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Experiments on the condensation and sublimation of water vapour at low temperatures

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Ref Ser Q21 l'~2t4 COPY NO. ,, -;, no. TT-60 BLDG

mc

PUB t I 1, 1

-.

NATIONAL

RESEARCH

COUNCIL

OF

CANADA

DIVISION OF MECHANICAL ENGINEERING

TECHNICAL TRANSLATION NO. TT

-

6 8

EXPERIMENTS ON THE CONDENSATION AND SUBLlMATlON

OF WATER VAPOUR AT LOW TEMPERATURES

I I

(VERSUCHE UBER DIE KONDENSATION UND SUBLIMATION DES WASSERDAMPFES BE1 TIEFEN 'TEMPERATUREN)

BY

ERlCH REGENER

OTTAWA 20 APRIL 1948

THIS REPORT MAY NOT BE PUBLISHED I N WHOLE OR I N PART WITHOUT T H E WRITTEN CONSENT O F

(3)

NATIONAL ilESEARCH LABORATORIES

Pages

-

7

Fig,

-

1

Ottawa, Canada

TECHNICAL TRANSLA TIOW

D i v i s i o n of Mechanical Engineering

Techo Trans. TT-68 Date

-

20 A p r i l , 1948. F i l e

-

12-R4-22

T i t l e : Versuche a b e r d i e Kondensation und Sublimation des Wasserdampfes b e i t i e f e n Ternperatwen.

By: E r i c h Regener

c

Reference: z\VB/DAL/S~, pp 17-24, Paper g i v e n a t t h e n i n t h s e s s i o n of r e g u l a r members of' the German

Academy of Aeronautical Research, 1 7 January, 1941,

S u b j e c t : EXPFHIlLlENTS ON THR CONDENSATION

AND

SUBLIMATION

OF WAmR VAPOUII AT LOW ilIJIPERA'I'UHES,

Submitted by:

J o

L o

O r r , T r a n s l a t e d by:

Head, D,A. S i n c l a i r .

Low Temperature Laboratory, Approved by:

J,H,

Parkin,

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Pago

-

1

Tech, Trans, TT-68

EXPERIMENTS ON THE; COVIIENSATION AND SUBLIMATION

OF

WATER

VAPOUZ AT LOW TEMPERATURE'S

-

One of t h e most i m p o r t a n t problems i n t h e p h y s i c s of c l o u d s i s t h e q u e s t i o n , under what c o n d i t i o n s c a n

s u p e r c o o l e d w a t e r d r o p l e t s form i n t h e f r e e atmosphere a t

sub-zero t e m p e r a t u r e s :, and under what c o n d i t i o n s may i c e c r y s t a l s o c c u r ,

From analogy w i t h c o n d i t i o n s a t h i e e r tempera- t u r e s i t i s a j u s t i f i a b l e c o n c l u s i o n t h a t a t low t e m p e r a t u r e s , t o o , when s u p e r s a t u r n t i o n s o c c u r i n the atmosphere, condensa- t i o n n u c l e i must always be p r e s e n t i f e i t h e r c o n d e n s a t i o n o r s u b l i m a t i o n i s t o t a k e p l a c e , But s i n c e u n g e r a p p a r e n t l y i d e n t i c a l c o n d i t i o n s some times s u p e r c o o l e d w a t e r d r o p l e t a and

a t o t h e r times i c e c r y s t a l s a r e obsesved i n t h e atmosphere, t h e m e t e o r o l o g i s t s have s o u g h t t o e x p l a i n t h e d i f f e r e n c e by t h e e x i s t e n c e o f two d i f f e r e n t t y p e s of n u c l e u s , There a r e s a i d t o be c o n d e n s a t i o n n u c l e i l e a d i n g t o t h e f o r m a t i o n o f w a t e r d r o p l e t s , and d i f f e r e n t l y c o n s t i t l x t e d n u c l e i on which

t h e w a t e r vapou from the a i r sublimos d i r e c t l y t o i c e ,

17

A l f r e d Wegoner

,

i n p a r t i c u l a r , e x p r e s s e d t h e h y p o t h e s i s t h a t s m a l l q u a r t z p a r t i c l e s might a c t a s s u b l f m a t i o n n u c l e i , s i n c e q u a r t z h a s t h e same c r y s t a l form a s i c e , and t h i s would

favour t h e c r y s t a l l i z a t i o n of w a t e r vapoyr on

it.

