Biomedical Engineering Reference
In-Depth Information
Fig. 8
The effect of wave vector on Fig. 4. The damping coefficient,
α
, is plotted vs. the real
capillary wave frequency,
ω
o
, for several different wave vectors. Only the isopleths for
ε
d
=
0and
= 0 are shown to give the outermost loop of Fig. 4. The plot was generated using
σ
d
= 71.97 mN m
-1
,
κ
= 0 mN s m
-1
,
= 997.0 kg m
-3
,
= 0.894 mPa s and
g
= 9.80 ms
-2
µ
ρ
η
vary with the surface tension unless it is depressed greatly, i.e., at high surface
pressures. Second, it shows a monotonic decrease in the wave propagation
rate as the surface tension increases as should be expected. Third, there also
is a monotonic depression in the damping with increase in the surface ten-
sion, meaning that the capillary wave damping on a film-covered surface at
high surface pressures can actually be less than the damping on a pure liquid
surface, as was first noted in 1989 by McGivern and Earnshaw [69]. We hasten
to add that we are dealing with the temporal damping.
Finally, we come to the effect of the wave vector
k
for a range used in the
experiment to be presented. Figure 8 shows that the polar plot profile changes
insignificantly over the range of
k
. Hence, it appears entirely justified in aver-
aging and collapsing onto a single profile the results of
α
and
ω
o
obtained at
different wave vectors over the indicated range.
4
Surface Light Scattering Method
Light scattering as an experimental method to probe liquids and solutions has
a long history since the demonstration by Tyndall in 1869 [70]. A vast litera-
ture exists on the subject of scattering in condensed matter (see for example,
Fabelinskii [71]). Application to liquid surfaces began at the beginning of the
20th century with work by Smoluchowski [72], Mandelstam [73], Gans [74],
