Multilayered Porous Media Research Articles

Integral transform solution for solute transport in multi-layered porous media with the implicit treatment of the interface conditions and arbitrary boundary conditions

Summary Solute transport in multi-layered porous media is of great importance in environmental engineering problems. Its important feature lies in the explicit existence of interface conditions. The previous analytical solutions require explicitly considering the interface conditions in the evaluation of coefficients or in the eigenvalue system. In the present study, an implicit treatment of interface conditions is presented to eliminate the interface conditions from the original system. The generalized integral transform technique is performed with respect to the transformed system to obtain the analytical solution. Compared to the pervious solution strategy, the present eigenfunctions are much simpler. The present analytical solution and eigenvalue system are expressed for the generalized boundary conditions by introducing two boundary factors in the boundary conditions, which applies to arbitrary assembly of boundary conditions without modification and can reduce the effort of programming. The developed analytical solution is validated against two experiments and one analytical solution. Good agreement is shown between the experimental data and analytical as well as numerical solutions.

Effect of Thermophysical Properties on Coupled Heat and Mass Transfer in Porous Material during Forced Convective Drying

The convective drying kinetics of porous medium was investigated numerically. A mathematical model for forced convective drying was established to estimate the evolution of moisture content and temperature inside multilayered porous medium. The set of coupled partial differential equations with the specified boundary and initial conditions were solved numerically using a MATLAB code. An experimental setup of convective drying had been constructed and validated the theoretical model. The temperature and moisture content of the potato samples were dynamically measured and recorded during the drying process. Results indicate that thermal diffusion coefficient has significant positive impact on temperature distribution and mass diffusion coefficient might directly affect the moisture content distribution. Soret effect has a significant impact on heat flux and temperature distribution in the presence of large temperature gradient.

Local mass non-equilibrium dynamics in multi-layered porous media: application to the drug-eluting stent

A solution for a model of mass diffusion from a drug-eluting stent to the arterial wall is addressed. The coating layer is described as a porous reservoir where the drug is initially loaded in polymer-encapsulated solid-phase, and then released both to the coating and to the arterial tissue in a liquid-phase. The endothelium, intima, internal elastic lamina and media are all treated as homogeneous porous media and the drug transfer through them is modelled by a non-homogeneous set of coupled partial differential equations that describe a local mass non-equilibrium diffusion problem. Drug concentration levels and mass profiles in each layer at various times are computed as a spectral decomposition: numerical results show a delayed release depending on the physico-chemical drug properties combined with the microstructure of the polymeric-coated stents.

A design of an impedance tube for teaching acoustic material properties and laboratory techniques

The design and implementation of an adaptable acoustic impedance tube for instructional use will be presented. This system, which was designed for use in a graduate-level laboratory environment, is in accordance with ASTM standard E1050-98. The system is configurable for both horizontal and vertical measurements. Vertical use enables acoustic property measurement of granular materials, allowing characterization of a wide variety of media. The academic content is delivered by engaging students in measurements using the impedance tube. Specific acoustics content objectives include modeling of sound propagation in porous materials and the role of acoustic parameters such as porosity, tortuosity, and flow resistivity in quantifying acoustic behavior of materials. Instructional goals also include mastery of computer based data acquisition and processing. This aspect of modern laboratory practice is a critical part of our graduate acoustics curriculum. Students participated actively in the development of the software used to collect data and calibrate the impedance tube. The system design required the students to solve practical problems such as cutting and positioning of the sample as well as more demanding tasks such as design of a multilayer porous medium with desired acoustic properties.

