a l
a i r s t r e a m away from any s o l i d boundaries.
3.2. THE PROBLEM OF TURBULENECE
3.2.1.
The e f f e c t o f t u r b u l e n c e on a supported p a r t i c l e
A l l methods of f r e e l y s u p p o r t i n g o b j e c t s i n v e r t i c a l a i r - s t r e a m s are
based on the p r i n c i p l e t h a t , i f a i r moves upwards w i t h a speed equal t o
the t e r m i n a l sppad o f t h e o b j e c t , then the upward drag f o r c e s on t h e
suspended o b j e c t w i l l balance the downward g r a v i t a t i o n a l f o r c e .
The c h i e f
problem i n t h e design o f usable a i r support system i s the tendency o f the
o b j e c t t o d r i f t t o t h e sides o f t h e t u n n e l .
An i n d i c a t i o n o f t h e d i f f i c u l t y
Direction
of motion
x is of rot at i on
Fig.3.1
A rotating
p r i s m at
fluid
C ONCAVE
>
(a)
+
+
<
CONVEX
+
High p r e s s u r e
Low p r e s s u r e
R e l a t i v e mo tions
of adjacent s t r e a m l i n e s
+
b
urface of
discontinuity
Fig.3-2
The f o r m a t i o n of e d d i e s
22.
i s t h a t as t h e t e r m i n a l v e l o c i t y o f an i c e sphere of 4mm
diameter i s
1
approximately 10 ms"" , a h o r i z o n t a l d r i f t o f o n l y 1% of t h e t e r m i n a l v e l o c i t y
w i l l cause the sphere t o cross a 150 mm diameter t u n n e l i n li seconds.
Even
i f t h e r e i s no systematic cause of h o r i z o n t a l m o t i o n , any random movement of
t h i s magnitude i s l i k e l y
minutes.
t o r e s u l t i n a chance c o l l i s i o n w i t h the sides w i t h i n
I t i s t h e r e f o r e e s s e n t i a l t o design a wind t u n n e l which possesses a
very low l e v e l of t u r b u l e n c e .
3,2*2* The a p p l i c a t i o n of B e r n o u l l i s theorum t o f l o w i n t u n n e l s
Although s t r i c t l y
concerned w i t h i n v i s c i d f l o w , B e r n o u l l i s theorem can be
used t o describe t h e c o n d i t i o n s which lead t o laminar f l o w becoming t u r b u l e n t
i n r e g i o n s away from t h e sides of the t u n n e l , where i n $ e r t i a l r a t h e r than
viscous f o r c e s dominate.
B e r n o u l l i ' s theorem can be expressed
p t p
constant »....*......«».•*«.**. 3.1
where p i s the s t a t i c pressure and p
^
and
as
the dynamic pressure
2
= i vv
p
3.2
where v i s the a i r v e l o c i t y and p the a i r d e n s i t y .
Equation 3.1 o n l y holds f o r d i f f e r e n t p o i n t s on the same streamline and i n
general d i f f e r e n t s t r e a m l i n e s w i l l have d i f f e r e n t values o f the c o n s t a n t ,
corresponding t o d i f f e r e n t energy d e n s i t i e s .
3.2.3. Flow along curved streamlines.
By c o n s i d e r i n g the t r a n s v e r s e a c c e l e r a t i o n of a curved s t r e a m l i n e one
can d e r i v e a s i m i l a r expression t o equation 3.1of f l u i d
the
r o t a t i n g with radius r .
Figure 3.1 shows a prism
There w i l l be a pressure g r a d i e n t due t o
motion o f the f l u i d , i n order, t o balance the c e n t r i f u g a l f o r c e .
can be expressed
as
2
^ *
=
r
where
This
h
3.3
os
ds i s the side of the prism along the p r i n c i p a l normal.
This i s the
j u s t i f i c a t i o n f o r the p r i n c i p l e t h a t i f t h e f l o w i s along p a r a l l e l streaml i n e s then no pressure g r a d i e n t can e x i s t across the f l o w .
So a h o r i z o n t a l
pressure g r a d i e n t w i l l cause a i r t o f l o w t o t h e side of the wind t u n n e l .
T
Boundary layer
7—7-~l—/
Fig. 3-3
/*////////////
The definition
of
/
boundary
^
Fig.3-4
The d e v e l o p m e n t
a)
Fig.3 5
Blunt
f / /
/ /
layer
Direction of decreasing pressure
of b o u n d a r y
layer
separation
object
b) S l e n d e r
Boundary layer separation
a t an o b s t a c l e
object
23.
3
t2*,4,JeynQulU§ tteasmn and stidy.
l&m&ism
I f one considers a surface of d i s c o n t i n u i t y o r an area bounding r e g i o n s
of
f l u i d w i t h d i f f e r e n t v e l o c i t i e s , then i t i s p o s s i b l e t o chose a frame of
r e f e r e n c e such t h a t t h e f l o w on one side o f t h e boundary i s i n the opposite
d i r e c t i o n t o t h e f l o w on t h e o t h e r ( f i g . 3.2).
I f a k i n k develops i n t h i s
surface ( F i g . 3.2a), then e q u a t i o n 3.3. p r e d i c t s t h a t the pressure a t a
convex surface w i l l be h i g h e r than a t a concave s u r f a c e .
This means t h a t
any i r r e g u l a r i t i e s which develop i n the s t r e a m l i n e s adjacent t o t h e boundary
w i l l be u n s t a b l e and w i l l
(Fig.
3.2b).
tend t o get b i g g e r , causing the p r o d u c t i o n o f eddies
This i s t h e reason why i n any low t u r b u l e n c e system t h e a i r f l o w
must be as u n i f o r m as p o s s i b l e across t h e s e c t i o n .
Two places a t which non-
u n i f o r m f l o w can a r i s e are a t o b s t r u c t i o n s and bends i n t h e t u n n e l .
3.2.^. ,Ed^y,iarmat;on.^t t v n n e l wails, - Boundary j a y e r s e p a r a t i o n .
Boundary l a y e r s e p a r a t i o n i s the p r i n c i p a l process by which t u r b u l e n t
eddies are i n t r o d u c e d i n t o a wind t u n n e l e i t h e r from t h e sides o r from o b j e c t s
placed i n the a i r s t r e a m .
I t i s p o s s i b l e t o take i n t o account the drag o f an
o b j e c t , due t o a f l u i d motion over i t s s u r f a c e , by assuming t h a t t h e f l u i d i n
c o n t a c t w i t h the o b j e c t i s moving w i t h t h e v e l o c i t y of the surface of the o b j e c t .
There w i l l be a v e l o c i t y g r a d i e n t i n t h e r e g i o n of the obstacle ( F i g . 3.3)
and t h e boundary l a y e r i s d e f i n e d as t h e r e g i o n of f l u i d
v e l o c i t y o f the f l u i d
Fig.
i n which t h e
i s l e s s than 99% of i t s u n d i s t u r b e d v e l o c i t y
3.4 shows a s e r i e s of v e l o c i t y p r o f i l e s a t ( a ) , ( b ) and ( c ) near
a f l u i d boundary where t h e r e i s a pressure g r a d i e n t opposing the motion of
the f l u i d .
As t h e f l u i d f l o w s along t h e boundary i t i s r e t a r d e d by the
pressure g r a d i e n t and e v e n t u a l l y at A t h e d i r e c t i o n o f t h e f l o w near the
boundary i s reversed.
This reversed f l o w p i l e s up a g a i n s t the f l u i d moving
i n t h e o r i g i n a l d i r e c t i o n and t h e s t r e a m l i n e s associated w i t h these f l o w s
leave t h e boundary.
T h i s i s c a l l e d boundary l a y e r s e p a r a t i o n and i t w i l l
produce a surface o f d i s c o n t i n u i t y , AB
S
separating regions o f " f l u i d w i t h
d i f f e r e n t v e l o c i t i e s and energy d e n s i t i e s .
This surface w i l l be unstable
and w i l l produce a t r a i n of eddies by t h e mechanism described i n Fig.3.2.
I/)
If)
0)
cn
O
0)
N
]
to
4>
to
0)
o
T5
Do
2
iO
C7)
0>
Q
to
to
CD
to
0)
T
to
0)
m
cn
cn
to
24.
,The causes of boundary l a y e r s e p a r a t i o n
Boundary l a y e r s e p a r a t i o n w i l l occur wherever there are l a r g e enought
adverse pressure g r a d i e n t s near a f l u i d boundary t o l e v e r s e the f l o w . I n a
d i v e r g e n t s e c t i o n o f t u n n e l , the angle o f divergence has t o be l i m i t e d t o
p r e v e n t s e p a r a t i o n o c c u r r i n g a t the w a l l s . Another cause i s t h e pressure
g r a d i e n t set up a t sharp bends, where equation 3,3 p r e d i c t s a pressure
g r a d i e n t across the f l o w due t o c e n t r i f u g a l f o r c e s , so the f l u i d a t the
o u t s i d e o f the bend v \ i l l be r e t a r d e d . I f o b j e c t s are placed i n the a i r s t r .a
then an adverse pressure g r a d i e n t w i l l be s e t up at t h e r e a r o f t h e o b j e c t .
The b l u n t e r t h e e x t r a c t i o n , tne more l i k e l y turbulence w i l l occur ( F i g . 3.5
3 ,b).
3.3.
3.3.1.
LAMINAR FLOW WIND TUNNELS
P r i n c i p l e s of o p e r a t i o n
One o f t h e ways o f ensuring t h a t t h e f r e e l y supported
particle
stays
away from the w a l l s i s t o reduce the turbulence t o such a l e v e l t h a t the
p a r t i c l e remains i n t h e p o s i t i o n i n which i t was placed.
Tunnels o f t h i s
type have been d e s c r i b e d by CHAPMAN (1953), LIST (1959), and PRUPPACHER and
NEIBURGER (1968).
These t u n n e l s are a l l l a r g e r than 4m i n v e r t i c a l
and r e q u i r e blowers from 4 t o 15 kW power r a t i n g .
They have wide
extent
working
s e c t i o n s of about 0»2m i n diameter and a great deal o f care has been taken
to ensure t h a t t h e a i r f l o w i n the working
s e c t i o n i s laminar.
This i s
achieved by the use o f honeycombs, gauzes and c o n t r a c t i o n s .
3 3„2.» The U n i v e r s i t y of C a l i f o r n i a Cloud Tunnel
U
The v e r t i c a l wind t u n n e l ( F i g . 3.6) described by PRUPPACHER and
NEIBURGER (1968) was b u i l t f o r the study of f r e e l y supported
s o l i d and l i q u i d p r e c i p i t a t i o n p a r t i c l e s .
artificial
I t i s a s e c t i o n t u n n e l powered
by a 15 kW vacuum pump and u t i l i z e s several common methods of reducing
turbulence.
The c o o l i n g i s provided by t h r e e l a r g e r e f r i g e r a t i o n u n i t s
and t h e h u m i d i t y o f t h e a i r f l o w can be a l t e r e d by the h u m i d i f i e r placed
upstream of t h e plenum.
Although i t was o b v i o u s l y out o f t h e question
t o b u i l d such a system a t Durham w i t h the l i m i t e d f i n a n c e a v a i l a b l e some
25.
of t h e techniques used t o smooth t h e a i r can be a p p l i e d t o t h e c o n s t r u c t i o n o f
a s m a l l e r wind t u n n e l .
3.3.3
Methods o f reducing turbulence.
The
f i r s t a i r smoothing s e c t i o n i n F i g . 3.6 i s t h e plenum o r s t i l l i n g oL>
chamber, which a c t s as a capacitance t o damp out o s c i l l a t i o n s .
The a i r then
passes i n t o a s e c t i o n c o n t a i n i n g a honeycomb and a s e r i e s o f gauze screens.
Honeycombs reduce eddies by f o r c i n g t h e f l u i d i n t o pipes which are a p p r e c i a b l y
narrower than the t u n n e l ; they also help t o keep the f l o w p a r a l l e l .
Screens
reduce d i f f e r e n c e s i n t h e l o n g i t u d i n a l v e l o c i t y across the s e c t i o n by
p r o v i d i n g more r e s i s t a n c e t o t h e f a s t e r moving regions of the f l u i d .
The
l a s t a i r s m o o t h i n g s e c t i o n i n the C a l i f o r n i a t u n n e l i s the c o n t r a c t i o n
where t h e cross s e c t i o n o f the a i r f l o w i s reduced and consequently the a i r i s '
accelerated.
I f t h e c o n t r a c t i o n i s designed
so t h a t the f a l l
i n pressure
experienced by each volume o f a i r i s the same and i f t h e f i n a l v e l o c i t y i s
a p p r e c i a b l y h i g h e r than t h e i n i t i a l v e l o c i t y then t h e main f a c t o r governing
the
o u t l e t v e l o c i t y w i l l be the pressure drop across t h e c o n t r a c t i o n and n o t
the
d i s t r i b u t i o n of v e l o c i t i e s a t the i n l e t .
I n the C a l i f o r n i a tunnel the r a t i o
cf the i n l e t area t o o u t l e t area was 7:1.
3.3.4
S u c t i o n versus
blowing
Because the i m p e l l e r o f a blower creates considerable t y r b u l e n c e as
w e l l as h e a t i n g the a i r s t r e a m , i t may be p r e f e r a b l e t o operate t h e t u n n e l
i n the s u c t i o n mode.
I n the C a l i f o r n i a t u n n e l a i r i s sucked through t h e
3 -1
system by a 15kW vacuum pump d e l i v e r i n g 0.2 m s
of a i r , w i t h a pressure
drop across t h e pump o f the order of 0.9 atmospheres.
This l a r g e pressure
drop appears t o have been necessary i n order t o place a sonic t h r o a t
upstream o f t h e pump i n order t o stop d i s t u r b a n c e s t r a v e l l i n g upstream from
the
impeller.
the
pipe where t h e a i r f l o w s a t supersonic speed, i s described by PRANDTL
(l952)»
This method of using a sonic t h r o a t , which i s a r e g i o n of
The c h i e f disadvantage
of t h e s u c t i o n tunnels i s t h a t they have
t o be c a r e f u l l y sealed i n o r d e r t o prevent a i r from l e a k i n g i n t o t h e system.
Back pressure c a p
S t a b l e support t o r particle
E x i t screen
Shaped gauze screen
f
Gauze
screen
Honeycom b
Fig.3-7
A
Blanchard-type
tunne
11
Air
speed
rl
ms
7-
\ /
P a r t i c l e stably supported
So
to
_L_
Distance from
side
m m
Fig.3-ff
Velocity profile
for
Fig.3-7
( C o t t o n and Gokhale, 1 9 6 7 )
O
26.
3,4. VELOCITY WELL SYSTEMS
3.4.1.
P r i n c i p l e of o p e r a t i o n
Several wind t u n n e l s have been made which support water drops by p l a c i n g
them i n a r e g i o n where t h e v e l o c i t y d i s t r i b u t i o n o f t h e a i r f l o w i s i n the form
of a w e l l .
This g i v e s t h e drop a p o s i t i o n o f stable e q u i l i b r i u m .
These t u n n e l s
f a l l i n t o two t y p e s , e i t h e r t h e drop i s supported i n a d i v e r g e n t s e c t i o n o f
t u n n e l e.g. GARNER and KENDRICK (1959) o r above t h e end of t h e t u n n e l as i n
BLANCHARD (1950).
These types of support have t h e advantage t h a t t h e a i r f l o w
does n o t have t o be as smooth as i n t h e laminar f l o w systems.
3.4.2.
'Blanchard-tvoe' t u n n e l s
The e s s e n t i a l f e a t u r e s of t h i s type o f wind tunnel are shown i n f i g u r e 3.7.
Tunnels o f t h i s t y p e have been b u i l t by BLANCHARD (1950) KINZER and GUNN ( 1 9 5 1 ) ,
KOENIG (1965) and COTTON and GOKHALE (1967).
The water drop tends t o s t a y a t
the edge o f the bottom of the v e l o c i t y w e l l ( f i g . 3.8).
by s p e c i a l l y shaped screen and t h e e x i t screen.
This w e l l i s created
The back pressure cap
prevents t h e drop from f l y i n g o u t of t h e system and also a s s i s t s t h e a i r t o
spread out on l e a v i n g the t o p o f the t u n n e l .
I t i s e s s e n t i a l t h a t the v e l o c i t y
p r o f i l e does n o t produce eddies due t o t h e e x i s t e n c e o f d i f f e r e n t v e r t i c a l
velocities i n a d j a c e n t regions o f the a i r . According t o B e r n o u l l i ' s theorum
the s'.des of t h e w a l l are unstable unless
t o spread o u t .
he a i r f l o w from the t u n n e l tends
I f such a p r o f i l e were c r e a t e d i n s i d e a c y l i n d r i c a l tube
eddies would f o r m a t t h e sides of t h e w e l l .
I t i s n o t known t o what e x t e n t the success of t h i s type o f system i s
due t o a b i l i t y o f waterdrops t o d i s t o r t when acted on by shear f o r c e s .
These
systems have never i n t h e author's knowledge been used t o s u p p o r t s o l i d
o b j e c t s which c o u l d n o t r e a c t i n the- same way as l i q u i d drops a t t h e
boundary o f t h e v e l o c i t y w e l l .
BLANCHARD (1957) found t h a t i c e spheres
could be supported f o r o n l y a few seconds.
A f u r t h e r advantage o f water-
drops i s t h a t they can be e a s i l y placed a t the s t a b l e p o s i t i o n by using a
hyp©*dermic s y r i n g e .
Location of water drop
Shaped gauze screen*
Screens
mini
"Honeycomb
5 0 m m-
Fig.3-9
Typical divergent tube support
t
Ffg.3-10
The tapered
( Kinzer and Gu nn )
tube
Fig/311
The air Jet
( Rog*rs,1967)
27.
Wind t u n n e l s i n which the watersrop i s supported i n s i d e a d i v e r g e n t tube
( F i g . 3 . 9 ) , which contains a v e l o c i t y w e l l , have been b u i l t by GARNER and
KENDRICK (1959) and IRIBARNE and KLEMES (1970), This method o f support has
the advantage t h a t t h e water drop does n o t have t o be c a r e f u l l y placed i n the
p o s i t i o n o f s t a b l e e q u i l i b r i u m ? bat can be allowed t o f a l l down the a x i s o f
the d i v e r g e n t s e c t i o n and f i n d i t s own s t a b l e p o s i t i o n - Both t h e "Blanchardtype* and d i v e r g e n t tube supports have t u n n e l sections o f about 150 mm i n
diameter and supported drops from 2mm up t o t h e maximum drop diameters o f
about 6mnw
3.4.4 A i r l e t s and tapered tubes
The t h i r d type o f f r e e support system does not r e q u i r e a h i g h l y smoothed
a i r f l o w and u s u a l l y c o n s i s t s o f an a i r s t r e a m which i s o f a s i m i l a r diameter
t o supported p a r t i c l e .
Examples of t h i s method are the tapered tube o f
KINZER and GUNN (1951) and t h e a i r j e t used by ROGERS (1967)*
The tapered tube ( F i g . 3.10) i s s i m i l a r t o t h e rotameter method of
measuring a i r f l o w r a t e , t h e water drop being kept away from the sides by t h e
a i r r u s h i n g past*
its axis.
Great care must be taken t o make the tube symmetrical about
ROGERS (1967) found t h a t water drops h i t the sides on f r e e z i n g and
i t i s d o u b t f u l i f a non-symmetrical p a r t i c l e could be kept away from the sides
of the tube*
The p r i n c i p l e
o f t h e a i r j e t i s not w e l l understood, b u t ROGERS found
t h a t t h e nozzle diameter had t o be a f a c t o r o f 5 s m a l l e r t h a n t h e diameter
of t h e supported i c e sphere.
The j e t can support i r r e g u l a r o b j e c t s b u t n o t
water drops and ROGERS found t h a t i c e spheres l a r g e r than 6mm i n diameter
could be supported i n d e f i n i t e l y .
He a l s o suggested t h a t s m a l l e r spheres
could be supported i f the nozzle diameter were reduced.
The a u t h o r t r i e d
reducing t h e size o f t h e nozzle down t o 0.5 mm but found t h a t i t was n e a r l y
impossible t o l o c a t e t h e a i r j e t and then place a small i c e sphere i n i t
w i t h o u t a s o p h i s t i c a t e d alignment system.
5
V eloc ity
pro t i l t
Air
Forces
d u e to
Y
/
»
B e r n o u l l i s tthhceoorruum
m \
/
\7AVj
7/ v
def l e c t e d by sphere
R e s u l t a n t force
on s p h e r e
/a 'A
(A)
Fig.312
(B)
Possible mechanisms for the air j e t
Momentum
system
force
(A)
(A)
Bernoulli
force
A
LOW
o
UNIFORM
VELOCITY
( B)
Momentum
to r c e
( B)
FLOW
GRADIENT
Bernoulli
LOW
HIGH
force i
H»GH
V e l o c i t y profile
1*5 I n c r e a s i n g p r e s s u r e
velocity-
Fig.313 D e f o r m a t i o n of
w a t e r drops
F i g . 314
Water
drops
a v e l o c i ty
in
well
28.
3.5.
3.5.1.
THE DESIGN OF THE SUPPORT TUBE
The gh^'.ce o f the type of support
I n t h e preceding s e c t i o n t h r e e types of f r e e support system were discussed?
namely t h e laminar f l o w , v e l o c i t y w e l l and the a i r j e t methods.
The choice
o f a system i s r e s t r i c t e d by the volume o f a i r i n the c o l d room and the l i m i t e d
c o o l i n g capacity a v a i l a b l e .
D u r i n g any s e n s i t i v e e l e c t r i c a l measurements the
r e f r i g e r a t i n g compressor would have t o be switched o f f as i t caused t h e c o l d
room t o v i b r a t e .
The o p e r a t i o n o f the wind t u n n e l would cause appreciable UACW*
due t o t h e compression o f a i r a t the blower"and t h e h e a t i n g o f the a i r i n the
working system.
So i f the temperature o f t h e a i r i n t h e r e g i o n o f the p a r t i c l e
i s t o be k e p t c o n s t a n t over a 10minutes p e r i o d the e q u i v a l e n t o* zold room
volume should n o t be c i r c u l a t e d f a s t e r t h a n about every t h r e e minutes.
laminar f l o w wind t u n n e l s have had a diameter o f a t l e a s t 150 mm which
Previous
would
mean t h a t a i r e q u i v a l e n t t o the volume o f the c o l d room woould be c i r c u l a t e d
1
every 18 s i f the a i r speed i n t h e working s e c t i o n was 10 m s " .
KINZER and
GUNN (1951) b u i l t a v e l o c i t y w e l l system w i t h a diameter o f 30 mm which
suggests t h a t such systems can be more r e a d i l y designed w i t h small diameters
than t h e low t u r b a t e n c e tunnels«
Although a i r j e t s provide more s t a b l e support
f o r ice spheres l a r g e r than 6 mm, i t i s c l e a r t h a t the f l o w round r e a l
stones i s f a r c l o s e r t o t h a t i n v e l o c i t y w e l l systems.
I n the
hail-
circumstances
t h i s l a s t system seems t o be the best compromise.
3.5.2. Problems o f s u p p o r t i n g s o l i d
particles.
A l l the v e l o c i t y w e l l systems have been designed t o support water
r a t h e r t h a n i c e spheres.
drops
BLANCHARD (1957) found t h a t ice spheres could be
supported i n h i s wind t u n n e l f o r o n l y few seconds, whereas waterdrops could
be supported i n d e f i n i t e l y p r o v i d i f t g t h a t - t h e r e , was no e v a p o r a t i o n . The
a i r j e t w i l l however support s o l i d p a r t i c l e s .
The mechanism of the a i r j e t i s sometimes e x p l a i n e d by B e r n o u l l i ' s
theorem by saying t h a t because the v e l o c i t y a t t h e a x i s o f the j e t i s
(greater than a t the edges, the a i r pressure i s l e a s t a t t h e c e n t r e (Fig.3.12)
T h i s n e g l e c t s the f a c t t h a t the p a r t i c l e i s o f s i m i l a r s i z e t o the j e t and
29.
the v e r t i c a l v e l o c i t y i n the centre beneath i t i s probably zero. An a l t e r n a t i v e
e x p l a n a t i o n i s described i n F i g . 3.12B, i n which the a i r j e t i s d e f l e c t e d by
the sphere and the change i n momentum of t h e a i r causes a f o r c e t o push the
p a r t i c l e towards the centre o f the j e t .
A. simple a p p l i c a t i o n o f B e r n o u l l i ' s theorem cannot be used t o e x p l a i n the
v e l o c i t y w e l l systems as the f o r c e on the supported water drop should be
d i r e c t e d towards the w a l l s o f the w e l l , where the a i r v e l o c i t y i s h i g h e r .
However i t i s p o s s i b l e t o e x p l a i n why l i q u i d drops can be supported w h i l e
s o l i d o b j e c t s cannot* by assuming t h a t the drop may be deformed by the
f o r c e s a c t i n g on i t .
I n a u n i f o r m a i r f l o w a water drop w i l l tend t o be
deformed by the d i f f e r e n c e i n pressures a t the side and the bottom (SPILHAUS*
1947), see f i g u r e 3.13 A,B.
According t o MASON (1957) t h i s deformation i s
very small f o r diameters l e s s than 1mm.
I f the drop i s i n a r e g i o n where the
v e r t i c a l a i r speed increases across the d r o p , then the pressure d i s t r i b u t i o n
w i l l be more complex, but i f one a p p l i e s B e r n o u l l i ' s theorem t o the a i r f l o w i n g
over the s u r f a c e the d i s t r i b u t i o n i s probably s i m i l a r t o F i g . 3.13C.
This
pressure d i s t r i b u t i o n w i l l tend to cause a deformation which w i l l be i n c l i n e d
to the v e r t i c a l ( F i g . 3.14).
This w i l l have the e f f e c t of i n c r e a s i n g the
f o r c e due t o the d e f l e c t i o n o f the a i r ( F i g . 14) and should help the water
drop t o be kept wway from t h e boundary of the a i r f l o w .
A solid particle
w i l l not deform and so w i l l be e j e c t e d from the w e l l by the B e r n o u l l i f o r c e s
(Fig.
3.14A).
3.5.3. P r e l i m i n a r y design c o n s i d e r a t i o n s
In o r d e r t o l i m i t the r a t e a t which the cold room was heated up, the
diameter o f t h e t u n n e l i n the r e g i o n where the p a r t i c l e would be supported
(the
working s e c t i o n ) , was r e s t r i c t e d t o 40 mm.
A
ssuming a maximum v e l o c i t y
1
i n t h i s s e c t i o n o f 10 ms" a volume o f a i r corresponding t o the c o l d room
volume would be c i r c u l a t e d every 5 minutes.
the
As t h e blower a v a i l a b l e heated
a i r by about 10°C, the a i r had t o be sucked through the t u n n e l r a t h e r
than blown.
This l i m i t e d the p o s s i b l e designs t o a d i v e r g e n t tube s i m i l a r
to t h a t b u i l t by GARNER and LANE ( l 9 5 9 ) r a t h e r than the open t o p type used
F i g . 3-15
The
divergent
tube
working
section
-AI u m i n i u m
Stable
Most
support
probable
of
cone
region
location
—\
particle
Gauze
cones
0
L
Air
flow
j
30.
BLANCHARD (1950).
I n f a c t a t t h i s stage of t h e design t h e author was unaware
of GARNER and LANE's work.
3.5,4, S t a b i l i t y i n t h e v e r t i c a l d i r e c t i o n
I n a d i v e r g e n t tube wind t u n n e l t h e a i r speed f a l l s o f f towards t h e t o p
of t h e tube so a t some h e i g h t i n the tube t h e p a r t i c l e i s supported by a i r
f l o w i n g a t i t s t e r m i n a l speed.
The degree o f s t a b i l i t y i s governed by the
r e s t o r i n g f o r c e onthe p a r t i c l e which increases w i t h t h e angle o f divergence.
However a l i m i t t o t h i s angle i s s e t by the p o s s i b i l i t y o f t h e f o r m a t i o n o f
eddies due t o boundary l a y e r s e p a r a t i o n a t t h e d i v e r g e n t w a l l s . POPE and
HARPER (1966) quoted t h e l a r g e s t angle between t h e tw> w a l l s f o r laminar f l o w
as 8 ° , b u t say t h a t angles up t o 45° can be t o l e r a t e d provided t h e f l o w i s
c a r e f u l l y guided round the c o r n e r .
the
I t was decided t o make t h e angle between
w a l l s 12° i n order t o increase t h e damping and to study methods o f
guiding the a i r into the divergent section.
A f t e r experiments w i t h various
flow-shaping devices i t was found t h a t two c o n c e n t r i c gauze conelets seemed
to s t a b i l i z e the motion o f small p l a s t i c t n e spheres.
The gauze used was
1
brass 'minimesh made by t h e Expanded Metal Company and had an open area o f
75$ and a s t r a n d t h i c k n e s s o f 0.13 mm.
This design was very s i m i l a r t o t h e
working s e c t i o n t h a t was f i n a l l y used ( F i g . 3.15).
3.5.$ S t a f r i U t Y jn a h o r i z o n t a l plane
The d i v e r g e n t tube was i n s t a l l e d above a smoothing s e c t i o n c o n s i s t i n g
of a honeycomb and a gauze screen and was connected t o a small 150 W blower.
I n i t i a l l y t h i s p i l o t t u n n e l was operated a t room temperature and p l a s t i c i n e
b a l l s were used t o t e s t v a r i o u s m o d i f i c a t i o n s aimed a t i n c r e a s i n g the
s t a b i l i t y of the p a r t i c l e .
The problem o f keeping t h e p a r t i c l e away from
the
w a l l s was o n l y p a r t l y solved and attempts t o create a v e l o c i t y w e l l i n
the
c e n t r e o f t h e tube by p l a c i n g screens below the gauze flow-shaping cones
did
n o t stop t h e b a l l s from r a t t l i n g around the bottom o f t h e support t u b e .
However, i t was found t h a t i f t h e gauze cones were a l i g n e d so t h a t t h e i r
sides were p a r a l l e l t o the upper aluminium cone, then t h e b a l l s tended t o
hover around the t o p of the gauze cones.
The b a l l could be dropped from t h e
31.
top of the aluminium cone and would stay i n the shaded r e g i o n of F i g . 3.16.
The p a r t i c l e showed a d e f i n i t e preference f o r s t a y i n g i n the h e a v i l y shaded
r e g i o n shown i n the diagram. A t t h i s stage the main d i f f i c u l t y i n improving
the system was t h a t t h e a i r f l o w e n t e r i n g the working s e c t i o n was probably not
very smooth. So i t was decided t o b u i l d a more permanent wind t u n n e l i n s i d e
the c o l d room.
3.5.6. A i r smoothing i n t h e main wind t u n n e l
The a i r was f i r s t passed through a 150 mm long honeycomb w i t h a 10 mm g r i d .
The next stage was a mesh screen w i t h holes 1.5 mm x 1.0 mm and f i n a l l y the
t u n n e l was c o n t r a c t e d from a diameter o f 75 mm t o 30 mm.
operated i n t h e sucking mode.
The blower was also
I d e a l l y s e v e r a l screens should have been placed
between the honeycomb and t h e f i n a l screen but t h e r e was not enough space.
U n f o r t u n a t e l y the t u n n e l had 2 r i g h t - a n g l e bends j u s t upstream of the honeycomb
and these should have been replaced w i t h a s e t t l i n g chamber i f the turbulence
i n the working s e c t i o n were t o be reduced
3.5.7 The performance
Ice
further.
o f the support system
spheres from 2 t o 5 mm diameter were supported i n a very s i m i l a r
way t o the p l a s t i c i n e b a l l s .
A f t e r about 10 t o 30 minutes f l i g h t they would
crash i n t o t h e w i r e s vh i c h supported the gauze cones and so g e t caught.
They
would go very near t h e sides every 2 t o 3 minutes and i t i s probable t h a t they
made c o n t a c t w i t h the w a l l s i n the 5 seconds t h a t elapsed before they moved
away.
The motion was d i s t i n c t l y d i f f e r e n t from t h a t i n t h e e a r l y attempts
at keeping the b a l l s away from the sides o f the t u n n e l and t h e r e was a
very marked tendency t o hover around the t o p o f the gauze cones.
1>
0)
\
s
\
s
s
Q
UJ
S
s
UJ
IQ D
32.
CHAPTER
4
THE CONSTRUCTION AND INSTRUMENTATION OF THE WIND TUNNEL
4.1. THE ADAPTATION OF THE COLD ROOM
4.1.1 The p r e p a r a t o r y of the c o l d room
To study the support o f i c e spheres» t h e t u n n e l was placed i n s i d e a c o l d
room.
