Film formation from solvent evaporation in polymer ternary solutions is relevant for several technological applications, such as the fabrication of organic solar cells. The performance of the final device will strongly depend on the internal morphology of the obtained film, which, in turn, is affected by the processing conditions. We are interested in modeling morphology formation in 3D for ternary mixtures using both a lattice model and its continuous counterpart in the absence of evaporation. In our previous works, we found that, in 2D, both models predict the existence of two distinct regimes: (i) a low-solvent regime, characterized by two interpenetrated domains of the two polymers, and (ii) a high-solvent regime, where isolated polymer domains are dispersed in the solvent background. In the significantly more intriguing 3D case, we observe a comparable scenario both for the discrete and the continuous model. The lattice model reveals its ability to describe morphology formation even in the high solvent content 3D case, in which the three-dimensional nature of space could have prevented cluster formation. To realize the simulations we have written specific codes using the languages C and julia. The codes closely follows the algorithmic dynamics governing the lattice and the continuum model.

Motivated by questions related to morphology formation in 3D involving interacting ternary mixtures, we propose a finite volume scheme to approximate numerically the unique weak solution to a coupled system of parab olic equations with nonlinear and nonlocal drift. The special feature of our system is that the coupling takes place precisely via the structure of the drift terms. We prove the convergence of the scheme towards the unique solution of the target evolution system and explore as well the stability of the solution with respect to selected parameters. We illustrate numerically in 3D the appearance of the wanted morphologies and compute as well the empirical order of convergence of the numerical approximations towards their limit.