Sophie Didierjean

Thermal dispersion in porous media: one-equation model

Abstract In this work, the methods of volume average and multiple scale expansion are employed to obtain one macroscopic equation governing thermal dispersion in a rigid homogeneous porous medium. The structure of the real porous medium is described here by a spatially periodic model. The theoretical longitudinal thermal dispersion coefficient for a stratified system is compared with numerical data obtained from a random walk method, and good agreement is achieved.

Dispersion in periodic porous media. Experience versus theory for two-dimensional systems

A method is presented for the experimental study of dispersion in saturated porous media for two-dimensional spatially periodic systems. The use of stereophotolithography laser as the basis of the porous media fabrication process made this investigation feasible. The porous media consist of a set of circular cylinders accurately positioned in an ordered (in line) or in a disordered (random) unit cell periodically reproduced in the plane of the study. For two directions of the average fluid velocity in the in-line array and one direction of the velocity vector in the disordered array, dye is injected in the form of a pulse at the entrance to the medium. The tracer concentration variations with time are measured by a video camera and are averaged over a unit cell. The measured time distributions are compared with computations using the macroscopic convection-diffusion equation in order to estimate the longitudinal dispersion coefficient. The variations of this coefficient with particulate Peclet number in the three geometries investigated are compared with the available numerical results. All the results agree, showing a significant influence of the direction of the average fluid velocity for the ordered medium. Concerning the random medium, the results appear to indicate that, in spite of its periodic character, this type of medium is capable of describing the behaviour of disordered porous media. This original technique is highly promising for the explanation of dispersion mechanisms in porous media.

Effect of Oxygen Depletion Along the Air Channel of a PEMFC on the Warburg Diffusion Impedance

The usual expression of the finite Warburg element used for analyzing electrochemical impedance spectroscopy spectra is obtained assuming that the reaction occurs at the electrode/membrane interface and that the oxygen concentration at the gas channel/gas diffusion layer interface is constant. A simple improvement of this expression consists in the oxygen concentration depletion along the gas channel. This pseudo-two-dimensional approach should be more appropriate for the investigation of mass transfer limitations in membrane-electrode assemblies of polymer electrolyte membrane fuel cells (PEMFC). Starting from experimental data from the literature, numerical simulations show that conclusions about the mass transfer limiting layer and its main characteristics can be significantly modified, which can contribute to a better understanding of oxygen transport in fuel cells. The results also put forward the existence of a critical value of the air stoichiometry below, which, close to the air channel exit, no oxygen can access to the active layer. However, the diffusion impedance model does not take into account time-dependent current variation effects on the gas concentration, although experimental proofs by Schneider et al. [J. Electrochem. Soc., 154, B383 (2007); 154, B770 (2007)] brought that they influence significantly the shape and the size of the measured impedance spectra

Experimental estimation of the transient free convection heat transfer coefficient on a vertical flat plate in air

Transient heat convection on a vertical plate has been interpreted both theoretically and experimentally, in terms of a variable heat transfer coefficient, by several authors. Few results concern the case were air is the fluid. Joule heating of a very thin vertical graphite foil has been tested experimentally here. Two different methods of inversion have been studied for estimating the local or global transfer coefficient, starting from infrared camera measurements. The second method has been able to provide the convective contribution to the measured global transfer coefficient. Experimental results with different levels of heating show that the early transfer coefficient decrease proportionally (in time t) to t−1, and not to t−1/2 as the early times conduction theory would anticipate. Other effects than those already presented in the literature remain to be investigated, in order to explain the discrepancy of this theory for air. Relaxation experiments show that enhancement of the wall/air exchange by a mastering of the transient heating of the whole wall seems to be quite difficult to obtain

Transport in PFSA Membranes

The proposed model allows estimating polymer membrane transport properties. It is based on a microscopic description of charge and water transport in a single capillary with a uniform distribution of charge at the wall. The equations are solved analytically for two geometries: cylindrical capillary and parallel plates. Macroscopic transport properties of the whole membrane are then deduced by upscaling the capillary model. Their variations with temperature and water content are evaluated and compared to data available in the literature. In addition, the influence of the pore size and of the effective charge density are studied.

Transient Dispersion in Porous Media: A Comparison between Exact and Approximate Solutions in a Case Study

Three methods are proposed for studying solute dispersion over short periods of time in the case study of a one-dimensional flow: the non-local method, the spatial moments method, and the volume averaging method distinguishing two zones using both rigorous closure and classical closure. The non-local method (exact) uses the Green function. Its application in calculating the generalized dispersion tensor and solving the macroscopic problem, is a cumbersome task. The methods of moments and volume averaging distinguishing two zones using rigorous closure can be used to find a correct description in terms of the spatial moments of the solute concentration distribution up to the second order. Nevertheless, the rigorous closure cannot, in general, be applied to periodic media. Volume averaging with classical closure gives coefficients which are different from those obtained by the method of moments. Surprisingly, the macroscopic solution is very similar to the exact one, in some of the tested cases.

A Simple Alternative to the Expression of Finite Warburg Diffusion Impedance in Porous Electrodes by Considering Oxygen Consumption Along the Air Channel

The classical expression of the finite Warburg element used for analysing electrochemical impedance spectroscopy (EIS) spectra is obtained assuming that the reaction occurs at the electrode/membrane interface and that the oxygen concentration at the gas channel/gas diffusion layer interface is constant. An alternative to this expression is proposed: it takes into account the variation in oxygen concentration along the gas channel due to the oxygen-reduction reaction (ORR). This pseudo-2D approach is well suited for investigating mass transfer limitations in the fuel cell membrane-electrode assemblies (MEA). Simple numerical applications starting from data already published by different authors show that with this new expression, conclusions about the mass transfer limiting layer and its main characteristics can be significantly modified. This improvement to the usual Warburg impedance could contribute to a better understanding of mass transfer limitation in fuel cells and eventually, to the design of MEAs in which diffusion losses are minimal.