Chapter 2: Literature survey
2.8 Wettability and Contact Angle
2.8.2 Different types of wetting
Osterhof and Bartell222 identified three different types of wetting: spreading,
adhesional wetting and immersional wetting. A brief overview of these various types
Chapter 2. Literature Survey
2.8.2.1
Spreading
Spreading occurs when a liquid in contact with a solid spreads on the solid and
displaces another fluid (air or immiscible liquid) also in contact with the solid (Figure 2-
13).
Figure 2-13: Evolution of a liquid drop (L) spreading on the solid (S) surrounded by vapour (V); a is the area covered by the spreading liquid.
During spreading, liquid L completely spreads out on the solid surface which results in
a decrease of the surface free energy of the system. If a is the surface covered by the
spreading liquid, the decrease in surface energy due to the decrease in area of the
solid/vapour interface will be aSV. Similarly, the increase in surface energy due to the increase in area of the solid/liquid interface is aSL. Since the liquid/vapour interfacial area increases as the liquid spreads over the solid, the increase in surface
energy due to the increase in area of the liquid/vapour interface is aLV. The total decrease in surface free energy is then given by:
SV SL LV
G a
(2.8)
The force that drives the spreading is quantified by SV SLLV. This quantity is called the spreading coefficient SL/S:
Chapter 2. Literature Survey
/
L S SV SL LV
S (2.9)
Note that the spreading coefficient was defined for vapour/liquid/solid systems. In the
same way it can be defined for liquid/liquid/solid systems, gas/liquid/liquid systems or
liquid/liquid/liquid systems:
liquid (L1)/liquid (L2)/solid:
1/ 2 1 1 2
L S SL SL L L
S , with L1 the liquid drop
spreading over the solid, and L2 the liquid surrounding the L1 drop;
gas/liquid (L1)/liquid (L2): SL L1/ 2 L V2 L L1 2 L V1 , where the liquid L1 is more dense than the liquid L2;
liquid (L1)/liquid (L2)/liquid (L3): SL L1/ 2 L L2 3 L L1 2 L L1 3, where density of the liquids is as follow:
1 2 3
L L L
.
In case the substrate is a solid (Liquid or gas/liquid/solid systems), the spreading
coefficient must be calculated by indirect methods, because the surface and interfacial
tensions of solid cannot be measured. Measurement of the contact angle θ between the
spreading liquid and the solid is necessary. When the system is at equilibrium, i.e. the
liquid has completely spread out or has stopped spreading, Equation 2.9 can be
combined with the Young’s equation (Equation 2.7), which gives:
/ cos 1
L S LV
S (2.10)
If θ is 0, the spreading coefficient will be zero and complete spreading occurs. If θ is 180, SL S/ 2LV and the solid is not wet at all by the liquid.
Chapter 2. Literature Survey
2.8.2.2
Adhesional wetting
Adhesional wetting occurs when a liquid, which is initially not in contact with a solid,
makes contact with the solid and adheres to it (Figure 2.14). Contrary to spreading, the
vapour/liquid interfacial area decreased as the liquid adheres to the solid. The change in
surface free energy is in this case:
SV LV SL
G a
(2.11) where a is the surface of the solid that the liquid covers. The force that drives the
adhesion of a liquid to a solid is quantified by SV LV SL. This quantity is known as the work of adhesion Wa, which is the force necessary to separate the liquid from the
solid.
a SV LV SL
W (2.12)
Combining Equation 2.12 with Equation 2.7, the work of adhesion can be expressed by:
cos 1
a LV
W (2.13)
In case that θ is 180, the work of adhesion is zero, which means that the liquid cannot wet the solid.
Figure 2-14: Adhesional wetting of liquid (L) on solid (S) surrounded by vapour (V), and schematic representation of the work of cohesion.
Chapter 2. Literature Survey
The work of cohesion Wc is defined as the work required to produce two units area of
interface from an original unbroken column of liquid (Figure 2-14) and quantified by:
2
c LV
W . The difference between the work of adhesion and the work of cohesion is the spreading coefficient:
/
L S a c
S W W (2.14)
If Wa > Wc the spreading coefficient will be positive, the contact angle will be zero and
the liquid will spread spontaneously over the liquid. If Wa < Wc the spreading coefficient
will be negative, the contact angle will be greater than zero and the liquid will not
spread over the liquid but will form droplets of a finite contact angle.
2.8.2.3
Immersional wetting
Immersional wetting occurs when a solid is immersed into a liquid through a fluid-fluid
interface. The surface free energy in case of complete immersional wetting (Figure
2.15a) is given by:
SV SL
G a
(2.15)
where a is the solid/liquid interface. Note that Equation 2.15 does not take into account
the interfacial tension between the liquid and the vapour because at equilibrium the
Chapter 2. Literature Survey
Figure 2-15: Position of a solid for immersional wetting type; (a) complete immersion, (b) partial immersion.
Nonetheless, during immersion, the solid goes through the interface (Figure 2.15b). The
spreading coefficient SL S/ defined in sub-section 2.8.2.1 is used to quantify the ability of the solid to completely immerse into the liquid. If
SL S/ 0, the contact angle θ will be zero and complete immersion will be spontaneous;
SL S/ 0, 0which means that the solid will only be partially immersed into the liquid. Thus, work must be done to “push” the solid into the liquid and achieve complete immersion. Modification of the interfacial tension, by using
surfactant for example, is required to facilitate the immersion.