Chemistry Reference
In-Depth Information
Articles by Miyano and Tamada (1992, 1993), and Wang et al. (1994)
also contain some experimental results indicating the influence of surface
film heterogeneity on the propagation of capillary waves. The authors no-
ticed that the lack of elaborate theory restrains further progress in this
field. The influence of the effects of multiple scattering on the propagation
velocity of surface waves is the main subject of this work.
2 Results and Discussion
At first we will consider the liquid-gas interface and linear surface waves
incident on a two-dimensional particle of the radius a (Fig. 1) under the
following main assumptions: the liquid is incompressible and Newtonian,
the two-dimensional particle has a circular shape, the amplitude of the
waves
A
is much less than the wavelength, the front of incident waves is a
straight line, the excess of the energy dissipation in the transitional region
at the border of the particle (Fig. 1) is negligible in comparison with the
whole energy dissipation in the liquid under the two-dimensional particle.
Fig. 1.
Scattering of surface waves by a single two-dimensional particle
The energy of the wave motion is mainly dissipated in the vortical layer
at the surface. The thickness of this layer G depends on the wave number
k
and, consequently, on the surface properties, which are different in the in-
ner and outer regions. This leads to a transitional region in the liquid at the
boundary between two-dimensional phases where the liquid motion is sig-
nificantly more complicated than at a distance from the boundary line.
