Biomedical Engineering Reference
In-Depth Information
faces will also be considered. The questions of chemically heterogeneous rough
surface, and rough hydrophilic surfaces, will be left aside for now. The wetting of
complex surfaces will be probed with surfactant solutions as models of the impure
liquids likely to be used in industrial applications (such as, e.g., antifouling and
self cleaning properties [1-6], oil spill cleanup [7], drop and liquid actuation in
microfluidics [8-13], decreasing fluid friction on immersed bodies and in channels
[14-21], decreased icing/snow accumulation on structures [22-25], and the use of
SHS as switches and sensors [26, 27]. Surfactant solution wetting will be compared
with wetting by aqueous and non-aqueous pure liquids to examine the similarities
and differences between the two. First the theories describing wetting by pure liq-
uids are presented, below.
1. Wetting of Pure Liquids
When a drop of pure liquid rests on a smooth, flat and homogeneous surface,
Young's equation relates the drop's intrinsic contact angle ( θ y ) to the interfacial
tensions ( γ lv sl and γ sv ,wherel , v and s represent liquid, vapor and solid phases,
respectively). These interfacial tensions depend upon solid and liquid chemistry and
purity. Young's equation is:
γ sv
γ sl
cos θ y =
.
(1)
γ lv
The highest (thermodynamically relevant) contact angle reported [22, 28] for pure
water on a smooth surface is
120 . On complex surfaces, higher contact angles
are possible, but their prediction is more difficult; traditionally, the two equations
of Wenzel [29] and Cassie [30] have been used.
If the liquid completely wets the surface by contacting the entire solid interface
beneath the drop, filling the pores/crevices, Wenzel's equation describes the Wenzel
contact angle ( θ w )as:
r γ sv
γ sl
cos θ w =
=
r cos θ,
(2)
γ lv
where the effect of topography is modeled by r , the roughness factor, which is the
ratio of actual surface area to projected surface area. By Eq. (2), it is seen that
for hydrophobic surfaces ( θ y > 90 ), r increases the apparent contact angle by in-
creasing the contact area/energy of the drop on the surface, whereas for hydrophilic
surfaces ( θ y < 90 ) roughness decreases the apparent contact angle.
The Cassie equation (3) is used to calculate the contact angle of a pure liquid
on a heterogeneous, flat, rigid and chemically inert surface, made up of m different
materials:
f m cos θ y m
cos θ c =
,
(3a)
m
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