Random Porous Materials Research Articles

Statistics of highly heterogeneous flow fields confined to three-dimensional random porous media

We present a strong relationship between the microstructural characteristics of, and the fluid velocity fields confined to, three-dimensional random porous materials. The relationship is revealed through simultaneously extracting correlation functions R_{uu}(r) of the spatial (Eulerian) velocity fields and microstructural two-point correlation functions S_{2}(r) of the random porous heterogeneous materials. This demonstrates that the effective physical transport properties depend on the characteristics of complex pore structure owing to the relationship between R_{uu}(r) and S_{2}(r) revealed in this study. Further, the mean excess plot was used to investigate the right tail of the streamwise velocity component that was found to obey light-tail distributions. Based on the mean excess plot, a generalized Pareto distribution can be used to approximate the positive streamwise velocity distribution.

A near-zero Poisson's ratio of Si with ordered nanopores.

The Poisson's ratio νij = -ε/ε, where ε and ε (i,j = x, y, z) are applied and resulting strain, respectively, are computed from first-principles for Si with an array of cylindrical, nanometer-sized pores aligned in the z direction (nanoporous Si, or np-Si). Through density functional theory calculations, it is demonstrated that the periodic arrangement of pores introduces strong anisotropy in the Poisson's ratio of np-Si: while νyz remains close to the Poisson's ratio of the bulk, νzx and νxy exhibit an increase and a sharp decrease from the bulk value, respectively, as the volume fraction of pores (ϕ) becomes large. It is shown that the characteristic dependence of the Poisson's ratio on ϕ originates from the difference in the actual stress on np-Si, which is caused by the dissimilar surface geometry. Unlike random porous materials, this finding signifies the importance of structural details in determining the mechanical response of ordered systems at a nanoscale.

An explicit formula for the coherent SH waves’ attenuation coefficient in random porous materials with low porosities

In this paper, the attenuation coefficient of coherent SH waves in random porous material with uniformly randomly distributed elliptical cavities of different aspect ratios is studied. Based on an analysis of the mechanism for attenuation, a simple macro model for the attenuation coefficient is proposed. The macro model says that the attenuation coefficient can be expressed as a function of the mean scattering cross section and the number density of cavities at low porosities. Then, large-scale numerical simulations using the pre-corrected Fast Fourier Transform (pFFT) algorithm accelerated Boundary Element Method (BEM) are conducted to specify this macro model. Finally, this macro model is compared with four theoretical models derived for composite/porous materials with circular inclusions at the porosity p=3.17% and 5%. Results show this macro model agree well with three of them. Compared to the existing theoretical models, the form of this macro model is simple and has a clear physical meaning. In addition, it is applicable to cases with relatively complex cavities.

Stochastic framework for modeling the linear apparent behavior of complex materials: Application to random porous materials with interphases

This paper is concerned with the modeling of randomness in multiscale analysis of heterogeneous materials. More specifically, a framework dedicated to the stochastic modeling of random properties is first introduced. A probabilistic model for matrix-valued second-order random fields with symmetry propertries, recently proposed in the literature, is further reviewed. Algorithms adapted to the Monte Carlo simulation of the proposed representation are also provided. The derivations and calibration procedure are finally exemplified through the modeling of the apparent properties associated with an elastic porous microstructure containing stochastic interphases.

Compressive behavior of pervious concretes and a quantification of the influence of random pore structure features

Properties of a random porous material such as pervious concrete are strongly dependent on its pore structure features, porosity being an important one among them. This study deals with developing an understanding of the material structure–compressive response relationships in pervious concretes. Several pervious concrete mixtures with different pore structure features are proportioned and subjected to static compression tests. The pore structure features such as pore area fractions, pore sizes, mean free spacing of the pores, specific surface area, and the three-dimensional pore distribution density are extracted using image analysis methods. The compressive stress–strain response of pervious concretes, a model to predict the stress–strain response, and its relationship to several of the pore structure features are outlined. Larger aggregate sizes and increase in paste volume fractions are observed to result in increased compressive strengths. The compressive response is found to be influenced by the pore sizes, their distributions and spacing. A statistical model is used to relate the compressive strength to the relevant pore structure features, which is then used as a base model in a Monte-Carlo simulation to evaluate the sensitivity of the predicted compressive strength to the model terms.

Fractal analysis for effective thermal conductivity of random fibrous porous materials

In this Letter, a fractal series-parallel model, which included numerous capillary channels both parallel and perpendicular to the heat flow direction, was established to predict the effective thermal conductivity of fibrous porous material (FPM). The prediction results from the proposed model are compared with calculated values from other theoretical models and experimental data.

