  We develop a mesoscopic lattice model to study the morphology formation in
interacting ternary mixtures with evaporation of one component. As concrete
application of our model, we wish to capture morphologies as they are typically
arising during fabrication of organic solar cells. In this context, we consider
an evaporating solvent into which two other components are dissolved, as a
model for a 2-component coating solution that is drying on a substrate. We
propose a 3-spins dynamics to describe the evolution of the three interacting
species. As main tool, we use a Monte Carlo Metropolis-based algorithm, with
the possibility of varying the system's temperature, mixture composition,
interaction strengths, and evaporation kinetics. The main novelty is the
structure of the mesoscopic model -- a bi-dimensional lattice with periodic
boundary conditions and divided in square cells to encode a mesoscopic range
interaction among the units. We investigate the effect of the model parameters
on the structure of the resulting morphologies. Finally, we compare the results
obtained with the mesoscopic model with corresponding ones based on an
analogous lattice model with a short range interaction among the units, i.e.
when the mesoscopic length scale coincides with the microscopic length scale of
the lattice.
