Macro Modeling of Reactive Infiltration Using Level Set Finite Element Formulations

The process of reactive melt infiltration can be used to fabricate ceramics and ceramic matrix composites. This process involves a liquid metal being allowed to infiltrate a medium with which the liquid reacts to form a resultant ‘matrix’ along with the already present reinforcing fibers. The authors’ previous work on this area revealed that the transient porosity and permeability of a porous medium can be determined for certain geometries from the reaction kinetics and coupled heat and mass transfer problem occurring at the pore level. But the formulation at the macro level, which is essential to optimize the process, has been limited. Towards this end, this paper solves the macro reactive flow problem in a porous medium analytically as well as numerically. The focus of this article will be on the solutions for the advance (displacement) of the ‘infiltration front’ with progressive chemical reaction occurring between the medium and the infiltrant. A finite element formulation is used to solve the problem computationally; a level set formulation is used to track the infiltration front during the process. Excellent agreement is obtained between the analytical and computational solutions thereby validating the level set finite element formulations.