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Asymptotic results for a barrier potential model

  • DAVID A. EDWARDS (a1) and CHRISTOPHER S. RAYMOND (a1)

Abstract

An enhanced understanding of the microstructure of oxide ceramics will help scientists and engineers improve their efficiency and design. A phase-field model for the composition and phase distribution of the oxide ceramic components is studied. The model, which includes an obstacle in the phase portion of the energy potential, results in a minimisation problem that characterises the distribution of the bulk phases. The transition region between them is studied in several mathematically plausible asymptotic limits. The behaviour of the system in these limits provides insights into the applicability of the model and indicates appropriate parameter regimes.

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[1]Blowey, J. & Elliott, C. (1991) The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. Part I: Mathematical analysis. Eur. J. Appl. Math. 2, 233280.
[2]Brown, J. & Sobsey, M. D. (2009) Ceramic media amended with metal oxide for the capture of viruses in drinking water. Env. Tech. 30 (4), 379391.
[3]Cogswell, D. A. & Carter, W. C. (2011) Thermodynamic phase-field model for microstructure with multiple components and phases: The possibility of metastable phases. Phys. Rev. E 83 (6, 1), 061602.
[4]Grashchenkov, D. V., Balinova, Y. A. & Tinyakova, E. V. (2012) Aluminum oxide ceramic fibers and materials based on them. Glass Ceram. 69 (3–4), 130133.
[5]Heulens, J., Blanpain, B. & Moelans, N. (2011) A phase field model for isothermal crystallization of oxide melts. Acta Mater. 59, 21562165.
[6]Keane, M. (2003) Ceramics for catalysis. J. Math. Sci. 38 (23), 46614675.
[7]Kim, I. J. (2010) Thermal stability of Al2TiO5 ceramics for new diesel particulate filter applications-a literature review. J. Ceram. Proc. Res. 11 (4), 411418.
[8]Nacken, M., Heidenreich, S., Hackel, M. & Schaub, G. (2007) Catalytic activation of ceramic filter elements for combined particle separation, NOx removal and VOC total oxidation. Appl. Catal. B 70 (1–4), 370376.
[9]Wei, G. C., Lapatovich, W. P., Browne, J. & Snellgrove, R. (2008) Dysprosium oxide ceramic arc tube for HID lamps. J. Phys. D 41 (4).
[10]Wheeler, A. A., Boettinger, W. & McFadden, G. (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45, 74247439.
[11]Wheeler, A. A., Boettinger, W. & McFadden, G. (1993) Phase-field model for solute trapping during solidification. Phys. Rev. E 47, 18931909.

Keywords

Asymptotic results for a barrier potential model

  • DAVID A. EDWARDS (a1) and CHRISTOPHER S. RAYMOND (a1)

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