Biomedical Engineering Reference
In-Depth Information
Tabl e 2. 1
The freezing temperature (for a droplet
of constant volume) is dependent on the number
and size of dust particles
Filter pore size (nm)
200
100
20
Freezing temperature (
ı
C)
53
58
65
Fig. 2.8
Illustration of ice nucleation on a rough surface of a foreign (dust) particle
.
Normally,
the surface of dust particles is rough. Therefore, the radius of the local curvature of the foreign
particles is smaller than the size of the particles.
r
, the radius of the ice nucleus;
R
s
, the radius
of the local curvature of the foreign particles. Reprinted with permission from ref. [
8
]. Copyright
(2004) Springer
particles had “disappeared” (cf. (
2.5
)and(
2.26
)). Notice that the other three curves
(B, C, D) share the similar characteristics. Such an effect on nucleation revealed by
foreign particles at low supercoolings is called the “zero-sized” effect.
Effective Curvature of the Surface Roughness of Foreign Particles
(Ice Nucleators)
R
0
is actually the ratio between the radius of the local curvature of the foreign
particles (substrate) and that of the critical nuclei
r
c
(
2.14
,cf.Fig.
2.8
).
For a given crystallization system,
R
0
is proportional to
T
(compare (
2.1
)and
(
2.14
)). As shown in Fig.
2.5
a, the
f
(
m
,
R
0
)versus
R
0
diagram can be divided into
three regimes based on
R
0
or
T
. Regime I (linear regime):
R
0
1 (relatively large
supercoolings and/or large
R
s
). In comparison to the critical nuclei, the foreign
particles can be treated as a flat substrate.
f
(
m
,
R
0
) then attains its lowest value
and becomes a constant with respect to
R
0
(or
T
), i.e., it assumes the form
f
(
m
).
According to (
2.26
), the plot of ln(£
V
)versus1/(
T
T
2
) is a straight line because
is constant for a given system (compare portion 1 of curve
A
in Fig.
2.7
b).
Regime II (nonlinear regime): as
T
deceases (or 1/(
T
T
2
) increases),
r
c
becomes
comparable with
R
s
(
R
0
1) (compare (
2.14
)). The ln(£
V
)
1/(
T
T
2
) plot becomes
a curve (compare the curved segment between portions 1 and 2 of curve
A
)as
f
(
m
,
R
0
) varies with
T
(or
R
0
). Regime III (zero-sized regime): further lowering
T
(or raising 1/(
T
T
2
)) leads to a much larger
r
c
than the radius
R
s
of the
