Maxwell-Stefan equations, flow-through

However, if convective transport of heat and species mass in porous catalyst pellets have to be taken into account simulating catal3dic reactor processes, either the Maxwell-Stefan mass flux equations (2.394) or dusty gas model for the mass fluxes (2.427) have to be used with a variable pressure driving force expressed in terms of mass fractions (2.426). The reason for this demand is that any viscous flow in the catalyst pores is driven by a pressure gradient induced by the potential non-uniform spatial species composition and temperature evolution created by the chemical reactions. The pressure gradient in porous media is usually related to the consistent viscous gas velocity through a correlation inspired by the Darcy s law [21] (see e.g., [5] [49] [89], p 197) ... 

Molecular diffusion is the mechanism of transfer of a substance either through a fluid which is motionless or, if the fluid is in laminar flow, in a direction perpendicular to the velocity of the fluid. The phenomenon has been studied from many points of view7ffequently conflicting, the most important of which are those of Fick and of Maxwell-Stefan. Fick (7) applied the well-known Fourier equation for rate of heat flow to the problem of diffusion. Unfortunately the mechanism of the two processes is not identical, since in the penetration of a liquid by a diffusing solute there will necessarily be displacement of the liquid and consequent volume changes arising for which the Fourier equation does not account. As an approxi-... 

Two standard methods (mercury porosimetry and helium pycnometry) together with liquid expulsion permporometry (that takes into account only flow-through pores) were used for determination of textural properties. Pore structure characteristics relevant to transport processes were evaluated fiom multicomponent gas counter-current difhision and gas permeation. For data analysis the Mean Transport-Pore Model (MTPM) based on Maxwell-Stefan diffusion equation and a simplified form of the Weber permeation equation was used. 

When setting up such a model, two building blocks are available which come from different modeling fields, namely, the Stefan Maxwell equations describing the flow of a gas mixture through a porous medium and the equations of multiphase flow in a porous medium. We will shortly describe both of them. After that, we make an attempt to join both of them into a combined model. The discussion of open problems and future directions concludes the section. 

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