Contact Angle Measurements over Macro, Micro and Nano Dimensioned Systems - Drops and Bubbles in Contact with Solid Surfaces - page 7

able to create hysteresis is a deviation from the real equilibrium and consequently
a severe obstacle to correct wetting evaluations. In the case of flat but chemical
inhomogeneous surfaces the ESA accepts to consider the advancing contact an-
gle as a good approximation of the effective equilibrium contact angle, while in
the case of physical irregularities this assumption is considered not satisfactory.
The necessity to deal with perfect, noninteracting, materials is a full requirement
for this theoretical approach that recommends not only to exclude polar surfaces
from the analyzed systems, due to their intrinsic capability to modify the liquid-
solid status, but also needed to develop a special experimental technology, known
as ADSA—(Axisymmetric Drop Shape Analysis) [149], able to further reduce any
dynamic deposition influence to the evaluation activities. By adopting this measure-
ment technique Gu et al. [200] proposed a Modified Young Equation (11) in order
to correlate the effects of line tension (i.e., the effective contact line among liquid
drop, solid surface and vapour) and drop curvature radius to the contact angle value:

σ
γ lv

1
R ,

cos θ = cos θ ∞ − (8)

where θ is the contact angle corresponding to a finite contact radius drop and θ ∞ is
the contact angle of a infinitely large drop. The same formula was also implemented
to be able to take account of eventual local inclination of the solid supporting ma-
terial, sounding therefore as (12)

σ
γ lv

cos β
ρ

cos θ = cos θ ∞ − , (9)

where β is the inclination angle and 1 /ρ the drop curvature [200, 201].
The Modified YE admits a direct dependence of contact angles by the line ten-
sion effects. Even if the features and the sign of line tension are still a point of
debate [43-56] among scientists, the direct consequence of it is a contact angle
dependence also by the size of the drop . This is a very important point in the frame-
work to create a link between the micro-nano observations and macro experiences.
The argument of the size effects dependence on contact angle values has been de-
bated by many Authors, approaching at final results sometimes contrasting each
other [146-158].

E. The Acid-Base Approach
Starting from a quite different point of view, that frequently determined cross crit-
icisms [167, 180, 181], the Acid-Base Theory shares with the ESA approach the
same aim to provide an explicit form of the solid-liquid energy γ sl by which it is
possible to calculate the work of adhesion , reported in (10) with its correlation with
the YE:

cos θ). (10)
The Theory is quite complex in all its details and the direct consultancy of origi-
nal works has to be considered mandatory for those who do not rely on a specific

W ADH = γ lv + γ sv − γ sl = γ lv ( 1 +