Phase separation and morphology formation in interacting ternary mixtures under evaporation: Well-posedness and numerical simulation of a non-local evolution system

TL;DR

This paper analyzes a nonlinear non-local PDE system modeling ternary mixture interactions with evaporation, establishing well-posedness and demonstrating how evaporation influences morphology evolution through numerical simulations.

Contribution

It introduces a well-posedness analysis for a non-local PDE system with evaporation and provides numerical simulations showing evaporation's impact on morphology.

Findings

Evaporation significantly alters morphology shapes.

Finite volume scheme effectively approximates solutions.

Model connects to particle systems and applications in material design.

Abstract

We study a nonlinear coupled parabolic system with non-local drift terms modeling at the continuum level the inter-species interaction within a ternary mixture that allows the evaporation of one of the species. In the absence of evaporation, the proposed system coincides with the hydrodynamic limit of a stochastic interacting particle system of Blume-Capel-type driven by the Kawasaki dynamics. Similar governing dynamics are found in models used to study morphology formation in the design of organic solar cells, thin adhesive bands, and other applications. We investigate the well-posedness of the target system and present preliminary numerical simulations which incorporate evaporation into the model. We employ a finite volumes scheme to construct approximations of the weak solution and illustrate how the evaporation process can affect the shape and connectivity of the evolving-in-time morphologies.