Spatial Distribution Of Pores Research Articles

Characterizing the effect of elastic interactions on the effective elastic properties of porous, cracked rocks

Elastic interactions between pores and cracks reflect how they are organized or spatially distributed in porous rocks. The principle goal of this paper is to understand and characterize the effect of elastic interactions on the effective elastic properties. We perform finite element modelling to quantitatively study how the spatial arrangement of inclusions affects stress distribution and the resulting overall elasticity. It is found that the stress field can be significantly altered by elastic interactions. Compared with a non-interacting situation, stress shielding considerably stiffens the effective media, while stress amplification appreciably reduces the effective elasticity. We also demonstrate that the T-matrix approach, which takes into account the ellipsoid distribution of pores or cracks, can successfully characterize the competing effects between stress shielding and stress amplification. Numerical results suggest that, when the concentrations of cracks increase beyond the dilute limit, the single parameter crack density is not sufficient to characterize the contribution of the cracks to the effective elasticity. In order to obtain more reliable and accurate predictions for the effective elastic responses and seismic anisotropies, the spatial distribution of pores and cracks should be included. Additionally, such elastic interaction effects are also dependent on both the pore shapes and the fluid infill.

Morphological analysis of high-impact polypropylene using X-ray microCT and AFM

Detailed visualization and understanding of high-impact polypropylene (hiPP) particle morphology and its evolution on the scale of entire particles is important for obtaining the required mechanical and optical properties of this material and for the quantitative description of mass transport in hiPP particles. Shape and size of hiPP particles as well as the spatial distribution of pores, PP homopolymer and ethylene-propylene rubber (EPR) phases in individual particles is visualized by micro-computed tomography (microCT) and atomic force microscopy (AFM) techniques. The morphology of each hiPP particle depends on many factors including catalyst system, the initial pore structure of porous catalyst and homopolymer particles, reactor conditions and particle history. These factors affect the required content, the constitution and the spatial distribution of EPR phase. To understand particle morphology and its evolution in a quantitative way we need a high-quality morphology data. The presented results include the AFM visualization of rubber layer on the surface of hiPP particles, the microCT visualization of not only porous homopolymer PP particles but also of large rubber domains in hiPP particles and the AFM mapping of the fine networked structure of EPR rubber and pores in hiPP particles.

Room temperature mechanical properties of polycrystalline YbAl3, a promising low temperature thermoelectric material

Intermetallic YbAl3 in the L12 (AuCu3) phase is a promising material for low temperature thermoelectric applications. However, there is no experimental data in the literature on the mechanical properties of YbAl3, although the design and development of thermoelectric modules incorporating YbAl3 will require mechanical property data. Using resonant ultrasound spectroscopy (RUS), the room temperature Young's modulus, shear modulus, bulk modulus and Poisson's ratio were determined as a function of volume fraction porosity, P, for specimens densified by both hot pressing (HP) and pulsed electric current sintering (PECS) polycrystalline specimens, where P ranged from 0.030 to 0.233 and mean grain sizes ranged from 0.5 to 1.4 μm. In addition, the longitudinal and acoustic wave speeds and the Debye temperature were measured. Using Vickers indentation, the hardness and fracture toughness of the specimens were also measured. Despite microstructural differences between the HP and PECS-processed specimens, the porosity dependence of the mechanical properties was a function of the total volume fraction porosity, P, independent of the details of the size and spatial distribution of pores within individual specimens.

Three-dimensional characterization of pores in Ti-6Al-4V alloy

The direct three-dimensional characterization of opaque materials through serial sectioning makes possible to visualize and better quantify a material microstructure, using classical metallographic techniques coupled with computer-aided reconstruction. Titanium alloys are used as biomaterials for bone implants because of its excellent mechanical properties, biocompatibility and enhanced corrosion resistance. The Ti-6Al-4V alloy (in wt. (%)) with porous microstructure permits the ingrowths of new-bone tissues improving the fixation bone/implant. This is important to understand connectivity, morphology and spatial distribution of pores in microstructure. The Ti-6Al-4V alloy compacts were produced by powder metallurgy and sintered at three distinct temperatures (1250, 1400 and 1500 °C) to obtain distinct microstructures in terms of residual porosity. The visualization of the reconstructed 3D microstructure provides a qualitative and quantitative analysis of the porosity of Ti6Al4V alloy (volume fraction and pore morphology).

