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

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.
Original languageEnglish (US)
JournalContinuum Mechanics and Thermodynamics
StatePublished - Aug 4 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-08-12
Acknowledgements: We are indebted to Professor Eliot Fried. We had many exhaustive discussions in which he gave us valuable ideas, constructive comments, and encouragement. This publication was made possible in part by the CSIRO Professorial Chair in Computational Geoscience at Curtin University and the Deep Earth Imaging Enterprise Future Science Platforms of the Commonwealth Scientific Industrial Research Organisation, CSIRO, of Australia. The European Union’s Horizon 2020 Research and Innovation Program of the Marie Skłodowska-Curie grant agreement No. 777778, and the Mega-grant of the Russian Federation Government (N 14.Y26.31.0013) provided additional support. Lastly, we acknowledge the support provided at Curtin University by The Institute for Geoscience Research (TIGeR) and by the Curtin Institute for Computation.

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Mechanics of Materials
  • General Materials Science


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