Biomedical Engineering Reference
In-Depth Information
tion voltage and denoted
V
sat
. This phenomenon is not yet completely understood;
some explanations have been put forward. In this section we present briefly a few
of them.
Possible Explanations for the Saturation Effect
The different explanations for the saturation limit of the contact angle are the trap-
ping of charges in the dielectric [13], an ionization at the triple line [10], an electric
resistance [5], a zero surface-liquid energy limit [14, 15], and—this is our theory—
the rapid increase of the vertical component
F
y
of the electric force according to
(4.17). A review of all these approaches is presented in [16].
Let us focus on the zero surface energy limit—which is a very useful approxima-
tion—pioneered by Peykov, Quinn, Ralston, and Sedev, which will be referred as
the “PQRS model.” The PQRS model considers that the saturation phenomenon
is a thermodynamic limit of stability. In this approach, the effective solid-liquid
surface tension decreases with the voltage according to
1
eff
2
γ
SL
V
(
)
=
γ
-
CV
(4.22)
SL
2
and the voltage dependant Young's law can be cast under the form
eff
γ γ
-
(
V
)
SG
SL
LG
cos (
θ
V
)
=
γ
At zero voltage, the force balance is that defined by the classic Young's law. As
the voltage increases, the effective solid-liquid surface tension decreases, and the
contact angle decreases (Figure 4.9). The lower limit for the effective solid-liquid
surface tension is zero; when this value is reached, the minimum contact angle is
obtained. This minimum value is the saturation contact angle
q
sat
.
At saturation
γ
SG
cos
θ
=
cos (
θ
V
)
=
(4.23)
sat
sat
γ
LG
which is equivalent to
æ
ö
γ
SG
θ
=
arccos
(4.24)
sat
ç
÷
è
γ
ø
LG
Figure 4.9
Sketch of the different contact angles depending on the applied voltage. (a) at zero
potential, the contact angle is determined by the classical Young law; (b) the contact angle decreases
when the applied voltage increases; (c) the lower limit of the contact angle is obtained when the
solid-liquid surface tension vanishes.
