Chemistry Reference
In-Depth Information
tems, where one can take into account the effects of multiple scattering of
surface waves.
If
A >> B
(scattering of transversal surface waves) (Fig. 2), one can ap-
proximately consider the liquid motion to be potential and to introduce the
scalar potential
ij
, which will satisfy the following equation
2
(
'
k
M
)
(
r
)
0
(8)
The exciting field acting upon the scatterer with the centre in the point
r
1
M
E
(/
1
is a sum of the incident wave
in
M
and the waves scattered
by other particles. The contribution of the given particle depends on the
distribution of the other scatterers. If the scattering is weak (
n
0
Q
s
/k<<1
,
where
Q
s
is the total scattering length and n
0
is the number density of the
particles), the configurationally averaged exciting field
M
E
is the solu-
tion of the following integral equation (Waterman and Truell 1961)
rr
³
E
inc
c
c
c
E
c
c
M
(
r
/
r
)
M
(
r
)
d
n
(
r
/
r
)
T
(
r
)
M
(
r
/
r
)
R
(
r
/
r
)
(9)
1
1
where
T
(c
is the scattering operator,
n(r
c
/r
1
)
the conditional density of
the scatterers,
R
a correction taking into account correlations between the
scatterers. In the following we will assume that
R=0
.
Fig.2.
Scheme of multiple scattering
The solution of Eq. (9) takes the form (Noskov 1998)
