Reactive [Formula presented]-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions

S. P. Clavijo; A. F. Sarmiento; L. F.R. Espath; L. Dalcin; A. M.A. Cortes; V. M. Calo

doi:10.1016/j.cam.2018.10.007

Reactive [Formula presented]-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions

S. P. Clavijo, A. F. Sarmiento, L. F.R. Espath^*, L. Dalcin, A. M.A. Cortes, V. M. Calo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We introduce a multicomponent Cahn–Hilliard system with multiple reversible chemical reactions. We derive the conservation laws of the multicomponent system within the thermodynamical constraints. Furthermore, we consider multiple chemical reactions based on the mass action law. This coupling reproduces phase separation under spinodal decomposition as a chemical reaction between the species takes place. Finally, we perform a numerical simulation to show the robustness of the model as well as the resulting patterns.

Original language	English (US)
Pages (from-to)	143-154
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	350
DOIs	https://doi.org/10.1016/j.cam.2018.10.007
State	Published - Apr 2019

Bibliographical note

Funding Information:
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. Additional support was provided by 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 ). Additional support was provided at Curtin University by The Institute for Geoscience Research (TIGeR) and by the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES.

Funding Information:
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. Additional support was provided by 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). Additional support was provided at Curtin University by The Institute for Geoscience Research (TIGeR) and by the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES.

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

Chemical reactions
Isogeometric analysis
Multicomponent Cahn–Hilliard
Spinodal decomposition

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2018.10.007

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title = "Reactive [Formula presented]-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions",

abstract = "We introduce a multicomponent Cahn–Hilliard system with multiple reversible chemical reactions. We derive the conservation laws of the multicomponent system within the thermodynamical constraints. Furthermore, we consider multiple chemical reactions based on the mass action law. This coupling reproduces phase separation under spinodal decomposition as a chemical reaction between the species takes place. Finally, we perform a numerical simulation to show the robustness of the model as well as the resulting patterns.",

keywords = "Chemical reactions, Isogeometric analysis, Multicomponent Cahn–Hilliard, Spinodal decomposition",

author = "Clavijo, {S. P.} and Sarmiento, {A. F.} and Espath, {L. F.R.} and L. Dalcin and Cortes, {A. M.A.} and Calo, {V. M.}",

note = "Funding Information: 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. Additional support was provided by the European Union{\textquoteright}s Horizon 2020 Research and Innovation Program of the Marie Sk{\l}odowska-Curie grant agreement no. 777778 , and the Mega-grant of the Russian Federation Government (N 14.Y26.31.0013 ). Additional support was provided at Curtin University by The Institute for Geoscience Research (TIGeR) and by the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. Funding Information: 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. Additional support was provided by the European Union's Horizon 2020 Research and Innovation Program of the Marie Sk{\l}odowska-Curie grant agreement no. 777778, and the Mega-grant of the Russian Federation Government (N 14.Y26.31.0013). Additional support was provided at Curtin University by The Institute for Geoscience Research (TIGeR) and by the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

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language = "English (US)",

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AU - Espath, L. F.R.

AU - Dalcin, L.

AU - Cortes, A. M.A.

AU - Calo, V. M.

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KW - Isogeometric analysis

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ER -

Reactive [Formula presented]-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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