The c o l d room a v a i l a b l e was f o r m e r l y a butcher's c o l d s t o r e , powered
by a 300 W compressor, which was capable o f h o l d i n g a temperature o f 30°C
3
below the ambient temperature.
and the i n s u l a t i o n c o n s i s t e d
polystyrene
The t o t a l volume of the cold room was 4m
o f 113 mm of cork and 55 mm o f expanded
( F i g . 4.1). The w a l l s and f l o o r were h e a v i l y engrained w i t h
d i r t so the room was e x t e n s i v e l y r e f i t t e d .
and used as a foundation
A new concrete f l o o r was l a i d
f o r a f a l s e f l o o r made of 15 mm plywood l y i n g on
a wooden frame which was f i l l e d w i t h expanded polystyrene
( F i g , 4.1 )*
The
plywood f l o o r was then covered w i t h a 6 mm rubber sheet which made a watert i g h t j o i n t w i t h t h e w a l l s t o prevent water seepage during d e f r o s t i n g .
The
surfaces o f t h e i n s i d e w a l l s and roof were removed w i t h sandpaper and were
f i n a l l y cleaned w i t h d e t e r g e n t t o remove a l l traces of grease and f a t .
F i n a l l y the i n s i d e o f t h e c o l d room was covered w i t h 3 coats of polyurethane
p a i n t which formed an i n e r t seal t o the w a l l s .
A new d e f r o s t i n g t r a y
capable of h o l d i n g about 20 l i t r e s of water was f i t t e d below the c o o l i n g
coils.
4.1.2
The window
Because o f t h e l i m i t e d space a v i l a b l e i n s i d e t h e cold room t h e
experiments were performed from the outside , using a double glazed window
f i t t e d w i t h glove ports'.
As the window would be an important
heat l o s s i t was made as small as p o s s i b l e .
source o f
The window was placed on the
i n s i d e w a l l s t o enable the o p e r a t o r t o reach as f a r i n t o t h e c o l d room as
possible
( F i g . 4.2).. PROBERT and HUB (1968) suggest t h a t 12 mm i s the
optimum thickness
of about 30°C.
o f a double glazed window f o r a temperature d i f f e r e n c e
I f the gap i s g r e a t e r convection tends t o b u i l d up,
reducing t h e advantage o f the e x t r a t h i c k n e s s .
12.5 mm perspex w i t h a s i m i l a r thickness
The two panes were made o f
of a i r gap. The windows were
Brass
Tubt
J L
—
Flfxible
Tube
lh
Fl o w m e t e r
60W
Lamp
M i rror
Perspex
H u m i di t y
tube
Hatch
measurement
Faraday
T o Wowed
Working
cage
section
Aluminium
cones
Thermocouple
i
Gauze
Heater
f
Fig.4.3
screen
A b s o l u t e filter
Steel wool
Vertical
Honeycomb
filter
s e c t i o n of
wind
tunnel
probe
33,
sealed w i t h perspex cement and p a i n t and never misted upon t h e i n s i d e ,
a l t h o u g h on very c o l d days condensation sometimes formed on:theuouter pane.
The glove p o r t s were never f i t t e d w i t h gloves as these would r e s t r i c t the
o p e r a t o r ' s ease o f movement and as most o p e r a t i o n s o n l y took a few seconds
no a p p r e c i a b l e heat l o s s was caused. When n o t i n use the glove p o r t s were
f i l l e d w i t h expanded p o l y s t y r e n e stoppers*
4.1.3 E l e c t r i c a l connections t o t h e c o l d room
I t soom became apparent t h a t a l a r g e number o f wires would have t o
pass i n t o t h e c o l d room t o enable the wind t u n n e l t o be instrumented. I n
the e a r l y stages o f experiments when t h e c i r c u i t y would have t o be c o n s t a n t l y
m o d i f i e d t h e r e was an obvious need f o r i n t e r c o n n e c t i n g plugboards on t h e
i n s i d e and o u t s i d e o f t h e c o l d room.
s i x t e e n 4 mm sockets.
sockets.
These were b u i l t and f i t t e d w i t h
The i n s i d e board was also equipped w i t h mains
Two 12-way cables and several mains and c o a x i a l leads were r u n
through the w a l l s ; these were a l l used i n the next two years.
4.2. THE WIND TUNNEL
4.2.1.
L i m i t a t i o n s on d e s i g n due t o the cold room
U n f o r t u n a t e l y the window was f i t t e d t o the c o l d room before t h e wind
t u n n e l was designed and i t soom became apparent t h a t t h e window was mounted
too low.
I d e a l l y as l a r g e a length of s t r a i g h t p i p i n g as p o s s i b l e was
r e q u i r e d upstream of the working s e c t i o n , but t h i s was l i m i t e d t o about
0-6 m by the h e i g h t o f the c o l d room f l o o r and windows.
This s t r a i g h t
s e c t i o n c o n t a i n e d a honeycomb, a gauze screen and a c o n t r a c t i o n but a bend
had t o be made i n t h e t u n n e l t o enable a heater t o be placed i n the a i r stream.
The blower had t o be mounted a t ground l e v e l t o minimize v i b r a t i o n s
so another bend
was r e q u i r e d downstream o f t h e working s e c t i o n .
The wind
tunnel as f i n a l l y b u i l t was about 7 m i n t o t a l l e n g t h and i n c l u d e d two
180° bends ( F i g . 4.3).
4.2.2 The blower
The blower used was a Siemens 0.7 kW 3-phase blower capable o f a
maximum volume f l o w r a t e o f 35 fts and a maximum pressure drop across
he blower e q u i v a l e n t t o 1.1m of water.
The blower was used t o suck
0)
1/1
U1
to
0)
(1)
DO
\
in
N
or
S
1
t I
0)
0)
CT
t-
34.
a i r t h r o u g h t h e working s e c t i o n a t a maximum a i r v e l o c i t y o f 20 ms * i n t h e
31 mm diameter s e c t i o n , which corresponds t o 20i s
the
1
o f a i r . The a i r l e a v i n g
blower was heated by about 10°C depending on t h e a i r f l o w r a t e , so t h e
o u t l e t from t h e blower was d i r e c t e d over t h e c o o l i n g c o i l s t o h e l p m a i n t a i n
the
of
temperature of t h e c o l d room.
The blower was b o l t e d t o t h e c o n c r e t e cap
a b r i c k p i l l a r and t h e v i b r a t i o n produced was n e g l i g i b l e .
For s a f e t y
reasons t h e blower was l o c a t e d o u t s i d e the c o l d room but i t was found t h a t
provided t h e pipes were w e l l lagged t h e heat losses were small compared
to t h e compression h e a t i n g o f t h e blower.
&»2sl^
ftlrflgw c o n t r o l -
The a i r f l o w was r e g u l a t e d by a b u t t e r f l y valve l o c a t e d i n a bypass p i p e
which met the main t u n n e l a t the i n l e t t o t h e blower ( F i g . 4#4)
The valve
was connected t o an e l e c t r i c motor and c o u l d be operated from the main c o n t r o l
panel o r a t the valve i t s e l f .
This method proved adequate and t h e a i r v e l o c i t y
could be r e g u l a t e d t o b e t t e r than 0.5 ms *•
4.2.4.. The wind t u n n e l l a y o u t
The l a y o u t o f the wind t u n n e l i s shown i n f i g u r e s 4.3 and 4.4.
was o n l y space f o r two a i r f l o w smoothing
of square tubes o f 10 mm side and a t o t a l
screen.
section.
stages, the honeycomb which c o n s i s t e d
,
l e n g t h o f 150 mm, and a minimesh
The h e a t e r , which was a h e a t i n g element from a water b o i l e r
3
Could
A l l t h e brass s e c t i o n s between the h e a t e r
and the working s e c t i o n were lagged w i t h a 50 W h e a t i n g t a p e , which
thermal time constant o f t h e system.
reduced
The a i r i n t h e working s e c t i o n
could then be r a i s e d from -8°G t o + 10°G i n about 4 minutes.
The p a r t i c l e i n the\ working s e c t i o n was viewed by the use o f a 50 mm
diameter m i r r o r which also served t o s h i e l d %he i c e from t h e d i r e c t
r a d i a t i o n o f t h e 60 W lamp which was used t o i l l u m i n a t e t h e working
section.
f
I t was n o t p o s s i b l e t o place any screens downwind o f the working
be operated a t up t o 200 watts*
the
There
The..heating e f f e c t o f t h e lamp was found t o be l e s s t h a n 0.2°C«
The i c e spheres used i n t h e f r e e f l i g h t experiment were i n s e r t e d i n t o t h e
t u n n e l t h r o u g h t h e hatchway which was placed j u s t below t h e m i r r o r .
35.
4.2.5. C o n s t r u c t i o n d e t a i l s
To enable as many as p o s s i b l e of the p a r t s t o be interchangeable
most o f t h e s e c t i o n s were made from 75 mm diameter t u b i n g f i t t e d w i t h 110 mm
f l a n g e s w i t h standard holes f o r the securing b o l t s .
The whole t u n n e l was
b u i l t around a 'Handyangle' frame which was b o l t e d t o the f l o o r o f the cold
room.
of
The t u n n e l sections were connected t o the frame by means o f sheets
aluminium f i t t e d w i t h a 75 mm hole and b o l t h o l e s t o match the f l a n g e s .
The Faraday cage was made from sheets o f aluminium.
The f l e x i b l e t u b i n g was
manufactured from neoprene impregnated f i b r e g l a s s on top o f a galvanized
screen s p r i n g and the maximum leakage quoted by the manufactuers was 0.1% of
the
volume f l o w r a t e per metre o f pipe under c o n d i t i o n s t y p i c a l o f i t s use
i n the wind t u n n e l . The f l e x i b l e t u b i n g was c a r e f u l l y sealed t o the brass
flanges by means o f P-V.C. tape and adhesive and some s e c t i o n s were f i t t e d
w i t h rubber gaskets t o reduce the leakage.
4.3, MEASUREMENT OF ELECTRIC CHARGE
4.3.1 The p r i n c i p l e o f measurement•
The two aluminium cones ( F i g . 4.3) i n s i d e the Faraday cage were i n s u l a t e d
from e a r t h a t both ends and were connected by means o f a low noise c o a x i a l
cable t o a v i b r a t i n g reed e l e c t r o m e t e r (V.R.E),
I f there i s a charge
separation process i n s i d e the upper cone w i t h one sign being r e t a i n e d on an
ice
p a r t i c l e i n t h e cone and the opposite s i g n being c a r r i e d away i n the
airstreamj
the Cones w i l l a c t as a Faraday p a i l and a charge equal t o t h a t
c a r r i e d by the i c e p a r t i c l e w i l l b e induced onto the o u t s i d e of the cones
12
and w i l l f l o w t o e a r t h through the 10
meter.
ohm i n p u t r e s i s t o r o f t h e e l e c t r o -
The e l e c t r o m e t e r w i l l t h e r e f o r e measure the charge s e p a r a t i o n c u r r e n t
i f t h e value o f the imput r e s i s t o r i s known.
The main a m p l i f i e r of t h e
V.R.E. was c a l i b r a t e d by a p p l y i n g an a c c u r a t e l y known voltage t o i t s
i n p u t stage.
The i n p u t r e s i s t o r was checked t o + 10% by passing a known
c u r r e n t through i t and n o t i n g the voltage i n d i c a t e d by t h e o u t p u t meter
on the V.R.E.
the
The background
noise l e v e l was found t o depend l a r g e l y on
design o f the i n s u l a t i o n and the space charge c a r r i e d by the a i r i n the
wind t u n n e l .
7
a uze
1
3 Absol ute
3 filter
3
3
7
Brass tube
Fig.4.6
The space
charge
filter
Pe r s p e x
n
A)
An early f o r m
1
of
1
1
S*"
insulator
Perspex
kO
mm
P.T.F.E.
P.T.F.E. T a p e
8)
Fig4.5
The f i n a l d e s i g n
The design
of
insulators
36,
4 * 3 , 2 * The p e r f o r m a n c e o f d i f f e r e n t t r Y P
fis
n
f
insulators
The i n s u l a t o r s were d e v e l o p e d by s t u d y i n g t h e i r p e r f o r m a n c e i n t h e
w i n d t u n n e l i n w h i c h t h e a i r was blown t h r o u g h t h e t u n n e l .
( F i g . 4 . 5 A ) c o n s i s t e d o f two p e r s p e x
perspex
spacers.
The f i r s t
pilot
design
r i n g s s e p a r a t e d by f o u r 4 mm d i a m e t e r
When t h e a i r s t r e a m was h e a t e d
or allowed to cool
after
h e a t i n g , t h e V . R . E . w o u l d r e c o r d a n o i s e l e v e l o f up t o 0 . 2 pA w h i c h was
suspected
t o be due t o t h e i n s u l a t o r s -
these n o i s y p e r i o d s o f r e c o r d .
A l a t e r design
( F i g . 4«5B) e l i m i n a t e d
The c h i e f m o d i f i c a t i o n was t o move t h e
away f r o m t h e a i r s t r e a m and r e p l a c e t h e p e r s p e x w i t h P . T . F . E .
a t t h e t i m e t h a t t h e n o i s e may have been caused by
metal
water
spacers
I t was t h o u g h t
condensing, on t h e
s i d e s o f t h e t u n n e l and b e i n g f o r c e d o v e r t h e i n s u l a t i n g a i r g a p .
This
seems an u n l i k e l y e x p l a n a t i o n as t h e dew p o i n t o f t h e a i r was u s u a l l y l o w e r
than t h e p r o b a b l e t e m p e r a t u r e
of the t u n n e l w a l l s *
When used i n t h e m a i n t u n n e l t h e i n s u l a t o r s were s e a l e d
with P.T.F.E.
tape and s i l i c o n e r u b b e r t o p r e v e n t a i r l e a k s due t o s u c t i o n t h r o u g h t h e
a i r gap.
A l l the surfaces
detergent
and hexane b e f o r e use
4 . 3 . 3 . N o i s e due t o space
o f t h e i n s u l a t o r s were c a r e f u l l y c l e a n e d
with
t o remove any g r e a s e .
charge
3 "^l
Because a p p r o x i m a t e l y 0 . 0 1 m s"
o f a i r passed t h r o u g h t h e t u n n e l one
might expect t h a t
t h e w o r k i n g s e c t i o n may behave as a crude space
collector despite
t h e e a r t h e d gauze s c r e e n u p w i n d .
f i l t e r was p l a c e
B e f o r e a space
i n t h e a i r s t r e a m , t h e c u r r e n t measured
c o u l d on some o c c a s i o n s
charge
by t h e
be a t t r i b u t e d t o space c h a r g e , e . g .
charge
V.R.E.
the noise
that
o c c u r r e d when t h e h e a t e r was used a f t e r a l o n g p e r i o d o f n o t b e i n g u s e d .
The most d r a m a t i c e v i d e n c e
f o r t h e e f f e c t o f space charge o c c u r r e d when a
n e a r b y b u i l d i n g was b e i n g d e m o l i s h e d and c l o u d s o f d u s t e n t e r e d
laboratory.
enter
When t h e c o l d room d o o r was opened and t h e d u s t a l l o w e d t o
the wind t u n n e l , t h e V . R . E . r e g i s t e r e d
which f e l l
the
a maximum c u r r e n t ' o f 0.4pA
back t o z e r o a b o u t 1 0 m i n u t e s a f t e r t h e door was s h u t .
space charge
filter
A
( F i g . 4 . 3 ) was t h e n i n s t a l l e d p e r m a n e n t l y i n the w i n d
37.
tunnelT h i s c o n s i s t e d ( F i g . 4 . 6 ) o f a s t e e l wool f i l t e r f o l l o w e d by a
f i b r e g l a s s a b s o l u t e f i l t e r o f t h e t y p e used by BENT (1964) as. a
*pmfliter
f o r a space c h a r g e c o l l e c t o r . W i t h t h i s f i l t e r i n s t a l l e d t h e r e was no
s i g n i f i c a n t V . R . E . d e f l e c t i o n when t h e door o f t h e c o l d room was l e f t o p e n ,
so i t was assumed t h a t t h e f i l t e r w o u l d be c o m p l e t e l y e f f e c t i v e under n o r m a l
operating conditions*
4»3 4«, N o f c e dye ta
effects
t
A n o t h e r s o u r c e o f n o i s e was a s s o c i a t e d w i t h t h e p r o b e s used t o measure
the temperature
of the working s e c t i o n .
which i s a piece o f s t i f f
l e a d , r u n s up t h e c e n t r e
walls.
As shown i n f i g u r e 4 . 3 , t h e
h
w i r e s u p p o r t i n g e i t h e r a -thermocouple o r
probe,
thermistor
o f t h e l o w e r cone w i t h o u t m a k i n g conta-ct w i t h
the
T h i s l e a d p e n e t r a t e s t h e F a r a d a y cage and may a c t as an a e r i a l as
i s a b o u t 4m l o n g .
it
N o i s e due t o t h i s s o u r c e reached up t o O . l p A when
t h e r m i s t o r s were used b u t l a t e r w i t h t h e r m o c o u p l e s as t h e s e n s i n g
t h e n o i s e was n e g l i g i b l e .
device
T h i s was p r o b a b l y because o f t h e h i g h R e s i s t a n c e
o f t h e t h e r m i s t o r , c i r c u i t , w h i c h was t y p i c a l l y 3 k f t as opposed t o t h e 5 t o 10
i l of the thermocouples,
I t was a l s o f o u n d n e c e s s a r y t o c a r e f u l l y s c r e e n
the
l i g h t b u l b y t h a t was used i n t h e F a r a d a y cage w i t h a l a t e r m o d i f i c a t i o n o f
the
tunnel.
4.3.5.
Additional
sources of
noise
One f u r t h e r cause o f n o i s e was t h e f a i l u r e t o remove the
l a y e r surrounding the d i e l e c t r i c i n low noise c o a x i a l c a b l e .
12
has a s m a l l r e s i s t a n c e compared t o t h e 10
and r e s u l t e d
e.g.
t u n n e l tended
input resistor
i n an i n t e r m i t t e n t s h o r t c i r c u i t when t h e
when t h e b l o w e r was s w i t c h e d o n .
not securely
ft
layer
of the
V.R.E.
I f t h e spacers i n the i n s u l a t o r
nose
through
were
the
level.
When a l l t h e s o u r c e s o f n o i s e m e n t i o n e d above had been
s u c c e s s f u l l y the background noise
This
c a b l e was v i b r a t e d ,
f i x e d , t h e i r movement when the a i r was p a s s i n g
t o cause an a p p r e c i a b l e
semiconducting
reduced
l e v e l was 0 . 0 0 2 pA t h r o u g h o u t a
h e a t i n g and c o o l i n g c y c l e l a s t i n g 30 m i n u t e s .
complete
Heater resistor
Dry bulb thermo
couple
3
Scopper
constanton
Cotton wick
Perspex
Brass tube
75 i*m
Eig.4.7
Humidity
measuring section
Cork
7
G l a s s tube
Vacuum flask
Mercury
0
Crushed
M ETHS TANK
Fig.4 8
AT
ice
0°C
Thermocouple reference j u n c t i o n
unit
38,
4 . 4 , THE MEASUREMENT OF TEMPERATURE AND HUMIDITY
4.4.1.
Temperature
In the p i l o t
variation
measurement
wind t u n n e l , temperature
i n current passing
was a p p l i e d a c r o s s i t .
was measured
by o b s e r v i n g
t h r o u g h a t h e r m i s t o r when a c o n s t a n t
To a v o i d h e a t i n g t h e t h e r m i s t o r , t h e
voltage
c u r r e n t had t o
be k e p t t o a minimum w h i c h made i t d i f f i c u l t t o use t h i s method t o
a signal
suitable
f o r r e c o r d i n g on a c h a r t r e c o r d e r .
the
produce
As m e n t i o n e d i n
s e c t i o n 4 . 3 . 4 the r e l a t i v e l y h i g h r e s i s t a n c e o f the t h e r m i s t o r tended
to
cause n o i s e
was
inserted
on t h e V . R . E . o u t p u t when t h e t e m p e r a t u r e
m e a s u r i n g probe
i n t o t h e w o r k i n g s e c t i o n o f the wind t u n n e l -
copper-constantan
So l o w r e s i s t a n c e
t h e r m o c o u p l e s were used w h i c h gave an E . M . F . o f
a p p r o x i m a t e l y 40 (A V °C * and t h e s i g n a l was a m p l i f i e d w i t h an
c i r c u i t D.C. a m p l i f e r .
The t e m p e r a t u r e s
of the c o l d room, t h e o u t l e t f r o m
t h e b l o w e r , and 2 - o t h e r p o i n t s i n the w i n d t u n n e l were a l s o
4 . 4 . 2 . Measurement
integrated
measured.
of h u m i d i t y
The h u m i d i t y m e a s u r i n g s e c t i o n was p l a c e d downwind o f t h e w o r k i n g
( F i g . 4 . 3 ) and c a r e was t a k e n t o e n s u r e t h a t t h e r e were no l e a k s
between t h e 2 p o i n t s .
copper-constantan
Dry b u l b and wet b u l b d e p r e s s i o n
thermocouples
as i n f i g u r e 4 . 7 .
section
i n the t u n n e l
were measured
using
The w a t e r h e l d i n t h e
p e r s p e x c o n t a i n e r c o u l d be m e l t e d by t h e h e a t e r r e s i s t a n c e and a l l l w w e d
wet t h e c o t t o n w i c k w h i c h c o v e r e d one j u n c t i o n o f a d i f f e r e n t i a l
mocouple.
aspirated
j u s t i f i e d as
i n c r e a s i n g the
bulb depression
T h i s was presumed t o be
f o r t h e r a n g e o f wind speeds u s e d .
r e l a t i v e h u m i d i t y was + 3%.
4.4.3
The t h e r m o c o u p l e r e f e r e n c e
The p r o b a b l e
error
junction
Four s e p a r a t e t h e r m o c o u p l e r e f e r e n c e
were c o n t a i n e d i n one u n i t
f o r an
a i r f l o w d i d not cause any i n c r e a s e o f wet
i n the
crushed
ther-
The v a l u e o f r e l a t i v e h u m i d i t y was r e a d o f f t h e t a b l e s
p s y c h r o m e t e r i n KAYE and LABY ( 1 9 7 0 ) .
to
(Fig. 4.8).
j u n c t i o n s were r e q u i r e d and t h e s e
A vacuum f l a s k , c o n t a i n i n g
i c e and t h e j u n c t i o n s , was p l a c e d i n s i d e a t a n k c o n t a i n i n g about
20 l i t r e s o f m e t h y l a t e d s p i r i t s w h i c h was h e l d about 0 ° C .
This
ensured
rV
/vWWA
hir*
K
7o9C
m
0
O ^ A W v
Hi*/
I nput
Output
Mi
1HP
A
Frequency Compensation
Oflset
voltage
vws^
33o
Fig.49
Am pi i f i e r
Basic d. c . ampl ifier c i r c u i t
Amplification
A,-
1
4 7 5L
J.Z0O
4-7W
I
SbSL
1,100
/ kSl
s-6 a
J10 51
1,200
6 00
1,100
3
4
5"
I33k»
610SL
/ AS.
—
6L0SL
8U>SL
I feSi
TEMPERATURE
13
[0
L
ko
I
60
RECORDER DEFLECTION
mm
FIG.4.10
TYPICAL AMPLIFIER CALIBRATION
(Workfng temperature)
39.
t h a t t h e i c e o n l y had t o be r e p l a c e d w e e k l y .
The m e r c u r y a c t e d as b o t h
a h e a t s i n k and a good t h e r m a l c o n t a c t w i t h t h e
ice.
4.4.4. The t'hprmo^'P.I^, w U f ^ r g t
The 5 D . C .
a m p l i f i e r s a l l used s i m i l a r
'Radiospares
1
Integrated c i r c u i t s
(709-OPA) w h i c h were powered by a + 15 V s t a b i l i s e d power supply-.
The
a m p l i f i c a t i o n c o u l d be v a r i e d by a l t e r i n g t h e v a l u e o f t h e f e e d b a c k
Rp and t h e i n p u t r e s i s t o r R j
N
( F i g . 4.9).
a p p l i e d t o the i n p u t t o ensure t h a t
current.
resitor
The o f f s e t v o l t a g e had t o be
t h e r e was zero o u t p u t f o r zero i n p u t
L a r g e v a l u e s o f f r e q u e n c y c o m p e n s a t i o n c a p a c i t o r s were used
to
p r e v e n t i n s t a b i l i t y caused by t h e a m p l i f i c a t i o n o f unwanted h i g h f r e q u e n c y
noise.
The b i g g e s t d i f f i c u l t y i n b u i l d i n g t h e 5 c i r c u i t s i n t o one r a c k
mounted p a n e l was t h e e l i m i n a t i o n o f e a r t h l o o p s w h i c h caused the a m p l i f i e r s
t o go o f f s c a l e .
circuit
as
T h i s was s o l v e d by c o n n e c t i n g e v e r y e a r t h p o i n t o f t h e
t o a common e a r t h and by s c r e e n i n g as much o f t h e t h e r m o c o u p l e
leads
possible.
4 . 4 . 5 . C a l i b r a t i o n o f the
thermocouples.
A. c a l i b r a t i o n j u n c t i o n c o n s i s t i n g o f a c o p p e r - c o n s t a n t a n
junction
in
a vacuum f l a s k f i l l e d w i t h p a r a f f i n was p e r m a n e n t l y a v a i l a b l e f o r c a l i b r a t i n g
the temperature
through the f u l l
measuring c i r c u i t s .
The j u n c t i o n c o u l d be r e a d i l y h e a t e d
range o f t e m p e r a t u r e s t h a t weie measured
i n t h e wind
tunnel.
One i m p o r t a n t s o u r c e o f e r r o r i n t h i s c a l i b r a t i o n was t h a t caused by t h e
c a l i b r a t i n g thermocouple having a d i f f e r e n t resistance
than the
measuring
o
thermocouple.
As t h e a m p l i f e r s were s e t
t o zero by s h o r t i n g o u t t h e
t h e r m o c o u p l e , t h i s c o u l d cause d i f f e r e n t zero r e a d i n g s
t h e r m o c o u p l e s , w h i c h w o u l d n o t be r e a d i l y d e t e c t e d .
f o r t h e two
A preset
resistor
was p l a c e d i n s e r i e s w i t h t h e c a l i b r a t i n g t h e r m o c o u p l e and b e f o r e
c a l i b r a t i o n the r e s i s t a n c e
adjusted.
A typical
of the reference
t h e r m o c o u p l e j u n c t i o n was
c a l i b r a t i o n c u r v e i s shown i n F i g . 4.10
c u r v e s were r e p r o d u c e a b l e
. These
o v e r the p e r i o d o f measurements t o + 0 . 2 ° C .
<z>
4
9
VWW*
L
<2)
UV
Li
U.V.
X60O
W £ 7 6&a6
XM*
Li
Fig.4-11
U.V.
Block diagram of temperature measuring c l r c u l t s
Bypass
St a
Main
tunnel
•^Blower
7=
Pitot-stat ic
tube
H oneycomb
Fig.4.12
ic t a p s
Location
of
o
pitot-static
tube
S t a g n a t i o n pressure
— s - ^ S t a t i c pressure
St at ic ,t ops
Fig.4.13
The pitot static head unit
Photo r e s i s t o r
SCHHITT
U . V.
Lamp
Fig.4.14
The run of w i n d device as a flowmeter
lOpmm.
40.
4 . 4 * 6 The a u t o m a t i c r e c o r d i n g o f t e m p e r a t u r e and h u m i d i t y .
F i v e t h e r m o c o u p l e a m p l i f i e r s were b u i l t o f w h i c h two were c a p a b l e o f
monitoring three
t h e r m o c o u p l e s each b u t gave o n l y a m e t e r o u t p u t -
These
were v e r y u s e f u l i n t h e e a r l y s t a g e s o f t h e e x p e r i m e n t and a l s o f o r
c h e c k i n g t h a t t h e h e a t i n g e l e m e n t s had c o o l e d down.
f o r the
two h u m i d i t y t e m p e r a t u r e measurements
The a m p l i f i e r s used
and t h e w o r k i n g
t e m p e r a t u r e were c o n n e c t e d t o b o t h m e t e r s and u l t r a
section
v i o l e t recorder
channels*
The r e c o r d e r g a l v a n o m e t e r s c o u l d be s w i t c h e d i n t o t h e o u t p u t c i r c u i t
a m p l i f i e r s by means o f a bypass
switch
(Fig. 4.1l).
r e p l a c e t h e g a l v a n o m e t e r w i t h an e q u i v a l e n t r e s i s t o r .
This switch
could
The r e c o r d e r
g a l v a n o m e t e r s were p r o t e c t e d a g a i n s t b o t h p o s i t i v e and n e g a t i v e
over-
l o a d i n g by Zener d i o d e s p l a c e d back t o back w i t h a s u i t a b l e l o a d
resistor.
The r e c o r d e r was used on t h e 50 mm min * s p e e d t h r o u g h o u t most o f
experiments.
Other channels
of the
the
were used t o r e c o r d a i r f l o w v e l o c i t y and t h e
e l e c t r i c c u r r e n t measured by t h e V . R . E .
4 . 6 . THE MEASUREMENT OF AIR SPEED
4.6.1.
The p i l o t - s t a t i c t u b e
A p i t o t - s t a t i c t u b e was c o n s t r u c t e d
( F i g . 4 . 1 3 ) and c a r e f u l l y
p o s i t i o n e d p a r a l l e l t o t h e wind t u n n e l a t a p o i n t u p s t r e a m f r o m t h e
o f t h e bypass p i p e and t h e main w i n d t u n n e l
(Figs. 4.3, 4.12).
junction
The p r e s s u r e
d i f f e r e n c e between t h e s t a t i c and s t a g n a t i o n p r e s s u r e s was measured by an
i n c l i n e d w a t e r manometer.
According t o the t h e o r y of the p i t o t - s t a t i c tube
t h i s d i f f e r e n c e i n p r e s s u r e s s h o u l d have been p r o p o r t i o n a l t o t h e s q u a r e o f
the a i r v e l o c i t y .
However? when t h i s i n s t r u m e n t was c a l i b r a t e d a g a i n s t a
c a l i b r a t e d r u n o f wind machine f h e p r e s s u r e . d i f f e r e n c e was f o u n d t o be
d i r e c t l y p r o p o r t i o n a l t o the v e l o c i t y .
if
Further? the c a l i b r a t i o n
t h e f l o w was r e s t r i c t e d by p l a c i n g a s l e e v e
changed
v a l v e i n t h e main t u n n e l .
The p r e s s u r e d i f f e r e n c e was a l s o an o r d e r o f magnitude g r e a t e r
than
expected.
A p r o b a b l e e x p l a n a t i o n f o r t h i s f a i l u r e i s t h a t t h e r e was a
static
p r e s s u r e g r a d i e n t down t h e t u b e i n w h i c h t h e p i t o t - s t a t i c probe was p l a c e d
41.
and t h i s caused an a p p r e c i a b l e s t a t i c p r e s s u r e d i f f e r e n c e between t h e s t a t i c
and s t a g n a t i o n ta.->s. T h i s was g r e a t e r t h a n t h e d i f f e r e n c e between t h e s t a t i c
and s t a g n a t i o n p r e s s u r e s a t any p o i n t on t h e p r o b e . A c c o r d i n g t o t h e HaganP o i s » e u i l l e law the f l o w r a t e i s d i r e c t l y p r o p o r t i o n a l to the pressure
g r a d i e n t down a t u b e f o r l a m i n a r f l o w , so one w o u l d e x p e c t t h e measured
s t a t i c p r e s s u r e d i f f e r e n c e between t h e two ' t a p s t o be p r o p o r t i o n a l t o t h e
air velocity.
4.6..2.
The r u n o f w i n d machine as a f l o w m e t e r .
A r u n o f w i n d machine w i t h vanes
the e n t r y p o i n t
fell
was f i t t e d
i n t o the wind t u n n e l near
( F i g . 4 . 3 ) The vanes chopped a l i g h t beam ( F i g . 4 . 1 4 ) w h i c h
on a p h o t o r e s i s t o r p r o d u c i n g a s e r i e s o f p u l s e s w h i c h were f e d i n t o
an a m p l i f i e r and a S c h m i t t t r i g g e r w h i c h was used t o produce square
of a r e g u l a r h e i g h t *
pulses
By u s i n g a d i o d e pump c i r c u i t t o produce an o u t p u t
p r o p o r t i o n a l t o t h e p u l s e r e p e t i t i o n f r e q u e n c y , t h e a i r v e l o c i t y c o u l d be
r e c o r d e d on a m e t e r and u l t r a
v i o l e t recorder.
