We propose a lattice model for three stochastically interacting components that mimicsthe formation of the internal structure of adhesive bands via evaporating one component(the solvent) by thermal gradient. We use high-performance computing resources toinvestigate the formation of rubber-acrylate morphologies. We pay special attentionto the role of varying temperature as well as of the changing the solvent interaction inconnection to the shape of the obtained rubber morphologies.In the lattice model, we start with microscopic spins of three particles in the latticewith short-range interactions between them. This microscopic model is approximatednumerically via a Monte Carlo Metropolis-based algorithm. High-performancecomputing resources and Python-based implementations have been used for thenumerical simulation of the lattice model. The numerical implementation highlights theeffect of the model parameters (volatility of the Solvent, temperature, and interactionbetween the particles) on the structure of the obtained morphologies. We demonstratethat one can utilize a reasonably simple model to explain the impact of parameters onthe creation of morphology in ternary systems when one component evaporates.