F'indeisenz) has a l s o r e c e n t l y proposed t h e same t h e o r y o

The p h y s i c a l chemists on the o t h e r hand have

l o n g had the s o = - c a l l e d Ostwald law of s t a t e s , ~ a c c o r d i n _ . : t o which when w a t e r vapour i s s u p e r s a t u r a b e d a t low temperaturea

the u n s t a b l e , s u p e r c o o l e d water o f h i g h e r energy c o n t e n t must f i r s t condense o u t from i t and can then, by f r e e z i n g , become i c e of lower energy c o n t e n t , The problem of s e p a r a t i n g t h e new phase h a s r e c e n t l y been f o r m u l a t e d mops p r e i s e l y and

37

g i v e n e x a c t t h e o r e t i c a l t r e a t x e n t by

M,

Volmer According t o Volmer t h e d e c i s i v e f a c t o r f o r c o n d e n s a t i o n and s u b l i m a t i o n

is t h e amount of ~ i , a r k which must be performed ~ g a F n s t t h e s u r - f a c e f o r c e s d u r i n g t h e formation oS a d r o p l s t o r c r y s t a l c o r e

(Traepfchen- o d e r ~ r l s t a l l k e i m ) , The s m a l l e r t h e a n ~ o u n t of work r e q u i r e d t o produce a g2ven c u r s , t h o g r e a t e r t h e pro- b a b i l i t y t h a t such c o r e s w i l l o c c u r , For the i c e c o r e , t h i s work, g e n e r a l l y speakq.ng, i s g r e a t e r , and, e x c e p t f o r t h e c a s e o f vary Low t enpei-atilr-es, c o n d e n s a t i o n d r o p l e t a always occur f i r s t * The work of c o r e f o r m a t i o n i s reduced by s o l i d , f l u i d

and chemlcal condensation n u c l e i , as w e l l as by e l e c t r i c a l charges on t h e i o n s , Thus c o n d e n s a t i o n i s f a c i l i t a t e d , a l -

3:- Known i n E n g l j s h a s : "Ostwaldl s Law of #

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Page

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2

Tech, Trans, TT-68

though i n c e r t a i n c a s e s , indeed, only h a b a r e l y d i s c e r d n i b l e manner, V l m e r P s t h e o r y has r e c e n t l y hecn d i s c u s s e d by

K r a s t a n o d g i n i t s a p p l i c a t i o n t o t h e problem of water vapour condensation i n the atmosphere, U n t i l now l a b o r a t o r y t e s t s t o determine the c o n d i t i o n s of conderlsation and sub]-imation of water vapour a t low t e m p e r a t u r e have been l a c k i n g , A

p r e l i m f n a r y r e p o r t of t h o a u t h o r own experiments i n t h i s f i e l d i s g i v e n h e r e ,

The w a t e r vapour s u p e r s a t u r a t i o n s were p r o - duced by sudden expansion of' a i r s a t u r a t e d w i t h water vapour, F i g u r e 1 shows t h e p l a n o f t h e best srrangement used, The expansion v e s s e l A can b e f i l l e d e i t h e r from a w i t h a i r con-

t a i n i n g condenaatron n u c l e i drawn from t h e a 6 0 s p k l e r e o r t h e room, o r from b w i t h a i r c o n t a i n i n g no n u c l e f d r a m through t h e ~ c h o t t - b a c t e r i a f i l t e r B and t h e s t o r a g e v e s s e l

C, A c o n t a i n s a q u m t f t y of w a t e r

or

i c e , By rneans of a

-

cold=bath i t can be brought o v a r i o u s t e m p e r a t u r e s , By

suddenly opening t h e v a l v e D t i ) $ l e a d i n g t o t h e p r e v i o u s l y evacuated space v9, t h e volume of a i r v c o n t a i n e d i n c a n

be silddenly expanded, cooled. slrlct s u p e r s a t u r a t e d a c c o r d i n g t o

v

+

VY

the degree of expansion

---

V 13y v a r y i n g vq t h e d e g r e e

of expansion car1 be varied,Frorn the s m a l l v e s s e l

g,

which i s connected a t t h e s i d e , given condensation n u c l e l c m be i n t r o d u c e d i n t o t h e expansion space

