Biomedical Engineering Reference
In-Depth Information
where
V
is the volume of the system. It follows then from (
2.20
)
ln.t
nucl
V/
D
kf .m/=.TT
2
/
C
G
kink
=kT
ln.f
00
.m/.f .m//
1=2
B
0
/
(2.26)
with
D
16
cf
2
=3kS
m
;
(2.27)
where B
0
D
BŒ.R
s
/
2
N
o
. For a given system, changes in the slope and/or the
intercept of the ln(
TV
)
1/(
T
T
2
) plot will correspond to the modifications in
f
(
m
,
R
0
)
,f
00
(
m
,
R
0
)andˇ
kink
.
“Zero-Sized” Effect of Foreign Particles (Ice Nucleators)
As discussed earlier, the ice nucleation process can be regarded as a kinetic process
for ice nuclei to overcome the so-called nucleation barrier G
, under a given
supercooling T (T
D
T
m
T ;
T
and
T
m
are the actual and the melting
temperatures, respectively). To obtain the ice nucleation kinetics, the correlation
between the nucleation induction time
T
, the time required for the first nucleus to
appear in the drop of water with a given volume
V
, and supercooling T ,was
examined. The precise ice nucleation experiments were carried out in a cell based
on the “micro water suspending” technology (cf. Fig.
2.7
a) [
51
].
The experiments by Liu et al. [
12
] show that under normal crystallization
conditions, it is almost impossible to eliminate the influence of dust particles. This
is evidenced by the fact that the freezing temperature (for a constant droplet volume)
decreases progressively as the pore size of the filters is decreased progressively
from 200 nm, to 100 nm, to 20 nm (cf. Table
2.1
). Actually, in most cases,
the term “homogenous ice crystallization,” to which most authors refer [
52
], is a
heterogeneous ice nucleation process promoted by dust particles. This implies that
the effect of the dust particles on ice crystallization is inevitable, and should be taken
into account in our discussion.
Just as an ice nucleation substrate does, so do foreign bodies always lower the
nucleation barrier by a factor
f
(cf. (
2.15
)). For an optimal interaction and structural
match between the nucleating phase and the substrate
m
!
1and
f
(
m
,
R
0
)
!
0,
meaning that the nucleation barrier is completely eliminated due to the occurrence
of foreign particles. When
f
(
m
,
R
0
)
D
1 (extremely poor structure match/interaction
between ice and foreign particles), the nucleation barrier is the highest (
G
homo
)
under the given conditions even when the foreign particles are still present, in which
case the foreign particles do not play any role in lowering the nucleation barrier.
If freezing were first controlled by heterogeneous nucleation and followed by
homogeneous nucleation as T increased
,
we would have obtained for a nucleating
system pair-wise intersecting straight-line segments in the ln(
V
)versus1/(
T
T
2
)
plot (cf. Fig.
2.7
b): one segment with a small slope at low T (or high 1/(
T
T
2
)),
the other segment with the largest slope at high T (cf. (
2.26
). The slope would