3-D consolidation of multilayered porous medium with anisotropic permeability and compressible pore fluid

3-D consolidation of multilayered porous medium with anisotropic permeability and compressible pore fluid

Visualization experiments and pore network simulations for invasion-percolation transport of a non-wetting fluid through multiple porous layers

A similarity model experiment was developed to investigate the liquid water transport in hydrophobic porous layers of polymer electrolyte membrane fuel cells (PEMFCs). The dimensionless numbers in the similarity model experiment were closely matched to those in operating PEMFCs. This allowed the visual inspection of invasion-percolation transport of a non-wetting fluid with active capillary fingering in multiple porous layers, similar to the liquid water transport in porous layers of PEMFCs. The experimental results showed that inserting an intermediate layer between a fine layer and a coarse layer suppresses the capillary fingering of the non-wetting fluid inside the coarse layer. Thus, it could be expected that the steady-state volume of the non-wetting fluid in the multiple porous layers decreases as the thickness of the intermediate layer increases. In fact, this trend was quantitatively verified by measuring the volume of the breakthrough droplets formed by the non-wetting fluid that emerged out of multiple porous layers. In addition, pore network simulations were also conducted to reproduce the observed non-wetting fluid transport in multi-layer porous media, and relatively good agreements between experimental and numerical results were obtained.

Analytical investigation of free surface flow in multi-layer porous media

In this paper, the free surface flow passing through a multi-layer porous medium is analyzed. An analytical model to describe the flow in multi-layer porous media driven by surface tension and vacuum pressure is proposed. The structure of the medium studied is modeled after those found in Rigid-Capillary-Press (RCP) dewatering devices. The capillary phenomenon is used in RCP to improve the water removal efficiency and the energy consumption in a paper making process. The porous medium is composed of six layers with complex woven fabric structures and pore sizes that range from 5 μm to 2 mm The dewatering performance predicted by the analytical model is compared to the pilot plant experiments with good agreements. The potential of the model to be applied as a parametric optimization tool for industrial RCP porous media design is discussed.

A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers

In this paper we propose a numerical scheme based on finite differences for the numerical solution of nonlinear multi-point boundary-value problems over adjacent domains. In each subdomain the solution is governed by a different equation. The solutions are required to be smooth across the interface nodes. The approach is based on using finite difference approximation of the derivatives at the interface nodes. Smoothness across the interface nodes is imposed to produce an algebraic system of nonlinear equations. A modified multi-dimensional Newton’s method is proposed for solving the nonlinear system. The accuracy of the proposed scheme is validated by examples whose exact solutions are known. The proposed scheme is applied to solve for the velocity profile of fluid flow through multilayer porous media.

An analytical solution for wave-induced seabed response in a multi-layered poro-elastic seabed

In this study, a new analytical solution for the wave-induced seabed response in a multi-layered poro-elastic seabed is developed. The seabed is treated as a multi-layered porous medium and characterized by Biot’s theory. The displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vector. Then, the Biot’s dynamic equation can be solved using Fourier transformation and reducing to Helmholtz equations. To obtain the general solutions for the multi-layered poro-elastic seabed in the frequency-wave-number domain, the transmission and reflection matrices (TRM) method is used to form the equivalent stiffness. Using the boundary conditions and continuous conditions, the frequency-wave-number domain solutions are obtained. Finally, the time-space domain solutions for the multi-layered poro-elastic seabed are obtained by means of the inverse Fourier transformation with respect to the horizontal coordinate. Based on the new solution, a parametric study is carried out to examine the effects of soil characteristics (number of layers, permeability and shear modulus) and wave characteristics (water depth and wave steepness) on seabed responses. The results indicate that the seabed response is affected significantly by permeability, shear modulus and relative water depth.

Numerical simulation of solidification of liquid aluminum alloy flowing on cooling slope