-

A by means of s u l t a h l e e v a c u a t i o n o

By i l l u m i n a t i n g from t h e s i d e with an a r c

lamp t h e u l t r a - m i c r o s c o p f c condensation phenomenon can e a s i l y be observed, A f i f t e e n - p o w e r b i n o c u l a r microscope i s very convenient f o r t h i s purpose, Tiny ice c r y s t a l s a r e s a u i l y d i s t i n w i s h a b l e from wa texa d r o p l e t s even wi th t h e naked e y e

by t h e i r g l i t t e r and s p a r k l e ,

F i r s t t h o s e experinlsnts w i l l be c o n s i d e r e d i n which the a i r was c l e a r e d o f condensation nucl-ei by t h e b a c t e r i a f i l t e r and which a l s o , from the o u t s e t , c o n t a i n e d

no i c e p a r t i c l e s , I t should b e e x p l a f n e d t h a t t i n y i c e

c r y s t a l s form a t t e m p e r s t u r e s below z e r o on t h e wal-1s of t h e expanslon chamber an6 i n %he air t n t a k e cube, I t 1s neces- s a r y , e s p e c i a l l y a t v e r y l o w t e m p e r n t u m s when t h e i c e de- p o s i t i s v e r y considerabbe a n d . t a k e s the f'omn of needleg,

t o i n t r o d u c e the a i r slowly I n o r d e r t o ensure t h a t n o t h i n g breaks away f r o m t h e s e s n : ~ , l T c r y s t a l s t o flout I n the air as i c e d u s t , I n t h e pr.escncs of s u c h i c e d u s t any expansions

w i l l r e s u l t i n a s u b l i m a t i o n of the w a t e r vapour on t h e s e a r t i c l e s , S t r e a k s of t h e s e i c s p a r t i c l e s then

---

ice dUShe v a r y l i g h t valve i s zpened by gas

p r e s s u r e i n 1 t o 2 x 10" second, The

expansf ~n i s t h e r e f o r e e n t f r e l y a d i a - b a t i c ,

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appear. They a r e r a t h e r c o a r s e and c l e a r l y v i s i b l e , t h e more s o , of c o u r s e , t h e g r e a t e r the expansion,

Hence i f c a r e i s t a k e n t o have no i c e dua t

i n

t h e a i r , then, i n accordance w i t h r e s u l t s a t h i g h e r tempera- t u r e s , no c o n d e n s a t i o n whatsoever w i l l o c c u r w i t h s m a l l ex- p a n s i o n s i n a i r f r e e from n u c l e i even a t temperaturaes below z e r o , The a i r w i l l t h u s bo l e f t s u p e r s a t u r a t e d with w a t e r vapour, The s i n g l e c o a r s e d r o p l e t s which a r e sometimes ob- s e r v e d a r e a p p a r e n t l y caused by chemical c o n d e n s a t i o n n u c l e i which a r e n o t h e l d back by t h e b a c t e r f e . f i l t e r , Not u n t i l t h e d e g r e e of expansion r e a c h e s a g r e a t e r v a l u e , about 1,3, does t h e number o f d r o p l e t s g r a d u a l 1 7 b e g i n t o i n c r e a s e , whfle a c o n d e n s a t t o n t a k e s p l a c e , a s i s known, on t h e i o n s which a r e always p r e s e n t i n t h e a i r * , However, t h i s c o n d e n s a t i o n i s s t i l l i n t h e form o f d r o p l e t s down t o -50°C, whore t h e p r e s e n t observatioxls have stopped, Hence ovsn with h i g h e r s u p e r s a t u r a t i o n o f water vapour i n the a i r ( t h e d e g r e e o f

exparlsion 1.3 corresponds t o more t h a n a f i v e f o l d s u p e r s a t u r a - t i o n ) the d r o p l e t s always form f i r s t a t low temperatures,

With expansions somewhat g r e a t e r t h a n about 1 , 4 t h e d r o p l e t cloud suddenly b e c m e s much d e n s e r , and a t

