Biomedical Engineering Reference
In-Depth Information
evolutions of the evaluated system. The accomplishment of true equilibrium condi-
tions over a real surface, unfortunately, is not an instantaneous set up and usually
it occurs, if possible, after a sequence of steps performed on different time scales,
strictly related to the specific liquid-solid system features and the adopted experi-
mental technique [155-158]. It is important to stress that a visual 'steady position'
of a liquid over a substrate does not have to be automatically considered as the fi-
nal equilibrium position. This means that there is no
apriori
certainty that a drop
placed on a real solid substrate has reached its deepest and therefore more stable
potential energy well. In the microscopic size range the presence of heterogeneities
or the evaluation of viscous fluids makes highly probable the existence of multiple
partial equilibrium positions [44, 72, 87, 117, 135, 191] that, independently of their
major or minor degree of stability, may provide misleading results, often difficult
to perceive.
Two main theoretical approaches, briefly described in the following, were born
after Young and still hold in the wetting community. A third version has to be
recognized in the works of the Russian school of Churaev, Starov
et al.
[118-123]
who developed, on the basis of the Derjaguin statements, a proper way to deal with
wetting problems by adopting a rigorous mathematical approach of the liquid-solid
energy minimization issue. Due to the specificity of this issue a direct consultancy
of the Authors papers is recommended.
D. The Equation of State Approach
Zisman and his collaborators [2-6] in the mid sixties performed very important
experimental and theoretical revisions of the contact angle problem. His analy-
sis provided the wide known correlation among the contact angles of homologous
series of fluids (n-alkanes) and their liquid surface tension values. This correspon-
dence was found linearly decreasing. By measuring series of liquids with different
properties he obtained band diagrams by which he determined the concept of
crit-
ical surface tension of wetting
. He approached the concept that later Neumann
et
al.
, by further implementing and expanding his data, developed and proposed in the
Equation of State Approach—ESA
[15]. To correctly apply the YE an extra equation
was in fact needed and this was therefore formulated as (4):
γ
lv
−
√
γ
sv
γ
sl
=
0
.
015
γ
lv
γ
sv
,
(4)
1
−
where
γ
sl
,
γ
sv
are respectively the
surface-liquid
and
surface-vapor
energies and
γ
lv
is the liquid surface tension. By combining this definition of the solid-liquid
surface energy with the YE Neumann and colleagues derived an expression in
which the solid-vapor surface energy was able to be determined by both the ex-
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