Chemistry Reference
In-Depth Information
If one assumes that there is no motion in the film it acts as a "wall".
Then the viscous stress W
visc
from standard theory would be distributed as
1
(10)
3
U
Q
W
#
0
.
33
U
visc
x
where
x
is the distance from the front of the 'plate'.
2
The viscous stress
must be balanced by a gradient in the surface tension, i.e.
d
V
W
visc
dx
Integrating over the entire film length when the film has obtained its criti-
cal length
L
c
one then obtains
(11)
U
3
3
V
V
0
.
66
U
Q
L
max
w
o
c
implying that
U
3
L
c
| constant, which is inconsistent with the experimental
findings described above.
The reason for the inconsistency of the 'plate'-model is presumably the
circulation pattern that was observed in the film:
a self-organized motion
of regularly spaced, unsteady channels, oriented parallel to the direction
of the substrate flow
. These channels, about 1 cm in width, extended most
of the length of the film and alternated in direction of flow. The circulation
velocity was d
U
/2.
It is questionable to apply the experimental results of Mockros and
Krone to a field situation. This is mainly because the role of the side walls
and the bottom in the formation of the streaming filaments is not known.
Another question is what happens when the substrate flow is non-uniform.
A new experiment is needed, looking into these questions. One possibility
is to make a down-welling zone with film accumulation symmetrically
around the stagnation line, and making the experiment broad enough for
side wall effects to be negligible.
2.4. Dimensional arguments
One might inquire what can be obtained on purely dimensional grounds
considering relations between the quantities Q,
k
,
U
k
and 3
max
/U. Since only
1
The Reynolds number in the boundary layer is sufficiently small so that laminar
flow can be assumed.
2
Obviously this is not a good model near the front where the curvature at the
Reynolds ridge modifies the stress distribution.