T h i s d e v i c e worked v e r y w e l l
a t room t e m p e r a t u r e , b u t t h e r u n o f w i n d machine t e n d e d t o be u n r e l i a b l e
low temperatures.
T h i s f l o w m e t e r was used i n a l t e r i n g t h e a i r f l o w t o
r e q u i r e d v a l u e b u t was o f l i t t l e
airspeed
use
f o r accurate
measurements.
the
As t h e
i n t h e w o r k i n g s e c t i o n c o u l d be j u d g e d t o + 0 . 5 ms ^ by n o t i n g
t h e movement o f w a t e r d r o p s n e a r t e r m i n a l v e l o c i t y i t was d e c i d e d n o t t o
a t t e m p t t o remedy t h e
fault.
at
42.
C H A P T E R
5
THE PREPARATION OF ARTICIFICAL CLOUD WATER
5.1.
5.1.1
THE SOURCE QF IMPURITIES I N HAIL
I m p u r i t i e s and h a i l
growth
The c o n c e n t r a t i o n o f i m p u r i t i e s i n h a i l
t h e c l o u d d r o p l e t s f r o m which i t was f o r m e d .
i s l i k e l y t o ' be t h e
I f the h a i l
grew by a c c r e t i o n
onto a f r o z e n water drop then t h r o u g h o u t i t s growth i t w i l l
from cloud d r o p l e t s .
same as i n
have been f o r m e d
A c c o r d i n g t o LUDLAM ( 1 9 5 0 ) even i f t h e k e r n e l o f
the
h a i l was f o r m e d by t h e d i r e c t c o n d e n s a t i o n o f t h e v a p o u r , g r o w t h f r o m 1mm
diameter w i l l
be m a i n l y by t h e a c c r e t i o n o f s u p e r c o o l e d w a t e r d r o p s .
5 . 1 . 2 The c o n t a m i n a t i o n o f c l o u d w a t e r .
True a e r o s o l s a r e n o t r e a d i l y c a p t u r e d by f a l l i n g w a t e r d r o p s o r h a i l ,
but
a c c o r d i n g t o BYERS ( 1 9 6 5 ) are c a r r i e d around i n t h e a i r s t r e a m .
Particles
l a r g e r t h a n a f e w m i c r o n s a r e adsorbed a t t h e s u r f a c e o f f a l l i n g p r e c i p i t a t i o n .
GREENFIELD ( 1 9 5 7 ) showed t h a t p a r t i c l e s s m a l l e r t h a n l j x m e n t e r
by c o a g u l a t i n g w i t h s m a l l c l o u d d r o p l e t s .
condensation n u c l e i w i l l
D r o p l e t s w h i c h have grown f r o m
be c o n t a m i n a t e d by t h e o r i g i n a l
5 . 1 . 3 C o n d e n s a t i o n n u c l e i and c l o u d w a t e r
cloudwater
condensation
nucleus.
purity
C o n d e n s a t i o n n u c l e i may be c l a s s i f i e d by s i z e
Giant
r a d i u s y 1H m
Large
r a d i u s between 0 . 2 and 1.0\im
Aitken
radius <
into
0.2f*m.
JUNGE ( 1 9 5 3 ) measured t h e n u c l e u s c o n t e n t o f t h e a i r b o t h n e a r F r a n k f u r t
and on t h e Z u g s p i t z e and f o u n d t h e number o f l a r g e n u c l e i v a r i e d f r o m
7
5 x 10
8
t o 4 x 10
-3
m
q
, w i t h a mean o f 1.3
x 10
_3
m
.
As WEICKMANN i and
AUFM KAMPE (1953) e s t i m a t e d t h e c o n c e n t r a t i o n o f d r o p l e t s i n F l o r i d a
8
t h u n d e r s t o r m s t o be 10
-3
m
i t appears t h a t l a r g e n u c l e i are
probably
t h e m a i n f o r m o f a c t i v j e c o n d e n s a t i o n n u c l e i i n t h u n d e r s t o r m s as
are e f f e c t i v e a t lower s u p e r s a t u r a t i o n s
than Aitken n u c l e i .
concentration of n u c l e i increases r a p i d l y with decreasing
they
Since
the
r a d i u s i t would
43.
seem t h a t t h e most common s i z e o f a c t i v e n u c l e u s
t h e l o w e r end o f t h e l a r g e n u c l e u s range
i n thunderclouds l i e s
i . e . 0 . 2 - 0.3 ji m r a d i u s .
The a c t u a l c o n c e n t r a t i o n o f t h e c o n d e n s a t i o n n u c l e u s
c l o u d w a t e r depends on t h e
of
f a s t e r by c o a l e s c e n c e , w h i c h w i l l
not g r e a t l y a l t e r the
MASON ( 1 9 5 7 ) c o n s i d e r e d t h a t d r o p l e t s w i l l
l i k e l y t o grow
impurity concentration.
grow t o a r a d i u s o f a b o u t 20^im by
however t h i s e s t i m a t e was based on p u r e l y h y d r o d y n a m i c a l
considerations.
SARTOR ( 1 9 7 0 ) has deduced t h e o r e t i c a l l y t h a t t h e mass g r o w t h
r a t e s o f d r o p l e t s o f 10 ^ m r a d i u s w i l l
even w i t h o u t c h a r g e s b e i n g p r e s e n t
-1
30 kVm
substance i n the
s i z e t o w h i c h t h e d r o p l e t s grow by c o n d e n s a t i o n
w a t e r v a p o u r , because above a c e r t a i n s i z e t h e y are
condensation;
at
be i n c r e a s e d by an o r d e r o f m a g n i t u d e ,
on t h e d r o p l e t s , i f t h e p o t e n t i a l g r a d i e n t
«3
.
S h o u l d c h a r g e s o f 3 x 10
a p o t e n t i a l g r a d i e n t 300 kVm
3 orders of magnitude.
t h e e x t r e m e case a r e
1
pG be p r e s e n t
then the growth r a t e s
on each l O ^ d r o p l e t
in
s h o u l d be enhanced
by
As t h e v a l u e s o f charge and p o t e n t i a l g r a d i e n t i n
s l i g h t l y s m a l l e r t h a n t h e maximum v a l u e s f o u n d by GUNN
( 1 9 5 0 ) i t seems l i k e l y t h a t t h i s p r o c e s s p r o v i d e s an e x p l a n a t i o n o f why
p r e c i p i t a t i o n can d e v e l o p so r a p i d l y i n a cumulonimbus c l o u d .
storm c e l l
In a thunder-
5km t h i c k w i t h an u p d r a u g h t o f 10 ms * c l o u d d r o p l e t s a t
have o n l y 10 m i n u t e s t o d e v e l o p i n t o p r e c i p i t a t i o n , w h i l e t h e
t h e base
time,
c a l c u l a t e d by BEST ( l 9 5 l ) t o reach lOp. m r a d i u s by p u r e l y c o n d e n s a t i o n f r o m
t h e v a p o u r i s o f t h e o r d e r o f one h o u r f o r a s u p e r s a t u r a t i o n o f 0.05%.
I t w o u l d t h e r e f o r e seem t h a t an u p p e r l i m i t
f o r m e d by c o n d e n s a t i o n
to the r a d i u s o f d r o p l e t s
f r o m t h e w a p o u r i n t h u n d e r c l o u d s i s p r o b a b l y 10^1 m#.
5 . 1 . 4 The c h e m i c a l n a t u r e o f c o n d e n s a t i o n
nuclei.
The most e f f e c t i v e c o n d e n s a t i o n n u c l e i are s o l u b l e i n w a t e r and g e n e r a l l y
hygroscopic.
likely
The c o m p o s i t i o n o f l a r g e n u c l e i i s n o t w e l l know^but t h e most
substances are
sodium c h l o r i d e f r o m t h e oceans and ammonium s u l p h a t e ,
w h i c h i s f o r m e d f r o m s u l p h u r d i o x i d e and ammonia f r o m t h e d e c o m p o s i t i o n o f
organic
matter.
ojcatsJyj
44.
5 . 1 . 5 E s t i m a t i o n of the
i m p u r i t y c o n c e n t r a t i o n i n c l o u d w a t e r due
to
gondqnsaUPP PiA&J&j.*
If
t h e most i m p o r t a n t n u c l e i have r a d i i between O . l and Q . 3 j i m and
c l o u d d r o p l e t s grow f r o m t h e vapour phase up t o l O j i m r a d i u s
to
estimate
5
o f ammonium s u l p h a t e
TABLE 5 . 1 .
Hm
n
10
10
10
20
20
20
0.1
ro
mgJL ~
i,n, c l o u d w a t e r due t o
pa&lgi.
5.1 the a c t u a l c o n c e n t r a t i o n o f i m p u r i t y
t o t h e r a d i i o f b o t h n u c l e u s and d r o p l e t
9
is
n e i t h e r of which
I t would seem l i k e l y t h a t t h e range o f c o n c e n t r a t i o n o f
i m p u r i t i e s i s about 2 t o 20 mgA
This, i t will
be seen l a t e r ,
w e l l w i t h t h e range o f t h e p u r e s t c l o u d w a t e r samples.
t h i s analysis that
1
2.0
16.0
54,0
0,3
2.0
6.8
0,3
0.1
0.2
0.3
Impurity concentrations
known a c c u r a t e l y .
is
Concentration
of impurity
0*0
can be seen f r o m t a b l e
very sensitive
( S . G . o f sodium c h l o r i d e
Radius o f
condensation
nucleus
condensate
of
possible
1.8).
Cloud d r o p l e t
r a d i u s produced
by g r o w t h f r o m
the vapour
As
i t is
( £ £ g . 5 . 1 ) t h e c o n c e n t r a t i o n o f i m p u r i t i e s , assuming a s p e c i f i c
g r a v i t y of 2.0 f o r the condensation nucleus.
2.2
9
the
agrees
I t is clear
i f e l e c t r i c f i e l d s do g r e a t l y enhance t h e
coalescence
c l o u d d r o p l e t s o f l e s s t h a n 10 p r a d i u s , t h e n t h u n d e r s t o r m r a i n
c o n t a i n a h i g h e r l e v e l o f i m p u r i t i e s t h a n non t h u n d e r y r a i n .
from
should
The o n l y
r e l e v a n t o b s e r v a t i o n by FISHER and GAMBELL ( 1 9 6 4 ) does n o t c o n f i r m t h i s .
Furthermore possible
a b s o r p t i o n o f s u l p h u r d i o x i d e and n i t r o g e n p e r o x i d e
by p r e c i p i t a t i o n has n o t been c o n s i d e r e d .
T h i s c a l c u l a t i o n has
n e g l e c t e d t h e _ e f f e c t o f t h e washout o f n u c l e i w h i c h w i l l
i n cumulonimbus t h a n i n s t r a t i f o r m c l o u d s .
also
p r o b a b l y be l e s s
is
i
x
in
^
O
co
CM
•
Ca
•
•
rH
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CO
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rH
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•
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2i
0
•
Thunderstorm
Riin - toy.iris
end of r a i n f a l l
clean funnel
Collection of
rain in clean
funnel
Collection of
rain in clean
funnel
Analysis of
snov/ and ice
3 flights
conductivity
high a t low
levels.
in
•
1
t
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a:
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North
Russia
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IUCL
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8.0
1
4 >H. :
CO
12.0
10.3
i
4»
•P
«0
m
-p
-P • rH-H
eHrf ! ,
71.8
.
CM
o
•H
•H
*t
rH
CO
c
3 - 120
o
i
CO
o
o
*
All types of
v/eather
Thermally
stable air
from S.VY.
-3 flights
All types of
v/eather
TOTAL
ELECTRIC
CONDUCTIVITY
cc
-X
fu
cc
13.0
CO
c•
o
<
O
O
a
a
•> o
±c
r>
<c x
O Z v O
q uj o
N QJ H
O H
cc: en
Q a,
_u ~>
O UJ
2 2 O
U J N hCC U J o^
H 3
H
UJ U J
d . CO
50 km South
of Washington D.C.
New Zealand
Antartica
300ml fron
coast.
Hawaii
Q
UJ
x
CO O C 0
< rHvO
O S ON X
O
[H
OS UJ
UU
CQ Q
i_
;
North
Russia
S.E.
England
' CM
vO
O
rH
KOMBAYASI
ISONO
1967
REFERENCE
CN
LOCATION
< a
50 ml S.E
of San
Fransisco
r—t aJ
<
UJ
x
^
uj vO
H ON
H
H
§
2:
O CO
to in
r-H 1
—1
3
•_u L U *r
X CQ vO
10 ^5 o\
r H a: rH
U_i
0
45.
5.2
5.2.1
MEASUREMENTS OF IMPURITIES IN CLOUD AND RAIN-WATER
Type? o f
measurement
There are t h r e e methods o f c o l l e c t i n g p r e c i p i t a t i o n f o r c h e m i c a l
namely
l)
cloud
analysis
collection
2) c o l l e c t i o n a t t h e g r o u n d where t h e f u n n e l used a l s o
collects
f a l l o u t between p e r i o d s o f p r e c i p i t a t i o n .
3) c o l l e c t i o n at the ground of r a i n f a l l
only.
U n f o r t u n a t e l y most measurements are o f t y p e 2 and t h e r e
are v e r y f e w m e a s u r e -
ments made i n c l o u d s .
5 . 2 . 2 The e f f e c t s o f t h e
g e o g r a p h i c a l l o c a t i o n o f the s a m p l i n g s i t e .
H i g h l e v e l s o f i m p u r i t i e s i n p r e c i p i t a t i o n b o t h i n and b e l o w c l o u d s
arise
n e a r a source
of n u c l e i .
T h i s may be an i n d u s t r i a l c e n t r e ,
where
s u l p h u r and ammonium i m p u r i t i e s p r e d o m i n a t e , o r n e a r t h e s e a ,
where sea
i s present
impurity
i n abnormally large concentrations.
concentrations
f o u n d i n c l o u d s are
salt
l i k e l y t o be a more r e l i a b l e g u i d e t o t h e
l e v e l s found i n thunderstorms, but i f the
stratus
G e n e r a l l y the
will
samples are t a k e n i n s l o w l y moving
c l o u d s o v e r an i n d u s t r i a l a r e a t h e c o n c e n t r a t i o n i s
l i k e l y t o be
much h i g h e r t h a n i n a c u m u l o n i m b u s .
5.2.3
The e f f e c t s o f washout on measurements a t
the
around.
PETRENCHUK and SELEZNEVA ( 1 9 7 0 ) have compared c l o u d measurements w i t h
g r o u n d measurements o f i m p u r i t y c o n c e n t r a t i o n s
parts
i n p r e c i p i t a t i o n , f o r various
o f t h e S o v i e t U n i o n , and deduced t h e amount o f c o n t a m i n a t i o n o c c u r r i n g
d u r i n g the f a l l
of the p r e c i p i t a t i o n
i n the n o r t h o f Russia
5.2.4.
f r o m cloud base.
T h i s r a n g e s f r o m 45%
t o 80% i n i n d u s t r i a l U k r a i n e .
The p u r i t y o f t h u n d e r c l o u d w a t e r .
A number o f r e c e n t measurements o f t h e
concentration of dissolved
i m p u r i t i e s i n p r e c i p i t a t i o n b o t h a t t h e g r o u n d and i n c l o u d s are
i n Table 5 . 2 .
I t can be seen t h a t
there
even f o r measurements w h i c h were s e l e c t e d
contained
i s a wide range f r o m 2 t o 13 mg 2.
f o r being e i t h e r i n cloud
c o l l e c t e d a t t h e g r o u n d u n d e r c o n d i t i o n s where washout was s m a l l *
or
The
46.
most common i m p u r i t i e s a r e
Concentrations
sulphate
(S0 ) , chloride
( C l ) and s o l d i u m ( N a ) .
4
w h i c h have been o b t a i n e d
i n v a r i o u s types o f weather
are
l i a b l e t o be h e a v i l y b i a s e d
by a f e w p e r i o d s o f r a i n f a l l d u r i n g i n v e r s i o n
c o n d i t i o n s , where t h e t o t a l
i o n i c c o n c e n t r a t i o n can be as h i g h as 100 m g £
(DROZDOVA and PETRENCHUK, 1 9 6 6 ) .
From T a b l e 5 » 2 t h e minimum c o n c e n t r a t i o n o f i o n i c s u b s t a n c e s i n c l o u d w a t e r
p r o b a b l y l i e s around t h e
2-0 m g i * "
1
v a l u e f o u n d by ODD IE
(1962) f r o m a i r b o r n e
measurements i n a c l e a n a i r m a s s and BROCAS and DELWICHE ( 1 9 6 3 ) f r o m snow i n
Antarctica.
An u p p e r l i m i t
to the concentration
b
to
estimate
f o r thunderstorms
is
hard
.-i
b u t i s p r o b a c y about
10 mgJt
which i s t h e average v a l u e f o r a l l
w e a t h e r c o n d i t i o n s i n a f a i r l y l o w - p o l l u t e d a r e a such as N o r t h e r n
(DROZDOVA and PETRENCHUK, 1970) and a l i t t l e
Russia
l e s s t h a n t h e average o f
the
a i r b o r n e measurements made o v e r s o u t h e r n E n g l a n d by 0 D D I E ( l 9 6 2 ) »
5*2«5
The l o w e r p o s i t i v e charge and t h e p u r i t y o f
cloudwater.
The c o n c e n t r a t i o n o f d i s s o l v e d s u b s t a n c e s i n t h e
thunderstorm w i l l
depend
the nearness o f o t h e r
cloud droplets
will
on t h e l e v e l o f a i r p o l l u t i o n n e a r t h e
s o u r c e s o f a e r o s o l s such as t h e s e a .
The l o w e r p o s i t i v e charge has
Many o f
been observed
area o f low p o l l u t i o n .
i n most t h u n d e r c l o u d s
I f the
the
come f r o m
a i r i s probably well mixed.
several
SCRASE ( 1 9 3 7 ) and SIMPSON and ROBINSON ( l 9 4 l )
t i m e s by SIMPSON and
a t Kew, w h i c h i s n o t i n an
l o w e r p o s i t i v e charge were f o u n d t o be p r e s e n t
t h e n any mechanism e x p l a i n i n g i t s o r i g i n must n o t be
t o the c o n c e n t r a t i o n o f i m p u r i t i e s *
c o n s i d e r i n g b o t h the t h e o r y of t h e
and r e c e n t
s t o r m and
f o r m near c l o u d base i n an u p d r a u g h t t h a t has
t h e l o w e s t 2 km o f the a t m o s p h e r e , where t h e
highly sensitive
cloudwater of a
Therefore, from
f o r m a t i o n of i m p u r i t i e s i n cloud water
measurements i t seems t h a t t h e mechanism o f t h e
c h a r g e must be e f f e c t i v e i n t h e
i m p u r i t y range 2 t o 10 mgH
lower p o s i t i v e
•
Fig.5.1
The
deionizing
apparatus
47.
5.3.
THE PREPARATION OF ARTIFICIAL CLOUD WATER
The a r t i f i c i a l
chemicals
c l o u d w a t e r was made by a d d i n g known q u a n t i t i e s
t o w a t e r w h i c h was a t l e a s t a f a c t o r o f 30 p u r e r t h a n t h e
solution.
The i m p u r i t i e s i n o r d i n a r y t a p w a t e r c o n s i s t
i o n s such as c a l c i u m , copper
These were r e d u c e d
T
5'3.2,, h
Ion
e
of
ion
mainly of
and s o | d i u m , and a l s o g r e a s e and
pure
final
dissolved
microorganisms.
t o a l o w l e v e l by a d i s t i l l a t i o n and d e i o n i z i n g u n i t .
^ i o n i z a t i o n of water.
exchange r e s i n s consist o f p o r o u s beads o f an i n e r t m a t e r i a l such
polystyrene
fall
of
c o n t a i n i n g f u n c t i o n a l groups which t e n d t o absorb i o n s .
The r e s i n s
i n t o two b r o a d c l a s s e s , c a t i o n and a n i o n e x c h a n g e s , d e p e n d i n g on t h e
i o n removed f r o m t h e s u r r o u n d i n g s o l u t i o n .
o f one s i g n and i t s r e p l a c e m e n t
expressed
as
type
The p r o c e s s o f r e m o v a l o f an
by a n o t h e r
ion is reversible
and can be
as:
CATION RESIN
R -
S0 H + Na C I
R - S0
R -
N H* OH" + H C l ^ = * R
3
3
Na + N C l
ANION RESIN
where
If
- NH^ C l 4- H 0
2
R i s t h e base and SO^H and NH^ OH a r e
the
f u n c t i o n a l groups of the
resins.
one r u n s a weak s o l u t i o n o f sodium c h l o r i d e t h r o u g h a c a t i o n r e s i n t h e n
resultant
outflow w i l l
c o n t a i n h y d r o c h l o r i c a c i d and i f t h i s
anion r e s i n the a c i d w i l l
All
t e n d t o be t u r n e d
i n t o pure
i o n s are n o t removed e q u a l l y and t h e
e x p r e s s e d i n terms o f an exchange p o t e n t i a l
i s r u n i n t o an
water.
s e l e c t i v i t y o f t h e r e s i n can be
for a particular ion.
In
general
m u l t i v a l e n t i o n s a r e more e a s i l y removed f r o m d i l u t e s o l u t i o n s because
have h i g h e r exchange p o t e n t i a l s ,
_. 4+
Th
>
c
Fe
3+ *
>
^2+
Zn
>
.„+
NH^ >
„+
K
A n o t h e f t y p e o f d e i o n i s a t i o n uses mixed bed r e s i n s w h i c h a r e
m i x t u r e o f c a t i o n and a n i o n r e s i n s .
at e f f e c t i v e l y neutral
they
namely,
_ 2+
Ba
>
the
an i n t i m a t e
These have t h e a d v a n t a g e o f w o r k i n g
pH and a r e h i g h l y e f f i c i e n t .
48.
5.3.3
The w a t e r p u r i f i c a t i o n
Figure 5 . 1
shows t h e c o m p l e t e u n i t ? w h i c h was c a p a b l e o f
appoximately 1 l i t r e
needed.
system.
o f pure w a t e r every hour w i t h v e r y l i t t l e
The l a y o u t o f t h e d i s t i l l i n g
R. Diawson and c o n s i s t e d
column t o p r e v e n t
condenser.
reservoir
alkaline
producing
of a 2 l i t r e
splashing,
and t h e
attention
a p p a r a t u s was recommended
by D r .
flask f i t t e d with a fractionating
s t r e a m was condensed i n t h e
Liebig
Water c o u l d be c o n t i n u o u s l y r u n i n t o t h e f l a s k f r o m t h e
w h i c h was r e f i l l e d e v e r y h a l f
hour.
The f l a s k c o n t a i n e d
s o l u t i o n o f p o t a s s i u m permanganate w h i c h was used t o
any o r g a n i c m a t t e r
t o c a r b o n d i o x i d e and
oxidise
water.
The d e i o n i s i n g columns were 0.7m l o n g and 10 mm i n t e r n a l
The r e s i n s was h e l d i n p l a c e by s i n t e r e d
pyrex chippings at the
top.
head o f w a t e r f r o m t h e
small reservoir.
an
diameter.
g l a s s p l u g s a t t h e b o t t o m and
The w a t e r r a n t h r o u g h t h e
system u n d e r
the
The f l o w r a t e f o r optimum
d e i o n i z a t i o n depends on t h e volume o f r e s i n and u s i n g t h e m a n u f a c t u r e r s
s p e c i f i c a t i o n t h i s worked o u t a t 900 ml p e r
hour.
The c a t i o n r e s i n used was m a r k e t e d by B . D . H . as A m b e r l i t e
and t h e
i n the
use
a n i o n r e s i n was A m b e r l i t e I R A - 4 0 0 .
The l a t t e r
c h l o r i d e f o r m and had t o be c o n v e r t e d
resir
was a j p p l i e d
to the hydroxyl
by w a s h i n g w i t h a measured volume o f I N r a d i u m h y d r o x i d e .
done i n t h e
a p p a r a t u s on t h e l e f t o f f i g u r e 5 . 1 .
IR-120
The t r e a t e d
form before
T h i s was
resin
c o u l d t h e n be t h o r o u g h l y m i x e d w i t h d e i o n i z e d w a t e r t o remove a l l
of
the a l k a l i .
of
IRA-4O0 and
5.3.4
The m i x e d bed r e s i n was c a l l e d MB-1 and was a m i x t u r e
IR-120.
P u r i t y o f the deionized
water.
The most abundant i m p u r i t y i n t h e d e i o n i z e d
which was
i n e q u i l i b r i u m w i t h atmospheric
removed by b u b b l i n g w i t h
0.8
t o 0 . 1 5 p mho cm
concentration
traces
w a t e r was c a r b o n d i o x i d e
carbon d i o x i d e .
When t h i s
n i t r o g e n the c o n d u c t i v i t y of the water f e l l
T h i s l o w e r v a l u e c o r r e s p o n d s t o an
o f s l i g h t l y l e s s t h a n 0 . 1 mgJC^.
ionic
was
from
49.
5 . 3 . 5 The . , r t l f i c i a l
cloudwater,.
E l e c t r i c a l e f f e c t s i n v o l v i n g t h e r u p t u r e of t h e d o u b l e l a y e r a t a
water surface
have been f o u n d by DRAKE (1968) and IRIBARNE and MASON ( 1 9 6 7 )
t o be i n d e p e n d e n t
the a c t u a l
o f t h e s p e c i e s o f i o n p r e s e n t 3 and t o depend
ionicj^ncentration.
impurity concentrations
constituents
are
only
I t w o u l d appear f r o m t h e measurements o f
i n cloudwater
(Table 5.3) t h a t the p r i n c i p a l
sodium $ c h l o r i d e and ammonium i o n s .
So i t was d e c i d e d
t o make up a r t i f i c a l c l o u d w a t e r c o n s i s t i n g o f o n l y sodium c h l o r i d e i m p u r i t i e s .
L a t e r 5 i f time p e r m i t t e d
ammonium s u l p h a t e
?
other
i m p u r i t i e s such as sodium s u l p h a t e
c o u l d be u s e d »
The c o n c e n t r a t i o n used was 4 . 5 mgSL ~
g i v i n g a c o n d u c t i v i t y o f 8 . 1 1 * mho cm *
range o f i m p u r i t y c o n c e n t r a t i o n s
pipette.
w h i c h f a l l s w e l l w i t h i n the
probable
Approximately
w e i g h e d o u t and d i s s o l v e d i n 250 m l o f d e i o n i z e d
T h i s was t h e n d i l u t e d f u r t h e r by t a k i n g o u t 10 ml samples w i t h a
F i n a l l y t h e w a t e r was s t o r e d d u r i n g t h e e x p e r i m e n t s
Pyrex b o t t l e .
in a 1 litre
A l l t h e g l a s s w a r e used i n t h e p r e p a r a t i o n o f t h e
c a r e f u l l y cleaned w i t h p r o p a n o l
?
1
lGmgif ).
h i g h l y p u r e g r a d e , m a n u f a c t u r e d by
' a n a l a r ' w i t h a maximum i m p u r i t y l e v e l o f 0 . 1 % .
2g o f s o d i u m c h l o r i d e was
water.
9
i n thunderstorm p r e c i p i t a t i o n (2 to
The c h e m i c a l s used were a s p e c i a l
B«DoH c a l l e d
and
detergent
w a t e r was
and t h o r o u g h l y r i n s e d i n r u n n i n g
t a p w a t e r and f i n a l l y r i n s e d and l e f t t o s t a n d
i n d e i o n i z e d water©
120platinum.
w ire
Brass h o l d e r
Mould f o r
freezing
water
drops onto
a 120 \*m
Platinum wire
loop
Mould
used
in t h e f r e e f l i g h t
Fig.6-1
Moulds
experiments
for f r e e z i n g w a t e r
drops
wire
50.
C H A P T E R
FREE FLIGHT EXPERIMENTS ON
6.1.
6.1.1 Preparation of the
6
MELTING AND EVAPORATING ICE PARTICLES
EXPERIMENTAL PROCEDURE
ice
particles.
The i c e p a r t i c l e s were made by f r e e z i n g w a t e r d r o p s suspended i n i c e
moulds
(Fig. 6.1).
These moulds c o n s i s t e d o f 3 t o 5 - mm d i a m e t e r
p l a t i n u m w i r e f r o m w h i c h d r o p s were h u n g .
loops o f
Each hoop was c o n n e c t e d t o an
a l u m i n i u m f r a m e by 2 b r a s s r o d s , one o f w h i c h was i n s u l a t e d f r o m t h e f r a m e
by a p e r s p e x
bush.
The w i r e c o u l d be c l e a n e d by h e a t i n g t o w h i t e h e a t by
an e l e c t r i c c u r r e n t f r o m an a c c u m u l a t o r .
The w a t e r d r o p s were l e f t i n a r e f r i g e r a t o r t o f r e e z e a t about
N u c l e a t i o n would o f t e n n o t occur f o r s e v e r a l
e x p e r i m e n t s no a t t e m p t was made t o c o n t r o l
the f r e e z i n g t e m p e r a t u r e .
h o u r s , but i n these e a r l y
t h e t i m e o f n u c l e a t i o n o r measure
When r e q u i r e d , t h e i c e p a r t i c l e s were
removed f r o m t h e r e f r i g e r a t o r and p l a c e d i n t h e c o l d r o o m .
were t h e n e i t h e r knocked o u t o f t h e i r hoops w i t h
released
by e l e c t r i c a l l y h e a t i n g t h e h o o p .
the i c e p a r t i c l e s t o f a l l
~15°C,
a tapered
rapidly
The i c e
samples
p y r e x tube
The frame was d e s i g n e d t o
clear i n t o a clean evaporating
or
enable
basin.
The i c e p a r t i c l e was p u t i n t o t h e wind t u n n e l t h r o u g h t h e h a t c h ( F i g .
4.3)
its
and a l l o w e d t o f a l l
i n t o t h e w o r k i n g s e c t i o n j where i t seen moved i n t o
p o s i t i o n of e q u i l i b r i u m .
tunnel
The p a r t i c l e was c a r r i e d f r o m t h e b a s i n t o t h e
i n t h e end o f a p y r e x tube and was sucked o u t as
p l a c e d i n t h e p a r t i a l l y open h a t c h .
the surfaces
i n contact with
to s t i c k i n the tube
i f i t started
was
Care had t o be t a k e n t o e n s u r e t h a t a l l
the i c e were b e l o w 0 ° C as t h e p a r t i c l e
The i c e p a r t i c l e s were shaped
from the hoops.
soon as t h e t u b e
tended
melting.
i n a s i m i l a r way t o t h e d r o p s h a n g i n g
They t e n d e d t o be somewhat e l l i p s o i d a l , w i t h a d e f i n i t e
t e n d e n c y t o be w i d e r a t t h e end w h i c h was i n c o n t a c t w i t h t h e
support.
t h e s e e x p e r i m e n t s t h e o n l y d i m e n s i o n measured was t h e maximum w i d t h .
In
51.
6.1.? Prfir^tjnriQ t
All
n
n
nY 11 ^ n t . a m i n a t i o n o f t h e
the glassware
used
i n s t o r i n g t h e pure w a t e r and m a n i p u l a t i n g t h e
i c e s p h e r e s was c a r e f u l l y c l e a n e d
i n p r o p a n o l and d e t e r g e n t ,
w i t h t a p w a t e r and d e i o n i z e d w a t e r f o r s e v e r a l
made f r o m b o r o s i l i c a t e g l a s s r a t h e r
would n o t d i s s o l v e
ice.
hours*
and t h e n
A l l the glassware
t h a n soda g l a s s t o e n s u r e t h a t t h e
s i l i c a t e s f r o m the w a l l s of the c o n t a i n e r s
e v a p o r a t i n g b a s i n s and t a p e r e d
rinsed
•
was
water
The
t u b e s were k e p t u n d e r d e i o n i z e d w a t e r when n o t
i n use and were c a r e f u l l y d r i e d w i t h warm a i r f r o m a h a i r d r i e r b e f o r e u s e .
t h e r e was any d o u b t as t o t h e c l e a n l i n e s s
allowed t o stand
o f a c o n t a i n e r , d e i o n i z e d w a t e r was
i n i t f o r a f e w h o u r s j any c o n t a m i n a t i o n was shown by an
increase i n the e l e c t r i c a l c o n d u c t i v i t y o f the water.
The a l u m i n i u m w o r k i n g
s e c t i o n and t h e b r a s s gauzes were a l s o c l e a n e d
w i t h metal p o l i s h ,
and r u n n i n g w a t e r , b u t c o u l d n o t be c o n s i d e r e d
clean i n the
detergent
present
investigation.
