Biomedical Engineering Reference
In-Depth Information
and
f
2
=
(
1
−
f)
leads to:
cos
−
1
cos
θ
c
γ
lv
+
f
sl
RT
+
K
sl
C
n
s
S
)
θ
c
(C
S
)
=
ln
(
1
n
sl
K
lv
C
n
l
S
)
(10e)
f)
lv
RT
n
lv
+
(
1
−
ln
(
1
+
γ
lv
−
K
lv
C
n
l
S
)
.
lv
RT
n
lv
ln
(
1
+
which is only valid for the case of flat topped pillars with no penetration/curvature of
the liquid-vapor interface into the crevices of the roughness (see Fig. 1). Equation
(10b) through (10e) can also be derived by substituting Eq. (10a) (describing the
effect of surfactant on the Young contact angle) into Eqs (2) and (3) directly.
Equations (10a)-(10c) are predictive tools to study the effect of surfactant ad-
sorption at the solid-liquid and liquid-vapor interfaces of drops on smooth and
rough surfaces. The above models are the first of their kind to describe the effect of
surfactant adsorption on the wetting of complex surfaces. See references [27] and
[52] for more details. For
r
=
f
1
=
1and
f
2
,...,
∞
=
0, Eqs (10b) and (10c) both
simplify to Eq. (10a), as expected.
Any integrable isotherm(s) could be used in place of Eq. (6), allowing for the
modeling of different 'types' of adsorption for different surfactant-interface pairs.
Having chosen the isotherm of Zhu and Gu [79], values must be determined for
the constants (
xy
,n
xy
,K
xy
,γ
xy
,θ
y
) specifying adsorption to each interface. This
has been performed for solutions of Sodium Dodecyl Sulphate (SDS) on smooth
Teflon AF coated silicon [27]; first Eq. (7) was fit to surface tension measurements
to find l-v constants. These constants were input into Eq. (10a), which was then
fit to contact angle measurements, to find s-l constants. Solid-vapor adsorption
was neglected due to the hydrophobicity of the surface. In a separate work [52],
Eq. (7) was fit to surface tension measurements take from reference [60] to find
l-v constants for aqueous solutions of modified inulin. These were then used with
Eq. (10a) to fit contact angle data of the same inulin surfactant on quartz glass,
a system displaying the autophobic effect. In this way, some plausible values for s-l
and s-v constants were found to allow a demonstration of the utility of the models
explained here. Others sets of constants were also chosen on an
ad hoc
basis, based
on characteristics described in the literature [52].
In this chapter, all of the above mentioned constants are used. The constants
for SDS on Teflon AF are used throughout the rest of the chapter both to explore
the model and to apply it to the wetting of SHS by surfactant solutions. The l-v
constants for modified inulin, and some of the other constants from reference [52]
are only used in this section to explore the model.
1. Model Results and Theoretical Behavior
Using the constants for all these systems, the surface plots in Fig. 2 were created.
Figure 2a-d show predicted contact angle for SDS solutions from 0 to 1 CMC on
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