Model and Experimental Study of Surfactant Solutions and Pure Liquids Contact Angles on Complex Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 198

of all three surfactants. The dotted line on Fig. 6b corresponds to the modified
Cassie model predictions when an f valueof0.12isused(insteadof f = 0 . 06 for

the solid curve). This value of f 0 . 12 was found by fitting the highest concen-

tration data point for SDS to Eq. (10e). It is found to predict the high concentration
data better than the modified Cassie prediction for f

=

0 . 06. A similar idea was put
forth by Ferrari et al. [76], where repeated advances of surfactant solution drops
across a SHS were seen to result in contact angle decreasing by

=

5-15 ◦ over three
cycles. They attributed the decreasing contact angle to an increase in solid fraction
(i.e., increasing f , indicating a partial penetration of solution into the roughness).
In Fig. 6b, hexadecane and bromonapthalene demonstrate extremely low contact
angles indicating either an advanced state of partial penetration or the fully pene-
trated Wenzel mode. Thus, even if the surfactant solutions are partially penetrating
the surface, the surfactants still inhibit penetration compared to non-aqueous pure
liquids of similar surface tension.
4. AKD Surfaces-Surfactant Solutions and Pure Liquids

∼

Figure 7a and b show contact angles of surfactant solutions and pure liquids on
Teflon AF coated AKD and uncoated AKD, respectively. Uncoated AKD naturally
presents a saturated hydrocarbon chemistry, with hydrophilic heterogeneities. It is
clear from the data that surfactant solutions again show contact angles higher than
pure liquids of similar surface tension. It is also clear that the topography of the
AKD is less repellent than that of PTFE (see Fig. 5) or coated aluminum (see Fig. 6)
since the AKD surfaces show generally lower contact angles.
Also shown on Fig. 7a and b are modified Cassie and Wenzel predictions of
surfactant solution contact angles. Values of r were measured (see Table 1) and f
values were found, as described for PTFE. The discrepancy in f values for the two
surfaces calculated with water contact angle is due to the incomplete coating of
Teflon AKD. This incomplete coating would result in a decreased intrinsic contact
angle (compared to a completely Teflon AF coated surface) and an overestimation
of f ,butthe f value for Teflon AKD will be used in order to allow progress. Again,
additional values of f were found by fitting higher concentration contact angle data
for SDS to Eq. (10e). Both AKD surfaces are heterogeneous and rough complex
surfaces. While the full modified Cassie equation (10c) could be used to model
both surfaces, it would require additional data regarding the distribution/adsorption
properties of the heterogeneities that is not available. For now, Eq. (10e) is used to
make progress as described below.
Regardless of the limitations posed by the heterogeneities of the AKD surfaces,
certain observations can still be made. Examining Fig. 7a and b shows that nei-
ther a single modified Cassie prediction, nor a single modified Wenzel prediction,
can successfully model the data. On Fig. 7b, one could instead attempt to model
the data using the modified Cassie model at low concentrations and the modified
Wenzel model at higher concentration, with r as an adjustable paramter. Modifying
the fit in this way gives even larger r values, resulting in even worse predictions. It