Probing Pore Connectivity in Random Porous Materials by Scanning Freezing and Melting Experiments

Freezing and melting behavior of nitrobenzene confined to pores of Vycor porous glass with random pore structure has been studied by means of nuclear magnetic resonance cryoporometry. The two transitions are found to reveal a broad hysteresis. To get deeper insight into the mechanisms leading to this phenomenon, scanning experiments exploiting temperature reversal upon incomplete freezing or melting have been performed. In this way, it was found that different cooling and warming histories result in different solid-liquid configurations within the pore system. Further evolution of the thus-attained configurations with changing temperature unveiled important information about the transition paths. In particular, these experiments indicated the occurrence of a pronounced pore blocking for freezing, resulting in freezing transitions via invasion percolation. The melting, on the other hand, is found to occur homogeneously over the whole pore network.

Alternative Routes to Porous Silicon Carbide

ABSTRACTA low-cost alternative route for large-scale fabrication of high purity porous silicon car-bide is reported. This allows a three-dimensional arrangement of pores with adjustable pore di-ameters from several 10 nanometers to several microns. The growth of SiC is here based on a combined sol-gel and carbothermal reduction process. Therein tetraethoxysilane is used as the primary silicon and sucrose as the carbon source. We provide two different sol-gel based ways for preparation of porous SiC, obtaining either a regular porous or a random porous type. Regu-lar porous SiC with monodisperse ordered spherical pores of predefined size is obtained via liq-uid infiltration of a removable opal matrix. Whereas random porous material with polydisperse pores of an adjustable size distribution range, but without order, can be achieved via free gas phase growth. This is performed by degradation of granulated sol-gel prepared material inside a sealed reaction chamber, resulting in a SiO/CO/SiC rich gas atmosphere, which causes SiC growth inside the granulate itself. For both types doping of the initially semi-insulating porous SiC is possible either during the sol-gel preparation or via the gas phase during the following annealing procedure. As probing dopants we have used P, N, B and Al, which are well known from 'conventional' SiC. Composition and structure of the obtained material was investigated using scanning electron microscopy, X-ray diffraction, nuclear magnetic resonance and Fourier transform infrared spectroscopy.

Particle deposition in random fibrous porous materials: effect of acoustic fields, fibres distribution and porosity

Porous filters are widely used to control air pollution and have different industrial applications since they constitute a reliable and low cost solution to separate particulate matter from an air stream. In this study, the particle deposition within 3D porous filters subjected to low-frequency acoustic fields is studied following a numerical approach. Findings demonstrate that the application of acoustic waves enhances the deposition of particles, which in turn improves filter performance. It is shown that frequencies ranging from 200 to 1000 Hz (intensity 120 dB) increase particle deposition up to 2.5 times. Besides, the manner in which fibres are distributed in the porous material and the filter porosity affect considerably the number of particles deposited, for filters subjected to the same filtration velocity.

Determination of the effective diffusion coefficient in porous media including Knudsen effects

A 3-D bond pore network model is presented and used to evaluate the effect of pore size and connectivity on the effective diffusion coefficient in random porous media. The control equations of the system are set up and the simulation method is discussed. The simulation results show that when the average pore size dm < 1 μm, the effective diffusion coefficient is strongly dependent on pore size. The analysis shows that Knudsen and bulk diffusion effects can be decoupled, and for any given diffusion conditions, the effect coefficient accounting for Knudsen diffusion can be obtained. Thus, the effect of pore size can been readily accounted for by correcting the bulk effective diffusivity with the Knudsen effect coefficient. The simulations also show that the percolation threshold in random porous materials decreases with increased pore network connectivity.

Miniature acoustic prime mover operating at 10 kHz

A miniature thermoacoustic prime mover was developed for interfacing with electronics and microcircuits where it will be used for thermal management. It operates at approximately 10 kHz; heat is injected to the hot part of the device, the cold part is thermally anchored at room temperature. It consists of a quarter wave resonator of cylindrical geometry, 9 mm long. It has a stack of random porous material between two heat exchangers and it operates with air at one atmosphere. Preliminary results show that this oscillator produces a sound intensity at 110 dB, 1 m away from the open end of the resonator. This level can be raised substantially by careful alignment of the hot and cold parts of the resonator, and by reducing the heat losses along the stack and supporting structure between the hot and cold side of the stack. Based on the high operating frequency, a high power density is expected; such device can be used as the basic unit in an array of acoustic prime movers. This work provides a new functional miniature element that can lead the technology toward even smaller devices and well into the ultrasonic range.

