frazil nucleation mechanisms - International Glaciological Society

J ournalo/ Glaci%g)" Vo l.
2 1,
No. 85, 19 78
FRAZIL NUCLEATION MECHANISMS
By THOMAS O 'D. HANLE Y , S.J. ':'
(Physics D epartment, Wheeling College, vVheeling, WV 26003, U.S.A. )
ABSTRACT. Prev iously the a utho r h ad sugges ted that fraz il nucleation occurs b y a mechanism a na logous
to spinoda l decompositi on , a ided b y turbul ence. After furthe r study the foll owing points are made: ( I ) No
c ri t ica l point ex ists be tween solid a nd liquid ; this rul es o ut tru e spinodal d ecomposition. (2) Pure water can
be supercooled to - 40°C; at - 40°C the theoretical ene rgy ba rri er to nuclea ti o n is a bout 10- 19 J. Frazil
fo rms after supe rcooling less tha n o. I d eg; a t this tempera ture the theoretica l e nergy barrier is about 10- 14 J.
(3 ) Theory shows th a t turbul ence in c reases the energy barrier. (4) Turbule nce may a id dissipatio n o f heat
o f so lidifica tion, but not sufficiently to account for observed fraz il form ation at small supercoolings. (5 ) The
a uthor's ev idence that fraz il ca n begin to form at supercoolings as mall as 0 .02 d eg sugges ts that n o nucl eus
ex ce pt ice itself ca n account for " hete rogeneous" nuclea tion o f frazil.
Ri.suME. A1ticanismes de nucleatioll du.frazil. Nous av io ns a upa rava nt, suggen! que la nucleation du frazil
se produisai t par un mcca nisme a nalogue a la decomposition spinodale, aidee par la turbul ence. Apres une
etud e plus poussee les points suiva nts so nt re leves. ( I) 11 n 'existe pas d e point critique entre le so lid e et le
liquide; ceci reje tte I' idee d'une vra ie d ecomposition spinod a le. (2) L'eau pure pe ut etre surfo ndue jusqu'a
- 40°C; it - 40 °C la ba rri ere e nergetique theorique est d' e n viron 10- 19 J. L e fraz il se form e a pres une
surfusion de m o in d e o. I deg ; a ce tt e te mperature la barriere energetiqu e t heo rique est a utour d e 10- 14 J.
(3) L a theori e m on tre que la turbulen ce a ugm en te la barriere e nergetiqu e. (4 ) La turbulence pe ut a id er la
diss ipa tion d e la cha leur d e solidifi cat ion , mais pas suffisa mme nt pour tenir compte d es formations de frazil
o bservees pour d es fa ibl es su rfusions. (5 ) L'observation sui va nt la quell e le fraz il p e ut commencer it se form er
a d es surfusions a ussi fa ibles que 0,02 deg suggere qu 'au cun noyau, sauf la g lace elle-meme, ne pe ut etre a
l'origine d e la nucl ea tion " heterogene" du fraz il.
ZUSAMMENFASSUNG . M echallismell.fiir die K eimbiLdullg .freischwebender EiskristaLLe. D er Verfasser h at fruher
vorgeschl agen, d ass d ie K eimbildung frei schwebend er Ei , krista ll e durch ein e n d e l' spinodalen Entmischung
iihnli chen M ec ha nismus erfolgt, d el' durch Turbu lenz unte rstutzt wird . Nach w eiteren Untersu chungen
we rd en folgend e F es tstellungen getroffe n: ( I) Es gib t kein e n kritischen Punk t zw ischen fester und f1u ss iger
Phase ; di es schli css t echte spinoda le Entmischung aus. (2) R eines 'v\Tasse r kann bis - 40°C unterkuhlt
werden ; bei - 40°C belragt d ie theore tisch c Energieschwe ll e fur di e K eimbi ldun g rund 10- 19 J. Freischwebend es Eis entsteht na ch U nterkuh lung vo n weniger a ls 0 , I d eg; bei diesel' T e mperatur ist di e theore tische
En erg iesch wel le rund 10- 14 J. (3) Di e Theorie zeigt, d ass Turbulenz die Energieschwell e erhoht. (4)
Turbul enz mag die Verteilun g der G e fri erwiirme ford e rn , a ber ni cht in a usre ich endem Masse, urn die
beo bachtete Bildung freisch webende r Eiskristall e bei geringe r Unterkuhlung z u e rkl iiren. (5) Di e Beweise
des Verfassers fur d en Beginn del' Bildung freischwebender Eiskrista lle bei Unterkuhlungen von nul' 0,02 cleg
legt na he, class ke in K eim , ausser Eis se lbst, fur die " he teroge ne" Keimbildun g d er freischwe be nd e n Eiskrista ll e vera ntwort li ch ist.