1,s

a few v e r y c o a r s e i c e p a r t i c l e s a r e u s u a l l y round w i t h i n t h i s c l o u d , The a u t h o r i s u n c e r t a i n whether t h e s e i c e p a r t i c l e s r e p r e s e n t p r i m a r i l y a s u b l i m a t i o n i n a g i v e n c r y s t a l form from the

w a t e r vapour, o r whether t h e y a r e a secondary phenomenon, i o e o , v e r y f i n e i c e p a r t i c l e s o r i c e n u c l e i , t o r n from t h e w a l l s , which a r e then a b l e t o grow very r a p i d l y owing t o

t h e h i g h d e g r e e of ~ u p e r s a t u r a t i o n ~

I f t h e expansion i s i n c r e a s e d t o 1 0 5 o r 1,6 t h e c l u s t e r s o f c o a r s e i c e p a r t i c l e s become more frequanb, Then f ce c l u s t e r s and supercooled w a t e r d r o p l e t s a r e u s u a l l y found s i d e by s i d e , , and i t i s i n t e r e s t i n g t o observe how t h e i c e c r y s t a l s q u i t e r a p f d l y i n one t o two minutes absorb t h e s u p e r c o o l e d water dr.oplets as t h e w a t e r vapour from the l a t - t e r sublimes i n t o i c e ,

With expansforls from 1 , 6 t o 1.8 (dependtng on the i n i t i a l t e m p e r a t u p s ) a n o t h e r phenomenon suddenly o c c u r s , Yiater d r o p l e t s covso t o fozn and i n s t e a d a c h a r a c t e r i s t i c , very f'lne, w h i t i s h i c e cloud a p p e a r s , r e c o g n i z a b l e as such b y i t s s p a r k l e , This s p a r k l i n g i n - c r e a s e s v i s i b l y , i n d i c a k i n g t h a t t h e m i s t i s becoining

c o a r s e r a s t h e s m a l l p a r t i c l e s sublime o v e r f n t c t h e l a r g e r ones o

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Tech, Trans, TT-68 The phenomenon j u s t d e s c r i b e d occurs more o r l e s s e q u a l l y a t a l l i n i t i a l temperatures between C0 and

approximately - 4 0 ° ~ ( i i ) , A t temperatures below these, obser- v a t i o n , e s p e c i a l l y of t h e t r a n s i t i o r ~ s t a g e s o f t h e v a r i o u s forms of i c e cloud from one i n t t h e q becomes more d i f f i - c u l t and t h e r e f o r e l e s s certainTi1 It should a l s o be

noted t h a t the lower t h e i n i t i a l ~ s r n p e r u t u r e b e f o r e expansion, the lower w i l l be tk~e wato~l vapour c o n t e n t of t h e a i r , which r e s u l t s i n an ever t h i n n e r drople'c o r i c e cloud, However, even a t -5G°C, with f a i r l y small expansions, d r o p l e t clouds have been d i s t i n c t l y observed by the a u t h o r , I n a d d i t i o n ,

the s p a r k l i n g of the i c o p a r t i c l e s d i f f e r s w i t h t h e t e a t

c o n d i t i o n s , s i n c e t h e i r form i s d i f f e r e n t f o r v a r i o u s degrees of s u p e r s a t u r a t i o n ,

E n t i r e l y analogous phenomena occur i f , i n - s t e a d o f a i r which has p c s s e d through t h e b a c t e r i a f i l t e r ant! i s t h e r e f o r e f r e e from n u c l e i , a i r c o n t a i n i n g condensation n u c l e i from the atmosphere o r from t h e room i s expanded, The

chief d i f f e r e c c e i s merely t h a t even a t very s l i g h t degrees of expansion, d r o p l e t cloud forms, and t h i s continues t o be t h e case ever* down t o temperatures of a p p r o x h a t e l . y -50°C. The degree of expansion a t which the t r a n s l k i a n from d r o p l e t t o i c e condensation t a k e s p l a c e appears t o b e somewhat r e - duced; but more a c c u r a t e measurements a r e only now bofng made, The a u t h o r tiould a l s o p r e f e r t o postpone t h e p r e c i s e

c a l c u l a t i o n of t h e temperature a t which i c e cloud appears a l o n g s i d e the d r o p l e t cloud u n t i l the d i f f e r e n c e between t h e occurrence of the c o a r s e r i c e c l u s t e r s and the fli-ner i c e

clouds a t somewliat h i g h e r expansions i s more c l e a r l y understood, The o b s e r v a t i o n s of the f r e e z i n g of supey-

cooled water d r o p l e t s a r e a l s o u n c e r t a i n , Under p r e s e n t t e s t c o n d i t i o n s the supercooled water d r o p l e t s a r e u s u a l l y main- t a i n e d o n l y from two t o t h r e e minutes, a f t e r which they d i s t i l onto t h e l a r g e r water o r i c e s u r f a c e which is always p r e s e n t i n the v e s s e l ,