6 . 2 , THE BEHAVIOUR OF THE SUPPORT SYSTEM,
6.2.1.
Solid ice
spheres.
The w i n d t u n n e l was c a p a b l e
o f s u p p o r t i n g an i c e p a r t i c l e f o r a b o u t
30 m i n u t e s b u t e v e n t u a l l y t h e p a r t i c l e w o u l d c r a s h o n t o t h e a i r f l o w
gauzes.
shaping
T h i s was l i k e l y t o o c c u r a t any t i m e b u t p r o b a b l y a f t e r 30 m i n u t e s
i n t h e t u n n e l t h e p a r t i c l e had l o s t so much mass by e v a p o r a t i o n t h a t
t e n d e d t o move up t h e w o r k i n g s e c t i o n i n t o a r e g i o n where t h e
it
f l o w was
u n i f o r m , and as a r e s u l t be l i a b l e t o c r a s h down o n t o t h e g a u z e s .
2 or 3 minutes the
less
Every
i c e p a r t i c l e would t e n d t o come near t h e w a l l s and
p r o b a b l y t o u c h e d f o r a f e w seconds b e f o r e m o v i n g away t o h o v e r
somewhere
else.
6.2.2. Melting
It
ice
spheres
was i m p o s s i b l e t o s u p p o r t an i c e p a r t i c l e
throughout i t s . m e l t i n g process*
temperature
rose from about
If
i n t h e ";ind t u n n e l
During-the m e l t i n g experiments
the
air
- 5 ° C t o + 7°C a t a r a t e o f a b o u t 2 . 5 ° C min
1
.
52.
H o w e v e r , because t h e wet b u l b d e p r e s s i o n
temperature
of the
foe
surface
would be o f t h i s o r d e r , t h e
was p r o b a b l y between 0 and +2°C on i m p a c t .
The r e a s o n f o r t h e p a r t i c l e s t i c k i n g t o t h e
is
probably that there
adhesion.
Whether t h e
s i d e s soon a f t e r r e a c h i n g 0 ° C
was a w a t e r f i l m , o v e r t h e
ice surface which
assisted
i c e p a r t i c l e s touched the sides every few seconds, o r
t h e p r e s e n c e o f t h e w a t e r f i l m made t h e p a r t i c l e s u n s t a b l e ,
disadvantage
actual
i s n o t known. A
o f t h e e x p e r i m e n t a l l a y o u t was t h e d i f f i c u l t y o f j u d g i n g t h e
p o s i t i o n o f a p a r t i c l e m e r e l y by l o o k i n g down i n t o t h e t u n n e l and so 2 b l a c k
r i n g s were p a i n t e d round t h e c o r e t o h e l p j u d g e t h e
6.2»3
Suggestions
The p r o b a b l e
f o r i m p r o v i n g the
support
perspective.
system
r e a s o n f o r t h e f a i l u r e o f t h e wind t u n n e l t o keep m e l t i n g
p a r t i c l e s away f r o m t h e s i d e s was t h a t t h e l e v e l
o f t u r b u l e n c e was t o o
high.
The f l o w s h a p i n g gauzes a t t h e b o t t o m o f t h e w o r k i n g s e c t i o n were c e r t a i n l y
an improvement i n h e l p i n g t h e
i c e spheres t o keep away f r o m t h e w a l l s .
How-
ever t h e a i r v e l o c i t y seems t o g u s t b o t h i n t h e v e r t i c a l and h o r i z o n t a l
directiOiis.
I f the height o f the w o r k i n g s e c t i o n
i n c r e a s e d t o e l i m i n a t e t h e need f o r 2 r i g h t a n g l e
the turbulence c o u l d have been reduced.
have been p l a c e d a t
A large
( F i g . 4 . 3 ) c o u l d have been
bends i n t h e t u n n e l
then
s e t t l i n g chamber c o u l d then
t h e entrance o f t h e t u n n e l and c o n n e c t e d
s e c t i o n by means o f a s p e c i a l l y shaped c o n t r a c t i o n .
to the
working
The e f f e c t o f t h e
i m p e l l e r b l a d e s o f t h e b l o w e r , t r a v e l l i n g u p s t r e a m as p r e s s u r e w a v e s , was
not
It
appreciated
and no s c r e e n s were p l a c e d downwind o f t h e w o r k i n g
section.
i s c l e a r t h a t t h e r e s t r i c t i o n s made on t h e d e s i g n o f t h e t u n n e l by t h e
need t o
avoid contamination o f the
i c e samples and t o measure v e r y s m a l l
c u r r e n t s make t h e d e s i g n o f a v i a b l e s u p p o r t system n e a r l y
I t may have been b e t t e r
wind t u n n e l r a t h e r
preconditions.
t o have c o n c e n t r a t e d
impossible.
on p r o d u c i n g a w o r k a b l e
t h a n a l l o w t h e d e s i g n t o be compromised by t o o many
53.
6*2.4
Conclusions
on t h e s-fcudV o f m e l t i n g e l e c t r i f i c a t i o n u s i n g w i n d
tunnels
A t p r e s e n t t h e r e does n o t appear t o be a w i n d t u n n e l d e s i g n w h i c h w i l l
f r e e l y support
small ice p a r t i c l e s ( f r o m the
by PRUPPACHER and NEIBURGER ( 1 9 6 8 ) ,
laminar f l o w tunnel
I f a s m a l l t u n n e l were b u i l t w h i c h
c o u l d p e r f o r m t h i s t a s k t h e n t h i s would be a u s e f u l t o o l
study o f Cloud Physics*
particle
However, a t u n n e l
that
will
i n the
support
laboratory
a melting ice
t h r o u g h o u t t h e t r a n s f o r m a t i o n f r o m s o l i d t o l i q u i d would p r o b a b l y
have t o be more s o p h i s t i c a t e d
particles.
will
described
than a t u n n e l which merely supports s o l i d
During the m e l t i n g process the
change w h i c h w i l l
mean t h a t
t e r m i n a l speed o f t h e
t h e a i r speed w i l l
have t o be
particle
changed.
As t h e f o r c e s on a s o l i d p a r t i c l e have d i f f e r e n t e f f e c t s t h a n on m o l t e n
d r o p s , w h i c h can be d e f o r m e d , i t is
will
support
an i c e sphere w i l l
6.3.
6.3.1.
quite possible
not suppoit a water
that
a system
that
drop.
THE ELECTRIFICATION OF MELTING ICE
E l e c t r i f i c a t i o n , i n f r e e fUqfrfc*
E l e c t r i c a l measurements were made on 9 i c e
w h i c h were f r e e l y s u p p o r t e d
melting.
sides d u r i n g the e a r l y stages of
The average d r y b u l b t e m p e r a t u r e a t w h i c h t h e y c r a s h e d t o the
was + 4 ° C .
Wet b u l b d e p r e s s i o n was n o t m e a s u r e d , b u t f r o m l a t e r
the a i r a t the
(Table 6 . 1 ) .
level
away f r o m t h e
spheres o f 3 t o 5 mm d i a m e t e r
surface of
the
sides
measurements
spheres was p r o b a b l y l e s s t h a n 2 . 5 ° C on i m p a c t
There was no e l e c t r i f i c a t i o n above t h e + 0 . 0 0 3 pA b a c k g r o u n d
f o r any o f t h e
samples.
This i s
i n agreement w i t h l a t e r
observations
w i t h i c e s p h e r e s m e l t i n g on p l a t i n u m w i r e s , when t h e e l e c t r i f i c a t i o n d i d
n o t commence u n t i l
water o f e l e c t r i c
t h e m e l t i n g was w e l l a d v a n c e d .
The i c e was made f r o m
c o n d u c t i v i t y 0 . 7 5 j i mho cm * i n e q u i l i b r i u m w i t h
laboratory
carbon d i o x i d e .
6.3.2.
The m e l t i n g o f i c e p a r t i c l e s
A f t e r the m e l t i n g i c e p a r t i c l e s
m e l t i n g p r o c e e d e d r a p i d l y and t h e
t o 120 So
on t h e
sides of the
had c r a s h e d on t h e
tunnel.
s i d e s o f the
i c e u s u a l l y was f u l l y m e l t e d w i t h i n
The i c e c o r e c i r c u l a t e d i n t h e m e l t w a t e r d u r i n g t h e
later
tunnel,
90
stages
54,
of m e l t i n g .
A l t h o u g h the
s i d e s o f t h e t u n n e l had been c a r e f u l l y
cleaned,
i m p u r i t i e s w o u l d c e r t a i n l y have e n t e r e d t h e m e l t w a t e r d u r i n g m e l t i n g .
The
charge p r o d u c e d d u r i n g t h e m e l t i n g o f a 9 i c e p a r t i c l e s made f r o m w a t e r o f
cm-'
c o n d u c t i v i t y 0 . 7 5 | i m h o ^ i s c o n t a i n e d i n Table 6 - 1 .
The r a t e o f c h a r g i n g
reached a maximum i n t h e l a s t s t a g e s o f m e l t i n g and t e n d e d t o p e r s i s t f o r
a b o u t 15 seconds a f t e r t h e l a s t t r a c e s o f i c e had v a n i s h e d .
TABLE 6 . 1
The charge p r o d u c e d by i c e p a r t i c l e s
on the s i d e o f t h e w i n d
melting
tunnel.
Charge
Diameter
Temperature o f &ir
Wet B u l b D e p r e s s i o n
+pC
mm
°C
°G
5.0
3
2.2
1.5
4.3
3i
3.5
2*5
3.3
4i
4.3
2.0
4.0
4
5.2
2.0
3.1
4i
4.1
4.0
1.4
5
4.2
2.0
2*9
4
4.5
2.5
0,8
3
3.0
1.7
2.1
4
3.0
1.8
T h e r e i s no s i g n i f i c a n t r e l a t i o n between t h e d i a m e t e r s o r t h e
temperatures
o f c r a s h i n g , and t h e charge p r o d u c e d .
The mean charge was
3.0pC w i t h a s t a n d a r d d e v i a t i o n a b o u t t h e mean o f 0 . 5 p C .
d i a m e t e r o f 4mm t h i s c o r r e s p o n d s
t o a r a t i o o f charge
For an
average
t o mass o f 0 . l p C mg
( 0 . 3 esu g * ) . A 1 1 i c e samples p r o d u c e d p o s i t i v e l y charged m e l t w a t e r
C pnst a n t a n
R g . 7-1 W i r e l o o p s u p p o r t s u s e d by D r a k e ( 1 9 G S )
Ice core
SKI
Air-flow
Fig.7.2
C o n v e c i i v e c u r r e n t s in a m e l t i n g ice
D r a k e a n d M a s o n ( 19G6 )
Air
sphere
flow
Platinum
a)
Ice
Fig.7. 3
sphere
Straight wire
b)
support
Partially
molten
C H A P T E R
7
EXPERIMENTS WITH MET.TTNG ICE SPHERES HANGING ON PLATINUM WIRES
7.1.
THE SUPPORT OF MELTING ICE SPHERES
7 . 1 . , ! P r e v i o u s methods o f
DRAKE (1968) has
support.
shown t h a t t h e way i n w h i c h t h e m e l t i n g i c e
are v e n t i l a t e d can a f f e c t t h e amount o f charge
magnitude.
of
particles
s e p a r a t e d by an o r d e r of
I n t e r m s o f t h e a i r bubble t h e o r y , v e n t i l a t i o n a i d s t h e r e m o v a l
t h e n e g a t i v e l y charged
j e t drops
f o r m e d by t h e b u r s t i n g b u b b l e s .
rate of v e n t i l a t i o n also
a s s i s t s the f o r m a t i o n of convection i n the
thus h e l p i n g the bubbles
to burst at a surface
Convection i n the meltwater w i l l
bubbles
bursting at
at the ice-water
the s u r f a c e
interface.
meltwater,
free from contamination.
also a l t e r the
spectrum o f s i z e s o f
by r e d u c i n g t h e c l u s t e r i n g o f
the
bubbles
C l e a r l y t h e a i r f l o w around t h e p a r t i c l e and
t h e way i n w h i c h i t r e a c t s t o t h e a i r s t r e a m g r e a t l y i n f l u e n c e t h e
of
A high
amount
c h a r g i n g p r o d u c e d by t h e m e l t i n g i c e .
DINGER and GUNN ( 1 9 4 6 ) and MAC CREADY and PROUDFIT (1965) m e l t e d b l o c k s
of
ice i n containers
i n an a i r s t r e a m .
They f o u n d a charge
was an o r d e r o f m a g n i t u d e l e s s t h a n t h a t measured
2 t'o 6 mm d i a m e t e r
separation
which
by DRAKE ( F i g . 7 * l )
using
i c e s p h e r e s h a n g i n g f r o m 1 mm l o o p s o f c o n s t a n t a n .
d i f f e r e n c e between t h e s e r e s u l t s
convection i n the m e l t w a t e r .
The
was a t t r i b u t e d by DRAKE t o the o n s e t o f
T h i s c o n v e c t i o n has been d e s c r i b e d
by DRAKE
and MASON ( 1 9 6 6 ) who m e l t e d f r o z e n w a t e r d r o p s suspended f r o m a mesh o f
10 jim f i b r e s .
i c e core
These c o n v e c t i o n c u r r e n t s
( F i g . 7 . 2 ) , and t h e i r v e l o c i t y
sometimes r a n d o m l y r o t a t e d
increased w i t h
the
increasing melting
r a t e and w i n d speed b u t n e v e r exceeded a f e w cm s
The w i r e l o o p s u p p o r t d i d n o t p e r m i t t h e m e l t i n g p a r t i c l e t o
and t h i s may i n c r e a s e t h e m o t i o n o f t h e
ice core.
T h i s t y p e of
rotate
support
a l s o a l l o w s a p a r t i c l e t o be h e l d i n an a i r s t r e a m w h i c h i s m o v i n g
considerably f a s t e r or slower
is
than i t s t e i m i n a l
speed.
I f the
h i g h e r t h a n t h e t e r m i n a l s p e e d , the m e l t i n g w a t e r s u r f a c e w i l l
airspeed
tend
it,
I c e sphere
on w i r e l o o p
C o l d gas
Filter
1
I
H o t gas
Fig.7. 4
Melting
c h a m b e r used by
Drake(19G*)
B rass h ol d e r
Ice p a r t i c l e
L
I
Thermocouple
Gauze
7.5
screen
Modified
probe
Insulator
tunnel
section
used w i t h w i r e
support
56.
t o v i b r a t e and r i p p l e more t h a n i n n a t u r e , p o s s i b l y e n h a n c i n g c h a r g i n g .
T h e r e f o r e i t was d e c i d e d t o t r y t o d e v e l o p a more r e a l i s t i c method o f
support.
Z&LL2
A s t r a i g h t wjrp
support
W a t e r d r o p s were f r o z e n o n t o a 130 Hm p l a t i n u m w i r e
and p l a c e d
i n the wind t u n n e l .
through the m e l t i n g drop u n t i l
(Fig. 7.3b).
I f the airspeed
( F i g . 7.3a.)
D u r i n g t h e m e l t i n g p r o c e s s t h e w i r e moved
i t was t a n g e n t i a l t o t h e w a t e r
surface
was n e a r l y e q u a l t o t h e t e r m i n a l speed o f
t h e d r o p t h e n i t would c o n t i n u e t o hang on t h e w i r e f i n a l l y f a l l i n g
f l y i n g o f f between 30 and 60s a f t e r m e l t i n g was c o m p l e t e .
the
J u d g i n g by"
speed w i t h w h i c h the p a r t i c l e l e f t t h e w i r e , the a i r s p e e d
w i t h i n 1 ms ^ o f t h e t e r m i n a l speed o f t h e d r o p .
t h e p a r t i c l e sometimes
like a jelly
or
was g e n e r a l l y
During the m e l t i n g process
r o t a t e d about a v e r t i c a l a x i s , and always v i b r a t e d
i n t h e l a t e r stages of m e l t i n g .
7 . 1 . 3 . Comparison o f t h e w i r e s u p p o r t w i t h D r a k e ' s
experiment.
I n t h e e x p e r i m e n t o f DRAKE ( l 9 6 8 ) , t h e m e l t i n g p a r t i c l e i s s u p p o r t e d
a j e t of a i r
particle.
a i r , the
( F i g . 7 . 4 ) w h i c h i s o f a p p r o x i m a t e l y t h e same w i d t h as
As i t i s
turbulence
in
the
l i k e l y t h a t t h i s j e t i s mixing w i t h the environmental
i n t h e r e g i o n o f t h e p a r t i c l e was p r o b a b l y g r e a t e r
than
i n t h e p r e s e n t i n v e s t i g a t i o n ( F i g . 7 . 5 ) , where t h e a i r f l o w has been smoothed
by a honeycomb, gauze and c o n t r a c t i o n s e c t i o n .
t h e m e l t w a t e r i s n o t c o n s t r a i n e d by t h e
to r o t a t e
i n a more n a t u r a l manner.
Because t h e s u r f a c e o f
s u p p o r t t h e whole p a r t i c l e i s
W h i l e i t m i g h t be a r g u e d
free
that
microturbulence i s probably present i n thunderclouds, t h i s low turbulence
system has t h e a d v a n t a g e o f g i v i n g t h e p a r t i c l e more d e g r e e s o f f r e e d o m
t h a n p r e v i o u s methods o f
7.2.
support.
THE EXPERIMENTAL PROCEDURE
7 . 9 . 1 P r e p a r a t i o n o f the ice
particles.
The i c e p a r t i c l e s were p r e p a r e d
c o u l d e a s i l y be c l e a n e d .
i n s p e c i a l moulds ( F i g . 6 , 1 )
which
The p l a t i n u m w i r e was s o l d e r e d t o t h e end o f
a s h o r t l e n g t h o f b r a s s r o d w h i c h c o u l d be p l a c e d i n a h o l d e r f i x e d t o
the
Stand
tor
ice p a r t i c l e h o l d e r
Double
L am p
glazed
/
1
77TTTT77.
v.
V,
V.
'a
\
\
Alunn in i u m
Ice r e J e a s e p r o b e
\
Fig.7.7
The
refrigerator
window
Wood
V,
57.
baseplate of the mould.
water drop which was
The wire then passed through t h e centre of the
t
suspended from the p l a t i n u m w i r e Jftoop.
The
drop was
nucleated e i t h e r by i c e c r y s t a l s produced by l i q u i d n i t r o g e n , or by small
c r y s t a l s on the end of clean p l a t i n u m w i r e .
A f t e r n u c l e a t i o n the drop
1
was allowed t o freeze completely before being released from the mould oy
h e a t i n g the w i r e loop w i t h an e l e c t r i c c u r r e n t .
wire and
The
brass rod w i t h the
i c e p a r t i c l e attached could then be removed from i t s mould w i t h
tweezers and screwed i n t o the h o l d e r ( F i g . 6.1).
The
i c e p a r t i c l e s were
f r o z e n i n a r e f r i g e r a t o r and t r a n s f e r r e d t o the c o l d room i n a perspex
box t o prevent m e l t i n g .
7.2.2
Examination
of the i c e p a r t i c l e s *
A r e f r i g e r a t o r was m o d i f i e d t o enable the ice p a r t i c l e s t o be studied
under a microscope before m e l t i n g ( F i g . 7.7).
capable of m a i n t a i n i n g temperatures
reach - 15°C
This r e f r i g e r a t o r
was
down to -13°G and on cool days could
and so was used t o freeze the water drops.
A,n Olympus Zoom -
Stereo microscope was placed on the wooden top o f the r e f r i g e r a t o r and
focused on t h e i c e sample which was held i n the stand.
The advantages of
t h i s microscope were the l a r g e working d i s t a n c e , and the wide f i e l d of
view which enabled the whole p a r t i c l e t o be s t u d i e d s i m u l t a n e o u s l y , even
at the maximum m a g n i f i c a t i o n of 40x.
The microscope could a l s o be
w i t h a camera but i n order t o speed up the experiments
only b r i e f
fitted
notes
of bubble s i z e spectrum, degree of o p a c i t y and the presence of cracks were
made.
The dimensions o f the p a r t i c l e s i n 3 m u t u a l l y p e r p e n d i c u l a r
d i r e c t i o n s were measured w i t h a r u l e r .
As the p a r t i c l e s were n o t r e g u l a r
a more accurate method o f assessing the mass was d i f f i c u l t w i t h o u t r i s k
of
contamination.
7.2.3. The m e l t i n g stage.
In o r d e r t o increase the m e l t i n g r a t e an attempt was made t o b u i l d
a h u m i d i f y i n g u n i t which would reduce the wet b u l b depression i n the working
section.
E a r l y experiments
w i t h passing steam i n t o the t u n n e l f a i l e d
Temperature
°C
Pi
Ambient
tern perature
10
Fig.7 ?
The s u r f a c e t e m p e r a t u r e
of a n
ice sphere during
freezing
58.
because o f condensation
and subsequent blockage due t o water f r e e z i n g i n t h e
pipes l e a d i n g i n t o t h e c o l d room.
A h u m i d i f i e r c o n s i s t i n g of a deep t r a y
of water and a 100 W lamp bulb d i d increase the h u m i d i t y s l i g h t l y b u t w i t h
the h i g h f l o w r a t e o f a i r i n t h e t u n n e l a more s o p h i s t i c a t e d device would
be needed t o b r i n g t h e r e l a t i v e h u m i d i t y up t o 90%.
capacity
The e x t r a h e a t i n g
d i d enable t h e m e l t i n g r a t e s t o be increased d e s p i t e t h e increased
wet b u l b depression*
A t t h e maximum m e l t i n g r a t e a t t a i n a b l e a 4 mm i c e
sphere melted i n 2.5 minutes*
MASON (1956) c a l c u l a t e d t h a t a 4 mm s o l i d i c e
sphere would m e l t i n 3 minutes w h i l e f a l l i n g from the Q°C l e v e l i n a c l o u d ,
assuming a s a t u r a t e d a d i a b a t i c lapse r a t e .
D u r i n g m e l t i n g t h e p a r t i c l e could be viewed through t h e m i r r o r i n t h e
w i n d t u n n e l and notes were made of the s t a t e and manner of m e l t i n g -
These
could be synchronised w i t h t h e records of temperature and charging c u r r e n t
by using t h e event marker o n t h e u l t r a v i o l e t r e c o r d e r .
An idea of the
airspeed was obtained by n o t i n g the path of t h e drop a f t e r i t l e f t , , the
wire._ A f t e r t h e m e l t i n g run was. completed any water l e f t i n t h e working ,
s e c t i o n was removed w i t h t i s s u e paper f i x e d t o the end o f a piece o f w i r e *
7.2.4
Precautions fp p r e v e n t contamination o f the ice p a r t i c l e s *
The w i r e fcoops i n t h e i c e moulds and t h e p l a t i n u m wire supports were
cleaned before use by e l e c t r i c a l l y h e a t i n g t o white heat.
experiments
Between
t h e wire supports were stored i n deionized water.
The p i p e t t e s
and t h e o t h e r glassware were cleaned i n t h e same manner as described i n
Chapter 6*
The tweezers were washed i n deionized water a f t e r use. A l l t h e
equipment used t o manipulate t h e water and i c e specimens was s t o r e d i n a
glove box t o prevent contamination by d u s t .
7f3 lf
t
PegcrtpUPft
The p a r t i c l e s were u s u a l l y misshapen spheres due t o t h e d i s t o r t i o n
o f t h e o r i g i n a l drop under g r a v i t y w h i l e hanging i n the mould.
Their
masses ranged from 25 t o 60 mg b u t t y p i c a l dimensions were 4*5mm x 4.5mm
x 4mm and a mass o f 36 - 40 mg.
opaque.
Usually t h e centre o f t h e p a r t i c l e
looked
A f t e r being examined under t h e microscope t h e p a r t i c l e s were
59.
c l a s s i f i e d i n t o 2 groups, namely m i l k y and bubbly.
I n bubbly i c e t h e bubbles
were g e n e r a l l y d i s t i n g u i s h a b l e w i t h c l e a r i c e v i s i b l e between them.
Milky ice
contained patches where the bubbles could n o t be e a s i l y r e s o l v e d and the i c e
looked opaque because o f a mass o f t i n y bubbles less than 20 Jim i n diameter.
In general t h e lower t h e f r e e z i n g temperature the more l i k e l y the i c e was t o be
m i l k y and the bubbles s m a l l .
I n the range
-6 t o -9°C the i c e was r a r e l y
m i l k y and u s u a l l y very c l e a r o u t s i d e the c e n t r a l bubbly area.
I n t h e range
-13 t o -15 C t h e i c e u s u a l l y contained a m i l k y c e n t r a l r e g i o n , or a t l e a s t
a v e r y opaque are made up o f a mass o f bubbles.
Large bubbles were l e s s
common i n such i c e , b u t i t was e v i d e n t t h a t more a i r was trapped than i n i c e
frozen a t h i g h e r temperatures.
This i s c o n s i s t e n t w i t h the increase o f gas
s o l u b i l i t y i n water as the temperature f a l l s .
7.3.2
The f r e e z i n g process
The behaviour o f t h e water drops d u r i n g f r e e z i n g was s t u d i e d by
C
r e p l a c i n g one of t h e i c e moulds w i t h a constantan feoop and making a copper
constantan thermocouple j u n c t i o n on the loop i n c o n t a c t w i t h the surface
of t h e water drop. ( F i g . 7.8) shows t h e v a r i a t i o n i n surface temperature
during the f r e e z i n g process f o r a 3-g- mm diameter water drop f r e e z i n g i n an
environment a t -11°C.
During t h e p e r i o d AB the temperature of t h e drop f a l l s
towards t h e ambient temperature o f the cold room.
At B the drop i s nucleated
by an i c e c r y s t a l and t h e s u r f a c e temperature r a p i d l y r i s e s t o about -3°C
and remains constant f o r about 5 minutes.
This may be e x p l a i n e d by assuming
t h a t i n i t i a l l y an i c e s h e l l raj. i d l y forms and the l a t e n t heat released heats
the
drop u n t i l the i c e - w a t e r i n t e r f a c e i s a t 0°G.
H e r e a f t e r t h e r a t e of
f r e e z i n g i s governed by t h e c o n d u c t i o n o f the l a t e n t heat through the i c e
s h e l l and i t s r e l e a s e t o t h e environment.
of
the p a r t i c l e w i l l be below 0°C.
Hence the s u r f a c e temperatures
At a time D the i f r e e z i n g i s complete
and t h e p a r t i c l e cools t o t h e ambient temperature E and f i n a l l y t o t h e
wet b u l b temperature FThis experiment confirmed t h a t l i t t l e e r r o r was i n t r o d u c e d i n t o t h e
measurement o f t h e f r e e z i n g temperature, provided thac n u c l e a t i o n d i d n o t
occur u n t i l t h e drop had been i n the r e f r i g e r a t o r f o r 5 minutes a t -11°C
60.
and
longer f o r higher temperatures.
A t t h i s time t h e r a t e o f c o o l i n g had
1
dropped t o 0.2°C min"* .
As only 10 - 15% o f the water freezes d u r i n g t h e i n i t i a l
growth phase (Equation
rapid ice
7.2), the a i r bubbles s t r u c t u r e i s probably g r e a t l y
i n f l u e n c e d by the r a t e o f l o s s o f heat d u r i n g the slow growth p e r i o d .
This
heat l o s s can be c a l c u l a t e d from t h e d u r a t i o n o f t h e slow growth phase and
the supercooling
of the drop
T.
The mass m o f t h e water f r o z e n d u r i n g
the f a s t phase i s r e l a t e d t o the t o t a l mass M o f the d r o p , t h e s p e c i f i c
heat s o f water and the l a t e n t heat L o f water by equation 7.1.
/
M
•*•
s
AT
—
..
mL
r:
jjj
a o « o » « o « «
s
* .
7« 1
~ F r a c t i o n of drop frozen ( f )
7.2
The r a t e o f heat l o s s H d u r i n g t h e slow growth phase i s r e l a t e d t o
the d u r a t i o n t o f t h i s phase by equation 7.3
H
=
M(l - f ) L
7.3
t
For the 3-£ mm drop i n F i g , 7.8 t h e heat loss as given by equation 7*3 i s
21 mW. This i s n e a r l y an order o f magnitude l e s s than from, a comparable
drop f a l l i n g a t i t s t e r m i n a l speed i n a s a t u r a t e d atmosphere a t t h e same
temperature ( c f . s e c t i o n 8.4).
7.4.
7.4.1
THE ANALYSIS OF THE MELTING EXPERIMENTS
The c o n t r o l o f the important parameters.
As has been described
ice
i n s e c t i o n 2*4, the e l e c t r i f i c a t i o n of m e l t i n g
i s h i g h l y dependent n o t o n l y on the m e l t i n g c o n d i t i o n s , b u t also on
the chemical composition o f t h e water and t h e way i n which the p a r t i c l e
was f r o z e n . DRAKE (1968) has suggested t h a t m e l t i n g r a t e and water p u r i t y
have t h e g r e a t e s t e f f e c t on m e l t i n g e l e c t r i f i c a t i o n , b u t e a r l y i n the
present i n v e s t i g a t i o n i t became apparent t h a t t h e temperature a t which
the water was f r o z e n was also i m p o r t a n t *
The c h i e f d i f f i c u l t y experienced i n analysing t h e data was t h a t t h e
experimental
c o n d i t i o n s could not be r e g u l a t e d a t w i l l -
time t h e thermostat
For most o f t h e
on t h e c o l d room was n o t o p e r a t i o n a l so t h e temperature
of the c o l d room depended t o a l a r g e e x t e n t on the l a b o r a t o r y temperature.
(D
if)
I*
0)
CD
en
en
(V
cn <
0) 3
I
o
61.
This was o f importance
because the m e l t i n g r a t e of the p a r t i c l e s depended
l a r g e l y on t h e r e l a t i v e h u m i d i t y of the a i r . This f e l l o f f r a b i d l y w i t h
increase o f the temperature
heated.
through which the a i r i n t h e wind t u n n e l was
The f r e e z i n g temperature
of the p a r t i c l e s could be c o n t r o l l e d
t o + 2°C and care was taken t o nucleate t h e drops when t h e y were w i t h i n
1°C of the environmental
temperature.
The mass of t h e ice p a r t i c l e s could be measured t o + 25%
9
a more
accurate measurement was made d i f f i c u l t by t h e need t o a v o i d c o n t a m i n a t i o n ,
Same
and t h e i r i r r e g u l a r shape.
of measurements.
T h e ^ p u r i t y o f t h e water was used f o r each s e t
The carbon d i o x i d e c o n c e n t r a t i o n i n t h e water would probably
depend on t h e temperature
a t which the i c e was melted
( c . f Chafer 9) and
so d i d not have t o be c o n t r o l l e d .
The maximum r a t e of performing t h e m e l t i n g experiments
was 3 per day
of which o n l y about 2 out of 3 could be s u c c e s s f u l , the o t h e r s being r e j e c t e d
u s u a l l y because the i c e p a r t i c l e was dropped o r t h e p l a t i n u m w i r e d i d n o t
pass through the c e n t r e of t h e p a r t i c l e .
This l i m i t e d the number o f p a r t i c l e s
studied and t h e r e f o r e made t h e a n a l y s i s o f m e l t i n g e l e c t r i f i c a t i o n i n terms
of a l l the i m p o r t a n t v a r i a b l e s d i f f i c u l t .
designing the experiment
support system.
This l i m i ^ t i o n was accepted i n
i n order t o attempt t o o b t a i n a more r e a l i s t i c
However, because of the d i f f i c u l t y cjj r e g u l a t i n g a l l the
v a r i a b l e s the conclusions are l i m i t e d i n a way which i s o f t e n found i n
outdoor
s t u d i e s i n atmospheric
electricity.
7.4.2. The e l e c t r i c charge produced by m e l t i n g i c e .
A l l t h e 150 i c e p a r t i c l e s melted on p l a t i n u m wires gained a p o s i t i v e
charge and on no occasion was negative charging observed.
p a t t e r n of e l e c t r i f i c a t i o n i s shown i n F i g . 7.9.
The t y p i c a l
For over h a l f the
m e l t i n g p e r i o d no c h a r g i n g was measured and t h e advent o f water
rippling
over t h e i c e surface was u s u a l l y accompanied by a small p o s i t i v e c u r r e n t
o f a few fA. When t h e p a r t i c l e s t a r t e d t o hang on t h e wire and became
f r e e t o move, t h e r a t e o f charging increased r a p i d l y t o a d e f i n i t e
maximum.
