Wetting at High Temperature - Drops and Bubbles in Contact with Solid Surfaces - page 307

Here r is the average roughness ratio (actual area/projected area). As r is always

1, this means that if θ> 90 ◦ ,θ m increases with increasing roughness; the contrary
when θ m < 90 ◦ .
The triple line can also be 'pinned' by the presence of surface heterogeneities. In
this case, the local situation must be analysed. Grooves, ridges are all imperfections
which must be overridden by the moving triple line. They alter the local geometrical
profile of the surface, with an orientation of the contact plane different from the
original reference one. On the basis of energetic arguments [65], it is possible to
establish the maximum value for advancing contact angles and the minimum value
for receding contact angles (the difference between the two is called hysteresis).
In the case of plane, heterogeneous surfaces, i.e., surfaces formed by two differ-
ent materials or different phases, the macroscopic contact angle can be calculated
using the Cassie equation [66]:

cos θ c = f 1 cos θ 1 + f 2 cos θ 2 , (10)

where θ 1 and θ 2 represent the contact angles on fractions f 1 and f 2 of the total
contact area, respectively.

2. Anisotropy

The Young (Eq. (1)) or Neumann (Eq. (7)) equations, dictate that the equilibrium
solid-liquid configuration at the triple line depends on the values assumed by the
solid-fluid interfacial energies. It is also well known that these energies are a func-
tion of crystallographic orientation at the surface, so that any anisotropy of the
solid-fluid interfacial energies should result in anisotropy of wetting. A thorough
discussion of this phenomenon can be found in recent papers by D. Chatain [67],
with specific reference to surfaces and by Rohrer [68] with respect to grain bound-
aries.
Surface energy anisotropy affects wetting in different ways. Following the vari-
ation of interfacial tensions with orientation, also the Young contact angle should
vary with the orientation along the surface, with the macroscopic consequence that
a sessile drop is no longer axisymmetric.
But, more subtly, the change in surface energy has a certain influence on the
adsorption and segregation processes which enter into play in the solid-liquid in-
teractions [69]. Thus, also the kinetics of spreading and the final contact angle can
be affected. Another point is related to the equilibrium 'shape' of the solid surface.
At high temperature, due to the increased atom mobility, the surface, if not part
of a monocrystal, tends to re-orient itself locally to expose the most stable crys-
tallographic planes. This means that local faceting can occur which increases the
surface roughness with the consequences on spreading and equilibrium contact an-
gles already discussed. As pointed out in Ref. [67], the more the crystal orientations
emerging at the surface are stable, the more the solid surface remains unchanged.
The 'resistance' of a certain crystallographic plane to rotate can be measured by the