OF the several forms of ice found in I a ture, frazil is interes ting b ecause of several unusual
c haracteristics of its formation a nd because it leads to an a nnual world exp enditure of mi llions
of dollars (or pounds). Frazil form a tion has been reviewed by Mic hel ( 197 1). One question
which has received much attention is how frazil begins to form in water supercooled by less
than one degree. Specula ting that the process might differ from th e usual nucleation
m echanisms, Ha nley considered the th eoretical approaches used to exp lain spinodal d ecomposition, a nd sugges ted (H a nley, (975 ) that such a study might also clarify the role of water
turbu lence in fra zil production. This paper describes attempts made to attack the problem in
five ways, by considering (1) the m etastable states involved in the process a nd the possibility
that some kind of critical point is associated with these states, (2) the e nergy barrier traversed
during frazil forma tion, (3) the effect of turbulence on the energy barrier, (4) the effect of
turbulence on the tempera ture gradient outside the nucleus, and (5) the possibility that
heterogeneous nucleation may account for frazil initiation. Although none of these approaches
has succeeded in identifying a new mechanism, it is hoped that further insight will be gained
by bringing them together and applying them specifically to frazil formation, especially when
the pertinent mechanisms become b e tter understood.
* Present address:
Campion College, University of R egin a, R egina, Saskatchewa n S4S OA2, Canacla.
58 1
JOURNAL
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Frazil was defined by Kivisild ([1971] ) as: "Fine spicules, plates, or discoids of ice suspended in wa ter. In rivers and lakes it is formed in supercooled turbulent waters." In international ice terminology it is distinguished from the terms Jrazil slush and Jrozen Jra zil slush.
Spinodal decomposition has b een discussed by Hillert (1961, unpublished) and further
d eveloped by Cahn (196 I , 1968) . It is a specific type of phase transformation which occurs in
some binary or multicomponent systems (usually m etals and glasses) when deeply quenched
near a critical point. For example, an AI- Zn melt at a composition and temperature which
place it near its critical point, when cooled at a suitable rate separates during solidification in
such a way that one component gathers in small regions randomly distributed through a
matrix of the other component. The term spinodal decomposition probably should not be
extended beyond such transformations, but certain aspects of the th eoretical treatment of
spinodal decomposition may be useful to understand frazil formation . The most interesting of
these aspects is that when the conditions for spinodal decomposition are fulfilled , the energy
barrier to solidification seems to disappear. Frazil formation has been observed in water at
temperatures less than 0.1 deg b elow the freezing point (Michel, 1963; Carstens, 1966;
Hanley and Michel, 1975)' Therefore this paper will discuss the energy barrier to solidification in an attempt to explain frazil formation at small supercoolings.
Hillert ( 1961) has approached spinodal decomposition by way of the metastable state ofa
substance approaching a phase change. While considering the use of metastable states as an
explanation for frazil formation, two conclusions were reached.
A familiar example of metastable states involved in phase transitions is illustrated by the
pressure- volume diagram for water (Fig. I). If a sample of water vapour at 360°C is subj ected
to an increase of pressure at constant temperature, it moves along the isotherm from A to B.
260
250
240
230
Cl)
Cl:
220
C(
III
'"Cl:
210
I
I
D
::l
Cl)
Cl)
'"
Cl:
200
CL
190
C
IBO
I
LIQUID
I
170
160
0
"
4
6
8
( SPEC IFI C VOLUME X 10 3 )
Fig.
Pressure P versus specific volume v for water. Continuous lines represent isotherms; the dashed line meioses a region of
metastable states.
I.
FRAZIL
NUCLEATION
MECHANISMS
A further increase of pressure will move it toward point M through a succession of metastable
states. Local fluctuations of pressure will eventually allow the vapour to liquefy and move to
point c, from which with further increase of pressure it will traverse the path C D. The region
for metastable equilibrium, enclosed by a dashed line in Figure I , has a maximum at the
critical pressure which corresponds to a unique critical point on a P, V, T surface.
