Biomedical Engineering Reference
In-Depth Information
where
Δ
P
= interfacial pressure difference in a column of fluid of density
ρ
and height
h
,
Δ
P
=
ρ
gh
and
g
is the acceleration due to gravity (9.8 m/s
2
).
γ
= interfacial tension (
γ
lv
),
R
1
,
R
2
= surface's radii of curvature of the drop.
Therefore, there are only two unknown parameters in Young's equation. An obvious
approach is to solve for the two unknowns simultaneously from the two simultaneous
equations generated by two test liquids (each with its own
γ
lv
value and
θ
generated).
However, the problem with this approach is the
γ
ls
, which is a function of the liquid's own
γ
lv
and the solid's
γ
sv
. That is to say, the
γ
ls
value should be different when two liquids are
used, and hence cannot be determined simultaneously. So a more appropriate method
is to combine the equations from the surface tension component approaches (
γ
sv
is the
sum of different surface tension components, e.g., dispersive or polar components) with
Young's equation and then solve simultaneously the equations generated by using two or
three liquids. If deionized water (which is polar in nature) is used, diiodomethane (which
is dispersive) can be a supplementary liquid to be used, as the
γ
lv
and
θ
values are more
prominently differentiated from that of deionized water.
Surface Tension Component
Fowkes
The approach of surface tension components was pioneered by Fowkes [36]. The total sur-
face tension can be expressed as a sum of different surface tension components, each of
which arises due to a specific type of intermolecular force:
γ
=
γ
d
+
γ
h
+
γ
di
+
×××
(2.14)
where
γ
,
γ
d
,
γ
h
, and
γ
di
are, respectively, the total surface tension, dispersive surface tension
component, and surface tension components due to hydrogen and dipole-dipole bonding.
Equation 2.14 is often rearranged into:
γ
=
γ
d
+
γ
n
(2.15)
where the total surface tension
γ
is a sum of only the dispersive
γ
d
and nondispersive
γ
n
surface tension components. The former arises from molecular interaction due to London
forces; the latter is from all the other interactions due to non-London forces. A geometric
mean relationship was postulated both of the solid-liquid and liquid-liquid interfacial
tensions:
d d
=
+
−
2
(2.16)
γ
γ
γ
γ γ
12
1
2
1
2
For solid-liquid systems, combining Equation 2.16 with Young's Equation 2.12 yields:
d
d
cos
=
2
−
(2.17)
γ
θ
γ γ
γ
l
Y
s
l
l
Typically, experimental contact angles of different liquids with known
γ
l
d
on a dispersive
solid surface (
γ
d
) are employed to determine the surface tension of a solid.
=
γ
s
s
