Biomedical Engineering Reference
In-Depth Information
3.5.2 Young's Law for Two Liquids and a Solid
Suppose that we know the contact angles of a liquid 1 and a liquid 2 on a sub-
strate
S
in air. What is then the contact angle if liquid 2 is immersed into liquid 1
(Figure 3.23)?
Young's law for the first liquid is
γ
cos
(
θ
)
=
γ
-
γ
(3.28)
L G
1,
L G S
1,
,
S G
,
S L
, 1
and for the second liquid is
γ
cos
(
θ
)
=
γ
-
γ
(3.29)
L G
2,
L G S
2,
,
S G
,
S L
, 2
The difference of (3.28) and (3.29) yields [12]
(3.30)
γ
cos
(
θ
)
-
γ
cos
(
θ
)
=
γ
-
γ
L G
1,
L G S
1,
,
L G
2,
L G S
2,
,
S L
, 2
S L
, 1
If liquid 2 is immersed into liquid 1, Young's law yields
γ
cos
(
θ
)
=
γ
-
γ
(3.31)
L L
1, 2
L L S
1, 2,
S L
, 1
S L
, 2
From (3.31) and (3.30), we deduce
γ
cos
(
θ
)
-
γ
cos
(
θ
)
L G
2,
L G S
2,
,
L G
1,
L G S
1,
,
(3.32)
=
cos
(
θ
)
L L S
1, 2,
γ
L L
1, 2
Surface tensions can easily be measured (by the pendant drop method, for ex-
ample), and if the two contact angles in air
q
L
1,
S
,
G
and
q
L
2,
S
,
G
are known, the con-
tact angle
q
L
1,
L
2,
S
is given by
é
ù
γ
cos
(
θ
)
-
γ
cos
(
θ
)
L G
2,
L G S
2,
,
L G
1,
L G S
1,
,
θ
=
arccos
(3.33)
ê
ú
L L S
1, 2,
γ
ê
ú
L L
1, 2
ë
û
Figure 3.23
(a) Contact of droplets of liquid 1 and liquid 2 surrounded by air or gas. (b) Contact
of a droplet of liquid 2 immersed in liquid 1.