In a cooling process in which frazil is produced , the d ecrease in temperature involves an
isobaric change as shown in Figure 2. W ater cooled at the ambient barometric pressure passes
a long an isobar from A to B and, as it supercools, proceeds m etas tably toward M. When
freezing begins, it tends to go to the state at C and th en, with furth er cooling, toward D.
Further advances to an explanation of frazil formation using fluctuations in the specific
volume are hampered by the fact that no complete theoretical description has been produced
for the volume- temperature relationship of water near the freezing point.
Figure I includes a region containing the metastable states possible during the phase
transition. At its peak is a critical point. In presenting the curve shown in Figure 2, the
possibility of a similar region and a critical point was considered. Bridgman ( 193 I) discussed
the possibility of a solid- liquid critical point for pure substances as raised by several investigators and concluded that, "the probability that there is a critical point between liquid and
solid is so remote that it can be dismissed without further discussion".
Therefore it seems cl ear that spinodal d ecomposition does not provide an explanation for
fra zil formation. It is likely, however , that when we understand more completely the intermolecular mechanisms which govern the behaviour of water near ooe , it wi ll be fruitful to
apply fluctuation theory to the isobaric transition from water to ice.
The next consideration is the height of the energy barrier. Several attempts have been
made to develop an expression describing the energy barrier as a function of some kind of
25
20
15
10
A
LlOUID
;>
5
'"a:
~
tia:
0
B~I________________________________~C
I
'"::E
Q.
'" -5
I-
I
I
I
\
-10
ICE
I
Mo
I
o
\
\
-15
-20
0 .09
\
\
\
\
1.04
1.06
1.08
( SPECIFIC VOLUME X 10 3 ) m 3 kQ-1
Fig.
2.
T emperalure I versus sjJecific volume v .for waler. The dashed line represenls supercooled waler.
JO U RNAL
OF
GLAC I OLOGY
concentration. N6nethy a nd Scheraga (1962) d efine a mole fraction which is a combination
of five possible molecula r structures, J ackson and others ( 1967 ) similarly u se the fraction of
possible sites on an interface, while Fletcher ( 1970) uses the number of molecules in an ice-like
cluster. But attempts to express free energy as a function of any such concentration-like
para m eter will necessarily involve poorly known quantities until more is understood about
embryo shapes and anisotropic surface energies. For the present we must work with approximate functions and average values. For example, the h eight !'1C* of the nucl eation barrier
can be expressed (Fletcher, 1970, equation 4. 3 1) by the equation
1617(j3
!'1C*
(I)
= 3 ( !'1Sv ) !'1T) 2'
where (j is the surface free en ergy (approxim a tely 0.022 J m - 2 ) , !'1 T is the temperature of
supercooling, a nd ( !'1Sv ) is the average entropy offusion over t he supercooling range!'1 T. For
water,
Under optimum conditions water cannot be supercooled below about - 40°C. This
sugges ts either tha t the energy barrier for solidification b ecom es very low at - 40°C or that
Auctuations in the thermal energy of the water at - 40°C enable it to surmount the energy
barrier. Equations ( I) a nd (2) indicate that at - 40°C th e h eight of the en ergy barrier is
1. 2 X 10- ]9 J (about 0.74 eV ) . But it has b een observed th a t frazil forms in water at temperatures less than 0.1 deg below the freezing point (Michel, 1963; Carstens, 1966 ; Hanley a nd
Michel , 1975). By the same equa tions th e b a rrier at this super cooling is 1.4 X 10- 14 J (about
87 keV ), five orders of mag nitude higher th a n at - 40°C.
H a nley ( 1975) suggested that turb ulence could aid in surm oun ting the en ergy barrier to
solidification. Upon further consideration it a ppears that turbulence, in fact, h as the opposite
effect. We must distinguish between turbulence produced by movement of water past a
sta tionary obj ect, in which case the bound a ry layer is thicker than a lamina r boundary layer,
and movement of an obj ect a long with a turbulent stream. Here we need only consider the
second of these situations. In this case turbulence decreases the thickness of th e boundary
layer which sepa rates the growing embryo from the surrounding water and hence increases in
magnitude th e gradients of temperature, cluster size, density, a nd so on. It is in the bound ary
layer that the clusters of water molecules become re-a rra nged into an orientation favourable
to regul a r crystal grow th. T hus increased turbulence mig ht b e expected to increase to some
extent th e supercooling r equired for successful frazil nucleation.
