Multi-component gas mixture diffusion through porous media: A 1D analytical solution Lorenzo Pisani Center for Advanced Studies, Research and Development in Sardinia (CRS4), Parco Scientifico e Tecnologico, POLARIS, Edificio 1, 09010 Pula (CA), Italy Received 10 February 2006 Available online 16 July 2007 Abstract In this paper, the equations governing the transport of gas mixtures through porous media in 1D geometry and in absence of mass sources are examined. When the mass fluxes are determined by external conditions, the transport equations can be solved to find the variations of gas composition through the media. For this class of problems, we show that the convective transport mechanism can be, in many cases, neglected, regardless of the physical properties of the porous media and of the flux intensities. An estimate of the maximum error made in neglecting the convective term is provided. A matrix analytical solution of the diffusion equations is given for the general case of N-components gas mixtures. Explicit analytical solutions are derived in two particular cases. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Stefan–Maxwell; Knudsen; Dusty gas model; Fuel cells 1. Introduction The transport of multi-component gas mixtures through porous media is a physical phenomenon that plays a funda- mental role in many important applications. At present, for example, gas separation devices and fuel cell electrodes are the subject of a large number of experimental and model- ling studies. The correct description of such phenomenon is, therefore, a living subject in the literature. Recently, Suvanwarangkul et al. [1] have compared different models commonly used in the description of gas transport inside porous fuel cells anodes: the Fick’s model [2–4], the Dusty Gas Model (DGM) [5,6] and the Stefan Maxwell model [7,8]. As a conclusion, they find that the DGM is, in gen- eral, the most suitable model, but, since it requires a com- plex numerical solution they suggest its use only in case of necessity. However, their study is limited to a few specific gas mixtures and, therefore, it lacks of generality. Further- more, they assume, without a rigorous justification, that the convective transport is negligible. This work aims to overcome these problems, as it provides (i) a general and rigorous analysis of the maximum error made in neglecting the convective term and (ii) a matrix analytical solution of the DGM diffusion equations. The flux equations describing gas transport through a porous media can be derived by simple momentum transfer arguments [9]. There are three mechanisms by which a given species may loose momentum:  Transfer to another species as a result of collisions between pairs of unlike molecules (Stefan–Maxwell).  Direct transfer to the pores walls through particle-wall collisions (Knudsen).  Indirect transfer to the wall via a sequence of molecule– molecule collisions terminating in a molecule–wall colli- sion (Darcy). 1.1. Stefan–Maxwell The Stefan–Maxwell equations [10,11] describe the diffu- sion in multi (n) component gas mixtures 0017-9310/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2007.04.043 E-mail address: pisani@crs4.it www.elsevier.com/locate/ijhmt Available online at www.sciencedirect.com International Journal of Heat and Mass Transfer 51 (2008) 650–660