Spatial distribution of pores in fly ash-based inorganic polymer gels visualised by Wood’s metal intrusion

Inorganic polymer cements, or ‘geopolymers’, are now finding use as a replacement for Portland cement in concrete production, and have a complex pore structure which has proven difficult to measure accurately by gas or mercury porosimetry. These materials consist of an alkali aluminosilicate-based gel binder phase, within which are embedded unreacted precursor (usually coal fly ash and/or blast furnace slag) particles. Impregnation of the inorganic polymer samples with Wood’s metal, a low-melting-point alloy which solidifies at room temperature, and examination by scanning electron microscopy, allows both the size of pores and their physical distribution within the gel to be determined. Pore sizes as small as 10 nm are directly observable in high-resolution imaging. Much of the difficulty in applying standard porosimetry techniques to inorganic polymers may be identified as being related to the presence of numerous ‘ink-bottle’ pores, as well as the very wide distribution of pore diameters (spanning several orders of magnitude). The effect of gel chemistry on pore structure, and in particular the presence of calcium in the inorganic polymer formulation, is also considered.

3D microanalysis of geological samples with nanofocus computed tomography

High resolution CT nowadays is a well established method for numerous industrial applications [Roth et al. 2003; Moller-Gunderson 2007; Nier et al. 2003] as well as for a wide range of research areas [Bonse 2004 and 2006]. During the last decade, Computed Tomography (CT) has progressed to higher resolution and faster reconstruction of the 3D-volume. Most recently it even allows a three-dimensional look into the inside of geological samples with submicron resolution. As shown by Brunke et al. [2008], nanoCT-systems in pursuit of high resolution images, the potential, convenience and economy can now compete in many application fields with high cost and rare available synchrotron facilities. Computed Tomography for geological purposes can lead to a new dimension of understanding of the distribution of rock properties. Especially spatial distribution of pores and pore-connections as well as cementation properties are of utmost importance in the evaluation of reservoir properties. Moreover rock analysis with the aid of X-ray Computed Tomography may lead to better analysis and prediction of well stimulation jobs. For example, a plug can be scanned before and after being stimulated with acid. The possibility to visualize the whole plug volume in a non-destructive way and to use the same plug for further analysis is undoubtedly currently the most valuable feature of this new type of rock analysis and will be a new area for routine application of X-ray Computed Tomography in the near future. The paper will outline the hard- and software requirements for high resolution CT. It will showcase several geological applications which were performed with the nanotom, the first 180 kV nanofocus CT system tailored specifically for highest-resolution scans of samples up to 120 mm in diameter and weighing up to 1 kg with exceptional voxel-resolutions down to <500 nm (<0.5 microns).

Quantitative evaluation of porosity in aluminum alloy die castings by fractal analysis of spatial distribution of area

High-pressure die-casting processes are widely used, especially for automotive products, but pores in the die-casting process occasionally occur during production. To identify the cause of porosity and to take corrective action in the die-casting process accurately and rapidly, a quantitative estimation of the morphology of pores can be an effective technique. In this study, fractal analysis is proposed to characterize porosity quantitatively in terms of the spatial distribution of a number of pores appearing in a target region. The purpose of the present investigation is to evaluate the proposed fractal analysis by comparing the porosity in two types of aluminum alloy die castings manufactured by different die-casting processes, and to confirm that fractal analysis of the spatial distribution of pores can quantitatively characterize the porosity.

Micro–macro numerical modelling of bone regeneration in tissue engineering

Bone tissue regeneration using scaffolds inherently attends to two well-differentiated scales, i.e., the tissue level where the scaffold is implanted and the scaffold pore level where bone regeneration occurs. In this paper, this phenomenon is mathematically described and implemented as a two-length-scale coupled problem. Mechanical and fluid flow scaffold properties are macroscopically derived by means of the homogenization technique while the variables at the microscopic level are obtained by invoking the localization problem. As a first approach, cell migration within the scaffold is macroscopically modelled as a diffusion process based on the Fick’s law, with the diffusion coefficient depending on the size and spatial distribution of pores. At the microscopic scale, bone growth at the scaffold surface is considered to be proportional to the cell concentration and regulated by the local strain energy density. The mathematical model proposed has been numerically implemented using the finite element method (FEM) and the Voxel-FEM at the macroscopic and microscopic scales, respectively. The model has been qualitatively compared with experimental results found in the literature for a scaffold implanted in the femoral condyle of a rabbit achieving a good agreement.

Spatial distribution of pores in lotus-type porous metal

The spatial distribution of pores in lotus-type porous magnesium has been studied with the second-order characteristics and the nearest-neighbour distance distribution by using statistical analysis methods. The results show that the spatial distribution of pores is short-range ordered. On the basis of the analysis, two structural indices deduced from the variance of nearest-neighbour distance distribution and the standard deviation of local porosity from Dirichlet tessellations were proposed for quantitatively characterizing the pore distribution.

Analysis of the effective thermal conductivity of fractal porous media

Several types of fractals are generated to model the structures of porous media, and heat conduction in these structures is simulated by the finite volume method (FVM). The influences of the thermal conductivity of solid k s, the thermal conductivity of fluid k f, the porosity ε, the size and spatial distribution of pores on the effective thermal conductivity k e of these structures are analysed in detail. The calculated results indicate that the relation of effective thermal conductivity k e with thermal conductivity of solid k s and thermal conductivity of fluid k f conforms to a power function, and the relation of effective thermal conductivity k e with porosity ε conforms to an exponential function. The porosity ε is the most important factor that determines the effective thermal conductivity of fractal porous media, but the size and spatial distribution of pores, especially the spatial distribution of the bigger pores, do have substantive influence. The numerical results are analysed by comparing with the available empirical formulas from literatures, and provide verification of these empirical formulas.

