The complete series solution for the reactant diffusion and reaction at two diffusion-controlled chemically reactive surface sites of radii a(1) and a(2), located in an inert plane an arbitrary center-to-center distance d apart, is presented. Rigorous, analytical forms are developed to calculate the site reaction rates in terms of the dimensionless intersite distance σ[=d/(a(1) + a(2))] and the site radius ratio γ(=a(1)∕/a(2)). Numerical simulation and approximate theoretical results from the recent literature are compared to the exact site reaction rates. While general agreement was noted over the ranges of γ and σ, significant errors in the Wilemski-Fixman-Weiss site rates were found at small γ and σ < 3.
In the resin transfer molding (RTM) densification process, a liquid synthetic pitch is injected at high pressure
into the void spaces of the carbonized porous carbon fiber−carbon matrix (C−C) composite and allowed to
solidify. To prevent the expulsion of this pitch during the subsequent high-temperature carbonization, this
thermoplastic pitch must be stabilized (thermoset) by crosslinking with oxygen and exposing the composite
to air at a fixed temperature of 160−220 °C. The distributed layer of reacted oxygen is strongly dependent
on the permeability of the gaseous oxygen across the solid mesophase pitch. The shape and penetration of
the reacted oxygen profile, obtained from Auger spectroscopy by ion etching, is used to estimate the
permeability of oxygen as 1.86 × 10-12 cm2/s. Furthermore, Photoacoustic sampling−Fourier transform infrared
spectroscopy (PAS−FTIR) was used to characterize the matrix of the C−C samples to determine the functional
group changes during oxidation, qualitatively.
De Gennes model for Knudsen diffusion and strong surface trapping kinetics is applied to slit, capillary, and spherical pores. The exact analytical survival probability-time expressions obtained for each case, which scale with the average pore diameter, are compared with numerical simulation curves for a densely packed hard sphere model porous bed.
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