Session EF: Porous Media III

Ionic transport characterization of carbon-based porous materials

In the last few years, the transport of ionic species through a porous media and an electric field has been subject of intense research because of its many applications. The objective of the present work is to characterize ionic transport through a carbon porous media in a capacitive cell correlating its transient electrical parameters with its ion absorption performance. For this, a constant and continuous power supply, and carbon aerogel were employed in three types of experiments. In the first type, the electrical assembly is submerged in a stationary solution and the parasitic elements of the electric circuit were estimated. In the second type, ion-saturated aerogel was used in a series of polarity inversion cycles to evaluate its behavior. Finally, in the third type, convective effects on the ion migration were evaluated when a constant flow rate is applied. For all the experiments, the total capacitor's charge was obtained from the experimental current data and compared to the amount of ions retained on the carbon media estimated by the variation in the aerogel's weight and in the solution's conductivity.   

Two phase flow in a porous Hele-Shaw cell

We present an experimental study of liquid-air flow inside a 500 x 500 x 1 mm square Hele-Shaw cell saturated with 1mm diameter glass spheres. The flow is characterized by using the light refraction at liquid-gas interface menisci as a marker to determine the time dependent position of the liquid-gas interface. In the flow analyzed, liquid motion is generated by partially filling the cell with water and then letting the water out through an outlet in the lower part of the cell. We have observed that in contrast to what occurs in a Hele-Shaw cell with no spheres where the interface is a horizontal line that moves downwards, for a Hele-Shaw cell filled with spheres, the liquid-gas interface is an irregular line that moves with localized sudden motions generated by surface tension effects occurring due the non-regular geometry of the sphere arrangements. The distance scale of these dynamic structures is approximately ten sphere diameters. These observations are potentially useful in the underground water flows and petroleum extraction.   

Dynamics of poroelastic foams

Soft poroelastic structures are widespread in biological tissues such as cartilaginous joints in bones, blood-filled placentae or plant organs. Here we investigate the dynamics of open elastic foams immersed in viscous fluids, as model soft poroelastic materials. The experiment consists in slowly compacting blocs of polyurethane solid foam embedded in silicon oil-tanks and studying their relaxation to equilibrium when the confining stress is suddenly released. Measurements of the local fluid pressure and foam velocity field are compared with a simple two-phase flow approach. For small initial compactions, the results show quantitative agreement with the classical diffusion theory of soil consolidation (Terzaghi, Biot). On the other hand, for large initial compactions, the dynamics exhibits long relaxation times and decompaction fronts, which are mainly controlled by the highly non-linear mechanical response of the foam. The analogy between this process and the evaporation of a polymer melt close to the glass transition will be briefly discussed.   

Quantitative Visualization of Water Distribution in an Operating Polymer Electrolyte Fuel Cell

The objective of this study is to visualize the temporal evolution of water in an operating (\textit{in situ}) polymer electrolyte fuel cell (PEFC). To achieve this, the synchrotron X-ray radiography with high spatial and temporal resolution is employed. X-ray images of water inside individual PEFC components, such as the polymer membrane, gas diffusion layer (GDL), and endplate, are captured consecutively. As a result, the in-plane water distribution of water in the PEFC components is quantitatively visualized by adopting image normalization method. The temporal evolution of water in the anode GDL exhibits the back diffusion effect clearly. To examine the water accumulation phenomenon in the PEFC, X-ray $\mu $-tomography method is adopted for visualizing the internal structure of GDL. The accumulation phenomenon seems to be attributed to the concentrated porosity in GDL structure. The water-saturation characteristics at the cathode GDL, including saturation time and speed, are found to be quite different from those at the anode GDL.   

Wicking/absorption of a liquid droplet into nano-porous fibers

Contrary to what happens on a planar wetting substrate, a droplet sitting on a wetting solid smooth fiber can stay without spreading. In a fiber with parallel grooves, the liquid wicks into the channels. Here, we are interested in characterizing nano-porous fibers where the wicking front propagates through longitudinal micron size grooves and the liquid also penetrates inside the nano-porous fiber with tuned pore size in the range of tens of nm. The difference in groove to pore sizes produces a faster longitudinal than transversal liquid movement, allowing for model simplifications and leading to analytical solutions for the model proposed, that couples absorption with wicking dynamics. Experimental data on the droplet shape/volume together with front propagation are compared with the solution of the model to extract information of the fiber's structure which is compared with SEM images of the cross-sections of the fibers. The nano-porous composite fibers produced by coagulation wet spinning, were proposed to be used as bio-sensing device, drug delivery systems and neuron-implantable electrodes.   