An increase in supercooling for frazil form ation with an increase in turbulence was
indicated in the results reported by Hanley a nd l'vIichel ( 1975 ) a nd shown in Figure 3. The
same conclusion is supported by the diffuse-boundary m odel for nucleation d eveloped by
Calm a nd Hillia rd ( 1958) . If we apply Cahn a nd Hilliard 's theory a nd their boundary
cond itions to a spherically symmetric nucl e us, the Gibbs free energy of the nucleus can be
wri tten
f
00
!'1C
= 417N v
[!'1 gv (p) + K
G; YJ
)"2
d)".
r= o
H ere N v is the number of molecules per unit volu me, p is the d ensity of the water a t a distance
r from the centre of the nucleus, 6gv is t he free cncrgy per m olecule of a solution of uniform
density p, a nd K is a constant for the condensing substance. The second term in the integrand
represen ts the effect of the d ensity gradient in the boundary layer. Because the square of the
gradient is involved, a bounda ry layer made thinner by turbulence results in a n increased free
energy, whatever may b e the sign of the gradient.
FRAZIL
NUC L EA TIO N
M EC H AN I S MS
0.0 5
I
I
I
•
0 .0 4
•
I
I
I
I
I
0 .03
~
I
><
0
"E
f-
•
<l
0 .0 2
•
I
I
•
•
I
I
I
I
I
I
I
0 .01
00
I
I
02
06
0 .4
WATE R S?EED
08
MS - I
Fig. 3 . EX/Jerimentalllleall values Jar the maximum supercooling observed ill a cold room tallk at various water speeds. Fra z i/
Jo rmed ill all experiments at s/Jeeds of 0.24 In s- , or greater.
But turbulence in t h e water, by m a king thinner t h e bound ary laye r surrounding th e
embryo, will also incr ease the magnitude of the temper a ture gradient o utside the nucl e us.
This sugges ts th a t t he h eat of conde nsation is more readily conduc ted away in turbule nt
water , wi th a conseque n t enha ncem en t of growth of the embryo. L o the a nd Pound ( 196 9)
ela bora ted the effect of h eat dissipa tio n o n nucl eation, a nd concluded (p. 145) tha t th e e ffect
of slow heat dissipa tio n is to r etard the r a te of nucleatio n slig htl y. If turbulence increases the
te mper a ture gradien t a nd the heat diss ipa tion by a r easonable fac to r , even an orde r of
m agnitude, the effect on nucl eation is fa r from the five o rders of m agnitude needed to expla in
n uclea tio n at - 0.1 QC. It should be n o ted a lso that, a fte r the discussio n referred to a b ove,
Lothe a nd Pound th e m selves ( 1969, p . 11 2), question th e va lidity of the ass umption th a t
macroscopic therm od yn a mic proper ties such as surface te nsion and volume free energy m ay
be a pplied in the d escri ptio n of sm a ll clusters.
I t must be admi tted , then, tha t the studies outlined a b ove have revealed no mecha nism
which can expl ain hom ogeneous nucl eation of ice in slig htly supercooled water.
H eterogeneous nucleation must a lso be considered . H owever, we must remember th at
frazil h as been observed to form after a bulk supercooling of less tha n o . I d eg (M ichel, 1963;
Carstens, 1966; H a nley a nd Michel, ( 9 75) a nd recen t evidence sugges ts tha t it has begun to
grow a t a bout - 0.02 °C (H a nley a nd Michel, 1977 ) . This is considera bly warmer th a n th e
nucl eation threshold of - 4°C ascribed to silve r iodide, the best-known inorganic icen ucleating agen t, or t h e - I. 3QC cited as the thresho ld for biogenic nucl eators by Schnell
and V a li ( 1972 ) . T hese va lues, it sho u ld be noted , are fo r nucleation of ice from the vapour.
586
JOURNAL
OF
GLACIOLOGY
In discussing nucleation thresholds, Fletcher ( 1958, 1970) defines an interface parameter
which is characteristic of the nucleating particle and by which h e correlates the nucleation
temperature and the size of th e nucleating particle. Despite the deficiencies which he points
out for this model, it shows clearly that nucleation at - 0.02 °C or even at - 0.1 °C requires
a lmost perfect compatibility be tween the nucleating particle and the ice. This suggests that the
nucleation is not truly heterogeneous.
