Mathematical Analysis and Optimization of In ltration Processes

A variety of in ltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial di erential equation describing the evolution of the solid phase, coupled to one or more partial di erential 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 in ltration. The results demonstrate that the process is controlled by only two parameters, and . The optimization problem associated with minimizing the in ltration time is also considered. Allowing and to vary with time leads to signi cant reductions in the in ltration 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.