Influence of the Processes Parameters on the Properties of The ...

Chapter 3.
Analytical Methods and Designs <strong>of</strong> Experiments
Figure 3.24: Vectorial equilibrium for a drop <strong>of</strong> a liquid resting on a solid surface to balance three forces.
SV
SL LV Cos
(3.16)
SV SL
cos
(3.17)
LV
where γ LV denotes <strong>the</strong> interfacial tension due to <strong>the</strong> liquid-gas surface, γ SL refers to <strong>the</strong> interfacial
tension due to <strong>the</strong> solid-liquid surface and γ SV indicates <strong>the</strong> interfacial tension <strong>of</strong> <strong>the</strong> solid-gas surface.
In Young-Dupré equation, two parameters can be measured directly: <strong>the</strong> liquid surface tension
(γ LV ) and <strong>the</strong> contact angle (θ). The two o<strong>the</strong>r parameters (γ SV and γ SL ) have to be derived. The contact angle
measurements give 3 informations:
The affinity <strong>of</strong> a liquid to a solid surface: if water is used to measure <strong>the</strong> contact angle, one can
deduce <strong>the</strong> hydrophobic (great angle) or hydrophilic (small angle) character <strong>of</strong> <strong>the</strong> surface.
If several reference liquids are used, <strong>the</strong> surface energy <strong>of</strong> <strong>the</strong> solid can be calculated, discriminating
between polar and dispersive components. The most common models used are <strong>the</strong> Good & Van Oss
and <strong>the</strong> Owens & Wendt models.
The measure <strong>of</strong> <strong>the</strong> hysteresis between advancing angle and recessing angle give informations on
non homogeneity <strong>of</strong> <strong>the</strong> surface (roughness , contamination, etc.).
Theoretically, <strong>the</strong> Young-Dupré’ equation is correct, but as it is based on ideal surfaces
(homogeneous, pure, smooth), it is experimentally difficult to obtain. Considering this, a range <strong>of</strong> contact
angles is obtained, depending on <strong>the</strong> smoothness <strong>of</strong> <strong>the</strong> surface and with a maximum and minimum possible
value. The difference between <strong>the</strong> maximum contact angle (θ A ) and <strong>the</strong> minimum or receding contact angle
(θ R ) is referred as <strong>the</strong> contact angle hysteresis (Δθ= θ A − θ R ) [Possart and Kamusewitz, 2003].
6.2.2.2 Model <strong>of</strong> Owens-Wendt : Two Components Theory
Owens and Wendt [1969] considered that <strong>the</strong> surface energy is expressed in <strong>the</strong> form:
S = γ S d + γ S
p
(3.18)
with γ S d dispersive (or apolar) and γ S p polar (or non-dispersive) components.
Following <strong>the</strong> work that Fowkes pioneered in 1962, [Fowkes, 1962] <strong>the</strong> different surface energy <strong>of</strong>
solid (γ SV , γ SL and γ LV ) can be split into two components: polar and dispersive fractions. Based on <strong>the</strong>
assumption that only <strong>the</strong> same type <strong>of</strong> interaction (polar and/or dispersive) can occur between both phases.
Owens and Wendt [1969] proposed <strong>the</strong> following equation:
d d 1/ 2 p p 1/ 2
12
1
2 2[( 1
.
2
) ( 1
.
2
) ]
(3.19)
- 81 -