DNS of inertial flows in porous media: Assessment of mesh quality and resolution

At modest flow rates $(10 \le Re \le 300)$ through porous media and packed beds, fluid inertia can result in complex steady and unsteady recirculation regions, dependent on the local pore geometry. We present methods to parameterize and simplify mesh generation for packed beds, with an eye toward obtaining efficient mesh independence for Reynolds numbers in the inertial and unsteady regimes. To handle the geometric singularity at the sphere-sphere and sphere-wall contact points, we use a \emph{fillet bridge model}, in which every pair of contacting entities are bridged by a fillet, eliminating a small fluid region near the contact point. A second order accurate, parallel, incompressible flow solver [Moin and Apte, AIAA J. 2006] is used to simulate flow through three different sphere packings: a periodic simple cubic packing, a wall bounded hexagonal close packing, and a randomly packed tube. Mesh independence is assessed using several measures including Ergun pressure drop coefficients, viscous and pressure components of drag force, kinetic energy, kinetic energy dissipation and interstitial velocity profiles. Progress toward large scale simulations of flow through randomly packed $10^3$ pores will be discussed.   

Pressure-driven flow in a channel with porous walls

The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers-Joseph model. It is found that the value of the slip coefficient is different for pressure-driven and shear-driven flow. A modification of the relation is suggested to deal with this feature. Furthermore, detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the the mobilization of bottom sediments.   

Modeling Deformable Fibrous Media Using Direct Numerical Simulations

A micro-mechanical approach is used in this work to investigate the behavior of deformation in saturated fibrous media. The geometry of the porous media is approximated using model geometry made of cylinders in orthogonal arrangement with appropriate boundary conditions. The approach is based on direct numerical simulation that uses a hybrid lattice Boltzmann and finite element method for modeling the fluid and solid phases respectively. It has already been shown that the macroscopic behavior of real porous media can be recovered using model geometry as long as the parameters, porosity, permeability and compressive modulus are matched. Thus based on these critical parameters it is found that cylinders in skewed orthogonal arrangement behave as real layered fibrous porous media during saturated compression. Further an analytical expression is developed to predict the compressive modulus of orthogonal arrangement of cylinders. The expression shows that there is no direct effect of fiber diameter on the compressive modulus of such arrangements, which is also confirmed through direct numerical simulations.   

Fingering Instabilities during Capillary Imbibition into Paper

When a porous medium, such as a piece of paper, is placed into contact with a liquid reservoir, capillary action drives the liquid through the porous medium. The penetration distance $L(t)$ of the liquid/air interface is typically described by the Lucas-Washburn equation, with any deviations normally occurring on a length scale set by the average pore size. Here we report that solutions with a sufficient amount of hydrophobic solute undergo a fingering instability during capillary imbibition into paper. The finger amplitudes are two to three orders of magnitude larger than the average pore size, suggesting that the typical capillary fingering mechanism is not operative. Instead, we demonstrate that the finger growth rate is directly proportional to the solute concentration, and is strongly mediated by the ambient relative humidity. We interpret the fingering in terms of an instability driven by solutal effects on the local imbibition velocity, and we discuss the implications for various applications including thin layer chromatography and paper-based microfluidics.   

Some Remarks on the flow of Viscoelastic Fluids in Porous Media

Flow of porous media plays important roles in many branches of science and engineering .Because of the complications involved, studies in porous media have, largely, been experimental and the progress in theoretical modeling has been very slow Thus the one dimensional empirical model of Darcy, proposed in 1856,was extended to a non-linear empirical model by Forcheimer in 1901,and a diffusive term was added by Brinkman in 1949. In sixties and seventies, Whitaker, Slattery and Lundgren applied volume averaging technique to Navier-Stokes equation and gave heuristic account of the above models. Apart from some minor issues,the flow of viscous fluids in porous media is now well understood. This is, however, not the case in viscoelastic fluid flows in porous media. The empirical models are being employed without recognizing their empirical nature. Linear models are being used which do not reduce to the viscous model as the elastic parameters are set equal to zero. There are serious issues with the averaging process. Our purpose is to elaborate on the above problems and hopefully, suggest a reasonable model equation.