Model and Experimental Study of Surfactant Solutions and Pure Liquids Contact Angles on Complex Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 178

surface chemistry) is greater ot less than the critical contact angle ( θ cr , constant for
a given surface topography), respectively. Alternatively one can say that Eq. (4)
suggests that the more stable wetting mode is the one that gives the lower contact
angle. However, a more thorough examination of favorable modes requires thermo-
dynamic analysis [33]. Experimental results for pure liquids or mixtures of pure
liquids confirm that there is a generally smooth decrease in the intrinsic contact an-
gle as liquid-vapor surface tension decreases [34]. On SHS, the decreasing intrinsic
contact angle eventually leads to transition from Cassie to Wenzel wetting [7, 26,
35], often with abrupt decrease in contact angle [35, 36] due to the high roughness
of the SHS amplifying the change in intrinsic contact angle. However, 'metastable'
Cassie wetting modes have been suggested for surfaces which should exhibit the
Wenzel mode with low contact angles [37-39], but instead display high contact an-
gles and the Cassie mode. These researchers [37-39] suggest energy barriers that
must be overcome for this transition to take place. This has again been seen in
literature where intrinsic contact angles as low as 46.6 ◦ (reference [40]) and 70 ◦
(reference [34]) have yielded advancing contact angles of 105.3 ◦ (reference [40])
and 140 ◦ (reference [41]), respectively, when they should instead result in much
lower contact angles due to the more favorable (according to Eq. (4)) Wenzel mode
wetting (Eq. (2)).
Both Wenzel's and Cassie's equations describe how the intrinsic equilibrium
value of contact angle is modified by topography/heterogeneities. However, ad-
vancing a drop across a surface increases the contact angle to the advancing contact
angles, resulting in a higher energy metastable state compared to the Wenzel or
Cassie angle. Likewise, receding a drop across a surface decreases the contact an-
gle, resulting in another higher energy metastable state, resulting in the receding
contact angle (Chapter 3 of reference [42]). The difference between the advanc-
ing and receding contact angle is called contact angle hysteresis (CAH). Prediction
of the advancing and receding contact angles apriori is difficult, and has been the
study of much work and debate, e.g., references [33] and [43-45]. However, Wenzel
wetting mode is expected to have a higher CAH due to the higher work of adhesion
necessary to remove the drop from the increased solid-liquid interface. In contrast,
Cassie wetting mode is expected to have a lower CAH because of its reduced solid-
liquid interface compared to the Wenzel mode. So, to design a SHS, researchers try
to roughen a low energy surface in such a way that the Cassie wetting regime is
favored. See references [33, 43] and [45] for more in-depth discussion.
All of the theories presented above were derived considering pure liquids on
clean surfaces. Various models for surfactant solution wetting on simple (i.e.,
smooth and homogeneous) surfaces have been available for many years (e.g., ref-
erences [46-49, 51]). Only recently however, were the first models for describing
contact angles on rough/heterogeneous surfaces developed [27, 52]. In Section C,
we show our derivations [27, 52] of modified Cassie and Wenzel models for the
contact angle of surfactant solutions on rough and/or heterogeneous surfaces. Ex-
perimental protocols are briefly described in Section D. The models are then applied