Biomedical Engineering Reference
In-Depth Information
Equations (
9.3
)and(
9.4
) have sometimes been combined to a more general
form: [
28
]
cos
C
D r
cos
Y
C 1
(9.5)
where
C
is the apparent contact angle on the rough surface and
r
characterizes to
the degree of roughness of the solid area that contacts with liquid.
9.2.3
Dynamic Wetting Behavior
Both Wenzel's and Cassie-Baxter's theories predict the apparent CA in the equilib-
rium state, describing the static behavior of a liquid drop. In order to characterize
the dynamic wetting behavior, advancing/receding angles and sliding angle (SA)
are measured to evaluate the repellency of a surface. By definition, the maxi-
mum/minimum values of CAs for a drop front which has been advanced/receded
over a surface are termed the advancing/receding angles; the difference between
advancing angle and receding angle renders the contact angle hysteresis. SA can be
measured as an inclined plate tilts at a critical angle, beyond which a liquid drop will
rolling off or sliding down the plate surface. The quantitative relationship between
the CA hysteresis and SA is provided by (
9.6
)[
29
]:
mg.
sin
˛/=
w
D
LV
.
cos
R
cos
A
/
(9.6)
where
A
and
R
are the advancing and receding angles, respectively,
g
is the
gravity force, and
m
and
w
represent the mass and width of the drop, respectively.
Equation
9.8
shows that small CA hysteresis results in small SA, indicating liquid
drop rolling off or sliding down surfaces effortlessly. This equation also interprets
one of the mechanisms of
Stenocara
beetle's back. Condensed water droplets roll
off easily to be collected due to small SA on superhydrophobic surfaces.
9.2.4
Three-Interface Contact Line-Related Wetting Behavior
As discussed above, even though Wenzel's and Cassie's theories achieve great
agreement with experimental results in many areas, unfortunately they make no
statement about hysteresis. In the case of Cassie's theory, it simply describes an
increasing “most stable” (in Marmur's notation) [
30
] contact angle in an equilibrium
state with decreasing solid fraction
. However, many experimental results show
that drops may behave quite differently on two patterned surfaces of identical
[
31
];
thus, the solid fraction should not be the only parameter determining the contact
angle hysteresis. Chen et al. suggested that the topology of rough surfaces plays an
important role in determining the contact angle hysteresis [
32
]. They concluded that
