Porosity experimentally determined

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

The value of r can be estimated as that of saturated liquid at the same temperature or related to supercritical properties at temperatures above critical. Critoph [2] found that for the practical purposes of modelling ammonia - carbon adsorption cycles, using experimentally determined porosity data, that the complexity of estimating both r and p at sub and supercritical levels was not justified. The measured porosity data could be fitted to a much simpler version of the equation with no loss of accuracy, as follows ... 

It is not worth while, therefore, to give a digest of experimentally determined corrosion rates , but Table 2.21 indicates some sources of such data and their nature. (Some references to data on compatibility of fused salts with non-metallic materials have been included for the sake of completeness.) It should be remembered, that in the case of alloys, failure usually arises from selective attack which causes porosity of the container, even though the wall may appear on casual inspection to be quite sound... 

Both dynamic melting and equilibrium transport melting require that the porosity when two nuclides are fractionated from one another is similar to the size of the larger of the partition coefficients for the two nuclides. Given the low values of the experimental determinations of Du and Dxh, the porosities required to explain the observational data in these models are generally less than 0.5% and often times closer to 0.1%. Such low porosity estimates have been criticized based on physical grounds given the low estimated mantle permeability derived from the extent of melt connection observed in experiments (Paul 2001). 

Since a permeability coefficient of 2 x 10 cm/sec was used in our theoretical calculation for case B, this is equivalent to a single porosity value for all calculations with Equation 6. For any given set of ethanol concentration at the boundary, the appropriate ethanol concentration distance profile was calculated from the experimentally determined profile for the pure ethanol/water system and taken as that of the system. For any given set of ethanol concentrations at the boundaries the appropriate portion of the experimentally determined ethanol concentration distance profile, was calculated from the experimentally determined profile for the pure ethanol/water system. For any given ethanol concentration distance profile, the corresponding solubility profile of 3-estradiol was obtained by interpolation of experimental solubility data (Figure 2). 

The coordination number, fe, presents a greater problem. Although k is strictly a function not only of the void fraction but also of the packing arrangement [2], experimentally determined coordination numbers may be correlated directly with porosity as an approximation. Thus, Rumpf [1] used the expression... 

At the optimum point corresponding to the maximum packing fraction, e1 = e11, since the porosity value at this point does not depend on whether fine or coarse particles form the mixture skeleton. The Equation (90) permit calculation of the porosity values for a mixture of fractions of any composition. A similar procedure can be used for calculating the porosity of mixtures of three or more fractions. A laboratory check of these Equations (90) confirmed good agreement between the calculation forecast and the experimental determination of porosity coefficients and wide variety of combinations of narrow filler fractions. 

The porosity of a catalyst or support can be determined simply by measuring the particle density and solid (skeletal) density or the particle and pore volumes. Particle density pp is defined as the mass of catalyst per unit volume of particle, whereas the solid density p, as the mass per unit volume of solid catalyst. The particle volume Vp is determined by the use of a liquid that does not penetrate in the interior pores of the particle. The measurement involves the determination by picnometry of the volume of liquid displaced by the porous sample. Mercury is usually used as the liquid it does not penetrate in pores smaller than 1.2/m at atmospheric pressure. The particle weight and volume give its density pp. The solid density can usually be found from tables in handbooks only in rare cases is an experimental determination required. The same devices as for the determination of the particle density can be used to measure the pore volume V, but instead of mercury a different liquid that more readily penetrates the pores is used, such as benzene. More accurate results are obtained if helium is used as a filling medium [10]. The porosity of the particle can be calculated as ... 

Experimentally, it is difficult to separate the effects of F and z on the effective diffusivity. Often, empirical values of the product Ft are reported as the tortuosity. This is particularly true in the literature of transport/reac-tion in porous catalyst pellets. For the large variety of catalysts, the tortuosity —equal to /h(SK in Equation 4-42—ranges from 1 to 10 [103]. Although it has been difficult to correlate these tortuosity values with experimentally determined pore structure parameters, the tortuosity almost always decreases with increasing porosity. 

In diffusional impregnation, the distribution of the solute inside the wet porosity of the pellet is assumed to be governed by two phenomena [24-27] (Figure 4.1a) the diffusion of the solute into the pores of the pellet, described by Pick s law, and the adsorption of the solute onto the support, which depends on the adsorption capacity of the surface and on the adsorption equilibrium constant. These two parameters are experimentally determined from adsorption isotherms, but the final distribution is not fundamentally changed if equilibrium is not reached and adsorption is ruled by kinetics [28]. 

In an effective properties model, the porous microstructures of the SOFC electrodes are treated as continua and microstructural properties such as porosity, tortuosity, grain size, and composition are used to calculate the effective transport and reaction parameters for the model. The microstmctural properties are determined by a number of methods, including fabrication data such as composition and mass fractions of the solid species, characteristic features extracted from micrographs such as particle sizes, pore size, and porosity, experimental measurements, and smaller meso- and nanoscale modeling. Effective transport and reaction parameters are calculated from the measured properties of the porous electrodes and used in the governing equations of the ceU-level model. For example, the effective diffusion coefficients of the porous electrodes are typically calculated from the diffusion coefficient of Eq. (26.4), and the porosity ( gas) and tortuosity I of the electrode ... 

The effective diffusion coefficient can be estimated with Equations A4.3 through A4.9. The highest uncertainty is involved in the estimation of particle porosity and tortuosity. The porosity can be determined by mercury or nitrogen porosimetry. The best way is to experimentally determine the effective diffusion coefficient at room temperature for a... 

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