Biomedical Engineering Reference
In-Depth Information
This remark is important to predict the contact angle when using two liquids
in a microfluidic system. It can be seen that very often films can form (i.e., one of
the liquid totally wets the wall), especially when surfactants are used. A graphical
construction explains this phenomenon (Figure 3.24). Relation (3.32) is scalar, but
can be considered as the projection a vector equation. If we note the radii
R
0
= 1,
R
1
=
g
L
1
G
/
g
L
1
L
2
, and
R
2
=
g
L
2
G
/
g
L
1
L
2
, and draw the circles
R
0
,
R
1
, and
R
2
, relation
(3.32) is the projection on the
x
-axis of the vector
OM
¢ =
OM
1
-
OM
2
=
OM
1
+
M
1
M
¢. It the projection of
M
¢ falls inside the interval [-1, 1] there is a partial wet-
ting (i.e., the two liquids have a Young contact angle at the wall); in the opposite
case, there is a film on the wall. Because often
g
L
1
G
/
g
L
1
L
2
>> 1 and
g
L
2
G
/
g
L
1
L
2
>>
1—this is the case when surfactants are added to one of the fluids—the projection
easily falls outside the [-1, 1] interval, and a film forms indicating the total wetting
of one of the liquids.
3.5.3 Generalization of Young's Law—Neumann's Construction
Let us come back to the derivation of Young's law. Young's law has been obtained
by a projection on the
x
-axis of the surface tension forces, but the force balance ap-
plies also to a
y
-axis projection. On a solid, fixed surface, the resulting constraints
on the solid substrate cannot be seen. However, there are two cases where the y-
projection of Young's law is of importance: the cantilever and the contact between
three liquids.
Figure 3.24
Geometrical construction of the resultant contact angle.