( i f ) Even above O°C an i c e cloud i s obtainod i n t h i s appar4atus with i t s quick a c t i n g valve when the expansions a r e suff'lc- c i e n t l y g r e a t , Eiowever i t m e l t s v e r y q u i c k l y and changes i n t o water d r o p l e t cloud. The h i & 2 r the temperatures a t

which o p o r a t i o n t a k e s p l a c e , t h e f a s t e r t h i s process vRll be,

(ill.) The i n c i d e n t a l experimental d i f i ' i c u l t i e s ( c r a c k i n g of v e s s e l s , c o a t i n g o f obser- v a t i o n windows) also i n c r e a s e g r e a t l y a t low temperatures,

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In any case one f a c t seems t o b e c l e a r : t h a t i n the a i r i n v e s t i g a t e d by t h e a u t h o r , -&i ch n ~ u s t have con- t a i n e d n u c l e i of every p o s s i b l e kind, t h e r e were no s p e c i a l s u b l i m a t i o n n u c l e i which would l e a d t o the d i r e c t formation of i c e p a r t i c l e s even i n low s u p e r s a t u r a t i o n s , as assumed p r e v i o u s l y by A l f r e d 'JVegener9s theory, I n view of' the impor-

tance of e s t a b l i s h i n g t h i s , an attempt was made t o confirm i t

b y even more d i r e c t experiments, Very f i n e , p u r i f i e d q u a r t z powder was mixed t o g e t h e r with m c l u u s - f r e e a i r i n a s m a l l ves- s e l (E i n F i g , l ) , and t h i s a i r , c o n t a i n i n g the q u a r t z d u s t , was tEen i n t r o d u c e d i n t o the p r e v i o u s l y evacuated expansion v e s s e l , With the p r e f e r r e d s i d e i l l u m i n a t i o n t h i s q u a r t z d u s t

could be i d e n t i t i e d a b s o l u t e l y a s q u a r t z , f o r t h e l a r g e r par- t i c l e s e x h i b i t e d a q u i t e unmistakable s p a r k l i n g undor the

microscope, \Wen expansion now took p l a c s slowly t h e p a r t i c l e s r a p i d l y grew l a r g e r and b r i g h t e r , and t h e i r s p a r k l e vanished, i n d i c a t i n g t h a t water vapour was condensing on the q u a r t z p a r t i c l e s , This process could even be r a v e r s e d , f o r when a i r was a g a i n admitted, i n c r e a s i n g the p r e s s u r e and temperature, the water evaporated f r m the q u a r t z p a r t i c l e s again and t h e pure q u a r t z p a r t i c l e s appeared once more, This behaviour of q u a r t z p a r t i c l e s could be observed v e r y c l e a r l y a t - l S O and

- 3 3 O C O A t high expansions the formation of i c e seems t o occur r a t h e r sooner with q u a r t z d u s t t h a n w i t h o u t o lfloaae a c c u r a t e measurements concerning t h i s a r e s t i l l t o be made, For con-

d i t i o n s i n the atmosphere, however, the h i g h expansions and extreme s u p e r s a t u r a t i o n s a r e of no importance, s i n c e t h e y r a r e l y occur, and moreover a t expansions of 1,25 t o 1,3 ( o r a l t e r n a t i v e l y a t the corresponding, s u p e r s a t u r a t i o n s ) the i o n s which a r e always p r e s e n t i n abundance i n t h e atmosphere a c t , of course, a s condensation n u c l e i , i n which case water drop- l e t s occur even a t low temperatures,

Experiments corresponding e x a c t l y t o the

q u a r t z d u s t t e s t s were a l s o c a r r i e d o u t a t approxima1;ely -15°C

u s i n g o r d i n a r y t a b l e s a l t , , Here, too, d r o p l e t condensation

always occurred a t low and moderate expansions, A t the moderate expansions, a few coarse i c e p a r t i c l e s sometimes appeared along with the d r o p l e t s , The dogres of expansion of 1,8, however,

again brought about the very c h a ~ a c t e r f s t i c formation of f i n e i c e clouds as p r e v i o u s l y d e s c r i b e d ,

