Biomedical Engineering Reference
In-Depth Information
experiencing an autophobic effect similar to that in reference [47]). Physically, this
could be thought of as a glass surface (
θ
y
|
2
=
0
◦
) with, e.g., a thin PMMA coating
(
θ
y
|
1
=
70
◦
) either completely covering the glass (
f
1
=
1), or imperfectly coat-
ing the glass (
f
1
<
1). Figure 2e shows the role of the
f
1
and
f
2
parameters in
weighting the effect of surfactant adsorption on each portion of the heterogeneous
surface. The effects of the combination on contact angle are non-linear (due to the
cosine terms in Eq. (8)). As a result, the contact angles predicted by the modified
Cassie model for 0
<f
1
<
1 are more complex than for
f
1
=
1. Specif-
ically, as concentration ranges from 0 to the CMC, multiple maxima and minima,
and inflection points and 'kinks' (abrupt changes in slope) in the graph are seen
for 0
<f
1
<
1. To illustrate this, Fig. 2f shows five traces across the surface plot
of Fig. 2e (at
f
1
=
0and
f
1
=
0,
f
1
=
0
.
1,
f
1
=
0
.
5,
f
1
=
0
.
9and
f
1
=
1). The curves all in-
tersect at
C/C
CMC
∼
|
2
and any
weighting of the contact angles will have no net effect. As can be seen, even a het-
erogeneous surface that is a 9:1 combination of two materials can display different
behaviors compared to
f
1
=
0
.
1, since at this concentration
θ
y
(C
s
)
|
1
=
θ
y
(C
s
)
0and
f
1
=
1 (all on Fig. 2f). The
f
1
=
0
.
9 plot could
correspond to a glass surface thinly coated in PMMA (
θ
y
|
1
=
70
◦
), with 10% bare
patches (
θ
y
|
2
=
0
◦
,
f
2
=
0
.
1) due to incomplete coating or coating damage. While
the wetting of this surface with pure water would barely show a difference in con-
tact angle between
f
1
=
1and
f
1
=
0
.
9, surfactant solutions would behave very
differently on a completely
versus
incompletely coated surface.
Looking at the
f
1
=
0
.
5 plot in Fig. 2f, the behaviors are the most complex,
showing local minima and maxima, inflection points, and abrupt changes in slope.
The
f
1
=
0
.
1 plot could correspond to a glass surface barely covered in PMMA,
or to a hydrophilic surface with some hydrophobic patches due, e.g. to oil residue.
In contrast to the
f
1
=
0
.
9 plot, the
f
1
=
0
.
1 plot shows little deviation from the
f
1
=
1) plot at high concentrations, and large deviations at low concentra-
tions. This emphasizes the idea that it is the pure material contact angle
at a given
concentration
that must be considered when judging the relative effect of small
amounts of contamination on surfaces. This can be understood by considering that
the
f
1
and
f
2
parameters acts on the cosine of the concentration dependent contact
angles. As a result, a small change in the cosine of the heterogeneous surface contact
angle at low contact angles results in a large change in contact angle. Conversely,
an identical small change in the cosine at contact angles closer to 90
◦
0(
f
2
=
results in a
relatively small change in contact angle.
Further discussion of surfactant solution wetting on smooth or rough heteroge-
neous surfaces are given in reference [52]. However, the great variations that are
possible in surfactant solution wetting of heterogeneous surfaces point to the ex-
treme importance in experimental work to either ensure the homogeneity of the
surface, or to characterize the heterogeneity fully. Therefore, presented below is
the setup and procedures (including surface preparation) for the experimental work
discussed in this chapter. Following this, the experimental results are presented in
Section E.
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