Extended Larch\'e--Cahn framework for reactive Cahn--Hilliard multicomponent systems

TL;DR

This paper develops an extended thermodynamic continuum theory for multicomponent Cahn--Hilliard systems, incorporating chemical reactions and configurational forces to better understand phase separation and microstructure evolution in reactive materials.

Contribution

It introduces an extended Larché--Cahn framework that accounts for multiple reactions and configurational fields in multicomponent phase separation modeling.

Findings

Simulation shows reaction-diffusion interactions influence microstructure evolution.

Configurational tractions drive interface motion during phase separation.

The theory captures the coupling between chemical reactions and microstructural changes.

Abstract

At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to describe the coarsening kinetics of the exsolution microstructure, we derive a thermodynamically consistent continuum theory for the multicomponent Cahn--Hilliard equations while accounting for multiple chemical reactions and neglecting deformations. Our approach considers multiple balances of microforces augmented by multiple constituent content balance equations within an extended Larch\'e--Cahn framework. As for the Larch\'e--Cahn framework, we incorporate into the theory the Larch\'e--Cahn derivatives with respect to the phase fields and their gradients. We also explain the implications of the resulting constrained gradients of the phase fields in the form of the gradient energy coefficients. Moreover, we derive a configurational balance that includes all the associated configurational fields in agreement with the Larch\'e--Cahn framework. We study phase separation in a three-component system whose microstructural evolution depends upon the reaction-diffusion interactions and to analyze the underlying configurational fields. This simulation portrays the interleaving between the reaction and diffusion processes and how the configurational tractions drive the motion of interfaces.