A s an exanple o f chemical condensation n u c l e i , ozone was next i n v e s t i g a t e d , Tho ozone was produced in a

small ozone tube and vras then added t o c o r e - f r e e a i r , Again only d r o p l e t s o c c u r r e d a t r e l a t i v e l y s m a l l and moderate de-

g r e e s of ex?ansion, The d r o p l e t s were very abundant i n t h i s case owing to the known, v e r y powerful condensation-promoting

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Tech, Trans, TT-68

p r o p e r t i e s of ozone, However t h e l i m i t s f o r i c e c r y s t a l formation were n o t n o t i c e a b l y chaqged,

F i n a l l y a s t r o n g a - r a y e m i t t e r was p l a c e d

In

t h e expansion s p a c e I n o r d e r t o determine whether a very

high, l o c a l l y c o n c e n t r a t e d i o n i z a t i o n had any e f f e c t on tihe f o r m a t i o n o f i c e , Even w i t h t h i s arrangement, however, i c e p a r t i c l e s o c c u r r e d o n l y a t h i g h d e g r e e s o f expansion,

I n c o n c l u s i o n t h e q u e s t i o n of how i c e clouds can form i n t h e f r e e atmosphere w i l l be j u s t b r i e f l y touched upon i n t h e l i g h t of t h e r e s u l t s o b t a i n e d i n t h e l a b o r a t o r y o

The experiments confirm Volmerfs t h e o r y t h a t a primary sub- l i m a t i o n o f w a t e r vapour i n t o ice can t a k e p l a c e o n l y a t low

t e m p e r a t u r e s

-

perhaps -600 o r oven lower

-

a l t h o u g h t h e

numerical v a l u s cannot b e r e g a r d e d a s v e r y r e l i a b l e u n t i l more a c c u r a t e t e s t s have been made, Secondly, i c e can, o f c o u r s e , form a s a r e s u l t of the f r e e z i n g o f t h e s u p e r c o o l e d w a t e r d r o p l e t s , i n which c a s e t h e most l i k e l y e x p l a n a t i o n seems t o be t h a t t h i s p r o c e s s i s one of impingenlent of s o l i d p a r t i c l e s on t h e s u r f a c e of t h e d r o p l e t , F i n a l l y i t a l s o a p p e a r s pos- s i b l e t h a t i n t h e f r e e atmosphere a t f a i r l y hip$ a l t i t u d e s t h e a i r always c o n t a i n s permanent i c e c o r e s , I n c o n t r a s t t o t h e l a b o r a t o r y t e s t c o n d i t i o n s ? t h e a i r at h i @ a1 t i t t r d e s remains at low t e m p e r a t u r e s , of course, f o r r e l a t i v e l y l o n g p e r i o d s , I t does n o t seem i n c o n c e i v a b l e t h a t under t h e s e c i r c u m s t a n c e s s t a b l e i c e c o r e s of mfcroscopic s i z e a r e formed which grow i n t o v i s i b l e i c e p a r t i c l e s a s t h e w a t e r vapour

c o n c e n t r a t i o n i n c r e a s e s , Even i n t h e l a b o r a t o r y t e s t s i t

was d i f f i c u l t t o a v o i d f i n e i c e d u s t which, when p r e s e n t , always l e a d s t o i c e f o r m a t i o n o

These b r i e f o b s e r v a t i o n s , o f c o u r s e , make no c l a i m t o completeness, n o r do t h e r e p o r t e d l a b o r a t o r y e x p e r f - rnents, The condensation and s u b l i m a t i o n o f w a t e r vapotlr,

n o t o n l y i n t h e f r e e atmosphere, b u t i n t h e l a b o r a t o r y exper%- rnents a s w e l l , a r e shown t o be very complex phenomena, and many more experiments w i l l a s s u r e d l y b e needed b e f o r e t h e y

can be b e t t e r u n d e r s t o o d , The a u t h o r b e l i e v e s , however, t h a t t h e l a b o r a t o r y t e s t s a r e n e c e s s a r y i f i t i s d e s i r e d t o g a i n a r e l i a b l e b a s i s .for t h e e x p l a n a t i o r l of t h e p r o c e s s e s i n t h e f ~ e o atmosphere,

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REFERENCES

1 ) A l f r e d Wegener: Thermodynamik d e r Atmosphaere (Thermodynamics of t h e Atmosphere), L e i p z i g , 1911,

2 ) W o F i n d e i s e n , cog,, M e t e o r o l , Zs, 55 ( 1 9 3 8 ) , Po 121,

3)

M,

Volmer: K i n e t i k d e r Phasenbildung

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