Chemistry Reference
In-Depth Information
1
x
xy
Ek
2
Ek
where
J
2 Q
2
,
D
,
x
and
y
.
0
2
1
/
2
3
/
2
1
2
x
2
x
U
(
2
Q
)
Z
4
UQZ
Here
U
denotes the water density,
E
the film elasticity modulus.
Description of wave damping due to contact line effects needs some
empirical data on meniscus velocities (Henderson 1998). Therefore, the
third component in (1) is not considered here because of the lack of our
knowledge about the phenomenon. One, however, can assume that the
contact line effects give a small contribution to wave damping, because the
dimensions of the container are large compared with the characteristic cap-
illary scale and the wave amplitudes are small. In particular, since we
study the parametric wave excitation near its threshold, i.e., at very small
amplitudes, the contact line is nearly “pinned” to the walls. Then, accord-
ing to Miles' theory of wave damping due to dynamic contact line, the ad-
ditional wave damping, which is proportional to the speed of the contact
line at small speed values (Miles 1991, Henderson 1998), is expected to be
small.
4 Results and Discussion
4.1 Clean water
Wave damping in the container with clean water was measured in the fre-
quency range 10 Hz - 32 Hz. Figure 1 shows the experimental total damp-
ing coefficients and the damping coefficients calculated for a plane wave
mode (m = 1) and “mixed” modes with m = 1,2.
It can be inferred from Figure 1 that the damping coefficient values for
the plane mode are practically the same as for the "mixed" modes, i.e., the
wall damping coefficient mainly depends on frequency, but not on the
mode structure. One, therefore, can conclude, that the mixed modes weak-
ly affect the wave damping coefficient, even if they are excited in experi-
ment. Furthermore, Figure 1 shows that experimental values of the damp-
ing coefficient are in reasonable agreement with theory. However, the
experimental values are a little smaller than theoretically predicted, thus
showing that the measured damping is smaller than a sum of the surface
damping and the wall damping for free contact line. This, probably, can be
due to the "pinning" of the contact line between the water surface and the
walls. According to Hocking (1987) “the damping rate when this edge
condition is used is probably less than that for the free-end condition be-
cause of the reduction in the movement of the interface at the contact”.
This assumption, however, needs further special investigations.
