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A variety of materials are produced by infiltration processes. In these techniques a fluid phase (i.e., a gas or a liquid) is transported into a porous structure, where it then reacts to form a solid product. These methods are particularly important for producing composite materials, where the initial porous perform is composed of the reinforcement phase (i.e., fibers, whiskers, or particles) and infiltration produces the matrix. A key difficulty in isothermal, isobaric chemical vapor infiltration is the long processing times that are typically required. With this in mind, it is important to minimize infiltration times. This optimization problem is addressed here, using a relatively simple model for dilute gases. The results provide useful asymptotic expressions for the minimum time and corresponding conditions. These approximations are quantitatively accurate for most cases of interest, where relatively uniform infiltration is required. They also provide useful quantitative insight in cases where less uniformity is required. The effects of homogeneous nucleation were also investigated. This does not effect the governing equations for infiltration of a porous body; however, powder formation can restrict the range of permissible infiltration conditions. This was analyzed for the case of carbon infiltration from methane.