Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states

TL;DR

This paper develops a comprehensive dynamical model for the coupled process of phase separation and surface profile evolution in binary mixture films, incorporating thermodynamics, fluid dynamics, and interfacial effects, with analysis of stratified base states.

Contribution

It introduces a new coupled model based on model-H for binary mixtures with detailed thermodynamic and interfacial considerations, extending previous models.

Findings

Model derived using non-equilibrium thermodynamics including Soret and Dufour effects.

Comparison with literature validates the model in isothermal conditions.

Analysis of stratified base states provides insights into film stability.

Abstract

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibrium thermodynamics for a general non-isothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.