Morphology formation in thin films produced from a ternary solution is crucial for the performance of organic solar cells. Both the separation of excitons into free charges as well as the charge transport that follows depend on the shape and connectivity of the distinct polymer regions (the morphology).In this thesis, we study morphology formation from two different perspectives:A lattice-based Blume-Capel model with Kawasaki dynamics, and then a continuum system of coupled parabolic equations with nonlinear and nonlocal drift. The objective of this licentiate thesis is to represent morphology formation in three space dimensions using these two models. We relate our work to previous two-dimensional results for different parameter regimes. At the technical level, we construct a semi-discrete finite volume scheme to approximate the weak solution of our continuum model and implement it in Julia. We prove a convergence result of our semi-discrete scheme as well as a stability result of the weak solution with respect to temperature variations - a key parameter in the model. Looking at both the lattice model and the continuum parabolic system, we quantify and compare growth rates of the formed domains. Finally, we perform numerical experiments confirming convergence of our scheme and the effect of parameters on the obtained solution. These results provide a solid foundation for future extensions, including the evaporation of a mixture component.