Structure and Properties of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 57

The presence of the substrate brings the surface energies between the substrate and liquid
(

˃ sc ) into the problem (see Michel 1978). The nucleation
temperature depends on the character of the substrate, and the key dimensionless
parameter,

˃ sl ) and substrate and crystal (

ʳ ,isde ned by:

r sl r sc
r cl

cos c ¼ ð 3 : 2 Þ

The parameter ʳ is usually taken as the angle of contact between ice and the nucleating

material.
In heterogeneous nucleation, there is a critical crystal size after which the crystal grows
freely, reducing the free energy of the system. The functional form of the critical radius is
as in homogeneous nucleation, and the corresponding Gibb

' is free energy is

2

r cl T 0
q w L f D T 0

tan p= n ð Þ

D G ¼ 4 p ð 1

cos cÞ r cl ð 3 : 3 Þ

p= n

Thus the supercooling in the heterogeneous nucleation relative to the supercooling in
homogeneous case equals

r

1

D T n
D T 0 ¼

cos c
2

ð 3 : 4 Þ

= 0 and no supercooling is needed. Considering suspended
particles, the best inorganic nucleators in nature have

Ice as a substrate has ʳ

, and consequently the
supercooling would be 3.5 K. This is, however, more than the observed supercooling in
lakes. Field studies as well as laboratory experiments have shown that in calm fresh water
crystallization starts at temperatures from

ʳ =10 °

− 0.5 to − 1.5 ° C.

flow conditions, the surface water layer is well mixed and supercooling
takes place across the whole layer. It has been observed that the amount of supercooling is
not more than about 0.1 K, which is much less than in spontaneous heterogeneous
nucleation. Several theories have been proposed for the nucleation at such high temper-
atures. Michel (1978) suggested that near the lateral boundaries (shore or ice) turbulence is
weaker, and steeper surface temperature gradient can be set up. Ice germs form at the
surface,

In turbulent fl

flow, and serve for forced nucleation in the turbulent
surface layer. The supercooling is in this situation

fl flow away to the turbulent fl

2 r cl

q w L f r l T 0

D T ¼ ð 3 : 5 Þ

where r l is the radius of the seed particle. For clay particles, rl l * 1 ʼ m, and the super-

cooling in forced nucleation becomes 0.05 C. The process of multiplication of crystals in

this way is very fast. The border ice mechanism has been questioned, however. Osterkamp

°