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A model for front evolution with a nonlocal growth rate

Published online by Cambridge University Press:  31 January 2011

Shi Jin,
Xuelei Wang and
Thomas L. Starr
Shi Jin
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Xuelei Wang
Affiliation:
Department of Chemical Engineering, University of Louisville, Louisville, Kentucky 40292
Thomas L. Starr
Affiliation:
Department of Chemical Engineering, University of Louisville, Louisville, Kentucky 40292
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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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Type
Rapid Communications
Information
Journal of Materials Research , Volume 14 , Issue 10 , October 1999, pp. 3829 - 3832
Copyright
Copyright © Materials Research Society 1999

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References

REFERENCES

1.Avrami, M., J. Chem. Phys. 7, 1103–1112 (1939); 8, 212–224 (1940).CrossRefGoogle Scholar
2.Besmann, T.M., Sheldon, B.W., Lowden, R.A., and Stinton, D.P., Science 253, 1104 (1991).CrossRefGoogle Scholar
3.Crandall, M.G. and Lions, P.L., Trans. Am. Math. Soc. 277, 1–42, (1983).CrossRefGoogle Scholar
4.Evans, L.C., Partial Differential Equations (Amer. Math. Soc., Providence, RI, 1998).Google Scholar
5.Johnson, W.A. and Mehl, P.A., Trans. Am. Inst. Min. Metall. Eng. 135, 416 (1939).Google Scholar
6.Kolmogorov, A.N., Bull. Acad. Sci., USSR Phys. Ser 1, 355 (1937).Google Scholar
7.Osher, S. and Sethian, J.A., J. Comp. Phys. 78, 12–49 (1988).CrossRefGoogle Scholar
8.Sahimi, M., Applications of Percolation Theory (Taylor & Francis, London, 1994).CrossRefGoogle Scholar
9.Sethian, J.A., Level Set Methods (Cambridge University Press, New York, 1996).Google Scholar
10.Sotirchos, S. and Zarkanitis, S., Chem. Eng. Sci. 48(8), 1487–1502 (1993).CrossRefGoogle Scholar
11.Stauffer, D. and Aharony, A., Introduction to Percolation Theory (Taylor & Francis, London, 1992).Google Scholar
12.Whitham, G.B., Linear and Nonlinear Waves (John Wiley & Sons, New York, 1974).Google Scholar