Biomedical Engineering Reference
In-Depth Information
Figure 3.66
Large-scale roughness: schematic view of a drop located on an angle of the solid sur-
face. The position of the drop might not be stable.
An important remark at this stage is that the scale of the roughness on the solid
surface is very small compared to that of the drop [35]. Indeed, if not, it would
not be possible to define a unique contact angle
q
*
; the drop would not be axisym-
metrical anymore, and the contact could be sketched as in Figure 3.66, with many
different contact angles depending on the location of the droplet.
3.8.2.2 Cassie-Baxter Law
The same analysis was done by Cassie and Baxter for chemically heterogeneous
solid surfaces. For simplicity we analyze the case of a solid wall constituted of mi-
croscopic inclusions of two different materials. We shall not present the derivation
of the Cassie law. It is classical and the reader can refer to many topics [8, 10, 34].
Let us denote
q
1
and
q
2
as the contact angles for each material at a macroscopic
size, and
f
1
and
f
2
are the surface fractions of the two materials (Figure 3.67).
The Cassie-Baxter relation states that
*
cos
θ
=
f
cos
θ
+
f
cos
θ
(3.87)
1
1
2
2
This relation may be generalized to a more inhomogeneous material
*
=
å
cos
θ
f
cos
θ
(3.88)
i
i
i
Note that
f
1
+
f
2
= 1 or
å
f
i
= 1 if there are more than two components.
Figure 3.67
(a) Contact on a homogeneous substrate. (b) Contact on a heterogeneous surface.