Mathematical Analysis and Optimization of Infiltration Processes

Authors:
H.-C. Chang;D. Gottlieb;M. Marion;B. W. Sheldon
Affiliations:
Norton Co., Worcester, Massachusetts;Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912;Department of Mathematiques, Ecole Centrale de Lyon, France;Division of Engineering, Brown University, Providence, Rhode Island 02912
Venue:
Journal of Scientific Computing
Year:
1998

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Abstract

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, α and β. The optimization problem associated with minimizing the infiltration time is also considered. Allowing α and β to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where α and β are treated as constants.