Effects of Fiber Orientation and Overlapping on Knudsen, Transition, and Ordinary Regime Diffusion in Fibrous Substrates
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EFFECTS OF FIBER ORIENTATION AND OVERLAPPING ON KNUDSEN, TRANSITION, AND ORDINARY REGIME DIFFUSION IN FIBROUS SUBSTRATES Manolis M. Tomadakis and Stratis V. Sotirchos Department of Chemical Engineering University of Rochester Rochester, NY 14627 ABSTRACT Wc prescnt effective diffusion coefficients of gases in porous media whose structure can be represented as an assemblage of cylindrical fibers, such as the media used as substrates in chemical vapor infiltration. Structures consisting of non-, partially, or freely overlapping fibers of various orientation distributions are considered, and effective diffusion coefficients are computed by means of a Monte Carlo simulation scheme. In order to be able to examine the interrelation of ordinary, transition, and Knudsen diffusivities and tortuosities, computations are carried out over the whole diffusion regime, i.e., from bulk to Knudsen. Our simulation results are compared with variational bounds and experimcntal values of tortuosity of fibrous beds reported by other investigators. INTRODUCTION Knowledge of the mass transport characteristics of fibrous structures used as preforms in chemical vapor infiltration (CVI) helps us better understand the mechanism of the CVI process. This in turn enables us to identify operating conditions and procedures for improving the process, both in its conventional isothermal, diffusion-driven form [1] and modified, temperature-pressure gradient (ORNL process [2]) and pulse- CVI [3,4] versions. Howvever, only a few diffusivity measurements for dilute beds in the slip [5] and the ordinary diffusion regime [6,7] are available in the literature, with the Knudsen and transition regimes left totally unexplored. Moreover, theoretical work in this area has primarily becn focused on the derivation of bounds using variational principles or other methods [S-11]. Simulation results for the variation of the effective diffusion coefficient of random fiber structures with the porosity in the whole diffusion regime, from bulk to Knudsen, are p~resented in this work. Effective diffusivities are computed by using a Monte Carlo simulation scheme to compute the mean square displacement of test molecules travelling in the pore space [121. We consider fiber structures formed by randomly overlapping cylindrical fibers distributed randomly in d (d = 1, 2, or 3) directions (d-directional, random fiber structures), that is, with their axes parallel to a line (d -- 1), parallel to a plane (d =-2), or oriented randomly in the three dimensional space (d = 3), and structures with fibers grouped into d (d = 1, 2, or 3) bundles of parallel, randomly overlapping fibers, with the bundles arranged in mutually perpendicular directions (d-directional, parallel fiber structures). Since the fibers in an actual preform do not overlap with each other, structures of freely overlapping fibers can be used as models of actual preforms only for relatively high porosities. Howcver, the initial porosity of the fibrous structures that are used as preforms in composite fabrication by ch
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