Biomedical Engineering Reference
In-Depth Information
perimental measurable parameters, i.e., the liquid surface tension and the contact
angle value. This formula may be appreciated in (5):
2
)
γ
sv
γ
lv
(
0
.
015
γ
sv
γ
lv
−
+
γ
lv
(
0
.
015
γ
lv
γ
sv
cos
θ
=
.
(5)
−
1
)
Later on the same Authors got aware of a discontinuity problem in the form of
(4) related to certain surface tension values able to make zero the numerator of the
formula. The supporting expressions of the ESA were therefore reformulated in the
fashion that became later known as (6) and (7):
2
√
γ
lv
γ
sv
e
−
β(γ
lv
−
γ
sv
)
2
,
γ
sl
=
γ
lv
+
γ
sv
−
(6)
2
γ
sv
γ
lv
e
−
β(γ
lv
−
γ
sv
)
2
.
cos
θ
=−
1
+
(7)
The complete review of the birth and genesis of this formula would also imply
to mention the studies based upon other Authors, like Antonow [198], Berthelot
[199], and may be fully appreciated in the wide scientific production of the Neu-
mann Group and his numerous students and colleagues. The validity of the ESA
approach depends upon the fact of being able to correctly evaluate the
β
factor, that
recently has been slightly corrected and expressed as an average value equivalent
to 0.000125 (mJ/m
2
)
−
2
. This number was derived by a huge amount of measure-
ments by which Neumann
et al.
determined the behaviour of numerous surfaces
with different liquids. This numerical dependence is also the most common cause
of disagreement with the ESA approach. By explicit admission of these Authors in
fact solid surfaces have to be distinguished in three families:
•
The perfect ones, either chemical either physical, that may be correctly evalu-
ated by the ESA approach and therefore can be interpreted by the YE.
•
Those that even being chemically heterogeneous are physically perfect. These
substrates may be analysed, even with special care.
•
Those who present physical irregularities. By the Authors these surfaces have
no chance to be reported in a YE/ESA meaningful frame.
The problem concerning nonperfect surfaces arises from the appearance, over the
most of real samples, of the contact angle hysteresis phenomenon, i.e., the simul-
taneously presence of an
Advancing
and a
Receding
contact angles, both different
from the unique, single, real thermodynamic one prescribed by the YE rule on ideal
substrates. This terminology comes through the experiences within tilting drops
[132] where a drop placed on a tilted plate shows a profile with a relevant dif-
ference between the front (
Advancing
) contact angle and the rear (
Receding
) one
[7]. A simple practical example of this fact is the shape of a water drop falling
down on a window glass. In the sense of YE and ESA approaches any condition
Search WWH ::
Custom Search