Geoscience Reference
In-Depth Information
5
4
3'
3
3
2'
2
2
1
1
0
0.5
1.0
1.5
2.0
2.5
3.0
PARTICLE SIZE (in units of
l
)
Fig. 3.18
Dependence of matching distance
R
(
a
) on particle radius
a
. The scale of both axes
is l
2D=
v
T
, the ion mean free path.
Curve 1
shows the function
R
(
a
) for the potential-free
condensation.
Curves 2 and 2
0
are the matching distances for the attractive potential at different
Coulomb lengths, l
c
D
D
3 (
dotted line
).
Curves 3 and 3
0
display the same
l (
solid line
)andl
c
D
for the repulsive potential
This consideration shows that the value of
R
is of the order of the mean free
path
l
. If we assume that the interaction contains a long-range potential, such as the
Coulomb potential, which is sufficiently strong at distances of the order of
l
or more,
and is short range potential effective at shorter distances (of the order of
a
), then it is
possible to find a general expression for
R
. The behavior of the short-range potential
at short distances is of no importance for the derivation described next. It can be
even singular at
r
D
a
.
It is clear what to do. We introduce an effective particle radius a
that is defined
from a specially formulated asymptotic condition imposed on
n
(
r
).