Preparation of semisolid slurry using a cooling slope is increasingly becoming popular, primarily because of the simplicity in design and ease control of the process. In this process, liquid alloy is poured down an inclined surface which is cooled from underneath. The cooling enables partial solidification and the incline provides the necessary shear for producing semisolid slurry. However, the final microstructure of the ingot depends on several process parameters such as cooling rate, incline angle of the cooling slope, length of the slope and initial melt superheat. In this work, a CFD model using volume of fluid (VOF) method for simulating flow along the cooling slope was presented. Equations for conservation of mass, momentum, energy and species were solved to predict hydrodynamic and thermal behavior, in addition to predicting solid fraction distribution and macrosegregation. Solidification was modeled using an enthalpy approach and a volume averaged technique for the different phases. The mushy region was modeled as a multi-layered porous medium consisting of fixed columnar dendrites and mobile equiaxed/fragmented grains. The alloy chosen for the study was aluminum alloy A356, for which adequate experimental data were available in the literature. The effects of two key process parameters, namely the slope angle and the pouring temperature, on temperature distribution, velocity distribution and macrosegregation were also studied.

Transient model for coupled heat, air and moisture transfer through multilayered porous media

Most building materials are porous, composed of solid matrix and pores. The time varying indoor and outdoor climatic conditions result heat, air and moisture (HAM) transfer across building enclosures. In this paper, a transient model that solves the coupled heat, air and moisture transfer through multilayered porous media is developed and benchmarked using internationally published analytical, numerical and experimental test cases. The good agreements obtained with the respective test cases suggest that the model can be used to assess the hygrothermal performance of building envelope components as well as to simulate the dynamic moisture absorption and release of moisture buffering materials.

Development of an analytical solution of modified Biot’s equations for the optimization of lightweight acoustic protection

During lift-off, space launchers are submitted to high-level of acoustic loads, which may damage sensitive equipments. A special acoustic absorber has been previously integrated inside the fairing of space launchers to protect the payload. A new research project has been launched to develop a low cost fairing acoustic protection system using optimized layers of porous materials covered by a thin layer of fabric. An analytical model is used for the analysis of acoustic wave propagation within the multilayer porous media. Results have been validated by impedance tube measurements. A parametric study has been conducted to determine optimal mechanical and acoustical properties of the acoustic protection under dimensional thickness constraints. The effect of the mounting conditions has been studied. Results reveal the importance of the lateral constraints on the absorption coefficient particularly in the low frequency range. A transmission study has been carried out, where the fairing structure has been simulated by a limp mass layer. The transmission loss and noise reduction factors have been computed using Biot's theory and the local acoustic impedance approximation to represent the porous layer effect. Comparisons between the two models show the frequency domains for which the local impedance model is valid.

The Characteristics of Fluid Flow Through Multilayer Porous Media

The characteristics of fluid flow through three porous layers are investigated. The two outer porous layers are considered to be of infinite width, while the middle porous layer is assumed to be of finite width. The mathematical model of the fluid flow in the middle region can be described as laminar fully developed flow and is assumed to be governed by Brinkman equations. The flow through the upper and lower porous media is governed by Forchheimer equations. At the two interface regions between the middle finite width porous layer and the outer infinite porous layers, the continuity of the velocity and of the shear stress are imposed. Under these matching conditions, the exact solutions for the set of equations describing the flow velocity are obtained. It is found that the flow velocity is affected by two parameters, namely, Reynolds number and Darcy’s number. The effects of these parameters on the flow velocity profiles through the flow regions are investigated and presented.

Tidal deformations and the electrokinetic effect in a two-layer fluid-saturated porous medium

The electrokinetically induced vertical component of the electric field in a multilayer fluid-saturated porous medium caused by tidal deformations of the Earth’s crust is calculated. Petrophysical properties change in a jumplike manner at the boundary between two media. The pore pressure gradient at the boundary abruptly reaches a maximum and then exponentially decays, forming a hydrodynamic skin layer. Due to the electrokinetic effect, the electric field behaves in the same way. Observations of the vertical electric field can be used, in principle, to determine the mechanical properties of the medium experiencing deformation. The magnitudes of the effects lie within a range accessible to measurement.

