Microdrops Evaporating from Deformable or Soluble Polymer Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 108

remains constant, while the height and the contact angle decreases. In the second
one, provided that the surface is sufficiently smooth, the contact radius diminishes
while the contact angle is approximately constant. The final stage shows the drop
disappearing in an irregular fashion, which is difficult to track experimentally.
Several models have been proposed to the evaporation kinetics of sessile drops.
Lebedev [6] and later Picknett and Bexon—like Maxwell, Morse, and Langmuir
did for spherical drops—assumed that the evaporation of a sessile drop is diffusion
driven only. They independently established that for a drop with the shape of a
spherical cap, the vapour concentration field around the top half of an equiconvex
lens is equivalent to the electrostatic potential field. Hu and Larson compared the
two previous models and implemented them in a FEM simulation [7] for the case of
constant contact radius evaporation. The agreement between the analytic models,
the simulations, and experimental data was very good. As well, Meric and Erbil
proposed a model considering a sessile droplet as having 'pseudo-spherical cap'
geometry, introducing a flatness parameter of the droplet, with good agreement with
experimental data on large drops [8].
In the last few years more and more groups started investigating also wetting and
evaporation of drops on deformable [9-21] or on soluble substrates [22-39].
In this work we intend to report the state-of-the-art research on evaporating
droplets from soluble polymer surfaces along with the physico-chemical processes
involved. In this respect, we want to address but a few peculiar properties of solu-
ble polymers [40], like that: (i) in the presence of a solvent they become soft to a
degree depending on the relative vapour pressure of the solvent in the surrounding
atmosphere; (ii) solvent diffuses into the polymer thereby swelling and softening
it; (iii) solvent and polymer can mix at any ratio since there is not a clearly cut
solubility for polymers.

B. Background, Materials and Methods

1. Drop in Equilibrium

For the sake of simplicity, let us first consider a drop deposited onto a non-
deformable and non-soluble substrate (Fig. 1). In equilibrium, i.e., when the drop is
not evaporating, Young's equation must hold. It establishes the relation among the
three surface tensions acting at the rim of the drop (three phase contact line, TPCL).

γ S − γ SL =

γ L cos , (1)

γ L is the surface tension at the interface liquid/gas, γ S is the surface tension at the
interface solid/gas, and γ SL is the surface tension at the interface solid/liquid. is
called contact angle, or wetting angle, of the liquid on the solid. Equation (1) is
strictly valid only if the drop is not evaporating and if gravity can be neglected.