30
FREEZE-DRYING
of growth from the pure liquid, or a weak solution, we may make the approximation that
Ts : T,, in Which case,
dm
4 1tCK
—
=
——
T ——T00
7
-
For a thin disc,
,
dr
4 K
—
=
——
T ———T
8
dt
Pd
( o
…)
[ 1
EXPERIMENTAL
The limitations of the simple theory outlined above become apparent when we explore
the nature of ice crystal growth under a variety of conditions. It is essential that the
temperature or supersaturation be specied carefully during all experimental work, and
also that solid surfaces do not interfere with the crystal growth. When for example, we
study growth in a glass capillary tube the glass itself has sufcient thermal capacity to
dominate the growth form of the crystals. Crystals grow more quickly on a glass surface
which acts as a heat sink and take a curved form like
“frost” crystals on awindow pane.
1. Growth of ice crystals in supercooled water
Ice crystals growing freely in bulk water may be easily studied by seeding the free surface
of a small volume of water, which has been allowed to supercool in a glass cell, with a
single crystal of ice of selected orientation 9.
With supercooling greater than about
0.2°C ice crystals grow as dendrites, with branches at 120 °, in the direction of the “a”
axes.
The velocity of crystallisation increases with supercooling,
=
0.08 (To - T)
“’ cm sec—1
_
at— 20°C.
The growth rate in the direction of the “0” axis is about 100 times less at a
few degrees supercooling, but increases to a value comparable with that in the “a”
axis direction by—— 16°C. This gives an initial growth in the form of an expanding hexagonal wine glass, with an angle which depends on supercooling 11.
This subsequently
lls in as the growth front passes. The size and separation of the dendrite branches de—
creases With increased supercooling, and are about 10 microns at—‘— 10°C. (gure 9). A thermocouple placed in
water rises to very close to 0°C just after the growth front has
'
passed. If the latent heat released is just taken up by the supercooled liquid, a fraction
‘
T —— T
,,
.
.
.
.
.
.
.
'
—°L_
Will change to me as the growth fr0nt passes, the rest remammg liqu1d at 0°C
_
it is frozen by heat loss at the boundaries of the sample. For supercooling less than
0;02?CgroWth inæthe direction of the “0” axis doesnottake place at all 12, showing that
the two types of surface smoothand rough, exist for ice in‘ contact with the supercoole‘d
liquid.
'
‘
J—M
—
—:
'
,
In the same…way as new orientations appear
“supercooled _drops:'arevnæleated
below—ç— 6°C'neW Orientations may appear“ where single crystals nucleate
samples
beloW—— 69C.Ü
_
"
î.
.
‘
,
.
:j'
FREEZE-DRYING
of growth from the pure liquid, or a weak solution, we may make the approximation that
Ts : T,, in Which case,
dm
4 1tCK
—
=
——
T ——T00
7
-
For a thin disc,
,
dr
4 K
—
=
——
T ———T
8
dt
Pd
( o
…)
[ 1
EXPERIMENTAL
The limitations of the simple theory outlined above become apparent when we explore
the nature of ice crystal growth under a variety of conditions. It is essential that the
temperature or supersaturation be specied carefully during all experimental work, and
also that solid surfaces do not interfere with the crystal growth. When for example, we
study growth in a glass capillary tube the glass itself has sufcient thermal capacity to
dominate the growth form of the crystals. Crystals grow more quickly on a glass surface
which acts as a heat sink and take a curved form like
“frost” crystals on awindow pane.
1. Growth of ice crystals in supercooled water
Ice crystals growing freely in bulk water may be easily studied by seeding the free surface
of a small volume of water, which has been allowed to supercool in a glass cell, with a
single crystal of ice of selected orientation 9.
With supercooling greater than about
0.2°C ice crystals grow as dendrites, with branches at 120 °, in the direction of the “a”
axes.
The velocity of crystallisation increases with supercooling,
=
0.08 (To - T)
“’ cm sec—1
_
at— 20°C.
The growth rate in the direction of the “0” axis is about 100 times less at a
few degrees supercooling, but increases to a value comparable with that in the “a”
axis direction by—— 16°C. This gives an initial growth in the form of an expanding hexagonal wine glass, with an angle which depends on supercooling 11.
This subsequently
lls in as the growth front passes. The size and separation of the dendrite branches de—
creases With increased supercooling, and are about 10 microns at—‘— 10°C. (gure 9). A thermocouple placed in
water rises to very close to 0°C just after the growth front has
'
passed. If the latent heat released is just taken up by the supercooled liquid, a fraction
‘
T —— T
,,
.
.
.
.
.
.
.
'
—°L_
Will change to me as the growth fr0nt passes, the rest remammg liqu1d at 0°C
_
it is frozen by heat loss at the boundaries of the sample. For supercooling less than
0;02?CgroWth inæthe direction of the “0” axis doesnottake place at all 12, showing that
the two types of surface smoothand rough, exist for ice in‘ contact with the supercoole‘d
liquid.
'
‘
J—M
—
—:
'
,
In the same…way as new orientations appear
“supercooled _drops:'arevnæleated
below—ç— 6°C'neW Orientations may appear“ where single crystals nucleate
samples
beloW—— 69C.Ü
_
"
î.
.
‘
,
.
:j'