Mathematical Analysis and Optimization of Infiltration Processes

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, c_ and _. The optimization problem associated with minimizing the infiltration time is also considered. Allowing a and _ to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where (_ and _ are treated as constants. *Research supported in part by AFOSR grant 96-1-0150, NSF grant DMS 95-00814 and NSF grant ECS9202961. Research was also supported in part by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the second author was consulting for the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 236810001.