Microdrops Evaporating from Deformable or Soluble Polymer Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 111

Figure 2. (A) Scheme of the deformation of an elastic surface by a sessile droplet. L,S and G stand
for liquid, solid and gas. The dotted line displays the solid surface without deformation. is the
equilibrium contact angle of the droplet, h is the maximum height of the ridge and d is the maximum
depth of the depression under the drop. (B) Magnified scheme of the contact point at the TPCL. The
surface tension acts over a surface layer of thickness t .

k 2 )K(k) ,and E(k) and K(k) are the total normal el-
liptical Legendre integrals of the first and second kind respectively, cos is the
difference between the macroscopic contact angle and the equilibrium contact angle
given by the Young's equation, t is the thickness of the liquid-gas interfacial layer,
v is the Poisson's ratio of the material, and the other parameters have been defined
before. Later, White [45] extended this model introducing the influence of the sur-
face stress transmission of a free liquid interface at the microscopic TPCL on the
elastic surface deformation, i.e., he considered the action of the disjoining pressure.
He concluded that the microscopic contact angle is zero and that the macroscopic
one obeys Young's equation after introducing a correction factor that depends on
the microscopic deformation height at the TPCL and the deformation as a result of
the disjoining pressure.

≡ − −

where G(k) E(k) ( 1

4. Evaporation of Solvent Droplets on Polymer Surfaces

In recent times, several technological applications based on the deposition of sol-
vent microdrops on soluble polymer substrates by inkjet devices have been pre-
sented, and the microstructures generated on the surface after solvent evaporation
have been discussed. The literature is vast and growing, therefore here is listed
a representative, but by no means complete, experimental [22-25, 27-35, 37-39,
46-50] and theoretical [26, 36, 51, 52] catalogue. The interest towards a more fun-
damental understanding of the processes involved is increasing. This will allow for
an improved knowledge of the technology and a better control of the resulting mi-
crostructures.
As it has been pointed out, among others in [52], the evaporation of a solvent
droplet from a soluble polymer surface is a very complex process, where several
independent, but correlated, physico-chemical phenomena occur. A sketch of the
situation, addressing some of the processes involved, is displayed in Fig. 3.
We can divide these processes into three main groups of action:
(i) First, when a solvent drop is deposited on a soluble surface, this wets the sur-
face and takes the shape of a flattened lens due to its high affinity with the
substrate material. The drop is pinned at the rim due to the roughness of the