Evidence of anisotropic quenched disorder effects on a smectic liquid crystal confined in porous silicon

We present a neutron scattering analysis of the structure of the smectic liquid crystal octylcyanobiphenyl (8CB) confined in one-dimensional nanopores of porous silicon films (PS). The smectic transition is completely suppressed, leading to the extension of a short-range ordered smectic phase aligned along the pore axis. It evolves reversibly over an extended temperature range, down to 50 K below the N-SmA transition in pure 8CB. This behavior strongly differs from previous observations of smectics in different one-dimensional porous materials. A coherent picture of this striking behavior requires that quenched disorder effects are invoked. The strongly disordered nature of the inner surface of PS acts as random fields coupling to the smectic order. The one-dimensionality of PS nanochannels offers perspectives on quenched disorder effects, of which observation has been restricted to homogeneous random porous materials so far.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Linear elastic properties of 2D and 3D models of porous materialsmade from elongated objects

Porous materials are formed in nature and by man by many differentprocesses. The nature of the pore space, which is usually the space leftover as the solid backbone forms, is often controlled by the morphology ofthe solid backbone. In particular, sometimes the backbone is made from therandom deposition of elongated crystals, which makes analytical techniquesparticularly difficult to apply. This paper discusses simple two- andthree-dimensional porous models in which the solid backbone is formed by differentrandom arrangements of elongated solid objects (bars/crystals). We use ageneral purpose elastic finite element routine designed for use on imagesof random porous composite materials to study the linear elastic propertiesof these models. Both Young's modulus and Poisson's ratio depend on theporosity and the morphology of the pore space, as well as on the propertiesof the individual solid phases. The models are random digital image models,so that the effects of statistical fluctuation, finite size effect anddigital resolution error must be carefully quantified. It is shown how toaverage the numerical results over random crystal orientation properly. Therelations between two and three dimensions are also explored, as mostmicrostructural information comes from two-dimensional images, while mostreal materials and experiments are three dimensional.

Chord-distribution functions of three-dimensional random media: approximate first-passage times of Gaussian processes.

The main result of this paper is a semianalytic approximation for the chord-distribution functions of three-dimensional models of microstructure derived from Gaussian random fields. In the simplest case the chord functions are equivalent to a standard first-passage time problem, i.e., the probability density governing the time taken by a Gaussian random process to first exceed a threshold. We obtain an approximation based on the assumption that successive chords are independent. The result is a generalization of the independent interval approximation recently used to determine the exponent of persistence time decay in coarsening. The approximation is easily extended to more general models based on the intersection and union sets of models generated from the isosurfaces of random fields. The chord-distribution functions play an important role in the characterization of random composite and porous materials. Our results are compared with experimental data obtained from a three-dimensional image of a porous Fontainebleau sandstone and a two-dimensional image of a tungsten-silver composite alloy.

Liquid–liquid equilibrium for fluids confined within random porous materials

Using the Gibbs Ensemble Monte Carlo (GEMC) simulation technique, we examine the liquid–liquid phase behavior for a symmetric binary LJ fluid confined in a disordered solid matrix. Increasing the matrix packing fraction and adsorption strength, and lowering the ratio of adsorbent to adsorbate particle size reduces the magnitude of the miscibility gap. We also employ Voronoi tessellations to analyze the distribution of cavity sizes in mono- and polydisperse matrices to help explain the observed phase behavior.

Polymers in Random Porous Materials: Structure, Thermodynamics, and Concentration Effects

The distribution of dissolved macromolecules between a bulk solution and the interior of a porous substrate occurs in a variety of technologically important systems. The partition coefficient K, which is the ratio of concentration in the pores to that in the bulk, is primarily determined by the effective size of the polymer molecules. For dilute solutions, K decreases rapidly as the effective polymer dimensions exceed the average pore size. We have used liquid-state theory to construct a rigorous integral equation model for the structure of concentrated flexible linear polymers in the presence of a rigid matrix of discrete repulsive obstacles. We have used the structural information to calculate the thermodynamic properties of the polymer in these model porous materials. In particular, we have been able to calculate the partition coefficient as a function of concentration. The model provides good agreement with thermodynamic properties obtained from previous computer simulations of bulk polymer solutions as well as with our own simulations of polymers in porous materials.

Surface Roughness of Porous Materials and Its Characterization by X-Ray Absorption Measurements

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Structure of random porous materials: Silica aerogel.

Using small-angle x-ray scattering, we show that porous silica aerogel has a fractal backbone structure. The observed structure is traced to the underlying chemical (polymerization) and physical (colloid aggregation) growth processes. Comparison of scattering curves for aerogel with silica aggregates confirms this interpretation.