If such a compatibility between the nucleating particle and the ice is necessary, one
explanation for the formation of frazil is by means of tiny ice particles falling to the surface of
the water from above, and drawn into the bulk of the flow by turbulence. This mech anism
has been studied in considerable detail by Osterkamp and others ( ' 974) and Osterkamp
(1977). It appears plausible th a t in the cold room in which the study of frazil formation led
to the conclusion that frazil began to form a t a supercooling of 0.02 deg, tiny ice crystals may
have been generated either in the air above the water tank or in the heat exchanger. Another
mechanism which might explain the onset offrazil formation is surface nucleation, as proposed
by Michel (1967). He is now attempting to describe this mechanism in a quantitative manner
(private communication from B. Michel).
The study of frazil formation as possibly analogous to spinod al decomposition has led to
the following conclusions which have been prese nted in this paper: ( , ) No critical point exists
between ice and water; this rules out true spinodal decomposition. (2) Pure water can be
supercooled to - 40°C at which temperature the theoretical energy barrier to nucleation is
about 10- 19 J. Frazil forms after supercooling less than o. I deg; at this temperature the
theoretical energy barrier is abo ut 10- 14 J. (3) Theory shows that turbulence increases the
energy ba rrier . (4) Turbulence may aid dissipation of heat solidification, but not sufficiently
to account for observed frazil formation at small supercoolings. (5) The author's evidence that
frazil can begin to form a t supercoolings as small as 0.02 deg suggests that no nucleus except
ice itself can account for " heterogen eous" nucleation of fra zil.
ACKNOWLEDGEMENT
The a uthor gratefully acknowledges the assistance of Dr Thomas Knorr for reading the
manuscript and making many helpful suggestions.
REFERENCES
Bridgman, P. W . 193 I. The physics of high /mssure. London, G. Bell a nd Sons.
Cahn, J. W . 196 1. On spinodal decomposition. Acta M etallurgica , Vo!. 9, No. 9, p. 795- 801.
Cahn, J. W. 1968. Spinodal decomposition. T ransaction s of the M etallurgical Society of AI ME , Vo!. 242, No . 2,
p. 166- 80.
Cahn, J. W. , and HiUia rd,]. E. 1958. Free energy of a non-uniform sys tem. I. Interfacial free e nergy. J ournal of
Chemical Physics, Vo!. 28, No. 2, p. 258-67.
Ca rstens, T . 1966. Experiments with supercooling a nd ice form ation in fl ow ing water. Geofysiske Publikasjoller,
Vo!. 26, No. 9.
Fle tcher, . H . 1958. Size effect in h e te rogeneous nucleati o n . J ournal ofChemical Physics, Vo!. 29, No. 3, p. 572- 76.
Fletcher, N. H. 1970. The chemical physics of ice. Ca mbridge, University Press. (Cambridge Monographs on
Physics. )
H a nl ey, T. O 'D . 1975. A note on the mechanism of frazil ini tiation. (In Frankenstein, G. E., ed. Proceedings,
third International Sym/Josium on I ce Problems, I B- 2 [ August [975, Hanover, New Hampshire. [Hanover, N.H.],
International Associa tion of Hydra ulic R esea rch, p. 30 1- 04. )
H a niey, T. O ' D. , and Mi chel, B. 1975. T empera ture patte rns during the formati on of borde r ice and frazil in a
laboratory tank. (In Franke nstein , G. E. , ed. Proceedings, third International Symposium on I ce Problems, I B- 2 1
August 1975, Hanover, New Hampshire. [Hanover, N.H.] , Internationa l A ssociation of Hydrauli c Research,
p. 21 1- 21. )
H a niey, T. O 'D. , and Michel, B. 1977. Labora tory form ation of border ice and frazil slush. Canadian J ournal of
Civil Engineering, Vo!. 4, No. 2, p. 153- 60.
Hillert, M. 1961. A solid-solution mod el for inhomogeneous sys tems. Acta M etallurgica, Vo!. 9, No. 6, p. 525- 35.
Hill ert, M . Unpublish ed. A theory of nuclea tion fo r solid metalli c solu tions. [Sc.D. thesis, Massachusetts
Institute of T echnology, 1956.]
FR AZ IL
NUC L EA TIO N M EC HA
I SMS
J ackson, K . A ., and others. 1967 . O n the nature o f cr ystal growth fro m the melt, [by] K . A . J ackson, D . R .
U hlma nn a nd J. D. Hun t. J ournal qfCrystal Growth, Vo!. I , No. I , p . 1- 36.
Ki visild , H . R . [1 97 1. ] Ri ver and la ke ice ter m in o logy. (Ill [Intern a ti o na l Assoc ia ti on o f H ydra uli c Resea rch .]
