Comment on “Frequency-dependent dispersion in porous media”

In a recent paper, Valdes-Parada and Alvarez-Ramirez [Phys. Rev. E 84 031201 (2011)] used the technique of volume averaging to derive a frequency-dependent dispersion tensor, D*(w), the goal of which is to describe solute transport in porous media undergoing periodic processes. We describe two issues with this dispersion tensor that become particularly apparent in the time domain. Firstly, we demonstrate that the definition of D*(w), and equivalently of D*(t), is erroneous, and derive its correct counterpart, D*c(t). With this modification, the approach becomes strictly equivalent to the one devised by Moyne [Adv. Water Res. 20 63 (1997)]. Secondly, we show that the term "frequency-dependent dispersion" is misleading in this case, because D*(t) and D*c(t) do not depend on the process operating frequency. The study carried out by Valdes-Parada and Alvarez-Ramirez represents a frequency-analysis of the relaxation of the dispersion coefficients towards their steady-state, independently of any periodic operation or excitation

A two-pressure model for slightly compressible single phase flow in bi-structured porous media

Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of pore-scale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the pore-scale are generally approximated by Darcy’s law at a larger scale. In this work, we develop an alternative model to Darcy’s law that can be used to describe slightly compressible single phase flow within bi-structured porous media. We use the method of volume averaging to upscale mass and momentum balance equations with the fluid phase split into two fictitious domains. The resulting macroscale model combines two coupled equations for average pressures with regional Darcy’s laws for velocities. In these equations, effective parameters are expressed via integrals of mapping variables that solve boundary value problems over a representative unit cell. Finally, we illustrate the behaviour of these equations in a two-dimensional model porous medium and validate our approach by comparing solutions of the homogenized equations with computations of the exact microscale problem

Influence of wettability on liquid water transport in gas diffusion layer of proton exchange membrane fuel cells (PEMFC)

Water management is a key factor that limits PEFC's performance. We show how insights into this problem can be gained from pore-scale simulations of water invasion in a model fibrous medium. We explore the influence of contact angle on the water invasion pattern and water saturation at breakthrough and show that a dramatic change in the invasion pattern, from fractal to compact, occurs as the system changes from hydrophobic to hydrophilic. Then, we explore the case of a system of mixed wettability, i.e. containing both hydrophilic and hydrophobic pores. The saturation at breakthrough is studied as a function of the fraction of hydrophilic pores. The results are discussed in relation with the water management problem, the optimal design of a GDL and the fuel cell performance degradation mechanisms. We outline how the study could be extended to 3D systems, notably from binarised images of GDLs obtained by X ray microtomography

Correspondence between one- and two-equation models for solute\ud transport in two-region heterogeneous porous media

In this work, we study the transient behavior of upscaled models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the time scale of interest (t) is smaller than the characteristic time (T1) for the relaxation of the effective macroscale parameters (i.e., when t ≤ T1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (T1) (i.e., when t » T1); and (3) a one-equation, time-asymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the time scale (T2) associated with exchange processes between the two regions (i.e., when t » T2). In order to obtain some physical insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in simple cases. The main result of this paper is to show that there is weak long-time convergence of the solution of (2eq) toward the solution of (1eq∞) in terms of standardized moments but, interestingly, not in terms of centered moments. Physically, our interpretation of this result is that the spreading of the solute is dominating higher order non-zero perturbations in the asymptotic regime

Solute transport within porous biofilms: diffusion or dispersion?

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behaviour by controllling nutrient supply, evacuation of waste products and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilmscale. We show that solute transport may be described via two coupled partial differential equations for the averaged concentrations, or telegrapher’s equations. These models are particularly relevant for chemical species, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterised by a second-order tensor whose components depend on: (1) the topology of the channels’ network; (2) the solute’s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion-dominated, this analysis shows that dispersion effects may significantly contribute to transport

Quality Assessment for CRT and LCD Color Reproduction Using a Blind Metric

This paper deals with image quality assessment that is capturing the focus of several research teams from academic and industrial parts. This field has an important role in various applications related to image from acquisition to projection. A large numbers of objective image quality metrics have been developed during the last decade. These metrics are more or less correlated to end-user feedback and can be separated in three categories: 1) Full Reference (FR) trying to evaluate the impairment in comparison to the reference image, 2) Reduced Reference (RR) using some features extracted from an image to represent it and compare it with the distorted one and 3) No Reference (NR) measures known as distortions such as blockiness, blurriness,. . .without the use of a reference. Unfortunately, the quality assessment community have not achieved a universal image quality model and only empiricalmodels established on psychophysical experimentation are generally used. In this paper, we focus only on the third category to evaluate the quality of CRT (Cathode Ray Tube) and LCD (Liquid Crystal Display) color reproduction where a blind metric is, based on modeling a part of the human visual system behavior. The objective results are validated by single-media and cross-media subjective tests. This allows to study the ability of simulating displays on a reference one

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid. Both the mechanical equilibrium solution and the monocellular flow obtained for particular ranges of the physical parameters of the problem are considered. The porous cavity, bounded by horizontal infinite or finite boundaries, is heated from below or from above. The two horizontal plates are maintained at different constant temperatures while no mass flux is imposed. The influence of the governing parameters and more particularly the role of the separation ratio, characterizing the Soret effect and the normalized porosity, are investigated theoretically and numerically. From the linear stability analysis, we find that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The role of the porosity is important, when it decreases, the stability of the equilibrium solution is reinforced. For a cell heated from below, the equilibrium solution loses its stability via a stationary bifurcation when the separation ratio >0(Le,), while for 0, while a stationary or an oscillatory bifurcation occurs if mono the monocellular flow loses stability via a Hopf bifurcation. As the Rayleigh number increases, the resulting oscillatory solution evolves to a stationary multicellular flow. For a cell heated from above and <0, the monocellular flow remains linearly stable. We verified numerically that this problem admits other stable multicellular stationary solutions for this range of parameters

Particle filtration: A comparison between theory and experiment

The process of filtration of non-charged, submicron particles represents an example of transport in homogeneous and heterogeneous porous media that can be analyzed using the method of volume averaging. In this article the authors develop the local volume averaged particle transport equation for a homogeneous filter and compare the results with experimental data. The particle continuity equation is represented in terms of the first correction to the Smoluchowski equation that takes into account particle inertia effects for small Stokes numbers. This leads to a cellular efficiency that contains a minimum in the efficiency as a function of the particle size, and this allows them to identify the most penetrating particle size. Comparison of the theory with experimental results indicates that the first correction to the Smoluchowski equation gives reasonable results for the most penetrating particle size and for smaller particles; however, results for larger particles clearly indicate the need to extend the Smoluchowski equation to include higher order corrections. The influence of local heterogeneities on the measured filter efficiency may account for some of the observed differences between theory and experiment

Particle filtration: An analysis using the method of volume averaging

The process of filtration of non-charged, submicron particles is analyzed using the method of volume averaging. The particle continuity equation is represented in terms of the first correction to the Smoluchowski equation that takes into account particle inertia effects for small Stokes numbers. This leads to a cellular efficiency that contains a minimum in the efficiency as a function of the particle size, and this allows us to identify the most penetrating particle size. Comparison of the theory with results from Brownian dynamics indicates that the first correction to the Smoluchowski equation gives reasonable results in terms of both the cellular efficiency and the most penetrating particle size. However, the results for larger particles clearly indicate the need to extend the Smoluchowski equation to include higher order corrections. Comparison of the theory with laboratory experiments, in the absence of adjustable parameters, provides interesting agreement for particle diameters that are equal to or less than the diameter of the most penetrating particle