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Computational Modeling of Mineral Unmixing and Growth.

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Title: Computational Modeling of Mineral Unmixing and Growth.
Authors: Kuhl, Ellen1 ekuhl@rhrk.uni-kl.de, Schmid, Daniel W.2 d.w.schmid@fys.uio.no
Source: Computational Mechanics. Apr2007, Vol. 39 Issue 4, p439-451. 13p. 1 Diagram, 5 Graphs.
Subjects: Finite element method data processing, Diffusion processes, Kirkendall effect, Mineral metabolism, Ostwald ripening, Surface tension, Decomposition method, Linear free energy relationship
Abstract: A new finite element based simulation technique for mineral growth governed by the classical Cahn–Hilliard equation is presented. The particular format of the underlying Flory–Huggins free energy for non-ideal mixtures is characterized through a double-well potential. It allows for uphill diffusion driven by gradients in the chemical potential and thus provides the appropriate framework to simulate phase separation typically encountered in mineral unmixing and growth. For the finite element discretization, the governing fourth order diffusion equation is reformulated in terms of a system of two coupled second order equations. For the temporal discretization, a heuristic adaptive time stepping scheme is applied in order to simulate not only the early stages of phase separation but also the long term behavior of ageing and grain fusion. The basic features of the Cahn–Hilliard equation are elaborated by means of selected geologically relevant examples. In particular, isotropic and anisotropic mineral growth and symplectite formation are studied and the long term response in the sense of Ostwald ripening is illustrated. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Kuhl%2C+Ellen%22">Kuhl, Ellen</searchLink><relatesTo>1</relatesTo><i> ekuhl@rhrk.uni-kl.de</i><br /><searchLink fieldCode="AR" term="%22Schmid%2C+Daniel+W%2E%22">Schmid, Daniel W.</searchLink><relatesTo>2</relatesTo><i> d.w.schmid@fys.uio.no</i>
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Apr2007, Vol. 39 Issue 4, p439-451. 13p. 1 Diagram, 5 Graphs.
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  Data: <searchLink fieldCode="DE" term="%22Finite+element+method+data+processing%22">Finite element method data processing</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+processes%22">Diffusion processes</searchLink><br /><searchLink fieldCode="DE" term="%22Kirkendall+effect%22">Kirkendall effect</searchLink><br /><searchLink fieldCode="DE" term="%22Mineral+metabolism%22">Mineral metabolism</searchLink><br /><searchLink fieldCode="DE" term="%22Ostwald+ripening%22">Ostwald ripening</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+tension%22">Surface tension</searchLink><br /><searchLink fieldCode="DE" term="%22Decomposition+method%22">Decomposition method</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+free+energy+relationship%22">Linear free energy relationship</searchLink>
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  Data: A new finite element based simulation technique for mineral growth governed by the classical Cahn–Hilliard equation is presented. The particular format of the underlying Flory–Huggins free energy for non-ideal mixtures is characterized through a double-well potential. It allows for uphill diffusion driven by gradients in the chemical potential and thus provides the appropriate framework to simulate phase separation typically encountered in mineral unmixing and growth. For the finite element discretization, the governing fourth order diffusion equation is reformulated in terms of a system of two coupled second order equations. For the temporal discretization, a heuristic adaptive time stepping scheme is applied in order to simulate not only the early stages of phase separation but also the long term behavior of ageing and grain fusion. The basic features of the Cahn–Hilliard equation are elaborated by means of selected geologically relevant examples. In particular, isotropic and anisotropic mineral growth and symplectite formation are studied and the long term response in the sense of Ostwald ripening is illustrated. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00466-006-0041-1
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        Text: English
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      – SubjectFull: Finite element method data processing
        Type: general
      – SubjectFull: Diffusion processes
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      – SubjectFull: Kirkendall effect
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      – SubjectFull: Mineral metabolism
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      – SubjectFull: Ostwald ripening
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      – SubjectFull: Surface tension
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      – SubjectFull: Decomposition method
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      – SubjectFull: Linear free energy relationship
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              Text: Apr2007
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