Environmental Engineering Reference
In-Depth Information
Fig. 7
The ideal modeling of the coating ripples of the wet film solution
The film thickness variation, expressed as d
;
will be reduced by the self-leveling
flow. We estimate the leveling time s. First the fluid speed (v) can be deduced from
the 1-dimensional Navier-Stokes equation. Then the flow rate Q can be deduced
from Young-Laplace equation:
2
v
oz
2
¼ 0
o
p
ox
þ
l
o
ð
10
Þ
Q
e
0
l
rq
3
de sin
ð
qx
Þ
ð
11
Þ
Considering the volume conservation,
o
Q
ox
¼
l
o
e
ð
12
Þ
ot
dde
dt
¼
de
ð
13
Þ
s
Solving the differential equation yields the leveling time as follows:
s ¼
lk
4
re
0
ð
14
Þ
If leveling time is smaller than evaporation time, the pattern will disappear due to
the leveling flow. However, if the leveling time is too long or evaporation time too
fast, the irregular pattern will remain. The leveling time depends on the viscosity
and surface tension of the solution. For instance, when the viscosity of the given
polymer solution is 100 mPa s, the surface tension is 25 m N/m, the characteristic
pitch of the stripes is 500 lm, the wet film thickness is 10 lm, and the leveling
time will be 250 s. To remove the irregular patterns, the solvent having higher
boiling temperature should be considered. By choosing a solvent that can evap-
orate slowly beyond the leveling time, flat and uniform films can be produced
(Fig.
8
).
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