Analysis of a viscoelastic phase separation model

TL;DR

This paper introduces a new thermodynamically consistent viscoelastic phase separation model, analyzing its mathematical properties and validating it through numerical simulations that align well with mesoscopic results.

Contribution

The paper presents a systematically derived conservative two-fluid model for viscoelastic phase separation, including dissipative effects and rigorous mathematical analysis.

Findings

Model is consistent with the second law of thermodynamics

Existence of weak solutions is proven

Numerical simulations agree qualitatively with mesoscopic results

Abstract

A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics, and we study well-posedness of the model, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. A good qualitative agreement with mesoscopic simulations is observed in numerical tests.