U s u a l l y t h e p a r t i c l e would then leave t h e w i r e and s t i c k t o the
F i g 7.10
Charge separated
Pilot
by m e l t i n g 4 m m
d i o m e t e r i c e particles
i nvest igat ion
Freezing temperature
Conductivity
*C
-1
of w a t e r = 7 5 ^ m h o s c m
Charge
PC
0
4
3
2
T
4
Melting
(arbitrary
rate
units )
T
5
6
7
62.
sides of the wind t u n n e l .
I f tine charging continued on t h e sides f o r more
than a few seconds i t was concluded
t h a t the
e l e c t r i f i c a t i o n process was
not complete a t the moment the p a r t i c l e l e f t t h e w i r e and the o b s e r v a t i o n
was
rejected*
This p a t t e r n o f e l e c t r i f i c a t i o n i s very s i m i l a r t o t h a t
observed by DRAKE (1968) , but no negative charge was observed e a r l y i n the
m e l t i n g process.
The
value of the charge produced was estimated by summing the average
i
charge produced i n 1 minute i n t e r v a l s up t o the time a t which the c u r r e n t
decayed w i t h the time constant o f the V.R.E. Values o f t h e d r y b u l b and
wet bulb depression as w e l l as the temperature
o f the a i r near the ice
p a r t i c l e were read o f f the r e c o r d e r c h a r t and used t o c a l c u l a t e the average
m e l t i n g r a t e d u r i n g t h e l a s t minute of m e l t i n g .
7.4.3
A n a l y s i s of e a r l y m e l t i n g experiments w i t h deionized water•
15 i c e p a r t i c l e s o f about 4 mm e q u i v a l e n t d i a m e t e r
i o n i z e d water w i t h c o n d u c t i v i t y 0.75^mho cm
made from de-
? were melted.
charge produced was + 3 . 5 + 0.5 pC, which corresponds
r a t i o o f + 0.11 + 0.03
?
The average
t o a charge/mass
pC mg ^ (0.37 esu g ^ ) ; the e r r o r s quoted
standard d e v i a t i o n s about the mean.
are
This compares w i t h 0.4 pC mg ^
measured by DINGER and GUNN (1946) a t m e l t i n g r a t e s n e a r l y 200 times
greater.
DRAKE found e l e c t r i f i c a t i o n of + 0.2 pC mg * f o r i c e spheres
of s i m i l a r water p u r i t y when vigorous convection d i d not develop i n the
m e l t w a t e r , but t h i s increased t o + 1.0 pc mg
w i t h the onset o f
convection.
U n f o r t u n a t e l y d u r i n g these experiments the h u m i d i t y measurements
were s u b j e c t t o a systematic e r r o r * and i t was not p o s s i b l e t o quote
an absolute value f o r the m e l t i n g r a t e .
I n F i g . 7-. 10 the charge
separated i s p l o t t e d a g a i n s t m e l t i n g r a t e f o r i c e f r o z e n between -11
and -13°C.
There i s a d e f i n i t e tendency f o r t h e charging t o increase
with melting rate.
DRAKE d i d not measure the m e l t i n g r a t e i n absolute
terms but i t i s probably t h a t these data correspond
t o the lowest
63.
m e l t i n g r a t e s t h a t he s t u d i e d , as the t o t a l time f o r the i c e t o melt was on
average 8 minutes compared w i t h 90 seconds t o 2 minutes shown i n the
' t y p i c a l records' i n DRAKE'S paper.
to
to
o
o
o
to
CO
00
to
in
2Ly
E
to
6
CO
to
0)
0>
0
T
o
o
o
0)
O
0
>
tn
0>
to
oo
0>
o
CM
64,
CHAPTER
8
THE EFFECT OF MELTING RATE AND FREEZING TEMPERATURE
ON MELTING ELECTRIFICATION.
8.1. MELTING RATE AND THE ENVIRONMENT.
8.1.1 The m e l t i n g o f f a l l i n g n a t u r a l small h a i l .
MASON (1956) has solved the heat t r a n s f e r equations f o r i c e spheres
f a l l i n g from the 0°C l e v e l i n a c l o u d , assuming a wet a d i a b a t i c lapse r a t e .
This c a l c u l a t i o n shows ( F i g * 8.1) t h a t a 4 mm diameter i c e sphere o f s p e c i f i c
g r a v i t y 0.9 w i l l have completely melted by t h e time i t reaches the +10°C l e v e l ,
approximately 3 minutes a f t e r t h e m e l t i n g s t a r t e d .
The average m e l t i n g r a t e
d u r i n g t h e l a s t minute of m e l t i n g i s 14 mg min * f o r a 4 mm p a r t i c l e and
9 mg min ^ f o r a 3 mm p a r t i c l e .
I f the m e l t i n g h a i l were t o f a l l out o f the
cloud then t h e m e l t i n g r a t e would be reduced because t h e heat gained by
condensation o f water vapour would be decreased.
MASON also showed t h a t i c e
p a r t i c l e s of lower d e n s i t y would melt more s l o w l y because of t h e i r lower f a l l
speeds.
An upper l i m i t t o t h e m e l t i n g r a t e s o f i c e p a r t i c l e s o f 4 mm diameter
and l e s s can be set a t 14 mg min "'*• As the a i r i n the wind t u n n e l was n o t
s a t u r a t e d i t was intended t o t r y t o a l t e r t h e a i r temperature and r e l a t i v e
h u m i d i t y so t h a t the i c e p a r t i c l e s could be melted a t r e a l i s t i c m e l t i n g
ra te s •
8.1.2
The m e l t i n g o f i c e p a r t i c l e s i n the wind t u n n e l .
The r a t e of heat f l o w t o a m e l t i n g i c e sphere has been g i v e n by LUDLAM
(1950) as
Heat Flow = 4 *
[«^ K ^ T - T ^ + C L D ( P - P , ^ ) j j
8.1
m
where b i s the r a d i u s o f the p a r t i c l e , T i t s surface t e m p e r a t u r e , T
s
the d r y bulb temperature o f the a i r away from the p a r t i c l e , P, P
(T )
sa "t s
:
are
the c o n c e n t r a t i o n s o f water vapour i n the remote environment and a t
the
water surface r e s p e c t i v e l y .
2.56 x lO^J kg
10~
5
2
_ 1
The l a t e n t heat of vaporization»
=
the d i f f u s i o n c o e f f i c i e n t of water vapour, D = 2.4 x
2
m s , t h e c o n d u c t i v i t y o f a i r ^ K - 2.5 x 1 0 " Wnf
1
1
°K~ .
65.
The
c o e f f i c i e n t s C, and C take i n t o account the e f f e c t of v e n t i l a t i o n on the
n
m
heat and vapour f l o w and are given by
C
h
= 1.6 + 0.3
C
m
= 1.0 + 0.23
For a 4 mm
16.3
and
(Re)^"
(KRAMERS, 1946)
(Re)^
(pROSSLINS, 1938)
sphere at t e r m i n a l speed, Reynolds number
C
=
Re = 2400
5
=
12.2.
m
The
d e n s i t y of w a t e r vapour P i s equal t o the s a t u r a t i o n d e n s i t y of the
air
a t t h e dew
point P ^ ( T ^ ^ ) -
may
be taken as 0°C
The
surface temperature of the m e l t i n g sphere
as t h i s i n t r o d u c e s a maximum e r r o r of 3^ i n t o the f i n a l
value o f the heat f l o w .
For values of dew
p o i n t between 0 and
-10°C the data given by KAYE and
LABY (1949) f i t s the f o l l o w i n g r e l a t i o n
P J
sat
T
where T,
dew
dew'
A
) - P
and T
2
x ( T ) = (5.0 T.
sat s'
dew
- 0.1 T , ) x K f
dew'
4
3
*g m"
y
°C"
1
...8.2
are measured i n °C.
s
So the r a t e o f heat f l o w i n t o a m e l t i n g i c e sphere f a l l i n g a t t e r m i n a l
speed may
be obtained
f l o w = 4 Ub[c,
t
K T + G
h
a
Equation 8.3 was
ice
by s u b s t i t u t i n g equation 8.2 i n t o 8.3.
I
m
D (P
v
. (T.
sat
) - P
dew
Rate o f heat
. (0)f\
sat*
8.3
J
used to evaluate the r a t e o f heat f l o w i n t o the m e l t i n g
p a r t i c l e s i n t h e wind t u n n e l .
between approximately
The e r r o r i n the r a t e o f heat f l o w v a r i e s
A0% f o r a heat f l o w r a t e of 30 mW to 25$ a t 100 mW.
At low heat f l o w r a t e s the dominant e r r o r i s associated
of dew p o i n t which could o n l y be estimated
to ±
w i t h the measurement
despite an e r r o r of
o n l y + l-£# i n the measurement of r e l a t i v e h u m i d i t y . At h i g h m e l t i n g r a t e s
the c h i e f source of e r r o r was the measurement of the r a d i u s of the p a r t i c l e
which was
8.2
8.2.1
e s t i m a t e d . t o + 10%.
THE
EFFECT OF MELTING RATE QN ELECTRIFICATION.
Mass, c o r r e c t i o n for e v a p o r a t i o n .
A t low m e l t i n g r a t e s ao appreciable
f r a c t i o n of the
d u r i n g the 15 minutes i t i s i n the a i r s t r e a m .
melted was
estimated
of the t u n n e l to 0°G
i n 2 stages.
ice may
evaporate
The mass o f i c e a c t u a l l y
F i r s t l y d u r i n g the i n i t i a l
the t o t a l amount o f heat l o s t due
slow h e a t i n g
t o evaporation
during
Fig. 8 2
The effect of m e l t i n g r a t e on m e l t i n g e l e c t r i f i c a t i o n
Artificial
cloudwattr
Electrification
p C mg-1
b e t w e e n -10 and - 1 3 C
Drops f r o z e n in still a i r
x
•0 6
•05 H
•04 -
k
*
x
-0%
*
-Hf
4-
*
Average melting r a t e
I
m
t
«
F
T
r
1
—r~
F
1
1
r-
. -1
10 m g m i n
E l e c t r f f i c a t ion
p C mg"
1
Drops
frozen at
-11*3**5*C
04 H
•o5 -j
• 0<# -
x *
•03 «
x
*
ol X
oi
X
-
A v e r a g e m e l t i n g rate
-i
1
>
r
""i
$°
1
i
'
1
r
IOO
?
J
1
1
1 —
i$o
. .
F i g . 8.3
The effect
of
melting r a t e
Artificial
Electrification
pC m g
Drops
frozen
in
on
electrification
cloudwater
still
air
1
r
at
#
-10*3t'5 C
1
04
•03
•oz
•O)
i
i
—i—
SO
r
1
r
S
10
frozen
at
>
I
.
1
ISO
-I
rate
for
last minute
of
~13-t*3C
Electrification
pC mg
1
OS
.0 3
•01
f
f
T
I
1
»
T
i
50
l
l
too
—f-
—r
10
IS
A v e r a g e melting
\
mW
20
)S
A v e r a g e meltfng
Drops
T
— i —
100
-
rate
10
?
-tmW
melting
66.
a time t , was
4 7rbfc
L
D ( P
.(T.
) - P
. ( i T.
))1
8.4
^ m v
sat dew
sat * dew «*
This f o l l o w s from e q u a t i o n s 8 . 1 and 8.2 assuming t h a t the average d i f f e r e n c e
i n temperature between the dew p o i n t and t h e surface of the i c e i s i T,
* dew
r
r
During the m e l t i n g process the temperature o f the surface i s approximately
0°C so the heat l o s t , i n t i m e t ^ , due to e v a p o r a t i o n i s simply
Ht = 3 . 9
b t_
2
Tl.09
*-
Using equations 8.4
+ 0.022
T
dew
and 8.5
T
1
2
8.5
dew •*
the t o t a l amount of water l o s t by
evaporation was c a l c u l a t e d f o r a l l the i c e p a r t i c l e s .
At a melting rate
corresponding t o 20 mW, 50% o f the mass evaporated and a t 100 mW only 5%
evapora ted.
9«2«2t
T^e
results
for a r t i f i c i a l
glgudwflter*
The charge separated by the m e l t i n g of the a r t i f i c i a l cloudwater samples
was always of the same s i g n , raamely the meltwater became p o s i t i v e l y charged.
I f a l l the samples which were frozen i n s t i l l
a i r between -10 and -15°C
were
considered then there was no apparent r e l a t i o n s h i p between maximum m e l t i n g
rate and charge separated.
For the range -10
t o -13°G "there i s a trend
towards an increase i n c h a r g i n g w i t h increased m e l t i n g r a t e ( F i g . 8 . 2 ) .
the
range -lOj- t o -11%
If
±s taken then t h e v a r i a t i o n becomes more marked
w i t h almost a f a c t o r 10 increase i n e l e c t r i f i c a t i o n between m e l t i n g r a t e s
of
10 and 15 mg min * ( F i g . 8 . 2 ) .
F i g . 8.3 shows s i m i l a r though less w e l l
defined v a r i a t i o n s of e l e c t r i f i c a t i o n w i t h m e l t i n g r a t e f o r water drops
f r o z e n a t about -10 and - 1 3 ° C .
of
f r e e z i n g o f t h e water drop has an i m p o r t a n t e f f e c t on m e l t i n g e l e c t r i f i - ?
cation.
of
The probable e r r o r i n t h e r a t i o of charge to mass i s i n the region
40 t o 50% due t o an u n c e r t a i n t y i n the mass of + 25% and i n the charge
of + 20%*
the
These r e s u l t s suggest t h a t the temperature
The e r r o r i n the measurement of charge i s due t o the f a c t t h a t
molten drops f a l l o f f the wire d u r i n g the l a s t stages o f e l e c t r i f i c a t i o n .
Fig 8.4
The effect
of
the type of
x
•
—
support
@
0
@ —
Electrification
30
p C m g1
20
O
0 0
10
O
0
0
t
»
•
1
1
1
I
Freezing
Conductivity
Melting
Drops
1
1
temperature
of
water
rate y 1 5 m g
frozen
1
in still
1
1
1
°C
10 p mho
min
air
1
cm
67.
8 > 2 . 3 Comparison w i t h p r e v i o u s w o r k .
These r e s u l t s a g r e e q u a l i t a t i v e l y w i t h the
that the e l e c t r i f i c a t i o n
melting rate
increased
o f DRAKE (1968)
by a b o u t an o r d e r o f magnitude when t h e
and wind speed became s u f f i c i e n t t o cause v i g o r o u s c o n v e c t i o n
in the melt water.
DRAKE d i d n o t measure t h e m e l t i n g r a t e a b s o l u t e l y so a
d i r e c t comparison i s not p o s s i b l e .
8.3 t h a t
observations
There i s
the l o w e r t h e f r e e z i n g t e m p e r a t u r e
some e v i d e n c e
the sharper
f r o m F i g s . 8.2?
the t r a n s i t i o n
between t h e low and h i g h e l e c t r i f i c a t i o n r e g i o n s o f the g r a p h s .
(1956) has c a l c u l a t e d t h a t t h e average m e l t i n g r a t e d u r i n g the
o f m e l t i n g o f a 4mm s o l i d
MASON
l a s t minute
i c e p a r t i c l e f a l l i n g f r o m the 0°C l e v e l
in a
cloud
-1
i s 14 mg m i n
.
So i t seems p o s s i b l e t h a t such a p a r t i c l e would d e v e l o p '
vigorous convection i n the meltwater ( c f F i g . 8 . 2 ) •
U n f o r t u n a t e l y i t was
d i f f i c u l t t o observe t h e p a r t i c l e c l e a r l y enough t o v e r i f y t h a t t h e
increase
i n e l e c t r i f i c a t i o n c o i n c i d e d w i t h the onset o f convection*
DRAKE f o u n d t h a t t h e t o t a l
/ ™4 \
comparable p u r i t y
(10
c h a r g i n g p r o d u c e d by m e l t i n g p a r t i c l e s o f
~1
M ; was about 0 . 4 pC mg
0 . 0 3 pC mg ^ i n t h e absence o f c o n v e c t i o n .
a t h i g h m e l t i n g r a t e s and
A l t h o u g h he does n o t quote
a c t u a l m e l t i n g r a t e s i t seems l i k e l y f r o m t h e d e s c r i p t i o n o f the
t h a t the
experiment
range o f m e l t i n g r a t e s was s i m i l a r t o t h a t i n t h e p r e s e n t
These v a l u e s
f o r the
i n F i g s . 8 . 2 and 8 . 3 .
r a t i o o f charge
Two p o s s i b l e
the
investigation.
t o mass are a f a c t o r o f 10 g r e a t e r
reasons f o r t h i s d i f f e r e n c e are
than
the
d i f f e r e n t methods o f s u p p o r t i n g t h e p a r t i c l e and t h e f a c t t h a t DRAKE f r o z e
the water drops
i n an a i r s t r e a m as opposed t o s t i l l
air.
8.3 THE EFFECT OF THE SUPPORT
To see w h e t h e r t h e d i f f e r e n c e i n t h e m a g n i t u d e o f c h a r g i n g was due
to
t h e d i f f e r e n t ways o f s u p p o r t i n g t h e i c e p a r t i c l e s 10 f r o z e n w a t e r d r o p s
were m e l t e d on ij?
mm d i a m e t e r l o o p s o f p l a t i n u m w i r e .
These r e s u l t s
compared w i t h t h o s e o f a s i m i l a r e x p e r i m e n t w i t h p a r t i c l e s on t h e
w i r e s u p p o r t used i n t h e e x p e r i m e n t d e s c r i b e d
i n Section 8.2.
seen i n F i g . 8 . 4 t h e r e was no s i g n i f i c a n t d i f f e r e n c e between
were
straight
As can be
the
00
LP
(I
i£>
Q
ft
n
10
0)
O O G
QO
OO
-J
N
0)
f
O
o
Fig.8 6
Heat
flow
from
a
w a t e r
drop
during
Heat
freezing
f I ow ra t e
mW
200
3 m m
d la
ventilated
at
11ms
1
l?0
( Theory)
I GO
ILo
HO
I00
60
( Exper imen t)
3 mm
dia
stagnant
lo
air
(corrected )
— i
1
1
-12
-jo
Air t e r n p e r a t u re
°c
1
-%
i
~&
»
r
-4
-2
68.
e l e c t r i f i c a t i o n p r o d u c e d by p a r t i c l e s on e i t h e r s u p p o r t .
I n both experiments
t h e m e l t i n g r a t e s were j u d g e d t o be h i g h enough f o r v i g o r o u s e l e c t r i f i c a t i o n
t o have o c c u r r e d .
C l e a r l y t h e d i f f e r e n t t y p e s o f s u p p o r t do n o t cause an
o r d e r of magnitude d i f f e r e n c e i n e l e c t r i f i c a t i o n a l t h o u g h p o s s i b l y the
higher turbulence present
i n DRAKE'S e x p e r i m e n t c o u l d be i m p o r t a n t .
f
8 . 4 FREEZING RATE AND MELTING ELECTRIFICATION
8*4.1
Water d r o p s f r o z e n i n s t i l l
a i r - Pure
water*
F i g . 8 . 4 shows t h a t t h e t e m p e r a t u r e a t w h i c h t h e d r o p s were f r o z e n has a
H
marked e f f e c t on t h e e l e c t r i c a t i o n p r o d u c e d on m e l t i n g .
The p r o b a b l e
accuracy
o f t h e f r e e z i n g t e m p e r a t u r e was + 1°C due to the t h e r m o m e t e r and d r o p b e i n g
l o c a t e d a b o u t 30 cm a p a r t .
temperatures
decreasing
T h e r e i s some e v i d e n c e t h a t
b e l o w - 12°C t h e charge
temperature.
separation
for freezing
increases r a p i d l y
with
I t was n o t e d i n C h a p t e r 7 t h a t b e l o w - 12°C t h e
ice
becomes more l i k e l y t o be m i l k y .
8.4.2.
Water d r o p s f r o z e n i n a t l l j L a i r - A r t i f i c i a l
The a r t i f i c i a l
c l o u d w a t e r samples
water.
showed a s i m i l a r v a r i a t i o n o f m e l t i n g
e l e c t r i f i c a t i o n w i t h f reezing temperature
r a t e was s u f f i c i e n t t o e n s u r e t h a t
cloud
( F i g . 8.5) provided t h a t the
s m a l l v a r i a t i o n s i n m e l t i n g r a t e were n o t
important.
Below a m e l t i n g r a t e o f 14 mg min ^ t h e e f f e c t o f f r e e z i n g
temperature
i s a l t e r e d by t h e s h a r p changes i n t h e m e l t i n g
- m e l t i n g r a t e graphs
8.4.3
(cf. Fig. 8.2,
The f r e e z i n g r a t e and t h e
The f r e e z i n g r a t e
g o v e r n e d by t h e
rate
electrification
8.3).
environement.
d u r i n g t h e main p a r t o f the f r e e z i n g p r o c e s s
o f heat
l o s s f r o m t h e s u r f a c e o f the p a r t i c l e .
h e a t l o s s f r o m t h e f r e e z i n g w a t e r d r o p s was d e t e r m i n e d by m o n i t o r i n g
d r o p t e m p e r a t u r e as d e s c r i b e d
heat
i n S e c t i o n 7.3<,2.
is
The
the
The v a r i a t i o n o f r a t e o f
l o s s w i t h a m b i e n t t e m p e r a t u r e i s p l o t t e d i n f i g . 8 . 6 f o r 3 . 5 mm d r o p s .
The d o t t e d l i n e shows a c o r r e c t e d v a l u e f o r 3 mm d r o p s assuming t h a t
heat
melting
loss
i s p r o p o r t i o n a l to the surface
The h e a t
loss
the
area*
f o r p a r t i c l e s i n an a i r s t r e a m was c a l c u l a t e d f r o m
e q u a t i o n 8 . 1 assuming t h a t t h e s u r f a c e t e m p e r a t u r e
o f t h e sphere was a t 0 ° C .
Fig.«.7
The effect
Deionized
Melting
of
freezing
water
rate
rate
on m e l t i n g
electrification
1-O^mhocm
) 1 4 mg
min
1
x
*
Frozen
@
0
Frozen
Drake
in
in
airstream
still
air
(196S)
E l e c t r i f ic a t i o n
1
pCmq
s
01
O
a
•
20
40
6o
Heat
IOO
flowrate
during
mW
120
i
I4.Q
freezing
160
190
69.
T h i s o v e r e s t i m a t e s t h e h e a t f l o w b u t as t h e s u r f a c e t e m p e r a t u r e v a r i e s b o t h
w i t h t i m e and f r e e z i n g r a t e
e s t i m a t e was n o t made.
i n an u n d e t e r m i n e d manner a more a c c u r a t e
I t can be seen f r o m F i g . 8 . 6 t h a t a 3mm d r o p f r e e z i n g
-1
i n an a i r s t r e a m moving a t 11 ms
similar particle
A particle
in s t i l l
d i s s i p a t e s 10 t i m e s as much h e a t as a
a i r even i f b o t h are
freezing at -12°C i n s t i l l
similar particle
i n an e n v i r o n m e n t a t
-12°G.
a i r d i s s i p a t e s as much h e a t as a
i n the a i r s t r e a m at - 2 ° C .
8 . 4 . 4 . The dependence
o f m a t i n g e l e c t r i f i c a t i o n on f r e e z i n g
rate.
The e l e c t r i f i c a t i o n s t u d i e s o f t h e m e l t i n g o f w a t e r d r o p s f r o z e n i n
a i r d e s c r i b e d i n s e c t i o n s 8 . 4 . 1 and 8 . 4 . 2 have shown t h a t t h e r e
f o r the c h a r g i n g t o i n c r e a s e
still
i s a tendency
as t h e f r e e z i n g t e m p e r a t u r e i s l o w e r e d .
The
e l e c t r i f i c a t i o n measured i n t h e s e e x p e r i m e n t s i s an o r d e r o f m a g n i t u d e l e s s
t h a n d e t e c t e d by DRAKE (1968) under s i m i l a r c o n d i t i o n s .
As t h e p a r t i c l e s
m e l t e d by DRAKE were f r o z e n i n an a i r s t r e a m t h e d i f f e r e n c e between t h e 2
s t u d i e s may be r e s o l v e d by s u g g e s t i n g t h a t t h e e l e c t r i f i c a t i o n was h i g h l y
dependent on t h e r a t e o f f r e e z i n g o f t h e w a t e r d r o p s .
The f r e e z i n g c o n d i t i o n s
were t h e r e f o r e a l t e r e d t o t e s t t h i s t h e o r y .
The w a t e r d r o p s were hung f r o m a l | ran l o o p o f p l a t i n u m w i r e and c o u l d
be f r o z e n i n an a i r s t r e a m , u s i n g a vacuum pump.
The a i r speed was 11 ms ^
and t h e a i r t e m p e r a t u r e c o u l d be m o n i t o r e d by means o f a c o p p e r - c o n s t a n t a n
thermocouple.
The r a t e o f heat
l o s s was c a l c u l a t e d as d e s c r i b e d i n the
p r e v i o u s s e c t i o n assuming t h a t t h e a i r was s a t u r a t e d .
As t h e a i r was sucked
f r o m t h e b o t t o m o f t h e r e f r i g e r a t o r where i t was i n e q u i l i b r i u m w i t h
ice,
and was n o t h e a t e d , i t seems p r o b a b l e t h a t t h e a i r was s a t u r a t e d .
The e l e c t r i f i c a t i o n was f o u n d t o i n c r e a s e
r a t e o f heat l o s s f r o m the f r e e z i n g d r o p .
d i s s i p a t i o n there
r a p i d l y w i t h the i n c r e a s i n g
A t low values o f heat
i s a good agreement between t h e r e s u l t s o f t h i s e x p e r i m e n t
and t h e e x p e r i m e n t w i t h the d r o p s f r o z e n i n s t i l l
air
(Fig, 8.7).
v a l u e s o f h e a t f l o w r a t e were p r o b a b l y o v e r e s t i m a t e s f o r t h e
As t h e
ventilated
O
mm
I mm
Frozen in still
air
at
-6-5'C
Frozen
in
0 too ^oo \xm
I t—i
Frozen
F i g . 8,B
The
still
I mm
0
in an
frozen
-1
11rns
water
0
airstream
drops
at
-12C
air
at~12-5C
Fig.g.9
Solubility
(Kayc
of a i r
and
in
water
Laby,196«)
Sol a b i l i t y
ml ml
1
• oS
>\
I
>
I
I
I
I
2-<?
i
i
I-9
oi
-0
OZ
o
T
20
- 10
Tempe ra t u r e
—?
~7—
10
20
30
70.
d r o p s t h e agreement may be b e t t e r t h a n i n f i g .
m a j o r s o u r c e o f i m p u r i t y i s a t m o s p h e r i c C®
2
a b o u t 0 . 1 pC m g "
1
when f r o z e n i n s t i l l
8.7.
F o r d e i o n i z e d w a t e r whose
the e l e c t r i f i c a t i o n increases
a i r a t a b o u t - 1 0 ° C t o 0 . 8 pC mg
1
from
when
f r o z e n i n t h e a i r s t r e a m a t t h e same t e m p e r a t u r e .
A d i r e c t c o m p a r i s o n w i t h t h e r e s u l t s o f DRAKE i s d i f f i c u l t because
a c t u a l s i z e , a i r s p e e d and r e l a t i v e h u m i d i t y were n o t g i v e n i n h i s
T a k i n g an a v e r a g e d i a m e t e r o f 3 mm and an a i r s p e e d o f 7 ms
s a t u r a t e d atmosphere
and assuming a
I f t h e a i r i n DRAKE's e x p e r i m e n t was n o t s a t u r a t e d
then
better.
AIR BUBBLES AND MELTING ELECTRIFICATION
K a t e r d r o p s f r o z e n i n an a i r s t r e a m a t l o w t e m p e r a t u r e s
w h i t e and opaque whereas d r o p s f r o z e n i n s t i l l
bubbly c e n t r e
variation
i s consistent with t h e r e s u l t s obtained
t h e f r e e z i n g r a t e s w o u l d be i n c r e a s e d and t h e agreement would be
8.5
paper.
d u r i n g f r e e z i n g i t i s p o s s i b l e t o show t h a t the
of e l e c t r i f i c a t i o n w i t h f r e e z i n g r a t e
a t Durham ( F i g . 8 . 7 ) .
1
the
(Fig. 8.8).
are c o m p l e t e l y
a i r near 0°C are c l e a r w i t h a
The e f f e c t o f f r e e z i n g r a t e on m e l t i n g
electrifi-
c a t i o n may be due t o d i f f e r e n c e s i n t h e a i r b u b b l e s t r u c t u r e o f t h e p a r t i c l e s .
8 . 5 . 1 . The e f f e c t of t h e
s o l u b i l i t y o f a i r on m e l t i n g
The s o l u b i l i t y o f a i r i n w a t e r i n c r e a s e s
the water decreases f o r temperatures
of a i r trapped i n the
temperatures.
electrification.
r a p i d l y as the t e m p e r a t u r e o f
above 0 ° C ( F i g . 8 . 9 ) j t h e t o t a l
ice i s probably greater
i n i c e formed a t
amount
lower
I n the absence o f d a t a f o r s u p e r c o o l e d w a t e r t h e v a l u e s o f
s o l u b i l i t y f o r temperatures
b e l o w 0 ° C have t o be o b t a i n e d by e x t r a p o l a t i o n .
P r o v i d e d no a i r escapes d u r i n g f r e e z i n g , t h e amount o f a i r r e l e a s e d a t
s u r f a c e o f a m e l t i n g i c e sphere
is proportional
s o l u b i l i t i e s o f t h e a i r i n w a t e r a t 0 ° C and a t
temperature.
at
t o the d i f f e r e n c e i n
the i n i t i a l
The r a t i o o f t h e volumes o f a i r r e l e a s e d
i s a p p r e c i a b l y l e s s than
the v a r i a t i o n
1.0.
As t h i s
i n t h e amount o f m e l t i n g
e l e c t r i f i c a t i o n f o r water f r o z e n at s i m i l a r temperatures
8.5)
supercooling
by i c e f r o z e n
- 1 5 , - 1 0 and - 5 ° C as deduced f r o m F i g . 8 , 9 i s 2 . 9 : 1 . 8 :
variation
the
( f i g . 8 . 4 and
i t seems l i k e l y t h a t t h e i n c r e a s e o f m e l t i n g e l e c t r i f i c a t i o n
f r e e z i n g t e m p e r a t u r e i s due t o d i f f e r e n t a i r b u b b l e s i z e
spectra
with
as
w e l l as t h e d i f f e r e n t amounts o f a i r t r a p p e d i n t h e i c e . T h i s c o n c l u s i o n
Fig.fc.10
Air
bubbles
in
water
drops
frozen
in still
air
A
N umber
of
Max
i ons
MHky
Bubbly
Cylinders
5 0 Hro
bubble
100
diameter
200
400
2o
1-1 3 t o -1 5 C
12-
* i
4 -
20 -
12
-1
0
to
-11-5 C
-
4 -
20
-
16
-
IZ
-
- 5 to-9 C
4 -
20
drops
in each
sample
71.
i s r e i n f o r c e d by f i g . 8 . 7 w h i c h shows t h a t
dependent
8.5.2.
on the r a t e
the e l e c t r i f i c a t i o n i s
of f r e e z i n g r a t h e r than the temperature of f r e e z i n g .
A i r b u b b l e s i n w a t e r drops f r o z e n i n s t i l l
Generally the drops f r o z e n i n s t i l l
by a s h e l l o f c l e a r
ice.
air.
a i r had an opaque c e n t r e
surrounded
The volume o f t h e c e n t r a l r e g i o n i n c r e a s e d as
f r e e z i n g temperature decreased.
bubbly or m i l k y .
highly
the
The i c e samples c o u l d be c l a s s i f i e d as
M i l k y samples had a r e a s w h i c h were hazy even u n d e r t h e
h i g h e r m a g n i f i c a t i o n r a n g e o f the m i c r o s c o p e and e i t h e r c o n s i s t e d o f
bubbles s m a l l e r than 1 0 o r
areas of small c r y s t a l s .
In bubbly ice
the
b u b b l e s were s e p a r a t e d by c l e a r i c e and f e w were s m a l l e r t h a n 40|im d i a m e t e r .
Fig,
8 . 1 0 shows t h a t
as t h e f r e e z i n g t e m p e r a t u r e
increases the ice
particles
are more l i k e l y t o be b u b b l y t h a n m i l k y and i n t h e r a n g e - 5 t o - 9 ° C about
80% were b u b b l y and o n l y b% m i l k y , whereas
-13 and
70% o f t h e d r o p s f r o z e n between
- 1 5 ° C were m i l k y and o n l y 15% b u b b l y .
The maximum s i z e o f b u b b l e s d i d n o t v a r y a p p r e c i a b l y w i t h f r e e z i n g
t e m p e r a t u r e but a t h i g h e r t e m p e r a t u r e s t h e mean s i z e was n e a r e r the maximum
than f o r i c e f r o z e n a t lower temperatures.
