Biomedical Engineering Reference
In-Depth Information
angle). For simplicity, the surfaces being modeled in Fig. 2a-d are assumed to have
flat pillar tops and flat liquid-vapor interfaces, allowing one to express
f
1
=
f
and
f
2
=
f)
(i.e., we consider surfaces of the type shown in Fig. 1a only here).
Figure 2e-f show predicted contact angle for an arbitrary surfactant solution wet-
ting a two material heterogeneous surface. In both plots,
θ
y
|
1
=
(
1
−
70
◦
and material
1 does not experience the autophobic effect, while
θ
y
|
2
=
0
◦
with material 2 ex-
periencing an autophobic effect similar to that in reference [47]. Figure 2e shows
predictions for a range of solid fractions from
f
2
=
0 (all material 1) to
f
2
=
1
(all material 2). Figure 2f shows five traces across the surface plot of Fig. 2e (at
f
2
=
1).
It is important to note that, in reality, if the intrinsic contact angle were to
change drastically from 120
◦
it is likely that the solid-liquid adsorption parame-
ters would also change. As such, for surface chemistries which are not fluorinated,
i.e., Fig. 2c, d, the results should be seen as describing general trends rather than
exact values.
As Fig. 2a and c show, increasing surfactant concentration decreases contact
angle for a surface with a given value of
r
being wet in the Wenzel mode. The
magnitude of this decrease changes for different values of
r
. For example, for
r
0
,f
2
=
0
.
1
,f
2
=
0
.
5
,f
2
=
0
.
9and
f
2
=
=
1
21
◦
as con-
(a smooth surface), the decrease in the Wenzel mode contact angle is
∼
centration changes from 0 to the
C
CMC
for a surface with
θ
y
=
120
◦
(Fig. 2a). For
62
◦
for concentrations from 0 to the
C
CMC
.
In this way,
r
can be thought of as amplifying the effects of surfactant adsorption.
Since
r
is a measure of the increased area available under the drop and around the
contact line, the increased area leads to increased surfactant adsorption and a greater
change in contact angle as concentration changes. The roughness factor also acts to
increase smooth surface contact angles, but only for those above 90
◦
r
=
3, the decrease in contact angle is
∼
as discussed
below.
The combined effects of intrinsic contact angle, concentration and roughness
factor on Wenzel mode wetting can be understood by considering 'travel' along the
r
and concentration 'directions' in Fig. 2a, c. For
θ
y
>
90
◦
there are initially two
competing influences, since in this case, as
r
increases the contact angle increases,
but as concentration increases, contact angle decreases. For lower values of
θ
y
(but
still
>
90
◦
)
, sufficiently high concentrations of surfactant allow the downward in-
fluence of concentration to overcome the influence of
r
. This can be seen in Fig. 2c
compared to Fig. 2a. Specifically, it is seen in Fig. 2c for
C
=
0
.
435
C
CMC
,where
θ
y
(the smooth surface contact angle for a given surfactant concentration) decreases
to 90
◦
.When
θ
y
=
90
◦
(or if
θ
y
=
90),
r
has no effect until surfactant adsorption to
one or both interfaces decreases smooth surface contact angle, which then allows
r
to amplify the effect. This can be seen in the rapid decrease of contact angle with
surfactant concentration in Fig. 2c once
θ
y
<
90
◦
. This also explains why it is much
easier to use surfactants to fully wet surfaces which are already hydrophilic, since
any roughness of the surface will act doubly to promote wetting.
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