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2 µm - eTheses Repository - University of Birmingham

2 µm - eTheses Repository - University of Birmingham

(ii) for non-isothermal

(ii) for non-isothermal infiltration by a pure metal, taking into account the influence of preform deformability, and (iii) for isothermal infiltration, taking into account the influence of capillary phenomena (113) . Most models consider only the case of saturated flow, either by ignoring any capillary pressure drop or using the ‘slug-flow’ assumption, which implies that the infiltration front is abrupt. It has been shown that when the applied pressure is low or when the preform pore structure exhibits a broad size distribution, this assumption breaks down, as metal penetrates the preform in a gradual manner, filling the largest pores first. This case is relevant for industrial practice, because it is desirable to maintain the applied pressure as low as possible, to minimize preform damage and to reduce costs. In practical cases, the applied pressure is not established instantly but follows a more or less rapidly increasing function before the final infiltration pressure is established. For most relevant metal/reinforcement systems, isothermal metal infiltration is similar to drainage in soil mechanics (113) . During drainage, wetting water is displaced by non-wetting air out of a porous soil. In MMC infiltration, air generally constitutes the wetting phase and metal the non-wetting one. Non-saturated flow through porous media and drainage phenomena have been treated in the soil mechanics literature (111) . Based on soil mechanics, Dopler et al. (113) developed a model for isothermal infiltration of ceramic fibres based on capillary phenomena. The relationship between local pressure and non-wetting fluid velocity is classically described by Darcy’s law (Equation 25). When neglecting gravity it is valid for laminar flow in a porous medium in the following form: v0 = −K ⋅∇P Equation 25 where v0 is the superficial velocity of the non-wetting phase, defined as the volumetric flow rate, P is the pressure and K is the permeability tensor. 43

The permeability K can be expressed as a function of three independent terms: s r μ K K ⋅ K = Equation 26 where Ks is the specific preform permeability tensor, Kr is the relative permeability, varying with saturation between 0 and 1, and µ is the dynamic fluid viscosity. The tensor of specific permeability describes the geometrical arrangement of the porous medium. The different components of the tensor depend on the type of preform, its volume fraction, the diameter of the reinforcement phase, its arrangement and homogeneity. The component values of Ks can be measured by permeability experiments, using, for example water as a fluid (114) . There is no direct way to measure the relative preform permeability Kr. It is generally back- calculated from infiltration experiments or from calculations based on simplified porous preform geometries such as capillary tubes. A general form with two empirical parameters A and B can be given (113) as: K ⋅ B r = A S Equation 27 with S the saturation of the porous body. The evaluation of modelling results showed best agreement with A and B both equal to 1. The saturation S is defined as the ratio of filled void space to initial void space as follows: θl S = 1−θ c 44 Equation 28 where θl is the volume fraction of the intruded liquid and θc the volume fraction of the ceramic phase. The saturation is expressed, in general, in soil mechanics as a function of pressure. The functional relationship is measured by establishing a drainage curve for the considered system, which represents the degree of saturation either of the wetting or of the

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