05/02819 Concept of a small-scale electron accelerator driven system for nuclear waste transmutation. Part 2. Investigation of burnup

A similarity model experiment was developed to investigate the liquid water transport in hydrophobic porous layers of polymer electrolyte membrane fuel cells (PEMFCs). The dimensionless numbers in the similarity model experiment were closely matched to those in operating PEMFCs. This allowed the visual inspection of invasion-percolation transport of a non-wetting fluid with active capillary fingering in multiple porous layers, similar to the liquid water transport in porous layers of PEMFCs. The experimental results showed that inserting an intermediate layer between a fine layer and a coarse layer suppresses the capillary fingering of the non-wetting fluid inside the coarse layer. Thus, it could be expected that the steady-state volume of the non-wetting fluid in the multiple porous layers decreases as the thickness of the intermediate layer increases. In fact, this trend was quantitatively verified by measuring the volume of the breakthrough droplets formed by the non-wetting fluid that emerged out of multiple porous layers. In addition, pore network simulations were also conducted to reproduce the observed non-wetting fluid transport in multi-layer porous media, and relatively good agreements between experimental and numerical results were obtained.

Steady-State Solutions of Multilayered and Cross-Anisotropic Poroelastic Half-Space due to a Point Sink

This paper presents analytical solutions for the steady-state response of displacements and stresses in a half-space subjected to a point sink. The half-space is modeled as a multilayered poroelastic medium with both the permeability and the poroelasticity being cross anisotropic. The basic governing equations are presented in dimensionless style, and the state vector method together with the Hankel transform technique is adopted to solve them and obtain a transfer matrix in a clearly arranged way. Forward and backward transfer matrix techniques are utilized in the analytical formulation of solutions for a multilayered half space. Numerical results are presented to conduct some parametric studies and illustrate the influence of layering and material inhomogeneity on the settlement of the soils. The numerical evaluations of the solutions in the multilayered porous media can be easily achieved with high efficiency and accuracy.

Analytical and numerical investigation of double diffusion in thermally anisotropy multilayer porous medium

Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media.

Numerical Analysis of Efficiency of Landfill Venting Trenches

A 2D numerical model for convection-diffusion flow of a multispecies mixture through a multilayer porous medium is used to analyze the efficiency of landfill venting trenches. By analyzing the way each of the components of the landfill gas flow within the repository and how they are collected by the trenches, it was possible to explain the low efficiency of this type of structure that was observed in landfill operations. Numerical results are also presented for the long-term behavior of the gases inside the repository and their release into the atmosphere.

DRM-MD approach for the numerical solution of gas flow in porous media, with application to landfill

In the present work two different Dual Reciprocity Method (DRM) formulations were developed, for convection–diffusion flow of a mixture of gases in a multi-layer porous media, with an application to landfills. The first method treated the whole problem domain as a single one, while the second formulation, the Dual Reciprocity Method Multi-Domain decomposition (DRM-MD), divides the initial domain into a large number of subdomains. The main advantage of the single domain formulation, in relation to domain methods, is that only surface elements are necessary, so the input data is reduced. A drawback of this approach is that it results in a fully populated matrix system, limiting it to small or medium size problems. On the other hand, the DRM-MD formulation extends the range of applications of the technique to large problems, since the final matrix of the system is sparse (band diagonal) and the matrix coefficients of geometrically similar subregions are calculated only once.

Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium

Diffusion of dissolved contaminants in multilayer porous media is an important phenomenon affecting both contamination and remediation in natural aqueous environments, including diffusion in groundwater aquitards and contaminated bed sediments. This study presents a new analytical solution for solute diffusion in a semi-infinite two-layer porous medium for arbitrary boundary and initial conditions. The solution was obtained by using the Green's function approach in the Laplace domain with the application of the binomial theorem to facilitate inversion back to the real time domain. Results based on this solution were found to be simple both in form and ease of calculation and to be in good agreement with those obtained using numerical calculations based on the Crank-Nicolson finite difference method. Applications of the solution are presented in the context of a contaminated groundwater aquitard to demonstrate how different boundary and initial conditions can greatly affect the contamination and decontamination of porous media, and to illustrate how diffusion modeling might be used in a forensic sense.