Geoscience Reference
In-Depth Information
Tabl e 3. 1
The values of
"
,
.
"
/
(Eq.
3.125
),
u
"
,and
2
"
=q
"
.
"
/
u
"
2
.
u
"
/
2
1
1.615
8.994
3.902
1.737
.
u
"
/ (the set of Eqs.
3.158
at different dielectric
permeability ") and the ratio
of particle-to-ion
charges Q=q
3
1
1.777
6.447
2.402
1.959
5
1
1.926
5.136
0.1.684
2.174
1
1
2.22
3.8
1.002
2.615
2
2
1.427
16.351
8.661
1.492
3
2
1.535
11.56
5.415
1.633
5
2
1.633
9.107
3.846
1.767
1
2
1.821
6.617
2.331
2.037
2
1/2
1.894
5.05
1.718
2.117
3
1/2
2.139
3.673
1.041
2.47
5
1/2
2.369
2.96
0.721
2.817
1
1/2
2.833
2.229
0.421
3.54
Now we come to the result similar to that for metallic particles (Eq.
3.150
):
s
ˇq
2
e
2
2a
"
C
2
2"
C
3
C
"
1
"
C
2
:
".a/
2
(3.153)
3.5.5.2
Opposite Polarities
No noticeable simplifications comes up at "
D1
(metallic particles).
The analytical results for arbitrary " can be found for small particles. We again
return to Eq.
3.115
, rewritten in the dimensionless variables:
Z
e
u
2
".a/
D
.
"
/
C
.
u
/d
u
;
(3.154)
0
where
"
is the zero of
u
./ at arbitrary ". The first term is
2
"
C
S.
"
/:
.
"
/
D
(3.155)
At large , the integral on the right-hand side of Eq.
3.154
can be easily
estimated, for again, small
u
/
1= contributes to the integral. We have
".a/
.
"
/
C
"
:::
(3.156)
The values of
"
and .
"
/ are collected in Table
3.1
for a number of values of
the dielectric permeability ".
