Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems

Clavijo, Santiago P.; Espath, Luis; Calo, Victor M.

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 component content balance equations within an extended Larché–Cahn framework. As for the Larché–Cahn framework, we incorporate into the theory the Larché–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 Larché–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.

Citation

Clavijo, S. P., Espath, L., & Calo, V. M. (2021). Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems. Continuum Mechanics and Thermodynamics, 33(6), 2391-2410. https://doi.org/10.1007/s00161-021-01045-9

• Journal Article Type: Article
• Acceptance Date: Jul 23, 2021
• Online Publication Date: Aug 4, 2021
• Publication Date: 2021-11
• Deposit Date: Jul 31, 2023
• Publicly Available Date: Aug 9, 2023
• Journal: Continuum Mechanics and Thermodynamics
• Print ISSN: 0935-1175
• Electronic ISSN: 1432-0959
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 6
• Pages: 2391-2410
• DOI: https://doi.org/10.1007/s00161-021-01045-9
• Keywords: General Physics and Astronomy; Mechanics of Materials; General Materials Science
• Public URL: https://nottingham-repository.worktribe.com/output/22186707
• Publisher URL: https://link.springer.com/article/10.1007/s00161-021-01045-9