The t e n d e n c y f o r c y l i n d r i c a l
b u b b l e s o f a b o u t 500 ^ m i n l e n g t h t o f o r m i n c r e a s e d w i t h t h e f r e e z i n g
temperature.
W a t e r d r o p s f r o z e n s l o w l y were l i k e l y t o l o s e a i r
during
f r e e z i n g and a i r b u b b l e s have been seen b u r s t i n g t h r o u g h t h e t h i n
s h e l l d u r i n g the f i r s t
8.5.3
ice
few minutes o f f r e e z i n g .
A i r b u b b l e s i n w a t e r d r o p s f r o z e n i n an a i r s t r e a m .
Water d r o p s f r o z e n i n an a i r s t r e a m a t 11 ms ^ and b e l o w a b o u t - 9 ° C
are c o m p l e t e l y opaque even u n d e r t h e m i c r o s c o p e .
They c o n t a i n a l a r g e
number o f b u b b l e s o f t h e maximum d i a m e t e r ? w h i c h i s i n t h e r a n g e 25 t o
40jim.
There a r e a l s o a l a r g e number o f s m a l l e r b u b b l e s o f a l l
down t o t h e l i m i t o f r e s o l u t i o n w h i c h was a b o u t 5 j i m.
temperature
increased
the bubble s i z e
As t h e f r e e z i n g
s p e c t r u m seemed t o b r o a d e n and
by - 6 ° C t h e r e were a f e w b u b b l e s o f 100 \wi and an a p p r e c i a b l e
of
50 ym d i a m e t e r .
As t h e
sizes
number
f r e e z i n g r a t e d e c r e a s e d t h e d r o p s became
Fig.
«H
The
charge
separated
bursting
air
Iribarne
and
of
bubbles
Mason
10
C h a r g e / v o l ume
1
per vol u m e
(1967)
Molar
theory
impurity
concentration
pC m g
10
o
10
I
10
10
40
Rubble
Co
diameter
u rn
80
I OO
IZO
I GO
72.
more c l e a r and a d r o p f r o z e n a t
about t h e p e r c e n t a g e
- 6 ° C was about 15% c l e a r
ice.
c l e a r ice i n a drop f r o z e n at -15°C i n
T h i s was
stagnant
air.
Melting, electrification annate fruftbl&&
9t5t4
The
o b s e r v e d v a r i a t i o n o f the amount o f m e l t i n g
with freezing rate
suggests t h a t a i r bubbles s m a l l e r than about
d i a m e t e r produce a p p r e c i a b l y more charge
If
electrification
50jim
separation than l a r g e r
bubbles.
l a r g e enough c o n c e n t r a t i o n s o f b u b b l e s o f 1 0 | i m and l e s s are
present,
t h e n t h i s s i z e range w i l l
of m e l t i n g
8.5.5.
electrification
ice.
The b u b b l e - b u r s t i n g t h e o r y o f m e l t i n g
The
(fig.
p l a y an i m p o r t a n t p a r t i n t h e
electrification.
b u b b l e - b u r s t i n g t h e o r y o f IRIBARNE and MASON ( 1 9 6 7 ) p r e d i c t s
8 . 1 l ) t h a t t h e charge
s e p a r a t e d p e r u n i t volume o f a i r f a l l s o f - f
-5
r a p i d l y as t h e b u b b l e d i a m e t e r i n c r e a s e s .
of
For a 10
molar s o l u t i o n
i o n i c i m p u r i t i e s c o r r e s p o n d i n g t o a c o n d u c t i v i t y of 1.0 | i mho cm *
t h e c h a r g e p e r volume i n c r e a s e s by an o r d e r o f m a g n i t u d e o v e r - t h e
b u b b l e d i a m e t e r range 80 t o 20 yn.
electrification
agreement
The
particle
on
the
The measured v a r i a t i o n o f m e l t i n g
w i t h f r e e z i n g r a t e and b u b b l e s t r u c t u r e i s i n q u a l i t a t i v e
with this theory.
volume o f a i r r e l e a s e d
f r o z e n a t about
by the m e l t i n g o f a 4 mm d i a m e t e r
-10 C i s o f t h e o r d e r o f 1 mm •
The
ice
charge
p a r t i c l e was measured t o be about 25 pC i f t h e i c e had a
-5
c o n c e n t r a t i o n o f i o n i c i m p u r i t y o f 10
11 ms * a i r s t r e a m a t
-10°C.
p a r t i c l e w o u l d be a b o u t 5 0 ^ m.
m o l a r and w e r e . f r o z e n i n an
The maximum b u b b l e d i a m e t e r i n such a
As b u b b l e s o f 100^ m d i a m e t e r produce
-3
as much as 500 pC mm
, i f a l l t h e b u b b l e s t r a p p e d i n the
t h e s u r f a c e t h e t h e o r y p r e d i c t s a f a c t o r o f 100 g r e a t e r
is
observed.
ice
reach
charging than
One p o s s i b l e e x p l a n a t i o n i s t h a t many o f t h e
smallest
will
d i s s o l v e b e f o r e r e a c h i n g t h e s u r f a c e and t h e b u b b l e s i z e
will
be g r e a t l y a l t e r e d by t h e c o a l e s c e n c e o f b u b b l e s .
bubbles
spectrum
Furthermore
t h e p r e d i c t i o n s o f t h e t h e o r y may be i n e r r o r f o r d i a m e t e r s as l o w as
73.
2 0 j i m as t h e t h e o r y depends on t h e b u b b l e - b u r s t i n g p r o c e s s r e m a i n i n g t h e
same f o r w i d e l y d i f f e r e n t s i z e s o f b u b b l e s .
The IRIBARNE and MASON t h e o r y
has o n l y been, c o n f i r m e d e x p e r i m e n t a l l y f o r b u b b l e d i a m e t e r s g r e a t e r t h a n
160 Rm.
8.5.6
A i r b u b b l e s i z e s and t h e
r a t e of advance of t h e
ice
sheet.
A c c o r d i n g t o BROWNSCOMBE and HALLETT ( 1 9 6 7 ) t h e s i z e s and number of
bubbles
f o r m e d by t h e f r e e z i n g o f w a t e r depend on t h e r a t e o f advance o f
t h e i c e s h e e t and t h e e x t e n t
has measured
t o w h i c h p r e s s u r e can b u i l d up*
the average d i a m e t e r o f bubbles
of water at various f r e e z i n g rates
TABLE 8 . 1 .
(Table
CARTE
f o r m e d by f r e e z i n g
(l96l)
layers
8.1).
The r a t e of advance o f %he i c e s h e e t and s i z e o f
bubbles,,
CARTE
d i a m e t e r pm
(l96l)
g r o w t h r a t e mm min ^
400
0.2
200
0.5
100
2*0
50
5.0
The r a t e o f advance o f t h e i c e s h e e t i n a w a t e r d r o p f r e e z i n g a t
- 1 2 ° C i n an a i r s t r e a m f l o w i n g a t 11 ms ^ i s 2 » 4 mm m i n
Table&L t h i s r a t e o f f r e e z i n g c o r r e s p o n d s
about 90 Jim.
According to
t o a mean b u b b l e d i a m e t e r o f
T h i s v a l u e i s 3 t o 4 t i m e s t h e mean bubble s i z e
observed
i n t h e f r o z e n w a t e r d r o p s b u t t h e d i f f e r e n c e may be due t o t h e
up o f p r e s s u r e d u r i n g t h e f i n a l
water drops f r e e z i n g i n s t i l l
stages o f f r e e z i n g o f the d r o p .
air a typical
that the observations
For
speed o f t h e i c e s h e e t w o u l d '
be 0 . 2 mm m i n * c o r r e s p o n d i n g t o a b u b b l e d i a m e t e r o f 400 jim.
expected
build-
I t would be
o f GARTE w o u l d a p p l y more c l o s e l y t o
f r e e z i n g o f ai w a t e r l a y e r on t h e s u r f a c e o f a
hailstone.
the
74.
8 . 6 COMPARISON WITH PREVIOUS EXPERIMENTS.
The m a g n i t u d e o f charge
s e p a r a t e d by t h e m e l t i n g o f a r t i f i c i a l
cloud
w a t e r was f o u n d t o be an o r d e r o f m a g n i t u d e l e s s t h a n t h a t o b s e r v e d
DRAKE ( 1 9 6 8 ) .
T h i s may be e x p l a i n e d by t h e d i f f e r e n t r a t e s o f f r e e z i n g
o £ t h e i c e samples.
n o t be o b s e r v e d
Although vigorous convection i n the melt water could
i t seems l i k e l y t h a t t h i s was t h e cause o f t h e
d i f f e r e n c e i n e l e c t r i f i c a t i o n a t h i g h and l o w m e l t i n g r a t e s
i n f i a s . 8 . 2 and 8..3
There i s .some e v i d e n c e
described
The
suggest t h a t t h e e f f e c t s o f c o n v e c t i o n on t h e e l e c t r i f i c a t i o n
i m p o r t a n t f o r melting r a t e s as l o w as 5 mg m m
large
t h a t the h i g h e r the f r e e z i n g
r a t e ^ a t which the increase o f e l e c t r i f i c a t i o n i s apparent.
enough a i r
by
provided the
results
are
ice
contains
bubbles.
I t has been shown i n s e c t i o n 8 . 3 t h a t
the o b s e r v a t i o n s
made u s i n g
the
l o o p s u p p o r t o f DRAKE do n o t d i f f e r n o t i c e a b l y f r o m t h o s e made w i t h a more
natural
support which p e r m i t s the p a r t i c l e t o r o t a t e .
can be used
So DRAKE*s
observations
i n assessing the importance of m e l t i n g e l e c t r i f i c a t i o n f o r i c e
which has been f o r m e d a t h i g h f r e e z i n g r a t e s and w h i c h c o n t a i n s many
b u b b l e s s m a l l e r t h a n 3 0 t o 40 p m d i a m e t e r .
present
The r e s u l t s
obtained i n the
i n v e s t i g a t i o n are a p p l i c a b l e t o t h e s t u d y o f i c e f r o z e n a t l o w
f r e e z i n g r a t e s where an a p p r e c i a b l e
contained
i n bubbles l a r g e r
f r a c t i o n of the trapped a i r
is
t h a n 40 t o 50 p m .
The o b s e r v e d dependence o f m e l t i n g e l e c t r i f i c a t i o n on t h e
size of
a i r b u b b l e s a g r e e s q u a l i t a t i v e l y w i t h t h e IRIBARNE and MASON (1967)
t h e o r y o f the e l e c t r i f i c a t i o n of b u r s t i n g bubbles at a water s u r f a c e .
T h i s c o n f i r m s t h e v i e w o f DINGER and GUNN ( 1 9 4 6 ) and DRAKE ( 1 9 6 8 )
t h a t t h e e l e c t r i f i c a t i o n o f m e l t i n g i c e i s due t o t h e b u r s t i n g o f a i r
bubbles.
lb.
C H A P T E R 9
THE EFFECT OF CARBON DIOXIDE ON MELTING ELECTRIFICATION
9.1 CARBON DIOXIDE AND LABORATORY EXPERIMENTS
9.1*1
The Matthews and Mason experiment
One of t h e reasons put f o r w a r d t o e x p l a i n why MATTHEWS and MASON (1963)
f a i l e d t o d e t e c t charging when i c e and snow were melted has been t h e r e g u l a r
use o f d r y i c e i n the l a b o r a t o r y .
A l s o i n two out o f three experiments the
water was frozen i n close p r o x i m i t y t o d r y i c e . DINGER (1964) has p o i n t e d
out
t h a t the presence o f carbon d i o x i d e near the apparatus was s u f f i c i e n t
to reduce the e l e c t r i f i c a t i o n found i n t h e Dinger-Gunn experiment (1946).
However? as contamination o f t h e w a t e r and t h e a c t u a l method o f m e l t i n g
also have a l a r g e e f f e c t on the charge separated? the presence o f carbon
d i o x i d e may not have been t h e only cause of the MATTHEWS and MASON n u l l
result.
9.1.2 The Dinaer-Gunn experiment.
DINGER and GUNN (1946) found t h a t water f r o z e n i n an atmosphere o f
carbon d i o x i d e produced no e l e c t r i f i c a t i o n when melted.
The i c e samples
had a t y p i c a l volume o f 2 ml and were melted i n t r a y s , w i t h some v e n t i l a t i o n .
9.1.3
Drake's experiment*
DRAKE (1968), i n c o n t r a s t t o most o f t h e previous workers? found t h a t
water f r o z e n i n the presence o f carbon d i o x i d e produced as much as +1.3
pC mg ^ on m e l t i n g .
The i c e was made from small water drops and carbon
d i o x i d e was bubbled t h r o u g h the water before use. However, i f vigorous
convection d i d not d e v e l o p i n the m e l t w a t e r , e l e c t r i f i c a t i o n was i n h i b i t e d
by the presence o f carbon d i o x i d e .
76.
9.2 THE IMPORTANCE OF CARBON DIOXIDE IN MELTING ELECTRIFICATION
9.2.1 The double l a y ^ r t h e o r y and the e f f e c t s of carbon d i o x i d e .
According t o the e l e c t r i c a l double l a y e r t h e o r y o f b u b b l e - b u r s t i n g
e l e c t r i f i c a t i o n , the e f f e c t o f d i s s o l v e d carbon d i o x i d e should be the same
as t h a t of a s i m i l a r c o n c e n t r a t i o n o f d i s s o l v e d ions o f any species. This
has been confirmed by the experiment o f IRIBARNE and MASON (1967). The
reason f o r carbon d i o x i d e being more a c t i v e than most atmospheric gases
i s t h a t i t i s h i g h l y s o l u b l e i n water and forms carbonic a c i d which
d i s s o c i a t e s i n t o hydrogen and b i c a r b o n a t e i o n s .
I f melting ice e l e c t r i f i c a t i o n
i s caused by t h e release of trapped a i r bubbles, then one would expect the
presence o f c arbon d i o x i d e i n the water would i n h i b i t e l e c t r i f i c a t i o n .
9.2.2 The e f f e c t o f atmospheric carbon d i o x i d e .
GLUCKAUF (1944) giyes examples o f carbon d i o x i d e c o n c e n t r a t i o n a t the
ground as 0.031
the
- 0.035% a t Kew and 0.035 - 0.037% i n c e n t r a l London.
Inside
l a b o r a t o r y the concent r a t i o n s tend t o be h i g h e r and can range from 0.04
to 0.1%.
1 away from t h e ground, the c o n c e n t r a t i o n of carbon d i o x i d e seems t o
be independent o f a l t i t u d e , c e r t a i n l y up t o 10 km. GLUCKAUF
g i v e s an
average value o f 0.025% f o r 4 t o 10 km over England and KEELING (1968) found
c o n c e n t r a t i o n s o f 0.031% over Hawaii and A n t a r c t i c a between the 500 and 700 mb
levels.
KAYE and LABY (1970) give t h e s o l u b i l i t y of c arbon d i o x i d e i n water
as loO ml of CO^ P
e r
m
l
or
* water a t 15°C and 1 atmosphere.
Taking the
c o n c e n t r a t i o n o f atmospheric carbon d i o x i d e as 0.03% and assuming a l l the
CO^ r e a c t s w i t h the w a t e r t o form carbonic a c i d , t h i s i m p l i e s a t y p i c a l
e q u i l i b r i u m c o n c e n t r a t i o n o f 5 x 10
Molar o f carbonic a c i d .
This value
w i l l remain n e a r l y c o n s t a n t w i t h a l t i t u d e as the e f f e c t s o f decreasing
pressure and temperature on the s o l u b i l i t y tend t o cancel o u t .
Unless carbon d i o x i d e i s more e f f e c t i v e i n r e d u c i n g e l e c t r i f i c a t i o n
than s i m i l a r c o n c e n t r a t i o n s o f o t h e r i o n i c species one would e x p e c t t h a t ,
i n the c o n c e n t r a t i o n found i n the atmosphere, i t would reduce the
77.
e l e c t r i f i c a t i o n t o about 60% o f the value f o r p u r e s t water (IRIBARNE and
MASON, 1967). The e f f e c t of dry i c e i n t h e l a b o r a t o r y may be more s e r i o u s ,
because o n l y a 3% c o n c e n t r a t i o n o f carbon d i o x i d e i n the a i r i s needed
t o reduce the charge produced by the b u r s t i n g o f a 100 j*m r a d i u s bubble
to an i n s i g n i f i c a n t l e v e l .
9.3 AN EXPERIMENT TO DETERMINE THE EFFECT OF ATMOSPHERIC CARBON DIOXIDE.
9.3.1 Experimental
details
Some o f the d i s s o l v e d carbon d i o x i d e was removed from d e i o n i z e d water
by bubbling w i t h n i t r o g e n and a l l o w i n g the water t o stand i n a n i t r o g e n
atmosphere.
The c o n c e n t r a t i o n o f carbon d i o x i d e could be r e g u l a t e d by
exposing the water t o t h e atmosphere..
This water was used t o make the
ice spheres, which were then melted under constant c o n d i t i o n s i n the wind
tunnel.
Care was taken t o nucleate the water drops 4 t o 5 minutes a f t e r
being placed
i n the r e f r i g e r a t o r , i n order t o reduce the amount o f carbon
d i o x i d e absorbed d u r i n g the c o o l i n g o f the dropo
The ice sphere was then
melted on a p l a t i n l u m w i r e support i n the wind t u n n e l .
903.2 The use o f e l e c t r i c c o n d u c t i v i t y measurements t o evaluate the CQ^
concentration.
Carbon d i o x i d e r e a c t s w i t h water t o produce carbonic a c i d , which i s
p a r t l y d i s s o c i a t e d i n t o hydrogen and bicarbonate
CO + H O ^
2
2
H
i o n s , thus
+
C0 ^H +HC0 ~
2
3^
*3
0
o
As carbonic a c i d i s weak a c i d , Ostwald's d i l u t i o n law (Eqrw 9.1) may be
used t o evaluate the v a r i a t i o n o f c o n d u c t i v i t y w i t h c o n c e n t r a t i o n o f a c i d ;
K=
L C
L ( L -L)
9.1
2
o
o
where K i s the i o n i z a t i o n
constant
(4.5 x 10
C i s t h e c o n c e n t r a t i o n of c a r b o n i c a c i d , L
at i n f i n i t e d i l u t i o n
Co
q
g equiv 1
a t 2b C)
the e q u i v a l e n t conductance
and L the e q u i v a l e n t conductance a t c o n c e n t r a t i o n
Equivalent conductance i s d e f i n e d as the conductance of a s o l u t i o n
c o n t a i n i n g one gm e q u i v a l e n t o f s o l u t e when measured between p a r a l l e l
e l e c t r o d e s which are 1 cm a p a r t and l a r g e enough i n area t o c o n t a i n the
F i g.9 1
T he e f f e c t of
dissolved
CO^on
de ion i zed
conductivity
water
C on d a c t i v i t y 0*7
ta mho c m
1
05
'
0-3 -
o\ -i
2
4
r
6
to
3
C o n c e n t r a t i o n of c a r b o n i c
x 1 C f Molar
acid
6
Fig.9-2
C h a r g e on the m e l t w a t e r
made f r o m w a t e r
of
with
4mm
diameter
different
ice
C O ^ levels
Charge
+ PC
6 -
4 -
2-
—?
1
p—
o 1
o-3
0
Co n due \ «v ity
p mho c m
1
4
— i —
0-6
a 7
spheres
78.
the necessary volume o f s o l u t i o n .
By r e w r i t i n g the Ostwald d i l u t i o n l a w and s u b s t i t u t i n g the value f o r
L
2
o f 395 Hmho cm gm e q u i v "
L =
b
- 9 x I0~
1
quoted by MACINNES ( l 9 6 l ) ;
8 x 10"
±
\
The
C
9
+
7 x l Q ^
2
9
#
2
C
s p e c i f i c c o n d u c t i v i t y can be obtained by m u l t i p l y i n g t h e e q u i v a l e n t
conductance by t h e c o n c e n t r a t i o n , e n a b l i n g the v a r i a t i o n o f t h e c o n d u c t i v i t y
of t h e s o l u t i o n o f carbonic a c i d t o be p l o t t e d against c o n c e n t r a t i o n ( f i g . 9.1)•
When n i t r o g e n was bubbled through the deionized water samples t o remove the
CO^j the c o n d u c t i v i t y f e l l
V
~*1
k
"1
from 0.75jimho cm
t o a minimum of 0.15 ^mho cm
which i m p l i e s t h a t t h e c o n d u c t i v i t y due t o carbon d i o x i d e i n e q u i l i b r i u m w i t h
the water was 0.6|i mho gm ^.
From f i g . 9-1, the c o n c e n t r a t i o n o f carbonic
a c i d was 6 x 10 ^ N which agrees w i t h t h a t c a l c u l a t e d i n s e c t i o n 9.2.2 caused
by a 0.03% c o n c e n t r a t i o n o f CO^ i n the atmosphere.
9.3.3
The e f f e c t o f GO^ c o n c e n t r a t i o n s on m e l t i n g e l e c t r i f i c a t i o n .
The
10
f r o z e n water drops were made f r o m water which contained from 7 x
M t o l e s s t h a n 10 M carbonic a c i d .
The a c t u a l value o f the lower l i m i t
of the carbonic a c i d c o n c e n t r a t i o n could n o t be determined because t h e
c o n c e n t r a t i o n o f metal and non metal ions was n o t known.
The icewas melted
s l o w l y , t h e 4 mm spheres t a k i n g about 8 minutes t o m e l t .
The
charge c a r r i e d by the meltwater f o r water o f d i f f e r e n t
concentrations
o f carbon d i o x i d e i s p l o t t e d i n f i g . 9.2. There i s l i t t l e s i g n i f i c a n t v a r i a t i o n
of the charging w i t h carbon d i o x i d e c o n c e n t r a t i o n .
These r e s u l t s may be
compared w i t h e a r l i e r measurements made w i t h water drops which had stood
f o r about an hour before f r e e z i n g and were t h e r e f o r e i n e q u i l i b r i u m w i t h
atmospheric CO^ (Table 9.1)•
The estimates o f CO^ c o n c e n t r a t i o n were
d e r i v e d by the method o u t l i n e d i n s e c t i o n 9.4.1.
79.
TABLE 9.1
E f f e c t of CO^ c o n c e n t r a t i o n on m e l t i n g e l e c t r i f i c a t i o n ,
Percentage o f the c o n c e n t r a t i o n o f CO,
present
i n e q u i l i b r i u m w i t h water a t
Charge
pC
+15°C
Number
o f drops
160
3.0 ± .8
7
180
4.0 ± 1.0
8
260
4.9 + 1.0
17
Table 9.1 suggests t h a t t h e r e i s no s i g n i f i c a n t d i f f e r e n c e between
the charging produced by any of t h e 3 sets o f m e l t i n g i c e spheres.
However,
i f carbon d i o x i d e does have an important e f f e c t on m e l t i n g e l e c t r i f i c a t i o n
these r e s u l t s could be explained by carbon d i o x i d e being absorbed by a
water drop d u r i n g the m e l t i n g process ( c f s e c t i o n 9.4.2).
9.4 THE ABSORPTION OF CARBON DIOXIDE BY A WATER DROP
9.4.1 Absorption
by a s t a t i o n a r y drop.
A review paper by LEWIS and WHITMAN (1924) shows t h a t the c h i e f cause
of r e s i s t a n c e o f a water drop t o absorbing
l i q u i d a t t h e surface o f t h e drop.
gaseous CO^ i s a t h i n f i l m o f
Inside t h i s f i l m , which i s t y p i c a l l y
3|nn t h i c k (WHITMAN, LONG and WANG 1926), t h e l i m i t i n g f a c t o r i s the
d i f f u s i o n o f CO^ through a r e l a t i v e l y h i g h c o n c e n t r a t i o n of carbon d i o x i d e
solution.
The r a t e of m i x i n g i n s i d e the drop only l i m i t s t h e a b s o r p t i o n
process by reducing the c o n c e n t r a t i o n g r a d i e n t across the surface film»
By a p p l y i n g the t h e o r y o f t h e d i f f u s i o n o f gases through a f i l m o f stagnant
l i q u i d (Appendix 2 ) , t h e f r a c t i o n f o f the f i n a l e q u i l i b r i u m amount-'of
CO
absorbed i n a water drop can be d e r i v e d .
For a 4 mm diameter drop f o r t < ! 0 0 s
n/2
2
t n
and f o r t > 100 s
3k
0.44e x p
H iooj <t-i°°)J
0>
0)
0>
0;
u
O
u
o
r-
00
cn
o
<
4
I
5
O
o o>
u o
O ^
O
0*
tn
80.
"•6
where the p e r m e a b i l i t y c o e f f i c i e n t k
l 0 Q
= 2.8 x 10
a f t e r the s t a r t o f a b s o r p t i o n and D i s the d i f f u s i o n
~1
ms
, t i s the time
coefficient.
The t w o equations 9.3 and 9-4 describe d i f f e r e n t stages i n the
a b s o r p t i o n o f gas.
In the f i r s t s t a g e , the p e r m e a b i l i t y o f the surface
l a y e r decreases as the GO^ l e v e l r i s e s , and i n the second the l a y e r i s
s a t u r a t e d w i t h CC>2 and the p e r m e a b i l i t y remains constant.
These r e s u l t s
are p l o t t e d i n f i g . 9-3, which shows t h a t a f t e r 2.5 min the drop has absorbed
66% o f i t s e q u i l i b r i u m value of CO^, and a f t e r 7 min 90% o f the C 0 has been
2
absorbed.
9.4.2. A b s o r p t i o n by a f a l l i n g drop.
Much o f the experimental work on a b s o r p t i o n by water drops has been
c a r r i e d out on f a l l i n g drops e.g. by GARNER and LANE (1959), LEWIS and
WHITMAN (1924) and LEWIS e t a l .
(1926).
A t y p i c a l value f o r the time taken
f o r 90% a b s o r p t i o n f o r a f a l l i n g 4 mm diameter drop i s 5 seconds (GARNER
and LANE (1959).
This i s two orders o f magnitude l e s s than f o r a drop
i n stagnant a i r and i s due t o the presence o f convection and the d i s t u r b e d
nature o f the surface f i l m i n a f a l l i n g
drop.
9.5 CARBON DIOXIDE LEVELS IN PREVIOUS LABORATORY EXPERIMENTS
9.5.1 The Dinoer-Gunn experiment.
I f t h e r a t e o f a b s o r p t i o n o f GO^ i s g r e a t l y enhanced by p l a c i n g a
water drop i n a s t r e a m of the gas, the r a t e o f d e s o r p t i o n o f CO^ w i l l a l s o
be increased i n a v e n t i l a t e d atmosphere.
Dinger-Gunn experiment
The r a t e of d e s o r p t i o n i n the
( s e c t i o n 2 . l ) may be estimated by c o n s i d e r i n g a
r e c t a n g u l a r shaped volume o f water, o f depth d and surface area A,
placed i n a cubic c o n t a i n e r so t h a t o n l y the area A has access t o the a i r I t seems l i k e l y t h a t , because the water was s h e l t e r e d from the f a n by the
s i d e s o f the small c o n t a i n e r , the surface f i l m was not d i s t u r b e d , and the
GO^ was t r a n s f e r r e d across the surface by molecular d i f f u s i o n .
Appendix 2.2 the value o f f i s given by
From
81.
I f we assume t h a t the surface f i l m i s s a t u r a t e d w i t h CO^, then k = 2.8
-6 ^ - l
x 10
m s
.
I n t h i s experiment the depth o f i c e was about 10 mm, so i f one
considers a l a y e r o f water 1 mm t h i c k on the surface o f t h e i c e t h e n , according
to e q u a t i o n 9.5, the time constant d/k w i l l be about 400 seconds.
As the
t o t a l time f o r a l l the i c e t o m e l t was o f t h e order o f 100 seconds i t i s
suggested
t h a t t h e meltwater d i d c o n t a i n approximately the same amount of
CO^ as t h e o r i g i n a l water from which t h e i c e was made.
This
experiment
would t h e r e f o r e measure t h e e f f e c t o f CO^ on m e l t i n g e l e c t r i f i c a t i o n .
9.5.2 The experiment o f DRAKE.
The time constant f o r t h e a b s o r p t i o n and t h e r e f o r e a l s o d e s o r p t i o n o f
CO^ by a f a l l i n g drop i s l e s s than
than the m e l t i n g t i m e .
the
b u r s t i n g bubbles
5 s, which i s over a f a c t o r o f 10 l e s s
So seems probable t h a t t h e meltwater surrounding
e
i n DRAKE's experiment contained v e r y l i t t l e
though t h e i c e was made from water w i t h a h i g h CO^ content.
v
e
n
The r a t e of
loss f o f CO^ from a small a i r bubble a f t e r release from t h e i c e can be
estimated (Appendix 2.3) using the f i l m t h e o r y o f gas a b s o r p t i o n ;
-g 2 -1
where r i s the r a d i u s of the bubble and D = 2 x 10
ms
For a t y p i c a l 2 0 ^ m bubble, 99% of t h e CO^ i s l o s t i n t h e f i r s t
0.8 s a f t e r water comes i n c o n t a c t w i t h t h e bubble.
This suggests
that
the
c o n c e n t r a t i o n of CO^ i n t h e meltwater w i l l govern t h e CO^ content of
the
double l a y e r a t t h e surface o f the bubble on b u r s t i n g , r a t h e r than t h e
i n i t i a l gas content o f t h e bubble.
As the meltwater loses most of i t s
CO^ i n seconds, t h e c o n c e n t r a t i o n o f CO^ i n t h e p a r t l y molten drop i s
probably very close t o t h a t due t o t h e m e l t i n g environment, and i s n o t
dependent on t h e f r e e z i n g
environment.
9.6
I t i s suggested
CONCLUSION
t h a t t h e reason f o r t h e f a i l u r e o f DRAKE t o f i n d
that
CO^ i n h i b i t s m e l t i n g e l e c t r i f i c a t i o n may be due t o t h e absence o f CO^ i n
the
meltwater of h i s samples.
The apparatus o f DINGER and GUNN would
82.
measure the e f f e c t of CO - The MATTHEWS and MASON n u l l r e s u l t s were
obtained w i t h ice i n bulk fcr^a, where any CO^ i n t r o d u c e d d u r i n g the
f o r m a t i o n o f the i c e would n o t e a s i l y leak away during m e l t i n g - I n
order t o confirm t h i s t h e o r y , i c e spheres should be melted i n an
atmosphere of CO^ when, according t o t h e double l a y e r t h e o r y of
m e l t i n g e l e c t r i f i c a t i o n , the charging should be reduced. I t i s hoped
t o c a r r y out t h i s experiment a t Durham s h o r t l y .
83.
CHAPTER10
THE
ELECTRICAL EFFECTS OF THE MELTING OF REAL PRECIPITATION
1Q.1 THE LOCATION OF THE LOWER POSITIVE CHARGE
10.1.1 The l o c a t i o n deduced from l a b o r a t o r y experiments.
The way i n which r e a l i c e p a r t i c l e s m e l t w h i l e f a l l i n g from the 0°C l e v e l
i n convective
clouds i s s i m i l a r t o the behaviour o f the m e l t i n g i c e p a r t i c l e s
i n the wind t u n n e l .
I n both cases the temperature r i s e s d u r i n g the course o f
m e l t i n g although the temperature of the a i r i n the wind t u n n e l
more s l o w l y d u r i n g the f i r s t minute of m e l t i n g .
increases
T y p i c a l l y 40% of the i c e
i s melted i n the l a s t minute of m e l t i n g i n the tunnel compared to 50%
as c a l c u l a t e d by MASON (1956) f o r a 4 mm s o l i d i c e sphere f a l l i n g i n a
saturated atmosphere from the 0°C l e v e l .
I n the l a b o r a t o r y between 50 and
90% of a l l the charge was separated
d u r i n g the l a s t minute o f m e l t i n g when the average m e l t i n g r a t e ranged from
7 to 18 mg min
As MASON c a l c u l a t e d t h i s average value t o be 14 mg min ^
f o r a 4. mm p a r t i c l e m e l t i n g i n a c l o u d , i t seems t h a t most of the charge
separation on such a p a r t i c l e occurs d u r i n g the l a s t minute of m e l t i n g
C e r t a i n l y the l a b o r a t o r y r e s u l t s show t h a t the amount o f charging d u r i n g the
f i r s t minute of m e l t i n g i s l i k e l y t o be n e g l i g i b l e ( c f . f i g . 7.9).