1.A. H.R . symposium : ice alld its actioll Oil hydraulic structures, R eykjavik, I celalld, [8] - 10 Sep tember ' 9io. [Del ft ,
In tern a tio na l Associa tion o f H yd rauli c R esea r ch] , paper 1.0. )
Lothe, J ., and P ound , G. 11. 1969. Statisti ca l mech a ni cs of nu clea ti o n . ([n Zettl emoyer, A . C. , ed. Nucleation .
New York, M a rcel Dekke r, p . 109- 49.)
Mi chel , B. 1963. T heory of form a tion a nd d e pos it o f fraz il ice. Proceedillgs of the Eastern Snow COI!ference, 20 1h
a nnua l m ee ting, p. 30- 48.
Mi chel, B. 1967 . From the nuel eati on of ice crysta ls in clouds to th e fo r mat ion of fraz il ice in ri vers. (Ill Qura,
H. , ed. Physics of snow alld ice : illternational conference 011 low tempera ture science. . .. ' 966. . .. P roceedings, \' o!. I ,
Pt. I. [Sapporo] , Institu te of Low Te mperature Science, H okka id o Un iversity , p . 129- 36. )
M ichel , B. 197 1. Winter regime of r ivers a nd la kes. U .S. Cold R egions R esea rch and E ng ineering La borato ry.
Cold regions science and engineering. H a nove r, N. H ., P t. lJI . Sect. B ra.
Neme thy, G., al/d Scheraga, H . A . 1962. Stru cture o f water a nd h ydro ph obi c bond ing in pro teins. I. A model
for the t he r modynam ic properti es of liq ui d water. J ournal of Chemical Physics, Vo!. 36, o. 12. p. 3382- 400.
Oste rka m p , T E 1977 . Fraz il-i ce nuclea tion by mass-excha nge processes a t th e air- wate r interface. J ournal of
Glaciology . Vo!. 19, No. 8 1, p . 6 19- 25.
Osterka m p, T. E ., and others. 1974. Detection of a irborne ice crysta ls nea r a supercoo led strea m, by T . E .
Ostcrkam p , T. O hta ke a nd D. C. Wa rn imen t. J ournal of the Atmospheric Sciences, Vo!. 3 1. No . 5, p. 1464- 65.
Schnell , R . C ., alld Va li , G . 1972 . Atmosph e ri c ice n uclei from d eco m posin g vege ta tio n . Nature, \'o!. 236,
No. 5343, p . 16 3- 6 5'
DIS CU SSIO N
W . B. K A MB: In your labora tory experime nts on frazil forma ti on in m oving wa ter, can you
not control the inpu t of ice particl es fro m the a tmosph ere, and hence test O sterka mp's
hypoth esis?
T. O ' D . HAN LE Y: U nfo rtuna tely, I a m n ow far removed from the labora tor y in which the
experim e nts were done. If I had access to th at la bora tory, I would wa nt to look carefu ll y fo r
ice crys ta ls coming from t he heat excha n ger in the cold room when the room was in equilibrium a t - 2°C . I have not been a ble to m a ke this search elsewhere, a nd I wou ld be glad to
hear th e result if a nyone else has done it.
J. HALLE T T :
W ould it b e a fair ass umptio n to say th at nuclea tion of a few cr ystals in the cold
analysing air could give cr ystals which cou ld then prop agate in the liquid b y secondary ice
productio n , by collision of the walls or with each other in the turbulent Ro w ?
I ce li tera ture rep orts studies of collision breeding- for example Garabedia n and
Strickl a nd- Constable ( 19 74). I am no t sure th at we have r elia ble values fo r th e ra te a t which
crystals multiply by collision . I was willi ng to assume th a t breeding could occur if a n y
crystals w er e present in th e water, but I w as concerned a b o ut how the first cr ystals come to
be in t he w ater.
H ANLE Y :
F. PROD! : As a possible nucleati on m ech a nism for frazil I sugges t the sedimentation on th e
wa ter surface of radia tively cooled aerosol pa rticles. R adia tion cooling may lower th e
tempera tu re of the aerosol p article by a r em a rka bl e a mount. If so, we should notice highe r
frazil frequen cies by nig h t, with cl ear sky.
REFERE N CE
Ga rabecl ia n, H ., and Strickla nd- Consta blc, R. F.
Growth , Vo!. 22, No. 3, p. 188- 92.
1974. Collisio n b reed ing of ice cr ys ta ls. J ournal of Crystal