Page 253 - Process Modelling and Simulation With Finite Element Methods

240 Process Modelling and Simulation with Finite Element Methods

E -0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0
ti rnc
Figure 6.18 Cumulative model. Combined compaction front translation and convective-diffusive
model for Pe=100, m=0.7, offset y0=2. Shown are times tE [0.:0.01:0.375]. Maximum surfactant
concentration in the profile at a time for three different operator splitting increments At=0.01, 0.005,
and 0.001. The time asymptotic convergence is a consistency check on the operator splitting
scheme. Comparison with Figure 6.14 leads to the conclusion that only At= 0.001 is asymptotically
convergent.

I 011, I
om
4 01
a
+ 00 6 om
= om
B 2 0.0
2 OM i
'B 001 ; OM
OO!
8 002
i 001
0
I I
4 01
O! 04 06 03 1 0 O! vcmcai coodinatc E 09 I
04
06
"rkk7l Cdd4h7Ie
Figure 6.19 (a) Left: non-cumulative model. (b) Right: cumulative model. Combined compaction
front translation and convective-diffusive model for Pe=100, m=0.5, offset y0=2 for times tE
[0.:0.01:0.375]. Note that the cumulative percentage variation runs from 8--10% in the cumulative
model. At=0.01.
the surfactant is modeled as non-volatile constituent, able to adsorb on the latices
in the layer, but not to evaporate itself. Howison et al. [18] show a substantially
greater range of concentrations of an evaporating solvent for a similar model, but
with no compaction front.
This is an industrially important problem. Hydrophobicity of coatings drops
considerably with large concentrations of surfactants. In addition channelling of
water through pores of surfactant can seriously corrode material protected by an
otherwise effective coating. For these reasons, models such as the one outlined
above are central to the current research on coating efficiency.