On the flow of a dusty gas with constant number density through granular porous media

Abstract

In this work, we apply the method of intrinsic volume averaging to Saffman’s dusty gas equations in an attempt to develop a dusty gas model of flow through isotropic porous media. We assume the particle distribution to be uniform and the porous medium to be of the granular type. The effects of the porous microstructure on the flow mixture are analyzed using the pioneering results of Du Plessis and his coworkers, [J.P. Du Plessis, Analytical quantification of coefficients in the Ergun equation for fluid friction in a packed bed, Transp. Porous Media 16 (1994) 189–207; J.P. Du Plessis J.H. Masliyah, Flow through isotropic granular porous media, Transp. Porous Media 6 (1991) 207–221; J.P. Du Plessis, G.P.J. Diedericks, Pore-scale modeling of interstitial phenomena, in: J.P. Du Plessis (Ed.), Fluid Transport in Porous Media, Computational Mechanics Publications, 1997, pp. 61–104], which facilitate classification of the developed model into two sub-models: one for low speed, and one for high speed flow through granular media. A dust-phase partial pressure is introduced to render the governing equations determinate. This work provides an extension to a previously developed model, [F.M. Allan, M.H. Hamdan, Fluid-particle model of flow through porous media: the case of uniform particle distribution and parallel velocity fields, Appl. Math. Comput. 183 (2) (2006) 1208–1213], in which the velocity fields of the phases involved were assumed to be parallel.