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A model for front evolution with a nonlocal growth rate

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Abstract

In this paper we provide a new mathematical model for front propagation with a nonlocal growth law in any space dimension. Such a problem arises in composite fabrication using the vapor infiltration process and in other physical problems involving transport and reaction. Our model, based on the level set equation coupled with a boundary value problem of the Laplace equation, is an Eulerian formulation, which allows robust treatment for topological changes such as merging and formation of pores without artificially tracking them. When applied to the fabrication of continuous filament ceramic matrix composites using chemical vapor infiltration, this model accurately predicts not only residual porosity but also the precise locations and shapes of all pores.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Shi Jin

  2. Department of Chemical Engineering, University of Louisville, 40292, Louisville, Kentucky, USA

    Xuelei Wang & Thomas L. Starr

Authors
  1. Shi Jin
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  2. Xuelei Wang
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  3. Thomas L. Starr
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Jin, S., Wang, X. & Starr, T.L. A model for front evolution with a nonlocal growth rate. Journal of Materials Research 14, 3829–3832 (1999). https://doi.org/10.1557/JMR.1999.0515

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  • DOI: https://doi.org/10.1557/JMR.1999.0515

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