Chemistry Reference
In-Depth Information
sional particles, which are held off at the interface by capillary forces, if
the wavelength exceeds their size.
In the general case transverse surface waves have a vortical component
and Eq. (8) is assumed to be an approximation only. This means that Eq.
(13) does not allow to calculate the damping coefficient. However, the real
part of the complex wave number
K
for slightly damped capillary waves
(
ReK >> ImK
) can be estimated.
Both the inhomogeneities of the surface tension and of the dynamic sur-
face elasticity scatter capillary waves. In the former case one can estimate
the effects of multiple scattering if the line tension and the particle size are
known. The existing experimental estimates of the line tension for the
boundary between two-dimensional fluidlike phases give too low values,
which cannot lead to any measurable scattering effects (Benvegnu and
McConnel 1992). The larger numbers can be expected for the boundary
between solid-like phases, especially under non-equilibrium conditions. In
this case a noticeable influence of the multiple scattering has been pre-
dicted (Noskov 1998). Although the fluctuations of the surface elasticity
usually almost do not influence the scattering of transversal waves, a spe-
cial situation arises when the continuous surface film contains regions of a
gaseous two-dimensional phase (two-dimensional bubbles). If the dynamic
surface elasticity of the scatterer tends to zero, large multiple scattering ef-
fects can be observed (Noskov 1998).
Although the Eqs. (13), (14) do not allow us to estimate the contribution
of scattering to the effective damping coefficient of surface waves within
the assumptions, which have been made in this work, this can be fulfilled
with the use of the total scattering length Q
s
(Chou and Nelson 1994)
2
Im
K
Im
k
nQ
/
(15)
s
The total scattering length was calculated in Noskov (1991). The notice-
able changes of the effective damping of surface waves arise simultane-
ously with the corresponding changes of the wavelength. In this case it is
possible to speak about a new mechanism of the wave damping: the effec-
tive damping coefficient, which can be measured experimentally, increases
at the account of scattering.
Acknowledgements.
This work was financially supported by the Euro-
pean Space Agency (FASES MAP AO-99-052). B. A. N. also gratefully
acknowledges financial support from the RFFI, NSC of Taiwan (Joint Pro-
ject 05-03-90580 HHC_a, Project RFFI 03-03-32366) and the grant of the
President of the Russian Federation (Leading scientific schools, NSh-
789.2003.3).
