Biomedical Engineering Reference
In-Depth Information
Owens-Wendt-Kaelble
Fowkes' concept was extended by Owens and Wendt [37] to cases where both dispersion
and hydrogen bonding forces may operate. The surface tension composes of two compo-
nents such that:
γ
=
γ
d
+
γ
h
(2.18)
where
γ
h
denotes the component of surface tension due to both hydrogen bonding and
dipole-dipole interactions. They postulated:
d
d
h
h
=
+
−
2
−
2
(2.19)
γ
γ
γ
γ γ
γ γ
sl
s
l
s
l
s
l
Combining this equation with Young's Equation 2.12 yields:
(
)
=
d
d
h
h
1
+
cos
2
+
2
(2.20)
γ
θ
γ γ
γ γ
l
Y
s
l
s
l
Around the same time, Kaelble [38] published a very similar equation in terms of dis-
persion and polar forces. Thus, Equation 2.19 is often called the Owens-Wendt-Kaelble
equation.
Equation 2.20 contains two unknowns:
γ
s
d
and
γ
s
h
. They can be determined by measuring
the contact angle of at least two different liquids on one and the same solid surface and
then solving the two simultaneous equations.
Lifshitz-van der Waals/acid-base (van Oss)
The Lifshitz-van der Waals/acid-base (van Oss) approach [39,40] is a generalization of
the Fowkes' approach, by considering perceived acid-base interactions at the interface.
van Oss et al. divided the surface tension into different perceived components (i.e., the so-
called Lifshitz-van der Waals (LW), acid (+), and base (−) components) such that the total
surface tension is given by:
LW
+ −
=
+
2
(2.21)
γ
γ
γ γ
i
i
i
i
where
i
denotes either the solid or liquid phase. The interfacial tension was postulated
both of solid-liquid and liquid-liquid systems as:
LW LW
+ −
− +
=
+
−
2
−
2
−
2
(2.22)
γ
γ
γ
γ
γ
γ γ
γ γ
12
1
2
1
2
1
2
1
2
For solid-liquid systems, combining Equation 2.22 with Young's equation yields:
(
)
=
LW
LW
+ −
− +
1
+
cos
2
+
2
+
2
(2.23)
γ
θ
γ
γ
γ γ
γ γ
l
Y
l
s
l
s
l
s
Equation 2.23 is used to determine the solid surface tension components (
γ
s
LW
,
γ
s
+
, and
γ
s
−
)
from contact angles, using three simultaneous equations by inserting the properties of the
test liquids.