For a 4 mm s o l i d i c e p a r t i c l e MASON estimated t h a t the l a s t 50% of the
0
raass melted below the +6i2 C l e v e l o r 1km below the 0°C l e v e l .
One might
t h e r e f o r e expect t h e centre o f charge s e p a r a t i o n to l i e a t about + 8°C
and 1.2 km below the 0°C l e v e l .
The smaller the m e l t i n g p a r t i c l e , the
higher i n the cloud i t w i l l m e l t , so 2 mm p a r t i c l e w i l l have h a l f melted
by 450 m below the 0°C l e v e l -
However small ice p a r t i c l e s which m e l t
higher i n the cloud w i l l m e l t a t a lower r a t e due t o t h e c o o l e r environment,
so t h e y may c o n t r i b u t e less t o the cloud e l e c t r i f i c a t i o n .
also m e l t higher i n the c l o u d ; according
Graupel w i l l
to MASON a 3 mm diameter
graupel
p e l l e t of s p e c i f i c g r a v i t y 0.3 w i l l lose the l a s t 50% of i t s mass between
300 and 600 m below the 0°C l e v e l .
C l e a r l y the l o c a t i o n o f the charged
Fig. 10*1
The
location
t
of
the
Schonland
No of
and
lower
positive
charge
Malan(1951)
observations
-3
-Z
22
/8
2
J4
Simpson
and
-2
R o b i n s o n (1941)
4
3
2
-2
Reynolds
and
-6
-lo't
-6
-\0°c
Neil! ( 1 9 5 5 )
3
2
6
2
Tempera ture
ALSO
Kuettner (1950)
12 out
C l a r e n c e and M a l a n ( 1 9 5 7 )
of 5 0
AO
#
higher than+2 C
observations
level
average + S°C
84.
r e g i o n caused by m e l t i n g p r e c i p i t a t i o n depends very much on the size and
density of the i c e p a r t i c l e s .
10.1.2
The e f f e c t of the downdrauaht.
I f t h e m e l t i n g p a r t i c l e s are fal l i n g i n a downdraught which may be up
1
to 10 ms" (BYERS and BRAHAM, #1953) then t h e p o s i t i o n of t h e charged r e g i o n
produced by the m e l t i n g i c e may be lower than i f the p a r t i c l e s melted i n t h e
updraught.
I n the downdraught the n e g a t i v e l y charged d r o p l e t s w i l l be
c a r r i e d down below t h e 0°C l e v e l and w i l l tend t o n e u t r a l i z e t h e p o s i t i v e
charge on t h e m e l t i n g p r e c i p i t a t i o n .
The speeds o f t h e downdraught measured
by BYERS and BRAHAM were i n t h e range 5 t o 10 ms * which i s o f the same
magnitude as t h e f a l l s p e e d s o f p a r t i c l e s o f 2 t o 5 mm diameter, so t h i s e f f e c t
may w e l l be i m p o r t a n t .
I f t h e downdraught i s i n c l i n e d t o the v e r t i c a l t h e
m e l t i n g p r e c i p i t a t i o n may f a l l c l e a r e i t h e r i n t o t h e updraught or i n t o a
r e l a t i v e l y motionless p a r t o f the cloud.
10.1.3 The measured l o c a t i o n o f the lower p o s i t i v e charge.
A summary o f some experiments i n l o c a t i n g t h e lower p o s i t i v e charge i n
thunderclouds i s o u t l i n e d i n Table 1.3.
The mean temperatures a t which the
charge was found v a r i e d from -3 t o +8°C.
A d i r e c t comparison o f these r e s u l t s
i s d i f f i c u l t because o f the d i f f e r e n t methods o f measurement and because the
v a r i a t i o n of temperature w i t h a l t i t u d e was u s u a l l y i n f e r r e d from d i s t a n t
radiosonde measurements and an estimate of t h e h e i g h t o f cloud base.
These
temperature measurements are l i k e l y t o be about 2°C too high according
to BYERS and BRAHAM (1949) i f the charge r e g i o n i s l o c a t e d i n t h e downdraught and 2°C too low i f i n t h e updraught.
F i g . 10.1 shows t h e
d i s t r i b u t i o n o f l o c a t i o n s of t h e charge found by 3 observers who published
i n d i v i d u a l as w e l l as mean values.
The r e s u l t s o f SCHONLAND and MALAN
( l 9 5 l ) p o i n t towards a charge d i s t r i b u t i o n which can occur a t any l e v e l
near and below the 0°C l e v e l and perhaps i s best explained by r i s i n g
p o i n t discharge ions caught i n the updraught (MALAN. (1952).) The r e s u l t s
of REYNOLDS and NEILL (1955) c e r t a i n l y do not j u s t i f y p l a c i n g the mean
l o c a t i o n o f t h e charge a t -3°C as i n Table 1.3.
KUETTNER (1950) has provided
85.
perhaps the most r e l i a b l e estimate o f t h e p o s i t i o n o f the charge by studying
the sign o f t h e p o t e n t i a l g r a d i e n t i n the c e n t r e o f p i e c f i p i t a t i o n o r
l i g h t n i n g a c t i v i t y i n thunderclouds on t h e Zugspitze.
On 50 occasions the
charge was l o c a t e d above t h e +8°C l e v e l and on 12 above t h e +2°C l e v e l . I t
i s p o s s i b l e t h a t t h e mountain may have a f f e c t e d the thunderstorm but these
r e s u l t s p o i n t t o a t h e o r y o f e l e c t r i f i c a t i o n t h a t does not i n v o l v e the
m e l t i n g o f i c e . CLARENCE and AAA LAN (1957) o n l y quote average r e s u l t s f o r
the l o c a t i o n of the lower p o s i t i v e
10.14
charge.
Conclusion
From t h e previous s e c t i o n i t appears t h a t i t i s not p o s s i b l e t o s t a t e
a l o c a t i o n f o r t h e lower p o s i t i v e charge o r even be sure t h a t t h e r e i s o n l y
one type o f lower p o s i t i v e charge.
I t may be t h a t the South A f r i c a n
measurements have described a cloud o f p o i n t discharge ions whereas the
European and American o b s e r v a t i o n s have described a charge c a r r i e d by the
precipitation.
C l e a r l y i t i s not p o s s i b l e t o say t h a t t h e measured l o c a t i o n
of t h e charge precludes o r supports a m e l t i n g i c e theory.
I f m e l t i n g i c e i s r e s p o n s i b l e then t h e l o c a t i o n o f t h e charge w i l l
depend on the mean d e n s i t y and diameter of the m e l t i n g p a r t i c l e s . The
motion of the a i r i n the r e g i o n o f t h e p r e c i p i t a t i o n may also be important
and t h e mechanism should be more a c t i v e a t the edge o f the downdraught
or i n t h e updraught.
This l o c a t i o n agrees w i t h t h e p o s i t i o n o f t h e lower
p o s i t i v e charge deduced by WILLIAMS (1958) from a study o f l i g h t n i n g
f l a s h e s t o ground.
10.2 SOLID PRECIPITATION IN THUNDERSTORMS
10.2.1
C l a s s i f i c a t i o n of s o l i d p r e c i p i t a t i o n . ,
There i s some confusion i n t h e l i t e r a t u r e concerning t h e c l a s s i f i c a t i o n
of s o l i d p r e c i p i t a t i o n and i n p a r t i c u l a r the word g r a u p e l .
The Japanese
e.g. NAKAYA and TERADA (1935) , d e s c r i b e graupel as having a mean s p e c i f i c
g r a v i t y o f 0.13 agreeing w i t h t h e American ARENBERG ( l 9 4 l ) who gives a
value o f 0.2 WEICKMANN(1953) and KEUTTNER (1950) r e f e r t o graupel as
having a s p e c i f i c g r a v i t y o f about 0.6 and LIST (1965) suggests an
86.
upper value o f 0.8. As LIST's s t u d i e s o f t h e s t r u c t u r e o f i c e p a r t i c l e s
were a main p a r t o f h i s work h i s c l a s s i f i c a t i o n w i l l be used i n t h i s t h e s i s .
Snow p e l l e t s
These are l i g h t and opaque e i t h e r roughly c o n i c a l o r
s p h e r i c a l p a r t i c l e s o f s p e c i f i c g r a v i t y 0„1 t o 0.3. They are formed
according t o ARENBERG (1941) and NAKAYA and TERADA (1935) by the a c c r e t i o n
of cloud d r o p l e t s onto a f a l l i n g snow c r y s t a l .
Graupel
Graupel p e l l e t s are white and opaque and r o u g h l y s p h e r i c a l
i n shape w i t h s p e c i f i c g r a v i t y up t o 0.8 and diameters up t o 5mm.
They
d i f f e r from snow p e l l e t s i n having an i c e framework i n which a c r y s t a l l i n e
s t r u c t u r e can be i d e n t i f i e d . WEICKMAN (1953), from h i s experiences on
Mount Hohenpeissenberg considers t h a t the f o l l o w i n g d e s c r i p t i o n o f LITTLE
(1940) describes them w e l l . " A l l the stones (average diameter some 5 mm)
examined showed a d e f i n i t e c r y s t a l l i n e s t r u c t u r e , being i n the
form o f a s e c t o r o f a sphere, t h e angle subtended
approximate
a t the c e n t r e being 90°.
I t was not p o s s i b l e t o i d e n t i f y the form o f the i n d i v i d u a l c r y s t a l s , but
they r a d i a t e d out from the apex of the s tone g i v i n g a s t r e a k y appearance
at the s p h e r i c a l face as i f t h e stone were composed o f a bundle o f f i b r e s " .
Graupel
can e i t h e r be formed on a c r y s t a l o r a f r o z e n cloud d r o p l e t .
Small h a i l
LIST (1965) describes small h a i l as being semi-transparent
p a r t i c l e s o f s i m i l a r size t o graupel but w i t h a more rounded appearance
and a s p e c i f i c g r a v i t y o f 0.8 t o Q.,99. They may c o n s i s t p a r t l y o f l i q u i d
water and grow from graupel by the i n t a k e of water* i n t o t h e a i r c a p i l l a r i e s
of the i c e framework.
Hailstones
H a i l s t o n e s g e n e r a l l y have a layered c o n s t r u c t i o n and are
l a r g e r than small h a i l .
They may take a v a r i e t y o f shapes sometimes w i t h
lobes.
10.2.?. Observations o f s o l i d p r e c i p i t a t i o n i n thunderclouds.
There are very few o b s ervations of p r e c i p i t a t i o n p a r t i c l e s which were
made i n thunderclouds and t h e d e s c r i p t i o n s t h a t are a v a i l a b l e were u s u a l l y
made as a s u b s i d i a r y p a r t of an e l e c t r i c a l o r dynamical
study. The
o b s e r v a t i o n s f a l l i n t o two types> those made from mountain
were immersed i n t h u n d e r c l o u d s , and a i r c r a f t o b s e r v a t i o n s .
s t a t i o n s which
87.
WEICKMANN (1953) observed t h a t graupel was t h e most common form o f
s o l i d p r e c i p i t a t i o n i n thunderclouds.
KUETTNER (1950) noted t h a t graupel
was present i n 60% o f t h e thunderstorms on the Zugspitze , small h a i l i n
20%5 l i q u i d p r e c i p i t a t i o n i n 20% and h a i l i n o n l y 10% of the stormso
was present i n 70% of the storms.
Snow
KUETTNER concluded t h a t h a i l was
r e l a t i v e l y r a r e and was by no means necessary
f o r the production of l i g h t n i n g .
BYERS and BRAHAM (1953) found t h a t snow and snow p e l l e t s were the most
common form' o f s o l i d p r e c i p i t a t i o n above the 0°G l e v e l i n summer thunderstorms
over Ohio.
However, graupel and small h a i l below 3 mm diameter were
p r a c t i c a l l y u n i d e n t i f i a b l e but i n o n l y 10% o f the storms could the p r e c i p i t a t i o n
be classed as h a l l .
BRAHAM (1963) found t h a t t h e most common s o l i d p r e c i p i t a -
t i o n i n c o n v e c t i v e clouds over M i s s o u r i was graupel which gave the appearance
of having grown by t h e r i m i n g o f cloud d r o p l e t s .
The average s p e c i f i c
of the graupel was 0.88 and a l l the 110 graupel p e l l e t s c o l l e c t e d
g r a v i t i e s g r e a t e r than 0.7.
gravity
BRAHAM
gravity
had s p e c i f i c
also found c l e a r i c e p e l l e t s o f s p e c i f i c
0.9 u s u a l l y near t h e t o p s of updraughts.
WEICKMANN and AUFM KAMPE (1953) found t h a t the l i q u i d water content of
-3
cumulonimbi v a r i e s from 1 t o 6 g m
. The a c t u a l
value w i l l depend on t h e
p a r t of the cloud s t u d i e d and the temperature of cloud base and the amount
of a i r e n t r a i n e d by the updraught.
From t h e o b s e r v a t i o n s o f KUETTNER,
WEICKMANN and AUFM KAMPE and BYERS and BRAHAM i t seems t h a t t h e most common
form o f s o l i d p r e c i p i fca'-ion i n thunderclouds i s smaller than 5 mm diameter
and can be c l a s s i f i e d as graupel o r snow.
ice w i l l depend on the
The d e n s i t y and s t r u c t u r e
o f the
c o n d i t i o n s under which i t i s formed and may be
d i f f e r e n t i n thunderstorm w i t h d i f f e r e n t cloud base h e i g h t s , updraught
speeds and l i q u i d water contents*
10 2°3
0
The e f f e c t of growth c o n d i t i o n s on the s t r u c t u r e o f so+id p r e c i p i t a t i o n
I f t h e r a t e a t which supercooled water drops a r r i v e a t an i c e surface
i s g r e a t e r than t h e r a t e a t which t h e water i s f r o z e n then water w i l l be
present on the surface and t h e growth can be said t o be wet. The
t r a n s i t i o n from wet t o d r y growth has been s t u d i e d by LUDLAM (1950)
88.
by c a l c u l a t i n g the heat balance a t the i c e s u r f a c e .
He deduced t h e
temperature a t which the growth becomes wet f o r d i f f e r e n t sized p a r t i c l e s
i n c l o u d s w i t h bases a t 10 and 20°C.
4 mm diameter i c e spheres w i l l grow
in t h e d r y phase a t h e i g h t s above t h e -10°C l e v e l i n both clouds w h i l e
p a r t i c l e s o f 10 mm diameter can grow by wet growth up t o t h e -25°C l e v e l .
I t seems u n l i k e l y t h a t a p a r t i c l e o f 4 mm diameter w i l l have grown by wet
growth i n a cumulonimbus provided t h a t the growth d i d n o t s t a r t on top o f
a f r o z e n water d r o p l e t .
One might expect a p a r t i c l e o f l e s s than 4 mm t o
have a l i q u i d l a y e r i f i t was surrounded by enough cloud d r o p l e t s as i t
f e l l towards the 0°C l e v e l .
10.2.4 A i r bubbles i n n a t u r a l s o l i d p r e c i p i t a t i o n .
Air
bubbles can e i t h e r be formed by the r e l e a s e of d i s s o l v e d a i r a t an
advancing ice-water i n t e r f a c e o r can o r i g i n a t e i n the spaces between i n d i v i d u a l
cloud d r o p l e t s which f r o z e on impact w i t h the growing p a r t i c l e .
Wet growth
The r a t e o f advance o f t h e i c e i s governed by the r a t e
of l o s s o f heat t o the environment.
For a 4 mm diameter p a r t i c l e f a l l i n g
at t e r m i n a l speed a t -10°C t h e heat l o s s as computed from e q u a t i o n 8.1 i s
approximately 170 mW, corresponding t o a r a t e o f advance o f t h e i c e sheet
of 2.4 mm min ^.
CARTE (1961) found t h a t t h i s r a t e o f f r e e z i n g
bubbles o f about 80 ^m diameter.
produced
At -20°C t h e mean bubble diameter would
be about 50 ^m. As t h e a i r would be f r e e t o escape from t h e surface the
c o n c e n t r a t i o n o f a i r bubbles may be g r e a t l y reduced.
Dry growth.
The a i r bubbles released by the freezing o f i n d i v i d u a l
supercooled cloud d r o p l e t s are l i k e l y t o be a few \xn as t y p i c a l cloud
d r o p l e t s i n cumulonimbus clouds have diameters i n t h e range 20 t o 40 urn.
(wEICKMANN, %1953)% A more i m p o r t a n t source of trapped a i r bubbles i s
probably t h e gaps between a d j a c e n t f r o z e n d r o p l e t s *
MACKLIN (1962)
e x p l a i n s the f o r m a t i o n of rime of s p e c i f i c g r a v i t y l e s s than 0.5 as
being due t o d i f f e r e n t degrees o f close packing o f f r o z e n water d r o p l e t s .
BftOWNSCOMBE and HALLETT ( l 9 6 7 ) suggest t h a t t h e i n c r e a s i n g d e n s i t i e s o f
rime o f s p e c i f i c g r a v i t y g r e a t e r than about 0.6 can be explained by the
89.
i n c r e a s i n g deformation of t h e c l o u d d r o p l e t s on impact.
L i g h t e r rime w i l l
be formed when the d r o p l e t s freeze before they have had time t o spread
out
over t h e s u r f a c e .
The a i r bubbles trapped i n rime of s p e c i f i c g r a v i t y l e s s than 0.6
will
probably be i n the diameter range 2 t o 200|Am assuming a range of cloud
d r o p l e t diameters of 5 t o 40 jim.
At very low d e n s i t i e s the gaps between
frozen d r o p l e t s w i l l t e n d t o be i n t e r c o n n e c t e d . Ice o f h i g h e r d e n s i t y
probably contains smaller a i r bubbles trapped between the f r o z e n d r o p l e t s
due t o the e f f e c t of d e f o r m a t i o n on the d r o p l e t s *
As the f r e e z i n g r a t e
w i l l be l e s s the bubbles trapped i n s i d e t h e d r o p l e t s may
become l a r g e r and
as the growth becomes more l i k e wet growth the bubble size w i l l
increase as
adjacent d r o p l e t s coalesce before f r e e z i n g .
1Q.3
MELTING ICE AND
THE
MAGNITUDE.OF THE
POWER POSITIVE CHARGEa
The charge separated by m e l t i n g ice has been shown to depend on the s i z e
of the a i r b u b b l e s
9
the m e l t i n g r a t e and the p u r i t y of the i c e . A l l these
p r o p e r t i e s would be expected
storms*
t o have a range of values f o r d i f f e r e n t thunder-
A f i g u r e f o r t h e magnitude o f charge t h a t can be produced by
m e l t i n g i c e under p e r f e c t c o n d i t i o n s can however be obtained*.
10.3*1 Electriffica-frion under i d e a l circumstances.
We w i l l assume t h a t the ice present i n t h e thundercloud contains a l a r g e
number of bubbles s m a l l e r than 50 jim diameter and has been formed a t high
enough f r e e z i n g r a t e s t o e l i m i n a t e an a p p r e c i a b l e l o s s o f a i i d u r i n g f r e e z i n g .
The range of c o n c e n t r a t i o n s of i m p u r i t i e s i n cloudwater has been estimated
in chapter 5 as 2 t o 20 mg 1 ^
C e r t a i n l y the l e v e l cannot be l e s s than t h a t
due t o an e q u i l i b r i u m c o n c e n t r a t i o n of atmospheric
from water i n e q u i l i b r i u m w i t h atmospheric
carbon dioxideo
Ice made
carbon d i o x i d e and c o n t a i n i n g an
a d d i t i o n a l i o n i c i m p u r i t y c o n c e n t r a t i o n of no more than 0°2 mg 1 * was
found
to produce 0.8 pC mg ^ o f e l e c t r i f i c a t i o n a t the maximum m e l t i n g r a t e s l i k e l y
to be found i n the atmosphere ( f i g 8.7 )• This corresponds t o a charge
-3
d e n s i t y of 0o8 G km
i f the m e l t i n g p r e c i p i t a t i o n i s present i n a
-3
~3
c o n c e n t r a t i o n o f 1 gm . I n p r e c i p i t a t i o n of 5 gm
t h i s corresponds t o
90.
3
4 C km" o
SIMPSON and ROBINSON ( l 9 4 l ) estimated
t h a t the lower p o s i t i v e
charge o f -4 C could be considered as being l o c a t e d i n a r e g i o n 500 m i n
-.3
radius.
This corresponds t o a charge d e n s i t y o f 8 C km o
4
DRAKE (1968) found t h a t the charge separated by m e l t i n g a 10
Molar
1
sodium c h l o r i d e s o l u t i o n (5.8 mg 1 ) a t high m e l t i n g r a t e s was 0.4 p C mg
-3
which would produce a charge d e n s i t y o f 0.4 C km
f o r a concentration o f
-3
-3
-3
m e l t i n g p r e c i p i t a t i o n o f 1 gm
and 2 C km
for 5 g m
p u r i t y o f the water i s probably
r e a l i s t i c e s p e c i a l l y as the measurements
1
. This value of
made by SIMPSON and ROBINSON were made a t Kew which was not an area o f low
pollution.
TABLE 10,1
p r e d i c t e d by l a b o r a t o r y experiments
Concentration of i o n i c i m p u r i t i e s
10"
5
4
1
M ( 0,6 mg l " )
concentration of melting
precipitation
-3
1 gm
c
»3
5 gm
1
1 0 ~ M ( 6 mg l " )
Charge
Density
0.8 C km
4.0 C km
1 gm
0-4 C km
5 gm
2.0 C km
SIMPSON and ROBINSON ( l 9 4 l )
10 3o2
o
8 C km
The e f f e c t of the nature o f the p r e c i p i t a t i o n .
As has been discussed i n s e c t i o n 8.1 the d e n s i t y o f a s o l i d
precipit-
a t i o n p a r t i c l e a f f e c t s the m e l t i n g r a t e o f the i c e as denser p a r t i c l e s f a l l
f a s t e r and reach warmer l e v e l s before f i n a l l y m e l t i n g . .
also m e l t slower f o r the same reason.
and
Smaller p a r t i c l e s
There w i l l be a l i m i t i n g d e n s i t y
s i z e below which the m e l t i n g r a t e i s i n s u f f i c i e n t t o s u s t a i n the
enhanced
meltwater.
separation
e l e c t r i f i c a t i o n associated w i t h vigorous convection
i n the
Such p a r t i c l e s w i l l produce an order o f magnitude less charge
than p a r t i c l e s w i t h higher m e l t i n g r a t e s and w i l l n o t c o n t r i b u t e
sign i f IcantLy t o the lower p o s i t i v e charge.
DRAKE (1968) suggests a
minimum diameter of 1 mm f o r f r o z e n water drops .as these w i l l m e l t a f t e r
f a l l i n g 500 m from the 0°C l e v e l according
-3
t o DRAKE and MASON (1966).
-3
Fig.10 2
The effect
on
of
melting
Electrification
water
purity
ice e l e c t r i f i c a t i o n
R a n g e of
impurity
clouds
concentration
( Na
pC mg
in
CI)
20
2
}
®
Range
e I e c t r t f ica tion
r
0
10
Molar
DATA
concentration
of i m p u r i t y
Drake(196%)
Particles
frozen
Convection
in
in
airstream
meltwater
of
ions
91.
MASON (1956) has c a l c u l a t e d t h a t 3 mm diameter p a r t i c l e s o f s p e c i f i c g r a v i t y
0.3 w i l l m e l t i n a s i m i l a r d i s t a n c e -
Snowflakes have f a l l
speeds less than
1 ms ^ and are u n l i k e l y t o m e l t a t a high enough r a t e t o charge s i g n i f i c a n t l y
by t h i s process.
H a i l and small h a i l which are o f t e n made o f c l e a r o r m i l k y i c e w i t h
most o f t h e a i r trapped i n bubbles l a r g e r than 50 ^m diameter are on the
basis o f t h e work d e s c r i b e d i n chapter 8, u n l i k e l y t o c o n t r i b u t e
to t h e charging process*
significantly
Opaque i c e c o n t a i n i n g many bubbles smaller than
40p m diamter would however be expected t o produce e l e c t r i f i c a t i o n up t o 0.4
"I
-J.
pC mg
i f made o f water w i t h an i m p u r i t y c o n c e n t r a t i o n o f about 5 mg 1
In chapter 5 an e s t i m a t e f o r t h e range o f i m p u r i t y c o n c e n t r a t i o n s i n thunderclouds was given as 2 t o 20 mg 1 ^.
Under t h e i d e a l c o n d i t i o n s discussed i n
s e c t i o n 10<3»1 t h i s corresponds t o a range i n e l e c t r i f i c a t i o n o f 0*2 t o 0*5 pC
mg ^ ( f i g . 10*2) The o b s e r v a t i o n s d e s c r i b e d i n chapter 8- c o n f i r m the magnitude
~5
of c h a r g i n g observed by DRAKE f o r water of i m p u r i t y c o n c e n t r a t i o n 10
M.
10.3.3 The e f f e c t o f the e l e c t r i c f i e l d due t o t h e negative charge c e n t r e .
MATTHEWS and MASON (1964) observed t h a t water drops s h a t t e r i n g i n an
electric field
can produce as much as a f a c t o r o f 100 more charge s e p a r a t i o n
in an e l e c t r i c f i e l d than i n t h e absence of t h e f i e l d *
4
-1
about 3 x 10 V m
field
The f i e l d s used were
which i s a p p r e c i a b l y l e s s than the expected breakdown
i n thunderclouds.
BLANCHARD (1963) s t u d i e d t h e e l e c t r i f i c a t i o n produced by b u r s t i n g
bubbles i n an e l e c t r i c f i e l d *
The charge on t h e j e t drops from a 200pm
3
-1
diameter bubble could be reversed by a f i e l d o f about 3 x 10 V m f o r
H
a 10 M sodium c h l o r i d e s o l u t i o n .
However? from t h e t h e o r y o f IRIBARNE
and MASON (1967) and the c o n c l u s i o n s reached i n chapter 8 i t seems
u n l i k e l y t h a t 200 \im bubbles w i l l p l a y an i m p o r t a n t p a r t i n m e l t i n g
e l e c t r i f i c a t i o n f o r water o f t h i s p u r i t y .
the
As BLANCHARD observed t h a t
i n d u c t i o n charging f e l l o f f r a p i d l y w i t h decreasing j e t drop size
and hence bubble diameter* t h i s mechanism w i l l n o t be so e f f e c t i v e i n
a l t e r i n g the charge separated by bubbles o f about 20 jim diameter i n
Charged
causing
region
the
field
0
Earth
Fig.10-3
of
the
Schematic
bubble
view
of
the e f f e c t
on a n i n d u c t i o n
of
charging
orientation
mechanism
92.
An i n d u c t i o n mechanism would also be i n f l u e n c e d by t h e way i n which the
b u r s t i n g bubbles were d i s t r i b u t e d over the s u r f a c e of t h e m e l t i n g p a r t i c l e
( F i g . 10.3).
I f the bubbles b u r s t a t a l l p o i n t s on t h e surface w i t h equal
frequency, then an i n d u c t i o n mechanism would be i n e f f e c t i v e as the sign
of charge produced a t t h e bottom o f a m e l t i n g p a r t i c l e would be opposite
t o t h a t obtained a t t h e t o p . DRAKE and MASON (1966) have observed t h a t a i r
bubbles o f l e s s than 100 y. m diameter tended t o go t o the bottom of m e l t i n g
ice spheres whereas l a r g e r bubbles g e n e r a l l y went t o the t o p . I f the f i e l d
i n t h e r e g i o n of t h e m e l t i n g h a i l were due t o t h e negative charge centre
above, then the i n d u c t i o n charging would then increase the m e l t i n g
e l e c t r i f i c a t i o n by g i v i n g the e j e c t e d j e t drops from t h e small bubbles more
negative charge.
The magnitude of t h i s e f f e c t i s unknown f o r bubbles l e s s
<
than lOOp. m diamtero
93.
C H A P T E R 11
THE ELECTRIFICATION OF EVAPORATING ICE SPHERES
1 1 o l PREVIOUS WORK
LATHAM and MASON ( l 9 6 l ) have shown t h a t i c e possesses a t h e r m o e l e c t r i c
p r o p e r t y which causes the warmer end o f a piece o f i c e t o be n e g a t i v e l y charged.
When an i c e specimen evaporates> i t s surface temperature
i s u s u a l l y lower than
the i n t e r i o r and one would expect the surface t o acquire a p o s i t i v e charge.
As t h i s surface i s l o s t by e v a p o r a t i o n the remaining ice should acquire a
net negative charge.
LATHAM and STOW (1965) evaporated
an i c e s h e l l surrounding a copper
sphere and found a good q u a l i t a t i v e agreement w i t h the p r e d i c t i o n s o f the
Latham and Mason temperature g r a d i e n t theory.
I n a l a t e r paper LATHAM and
STOW (1966) showed t h a t the p r o b a b i l i t y o f a charged molecule l e a v i n g the
-57
ice
surface was 10
times l e s s than f o r an uncharged molecule.
The
charging a t t r i b u t e d t o evaporation could be explained i f the charged molecule
l e f t t h e ' s u r f a c e i n the centre o f a c l u s t e r o f about 1000 n e u t r a l molecules.
CROSS and SPEARE (1969) monitored the e l e c t r i c ch arging o f a p o l y c r y s t a l l i n e i c e specimen due t o evaporation i n vacuo and showed the
e l e c t r i f i c a t i o n t o be n e g l i g i b l e compared t o t h a t found by LATHAM and
—2
STOW (1965).
The l a r g e s t c u r r e n t recorded was -0.0011 fA mm
evaporation r a t e o f 45 j i g s ^ and a temperature
0.3°C mm
w i t h an
g r a d i e n t i n the surface of
The mean value o f c u r r e n t f o r evaporation ratec between 35
and 70 pgs ^ and temperature g r a d i e n t s o f 0.3 t o 0.6°C mm ^ was - 0.004 fA
-2
-1
mm o For an e v a p o r a t i o n r a t e of 54 JJ qs
the r e s u l t s of the Latham and
Stow experiment p r e d i c t a charging c u r r e n t o f - 38 fA f o r the sample used
3
2
by Cross and Speare (3.5 x 10 mm ) .
The l a r g e s t c u r r e n t observed by
Cross and Speare a t t h i s e v a p o r a t i o n r a t e was -7 fA and the mean value
-2.7 f A .
Cross and Speare also found t h a t p o l y c r y s t a l l i n e i c e evaporating i n
vacuo i s c h a r a c t e r i z e d by the development o f a f i b r o u s o r whiskery
surface.
They suggest t h a t t h e presence o f an a i r s t r e a m w i l l f r a c t u r e these
whiskers
0>
CD
0>
CD
O
CO
o4
0>
uJ
O
1
94.
and cause them t o be c a r r i e d away*
They also suggest t h a t these fragments
w i l l be charged by a temperature g r a d i e n t mechanism i n a s i m i l a r way t o t h a t
proposed by LATHAM (1963) f o r the e l e c t r i f i c a t i o n of f r o s t d e p o s i t s .
11.2 THE ELECTRIFICATION OF E E PARTICLES
EVAPORATING IN THE WIND TUNNEL
Ice
spheres o f about 4 mm diameter were f r o z e n onto 120 ^m p l a t i n u m w i r e s
and allowed t o evaporate i n t h e wind t u n n e l .
The i c e was made f r o m a r t i f i c i a l
- i
cloudwater o f sodium c h l o r i d e content 4,5 mg 1 ' •> The d r y b u l b temperature
of t h e a i r was about 0°C and t h e r e l a t i v e h u m i d i t y ranged from 50 t o 70%*
The wet b u l b depression was s u f f i c i e n t t o prevent the i c e m e l t i n g .
The
values o f e l e c t r i f i c a t i o n d e s c r i b e d i n f i g . 11*1 are averages over a 2 min
12
period of t h e c u r r e n t o u t p u t from t h e V.R.E. which was used w i t h a 10 fl .
input r e s i s t o r .
The maximum average c u r r e n t was + 3 fA and themean + 0.1 f A .
The average r a t e o f e v a p o r a t i o n was computed by equation 8.5 t o be 27 \ig s
1
corresponding t o a r a t e o f heat l o s s o f 68 mW. As the surface area o f t h e
2
ice spheres was about 50 mm , t h e maximum c u r r e n t d e n s i t y corresponds t o
~2
-2
+ 0.06 fA mm
and t h e mean t o + 0*002 fA mm . These values are o f t h e
same order as the background
section of the tunnel-
c u r r e n t s w i t h no i c e present i n t h e working
No c o r r e l a t i o n i s apparent between r a t e o f
evaporation and t h e V o R o E o
reading.