Quantitative analysis of pores of two types in a plasma-sprayed coating

Quantitative microstructural analyses of thermally sprayed coatings are reviewed. Then a ceramic plasma-sprayed coating is analysed using light microscopy and image analysis. Globular pores and interlamellar flat pores are reconstructed from serial sections of a specimen and their volume and surface area histograms are estimated. The spatial distribution of pores is described using a method based on 3D distances and testing of complete spatial randomness is performed. Interpretations of results in terms of the physical background of the material are discussed.

Micromorphology and image analysis of a hardsetting Ultisol (Argissolo) in the state of Ceará (Brazil)

A detailed examination of soil porosity employing micromorphology and image analysis can provide a better understanding of the peculiar behavior of hardsetting horizons. Owing the fact that hardsetting layers exhibit high bulk density values, we hypothesize that natural soil compaction in hardsetting horizons influences total porosity and pore shape and orientation. The aim of this study is to evaluate pore spatial distribution, and to establish the shape, size and orientation of pores using micromorphological and image analysis techniques, in hardsetting and non-hardsetting horizons of an Ultisol (Argissolo Acinzentado), located in the state of Ceará (Brazil). Micromorphological and image analysis studies were performed on soil thin sections and blocks. The results support the hypothesis proposed and suggest that the more dense areas, as measured by image analysis, are associated with the special behavior of the hardsetting horizons.

Determination of the pore connectivity and pore size distribution and pore spatial distribution of porous chromatographic particles from nitrogen sorption measurements and pore network modelling theory

The pore connectivity, pore size distribution and pore spatial distribution of the porous structure of native and silanized silica particles were determined by matching the experimental nitrogen sorption data with the theoretical results obtained from pore network model simulations. The agreement between theory and experiment is found to be good. The results clearly indicate that the deposition of the silane layer to the pore surfaces of the native silica particles produces a silanized silica particle with a mean pore diameter and pore connectivity smaller than that of the native silica particle. Furthermore, the evaluation of the pore diffusivity of ribonuclease under unretained conditions shows that the lower values of the pore connectivity found in the samples of silanized silica particles, when compared with the values of the pore connectivity obtained for the native silica particles, increase the diffusional mass transfer resistance within the porous structure of the silanized silica particles.

Densification of porous materials by power-law creep

The densification of a porous intermetallic alloy (Ti-14wt%Al-21wt%Nb) during the final stage of densification has been investigated under various states of stress and compared with the predictions of current models for densification by power-law creep. The experiments generally confirm the model predictions that the densification rate is a sensitive function of the stress state. Experimentally, unconstrained uniaxial compression resulted in the largest densification rates, while constrained uniaxial compression resulted in the lowest. Hydrostatic loading resulted in a densification rate similar (but slightly higher) than that of constrained compression. This ordering of the densification rates agreed well with the model predictions. However, the magnitudes of the measured densification rates are found not to be accurately predicted. A number of factors, including pore shape, pore spatial distribution and matrix microstructure have been observed to affect the densification rate, and the significance of each of these factors to predictive modelling of creep consolidation processes is assessed.

Gaseous diffusion in porous media. Part 3 - Wet granular materials

The diffusion of hydrogen through granular materials partly saturated with water was measured by a non-steady state technique previously described. The two types of sample used consisted of solid particles (unimodal poresize distribution) and porous particles (bimodal pore-size distribution), and all measurements were made on samples being dried from saturation. Coefficients of diffusion D were calculated, and for the range over which the larger pores were emptying the empirical equation D = Dv(/v)σ fitted all materials, where epsilon is the fractional air-filled volume, v is the volume occupied by the larger-pore phase, and where Dv is the diffusion coefficient when only this phase is air-filled. For all materials σ approximately equals 4 whether the samples were uniform or of mixed sizes. No such relationship existed over the subsequent range in which the smaller pores were drained. Over this range D must be a function of at least five independent variables - the total porosity T, the crumb porosity c, the shape factor for the crumbs or inter-crumb pores k, the shape factor for the particles forming the crumbs or crumb pores kc, and the moisture content of the sample. The spatial distribution of pores within a porous medium can be as important as the sizes of the pores. The factors k and m, previously introduced as particle-shape factors, now have a greater significance as measures of the geometrical complexity of a porous system. Adding water can either increase or decrease the complexity, depending on the amount added and the nature of the system. The agricultural significance of diffusion between the crumbs Dv and within the crumbs Dc is discussed, and it is suggested that Dc, or its associated complexity factor kc, might be used as an index of soil structure.