11,3 INTERPRETATION OF THE WIND TUNNEL EXPERIMENT
The wind t u n n e l experiment has enabled the e l e c t r i f i c a t i o n of simulated
s o l i d p r e c i p i t a t i o n p a r t i c l e s t o be studied i n c o n d i t i o n s which are probably
s i m i l a r t o t h e environment o f e v a p o r a t i n g graupel and small h a i l i n the a
atmosphere.
The amount o f charging i s c l e a r l y o f l i t t l e importance i n
cloud e l e c t r i f i c a t i o n
?
as even a t the maximum charging r a t e , the p a r t i c l e
would take 50 min t o a t t a i n a charge e q u i v a l e n t t o t h a t due t o i t s m e l t i n g
™X
""X
D
(0»3 pC mg
o r 1 esu g ) •
The values o f the temperature g r a d i e n t s expected are l i k e l y t o be
1
c o n s i d e r a b l y l e s s than t h e 9°C mm"
value estimated by LATHAM and STOW
(1965) f o r t h e i c e s h e l l on t h e copper sphere used i n t h e i r experiments.
95.
MASON (1956) has c a l c u l a t e d the theimal r e l a x a t i o n time o f a 4mm diameter
ice
sphere f a l l i n g a t t e r m i n a l speed t o be 7s. I t seems l i k e l y t h a t such
a p r e c i p i t a t i o n p a r t i c l e would soon reach a c o n s t a n t temperature w h i l e
evaporating i n an i s o t h e r m a l atmosphere.
I f the e v a p o r a t i n g p a r t i c l e i s
f a l l i n g i n a r e a l atmosphere where the temperature increases as t h e p a r t i c l e
f a l l s , t h e o u t e r surface w i l l be warmer than t h e c e n t r e .
i s f a l l i n g a t 7 ms
I f the p a r t i c l e
through an atmosphere w i t h t h e d r y a d i a b a t i c lapse r a t e
of 10°C km ^ the increase i n temperature o f t h e environment d u r i n g a p e r i o d
equal t o t h e r e l a x a t i o n time o f the p a r t i c l e w i l l be 0.5°C«
Assuming t h i s
i s the temperature d i f f e r e n c e between the centre and the surface o f a 4 mm
diameter p a r t i c l e , t h e mean temperature g r a d i e n t w i l l be approximately 0.25°C
mm *
o r a f a c t o r of 30 l e s s than i n the Latham and Stow experiment.
One would a l s o expect the s i g n o f t h e charge s e p a r a t i o n t o be opposite
to t h a t found by Latham and Stow and the e v a p o r a t i n g p a r t i c l e t o become
p o s i t i v e l y chargedo
A temperature g r a d i e n t should a l s o develop i n t h e
whiskers o f i c e formed d u r i n g t h e e v a p o r a t i o n , due t o a g r e a t e r e v a p o r a t i o n
rate o c c u r r i n g a t t h e t i p s o f the whiskers than near t h e surface of the
particle.
This gradient would be o f the same s i g n as i n the Latham and Stow
experiment.
I t i s suggested t h a t the one reason f o r t h e low l e v e l of charging
produced by t h e e v a p o r a t i o n of the small ice spheres was t h e low temperature
g r a d i e n t s i n the i c e samples.
This c o n d i t i o n i s l i k e l y t o be found i n t h e
evaporation o f p a r t i c l e s s m a l l e r than 10 mm diameter i n the r e a l atmosphere.
While i t i s not know whether whiskers d i d develop on the surface d u r i n g
e v a p o r a t i o n , i f t h e y d i d f o r m , then presumably
t h e temperature g r a d i e n t s
i n them were i n s u f f i c i e n t t o produce a measureable e l e c t r i f i c a t i o n .
96.
C H A P T E R 12
CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK
12.1 THE DESIGN OF A WIND TUNNEL TO STUDY THE
ELECTRIFICATION OF PRECIPITATION
The design o f t h e wind t u n n e l which supported small i c e spheres has
enabled some o f the problems associated w i t h t h i s type of research t o be
studied.
The design o f a windtunnel which w i l l support both s o l i d and
l i q u i d p a r t i c l e s i s c l e a r l y more d i f f i c u l t than a system which w i l l support
only water drops $ as the way i n which these p a r t i c l e s r e a c t t o pressure
g r a d i e n t s and shear f o r c e s i s d i f f e r e n t .
As no small wind t u n n e l appears t o
have been designed which w i l l support a p a r t i c l e throughout i t s m e l t i n g p e r i o d ,
the
a d d i t i o n a l c o n s t r a i n t s t o design caused by the need t o measure small
e l e c t r i c c u r r e n t s and t o keep the p a r t i c l e s very clean make the design o f
such a t u n n e l even more d i f f i c u l t .
Even w i t h a wind tunnel working s e c t i o n as small as 40 mm diameter the
r a t e of f l o w of a i r was so g r e a t t h a t the a i r i n the cold room of volume
3
o
4m was heated t o about 2 C a f t e r a m e l t i n g r u n l a s t i n g 1G min.
This
l i m i t e d t h e r a t e o f p e r f o r m i n g experiments t o one (.-very 3 hours? as the cold
room temperature had t o be r e s t o r e d t o below f r e e z i n g .
Stringent precautions
to avoid c o n t a m i n a t i o n a l s o slow down t h e e x p e r i m e n t a t i o n and some r e s u l t s
were r e j e c t e d because o f p o s s i b l e c o n t a m i n a t i o n . I n the present work? on
average o n l y 2 experiments per day gave useable r e s u l t s .
These problems
would a r i s e w i t h almost any system of s u p p o r t i n g i c e p a r t i c l e s i n a t u n n e l .
Another problem a s s o c i a t e d w i t h . t h e h i g h f l o w r a t e o f a i r i s t h e d i f f i c u l t y
i n r e g u l a t i n g the r e l a t i v e h u m i d i t y i f the a i r i s heated c o n s i d e r a b l y t o
enable t h e i c e p a r t i c l e s t o m e l t .
The h u m i d i f i c a t i o n o f a i r f l o w i n g a t
-1
the
r a t e o f 10 1 s
was found t o r e q u i r e more s o p h i s t i c a t e d
than a heated t r a y o f water.
a commerical h u m i d i f y i n g u n i t .
equipment
Probably the b e s t method would be t o use
Clearly, trying t oattain realistic
c o n d i t i o n s by f l y i n g or s u p p o r t i n g p a r t i c l e s i n a r e l a t i v e l y laminar
97o
f l o w environment does severely l i m i t t h e v e r s a t i l i t y o f the apparatus and
the c o n c l u s i o n s t h a t can be drawn from such experiments- The d i f f i c u l t y of
measuring t h e mass o f i r r e g u l a r i c e p a r t i c l e s 9 which a l s o had t o be kept
very clean? i n t r o d u c e d an e r r o r o f about 30% i n t o the f i n a l value of t h e
charge t o mass r a t i o . T h i s e r r o r n e c e s s i t a t e s a l a r g e number o f
experiments t o deduce the e f f e c t of environmental c o n d i t i o n s on the m e l t i n g
e l e c t r i f i c a t i o n . Furthermore t h e slow r a t e o f e x p e r i m e n t a t i o n w i t h a l a r g e
wind t u n n e l can be a great hindrance t o g e t t i n g meaningful r e s u l t s i n the
time a v a i l a b l e . I t may w e l l be t h a t these disadvantages of a l a r g e tunnel
capable o f f r e e l y f l y i n g a m e l t i n g p a r t i c l e make such a system of l e s s
use than t h e more simple and v e r s a t i l e system used by CRAKE ( l 9 6 8 ) o
1 2 . 2 THE ELECTRIFICATION OF MELTING ICE
The e l e c t r i f i c a t i o n o f m e l t i n g i c e has been shown t o be h i g h l y
on the r a t e a t which t h e i c e was formed i n i t i a l l y .
dependent
Water drops f r o z e n i n
s t i l l a i r were found t o produce an o r d e r of magnitude l e s s c h a r g i n g on
m e l t i n g than drops f r o z e n i n an a i r s t r e a m f l o w i n g a t 11 ms ^. The
d i s t r i b u t i o n and sizes o f t h e bubbles were found t o be d i f f e r e n t f o r the
drops f r o z e n i n moving and s t i l l a i r *
I t appeared t h a t a t low f r e e z i n g r a t e s
l e s s a i r was trapped because the a i r could escape w h i l s t the i c e s h e l l was
s t i l l thin.
Ice f r o z e n i n t h e a i r s t r e a m below about -8°C contained no a i r
bubbles g r e a t e r than 50 \im diamter? whereas i f the i c e were formed I n s t i l l
a i r the l a r g e s t bubbles were u s u a l l y from 100 t o 200jim i n diameter. The
o b s e r v a t i o n s t h a t a l a r g e number of small bubbles of diameter l e s s than
50|Am w i l l produce c o n s i d e r a b l y more e l e c t r i f i c a t i o n than a s m a l l e r number
of l a r g e r bubbles agrees w e l l w i t h the IRIBARNE and MASON (1967) theory o f
the
e l e c t r i f i c a t i o n o f b u r s t i n g a i r bubbles.
Evidence was found t h a t carbon d i o x i d e was r a p i d l y absorbed by a
m e l t i n g water drop f a l l i n g i n a i r and i t was suggested t h a t the d i f f e r e n t
r e s u l t s o f the e f f e c t o f CO^ on m e l t i n g e l e c t r i f i c a t i o n noted by DRAKE
(1968)
and DINGER and GUNN
(1946)
can be e x p l a i n e d by t h e way i n which
98.
C0 escaped from the i c e d u r i n g m e l t i n g . A r a p i d increase o f an order o f
magnitude i n m e l t i n g e l e c t r i f i c a t i o n over a small range of m e l t i n g r a t e s
was observed, and t h i s may be the same as t h a t observed by DRAKE t o be due
to t h e onset o f vigorous c o n v e c t i o n i n the meltwater. I t was shown t h a t
t h i s increased e l e c t r i f i c a t i o n could occur a t m e l t i n g r a t e s l i k e l y t o be
found i n the atmosphere. No s i g n i f i c a n t d i f f e r e n c e was noted between the
e l e c t r i f i c a t i o n o f ice melted on s t r a i g h t 100 Jim p l a t i n u m wires and 1.5 mm
loops o f w i r e . As the loop support i s e a s i e r to use t h i s i s probably the
best type of support.
2
F u r t h e r work on the e l e c t r i f i c a t i o n o f m e l t i n g ice should i n c l u d e an
e v a l u a t i o n o f the e f f e c t s o f e l e c t r i c f i e l d s .
The e f f e c t o f CO^ on the
e l e c t r i f i c a t i o n should be reexamined i n order t o see whether i t s bejaviour
i s c o n s i s t e n t w i t h a b u r s t i n g bubble mechanism.
Work on the e l e c t r i f i c a t i o n
produced by the b u r s t i n g o f bubbles o f less than ICO^im diamter would enable
the
IRIBARNE and MASON t h e o r y t o be checked f o r t h e range o f bubbles
l i k e l y t o be found i n small s o l i d p r e c i p i t a t i o n p a r t i c l e s .
sizes
The present
work, and t h a t o f DRAKE, s t r o n g l y suggest a bubble b u r s t i n g mechanism
f o r the f o r m a t i o n of the p o s i t i v e charge on the meltwater.
12.3
THE ROLE OF MELTING ICE IN CLOUD EIECTRIFICATION
Using the i n f o r m a t i o n gained i n the present i n v e s t i g a t i o n and the
work o f DRAKE (1968), the e f f e c t o f some o f the important v a r i a b l e s
i n f l u e n c i n g m e l t i n g e l e c t r i f i c a t i o n can be assessed.
I t has been shown
t h a t p r e c i p i t a t i o n p a r t i c l e s o f approximately s p e c i f i c g r a v i t y 0.9 and
diameter 4 mm m e l t i n g i n a cloud w i l l probably d i s p l a y the enhanced
e l e c t r i f i c a t i o n which Drake associated w i t h vigorous convection i n the
meltwater.
I t was found t h a t the volume of a i r and the s i z e o f the a i r
bubbles trapped i n t h e i c e could i n f l u e n c e the e l e c t r i f i c a t i o n by an
o r d e r o f magnitude.
formed i n s t i l l
Ice which was m i l k y i n appearance and which was
a i r produced t e n times l e s s charging than completely
opaque i c e formed i n an a i r s t r e a m .
a i r bubble
I t i s t h e r e f o r e suggested
t h a t the
s t r u c t u r e o f the i c e i s v e r y i m p o r t a n t i n i n f l u e n c i n g the
99.
the amount of e l e c t r i f i c a t i o n produced
by t h i s mechanism, and t h a t i c e formed
by d r y growth may be more e f f e c t i v e than i c e formed by wet growth.
The m e l t i n g r a t e and p a r t i c l e size can i n f l u e n c e the- development of
-enhanced e l e c t r i f i c a t i o n which may be associated w i t h v i g o r o u s convection
i n the meltwater.
The m e l t i n g r a t e depends on the speed o f the downdraught
and the d e n s i t y o f the p a r t i c l e s , as w e l l as the size of t h e p a r t i c l e s and
the a c t u a l lapse r a t e o f the temperature i n t h e c l o u d .
The e f f e c t o f
i m p u r i t i e s i n the cloudwater may be l e s s than the e f f e c t of the a i r bubble
s t r u c t u r e and m e l t i n g r a t e s , according t o the experiments described i n
Chapter 8.
I f t h e c o n t r i b u t i o n of the m e l t i n g i c e t o the e l e c t r i c a l
s t r u c t u r e o f a thunderstorm i s t o be assessed, then more i n f o r m a t i o n i s
needed of the a c t u a l m e l t i n g i c e p a r t i c l e s and the m e l t i n g environment.
I t was p o i n t e d out i n Chapter 10 t h a t the amount of i n f o r m a t i o n o f
the l o c a t i o n , magnitude and frequency of occurrence of the lower p o s i t i v e
charge i s very s m a l l .
I t i s n o t even p o s s i b l e t o say t h a t t h e r e i s only
one type of lower p o s i t i v e charge.
Certainly there i s i n s u f f i c i e n t
i n f o r m a t i o n t o r u l e out a m e l t i n g i c e o r i g i n , but on the evidence
a v a i l a b l e i t was suggested t h a t such a mechanism could o n l y e x p l a i n the
charge under t h e best circumstances p o s s i b l e , unless the mechanism was
more e f f e c t i v e i n the presence of e l e c t r i c
fields.
The process of m e l t i n g e l e c t r i f i c a t i o n and t h e c o n d i t i o n s t h a t might
cause i t t o be an e f f e c t i v e means o f charge p r o d u c t i o n i n clouds are
r e l a t i v e l y well'understood.
However i t i s not p o s s i b l e t o decide on the
mechanism f o r t h e f o r m a t i o n of the lower p o s i t i v e charge u n t i l more
i n f o r m a t i o n i s a v a i l a b l e on t h e magnitude and p o s i t i o n of the c h a r g e
9
on the nature of the p r e c i p i t a t i o n and the evironmental c o n d i t i o n s
associated w i t h t h e charge.
This l a b o r a t o r y i n v e s t i g a t i o n has suggested
several p r o p e r t i e s of clouds which may w e l l i n f l u e n c e the cloud e l e c t r i fication.
These p r o p e r t i e s must now be studied i n d e t a i l i f the physics
of the lower p o s i t i v e charge i s t o be understood.
100,
APPENDIX 1
WIR,^
A l . l THE ELECTRIFICATION OF ICE SPHERES MET.TTNG ON, PI,A,nM
Ice f r o z e n i n stagnant a i r
ARTIFICIAL CLOUD WATER - 4.5 mg l "
1
sodium c h l o r i d e .
C o n d u c t i v i t y 8.4 jimho cm *
No
Dry Bulb
Temperature
°c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
12.5
10.0
10.1
10.6
11.6
11.3
11.4
9.8
10.4
10,1
8.7
11.5
9.2
10.6
10.9
9.8
11.0
11.2
12.0
9.8
9.8
8.9
8.8
11.6
9.6
10.0
11.2
9.5
6.6
8.8
10.4
9.3
9.8
11.2
8.4
10.0
10.1
10.5
10.0
10.9
10.4
10,4
9.0
9.6
10.6
Dew Point
Melting
Heat
Initial
Mass
Mass
Melted
- °c
mW
mg
mg
64
32
32
32
48
32
32
32
36
32
32
32
40
48
40
41
48
36
60
48
48
36
40
48
40
36
48
48
40
32
40
32
32
40
24
64
48
40
36.
48*
48
36
40
40
36
56
25
24
22
35
21
19
21
26
27
22
25
34
35
36
43
43
17
20
23
45
32
38
39
34
33
43
37
36
29
34
29
29
35
20
56
45
38
34
44
41
28
18
35
31
5.7
5.8
6.5
7.8
7.9
8.4
9.1
7.3
7.0
4.b
6.2
6.3
4.5
7.4
3.9
3.7
4.1
9.5
9.2
8.5
3.8
3.8
2.8
6.4
4.6
3.5
4.5
6.4
2.6
3.5
4.5
3.5
3.7
4.7
4.5
4.4
2.5
2.0
2.2
3.1
4.6
5.9
7-9
3.5
4.5
96
49
43
34
47
38
27
31
44
63
32
60
68
42
86
75
85
21
26
20
85
58
73
66
83
73
83
44
50
60
74
72
69
81
44
80
92
101
84
99
73
53
18
75
69
101
No
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Dry bulb
Temperature
Dew point
°C
-°C
Melting
Heat
mW
10.1
10.4
10*4
10.5
11.6
11.6
.14.0
11.1
12.6
10.6
13.1
11.2
14.9
11.9
3.8
3.9
2.5
2.9
1-8
1.6
2.7
1.6
2.0
2.7
1.9
2.7
1.7
2.1
81
80
95
96
105
118
142
112
125
99
136
93
141
106
No
Freezing Temp
Cha rge
- °C
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
12
12.
11.5
13
12.5
13
12.5
12
11.5
11.5
12
11.5
11.5
13
12
11.8
11.5
14.5
14
10.5
10
10
10.5
13
12
10.5
11.5
14
13
11
11
12.5
11.5
11
11.5
11
+ pC
4.5
0.2
0
0.2
2*0
1.3
0.7
0.2.
0.1
0,1
Ool
0.2
0.4
0.8
0.6
2.2
0.7
1.0
0
0.1
0.8
0.1
0.9
2.4
1.3
4.2
2.0
3.1
2.3
0.3
0.5
1.3
0.5
1.3
0.»9
0,1
Initial
Mass
Mass
Melted
mg
mg
48
40
40
48
48
40
48
48
40
48
40
36
36
32
43
36
38
45
46
39
46
46
38
44
38
33
35
31
Charge/mass
pC mg *
0.08
0.008
0
0.009
0o058
0*060
0.038
0.009
0.004
0o004
0.005
0..008
0.012
0o023
0.016
0.051
0.016
0.057
0
0.004
0.018
0.003
0.024
0.062
0.038
0.129
0.047
0.106
0.063
0.008
0.017
0.038
0.017
0.045
0.026
0.005
!
A 3 APR 1972
MOTION
[BRA!
102.
No
Charge
Freezing Temp
37
38
39
40
41
42
43
44
4b
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
- ° c"
+C
13
10.5
11
12
10
11
12
14
14.5
10o5
12
11.5
14o5
12
11
11.5
14o5
13
15
14.5
11
11
10.5
10
3.1
1.3
Charge/ma:
pC mg
P
0.055
0.029
0.031
1.2
0.4
1.6
0.7
1.2.
1.6
1.0
1.0
2.2
1.7
4.1
1.0
1.5
0.7
3.4
2.6
4.4
lo4
1.3
0.012
0,036
0.017
0.043
0.088
0.02.8
0.032
0.051
0.048
0.109
0.022
0.032
0.018
0.074
0.056
0.114
0.031
0,034
0.027
0.031
0.033
0.9
1.1
1.0
A 1 . 2 THE ELECTRIFICATION OF ICE SPHERES MELTING ON PLATINUM WIRES
Ice frozen i n stagnant a i r .
E E IONIZED WATER
No
Dry Bulb
Temperature
C
5
61
62
63
65
66
67
68
69
70
71
72
73
74
75
13.0
13.7
14.0
14.1
1^3
13.2
13.5
12.0
13.6
13.7
15.0
13.8
13.2
14.7
14.0
Conductivity
Dew Point
1 . 0 pmho
-1
cm
-°C
Melting
Heat
mW
Initial
Mass
mg
Mass
Melted
mg
1.2
3.3
2.0
2.5
2.4
0„8
2.5
1.4
2.5
2.5
2.6
2.5
2.2
3.2
2.8
138
119
154
138
141
157
131
125
126
121
154
140
130
137
133
40
36
48
40
40
48
40
46
32
32
48
48
46
40
46
39
34
46,
38
38
47
38
45
30
31
46
46
44
38
44
103.
No
61
62.
63
64
65
66
67
68
69
70
71
72
73
74
75
Freezing
Temperature
Cha rge
Charge/mass
-°C
+pC
pC mg ^
12
9
9.5
11.5
14
10.5
12
13
7.5
50
6.5
6.8
14.5
12.5
13.0
5.7
3.9
3.2
4.6
11.1
3.8
7.6
8.2
2.9
1.1
1.2
2.2
4.0
3.8
4.5
0,15
0.12
C.069
0.12
0.29
0.08
0„20
0.18
0..10
0.036
0.026
0,»05
0.09
0.10
0.10
A l . 3 THE ELECTRIFICATION OF ICE SPHERES MELTING ON PLATINUM LOOPS
NO
76
77
78
79
80
81
82
83
84
Dry Bulb
Temperature
C
Dew Point
12.5
14.0
12.3
14.2
13.7
13,2
13.5
13.7
12.0
No
76
77
78
79
80
81
82
83
84
- C
Melting
Heat
mW
Initial
mass
mg
Mass
Melted
mg
1.0
2o4
2.5
4.7
1.1
1.7
1.5
1.3
2.0
115
100
90
94
127
118
109
99
81
24
18
18
21
27
24
18
14
14
24
17
17
19
27
23
18
14
14
Freezing
Temperature
Charge
Charge/mass
-°C
+pC
pC mg ^
11
9
8.5
10
11.5
11.5
7
4
8
5.0
0„8
1.2
2.0
5.0
4.4
2.0
0„1
3.9
0.21
0.046
0.07
0.11
0.19
0>19
0.11
0.007
0.29
104.
A1.4
THE ELECTRIFICATION OF ICE SPHERES MELTING ON PLATINUM I POPS
DEIONIZED WATER
Conductivity 1 . 0 mho cm"
1
Drops frozen i n an a i r stream moving at 11 ms
No
85
86
87
88
89
90
91
92
93
94
95
Dry Bulb
Temperature
~C
12.0
11.0
14.5
11.8
14.0
12.0
12.8
13.1
12.7
13.1
11.2
NO
85
86
87
88
89
90
91
92
93
94
95
Dew Point
- C
Melting
Heat
mW
Initial
Mass
mg
Mass
Melted
mg
2.0
1.5
4.5
6.2
1.3
2.5
2.0
2.0
1.2
2.0
1.3
86
81
82
48
108
82
87
89
98
95
85
18
18
14
16
18
18
14
14
18
18
18
17
17
13
13
18
17
13
13
18
17
18
Freezing
Temperature
-°C
Cha rge
+pC
12o0
12.5
5.2
12.3
8.5
3.5
11.5
6.6
2.4
5.3
12.5
11.2
13.5
6.9
12.2
12.0
2.9
15.3
12.5
0.4
4.6
11.1
Charge/mass
pC mg
0.65
0.77
0,54
0.94
0.68
0.17
0.14
0o93
0.023
0,27
0.63
Melting heat is defined as the heat f l o w rate to the melting sphere
which causes the ice to melt and i s corrected f o r the loss of heat due
to evaporation using equation 8 . 1 „
The value of mass melted melting
heat and charge/mass were worked out on the
computer using the program outlined i n A l . 5 .
9
NoU.M.AoC.
IoB.M.
360
105.
A l . 5 FORTRAN PROGRAM USED TO PROCESS THE WELTING ELECTRIFICATION DATA
DIMENSION TW (lOO) , HTM (lOO), TIME (lOO), TIMM (lOO), AMASS (lOO), Q (lOO),
TDEW (100), RAD (lOO) , HMELT (lOO), TF (lOO)
lo
FORMAT (12 F 5.1)
2.
FORMAT (8 x, 'TEMPW , 2x, HT. MELT', 2x, 'TIMM', 2x, 'HT,EVAP' , 2x,
1
,
1
'TIME • , 4x, 'INMASS , 2x, 'CHARGE', 2x, 'FRACTM' , 2.x, 'MASS MLT*,
1
1
2x, 'RATE', 4x, 'QPM , 5x, 'RAD', 6x, 'TDEW , 3 , 'TEMPF')
X
3.
FORMAT (2x, 13, 14 F 8.3)
READ (5,1) (TW(I), HTM(I), TIME ( I ) , TIMM ( i ) , AMASS ( i ) , Q ( l ) , I =1,36)
READ (5,1) (TDEW ( i ) , RAD ( i ) , TF ( I ) , I =
1,36)
WRITE (6,2)
DO 10
I = 1,36
HT MELT ( I ) = 3 . 9 * RAD ( I ) * (TW ( I ) j p l . 3 4 - 1.09
0.022
TDEW ( I ) -
TDEW ( l ) J t * . 2 .
HTE = 3.9 + RAD ( I ) ^
(.U0( ^ TDEW ( i ) + 0.022
TDEW ( 1 ) ^ 2 . )
A = H MELT (I)-Jf 8. ^ T I M M ( I )
B = HTE j|LTIMM ( I )
C = 3 . 9 ^ RAD ( I ) % ( . 5 5 ^ 7 DEW ( I ) + .005 Jjf TDEW ( l ) # ^ 2 . )
D - C *(TIME ( I ) - TIMM ( I ) )
FRACTM = A / (A+B+D)
AMELT = FRACTM
AMASS ( I )
RATE - AMELT/TIMM ( i )
QPM - Q ( I ) / AMELT
10. WRITE (6,3) I , TW(I), H MELT ( i ) , TIMM ( i ) , HTE, TIME ( I ) , AMASS ( i ) ,
Q ( I ) , FRACTM, AMELT, RATE, QPM, RAD ( i ) , TDEW ( I ) , TF ( i )
STOP
END
In the above program the names of the variables are as follows
I
index number of the ice p a r t i c l e
TW average dry bulb temperature during l a s t minute of melting °C
106
HTM
melting heat mW
TIME
Time p a r t i c l e was evaporating min.
TIMM
Time p a r t i c l e was melting
min.
(This is defined by the time between the moment when
the a i r temperature has been raised halfway between
0°C and i t s f i n a l value at the end of melting and
the end of the melting process).
AMASS The i n i t i a l mass of the p a r t i c l e as deduced from i t s
dimensions mg<»
Q
The charge on the meltwater at the end of melting pG
(This was calculated by integrating the current over the
melting period using the
U»Vo
chart record).
TDEW Modulus of the dew point temperature of the a i r i n the
tunnel during the l a s t minute of melting.. °C
RAD
Mean radius of the p a r t i c l e
mm
TF
Modulus of the temperature of the freezing environment
FRACTM Fraction of the ice actually meltedo
AMELT Mass of ice actually melted mg
QPM
Charge/mass melted pC mg
107
APPENDIX 2
THE ABSORPTION AND DESQRPTION OF
A2.1
CARBON
DIOXIDE
BY WATER
Absorption by a stationary drop.
The chief cause of resistance to the d i f f u s i o n of CO^ i n t o a water drop
i n stagnant a i r i s the t h i n surface f i l m of l i q u i d .
This f i l m has a
permeability which r a p i d l y decreases a f t e r the i n i t i a l exposure to CO^ due
to the increasing saturation of the layer.
permeability remains constant.
When the f i l m is saturated the
The rate of absorption can be related to
the concentration gradient i n the surface f i l m by
|~
= k A (Cg - C )
..........
x
A2.1
where W i s the volume of gas absorbed, A the surface area, k the permeability
c o e f f i c i e n t and C the concentration of CO^.
The subscript 1 r e f e r s to the
l i q u i d remote from the f i l m and g to the g a s / l i q i d boundary.
u
RIDEAL and DAVIES (l963) show, by solving the d i f f u s i o n equation f o r
a stagnant l i q u i d of i n f i n i t e e x t e n t , that the permeability c o e f f i c i e n t
is related to the d i f f u s i o n c o e f f i c i e n t D by
k
=
/ D
..........
A2.2
7 TTt
provided that the f i l m i s not saturated.
A f t e r the f i l m becomes saturated
at a time t
k -
/
#JD
^s
By i n t e g r a t i n g A2.1 with respect to time and s u b s t i t u t i n g f o r k
we have , f o r a water drop of radius r ,
W=
t
\
2
fair?
(Cg-C^
PD" j
dt . . . . . . . . .
A2.3
A f t e r a time t , the f r a c t i o n f of the amount of C0 absorbed at
2
e q u i l i b r i u m may be w r i t t e n as
W
f
=
.
——
{4VTCg/3)
a
~
|
[ C g - C,)
ftz>\
dt . . . A 2 . 4
108
I f we assume t h a t once the CO^ has passed through the surface f i l m i t i s
r a p i d l y d i s t r i b u t e d throughout the drop
then
C = f Cg
t
=
f/sj J
a
r
1
izf.
d
t
A 2
.
5
This equation has a s o l u t i o n
:
<
1
2
n
f - V " - - ' ° - (;> (I)"
which converges r a p i d l y i f t «
value of t = ^
r
72
t n / 2
2 6
- «-
2
2
. but tends to i n f i n i t y if t > 5-
.
The
corresponds to the time when the permeability has reached
a minimum value due to the saturation of the layer and may be designated
as t .
s
WHITIMAN et al (1926) quote the permeability c o e f f i c i e n t f o r t > t
as 2.8 x 10
1
ms , which approximately corresponds to a saturation time t
of
s
100s.
For t ^ 100 s
t = 100s, and k
f
f can be expressed i n terms of f-^QQj the value of f at
1 Q 0
, the permeability c o e f f i c i e n t f o r t
= f
l Q 0
+
3 k
l00
r
/
100
( l - f ) dT
A2.7
J
o
where T = t -100.
3
D i f f e r e n t i a t i n g A2.7 and w r i t i n g a = - k^00
df
a
a (i-f)
A
dT
2
,
b
This has the s o l u t i o n
f = 1 - (l-f
1 0 0
) exp (-a(t-lOO))
For a 4 mm diameter water drop A2.6 gives f^oO
A2.9
=
s
^^^ations
A2.6 and A2.9 are p l o t t e d i n f i g . 9.3.
A2.2 The desorption of a t h i n water layer i n a container.
The desorption of a t h i n water layer on the surface of a block of
ice i n a container can be treated i n a s i m i l a r way to the absorption of
gas by a water drop, provided that the process is by molecular d i f f u s i o n
109
through an undisturbed surface f i l m .
I f the surface f i l m has been present
f o r longer than 100 then i t can be said to be saturated and the permeability
can be taken as constant.
S
For a layer of area A and depth d , f may be w r i t t e n i n a similar way to
equation A2.5:
/
f
k A ( l - f ) dt
/ k
Ad
J
( l - f ) dt
A2.10
J d
The s o l u t i o n of A2.10 w i l l be
f = 1 - exp - ( k t / d )
A2.ll
The time constant of the desorption of a layer d due to i t s formation from
Co^ saturated ice w i l l be d / k .
WHITMAN
A2.3
F r a 1 mm layer with kjs
0
2.8 x 10 ^ ms
1
et a l . (1926) , the time constant w i l l be approximately 400 .
s
The release of carbon epoxide from a bubble immersed i n an unsaturated
liquid.
I f one assumes t h a t the gas w i l l d i f f u s e through the bulk l i q u i d f a s t e r
than through the surface f i l m , and i f the concentration of GO^ i n the water
is n e g l i g i b l e compared to that i n the bubble, the volume of CO^ removed from
the bubble i s
Q =
I
k A Cg dt
A2.12
where A i s the surface area of the bubble and Cg the concentration of CO
inside the bubble.
The f r a c t i o n f of the i n t i a l concentration Co of Co,
>2
in the bubble i s given i n a s i m i l a r way to A2.5 as
f =
3
/I
Co.47Tr
rI rD
3
J
i
r
2
4 t7t r r Co f dt
A2.13
t
D i f f e r e n t i a t i n g both sides of A2-13 by t we have
4E
dt
=
2
3
-
r
r
^
v
|
D
-
.f
TTi
f t
which may be expressed as
d£
=
3
3
/; D
5
f
r
\ J Trt
I n t e g r a t i n g equation A2.14 we have
dt
A2.14
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13 APR 1972
LlBBAgJ