Coupled Transports in Heterogeneous Media

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

“…It would allow to derive and validate the macroscopic models used for engineering simulations (see the works of Adler and collaborators [2], [3], [15], [30], [38], [51], [71]). The typical length scale for which the continuum mechanics equations are valid is confirmed to be both experimentally (see e.g.…”

Homogenization of the Ionic Transport Equations in Periodic Porous Media

“…Phenomenological equations relating the transport of ions and solvent to electrical potential, pressure and concentration gradients have achieved widespread acceptance in the literature (Gross and Osterle, 1968;deGroot and Mazur, 1969;Auriault and Strzelecki, 1981;Auriault and Lewandowska, 1994;Edwards, 1995;Coelho et al, 1996;Marino et al, 2000Marino et al, , 2001Adler, 2001;Adler and Mityushev, 2003;Revil and Leroy, 2004;Rosanne et al, 2004). For a one-to-one electrolyte they typically have the form (Marino et al, 2001):…”

Electroosmosis in homogeneously charged micro- and nanoscale random porous media

“…Second, numerically solving the governing equations of EOF in porous structures is still badly challenging for the present computational methods [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66]. The coupled electrostatic, hydrodynamic and mass transport problems subjected to complex geometrical boundary conditions represented by the solid-liquid interface in random porous media require huge or even unacceptable computational resources.…”

“…Coelho et al [29] developed a direct numerical solution for the EOF in porous media in the linear limit when the EDL thickness was much larger than the elementary grid size, and the method was applied to analyze the electroosmotic phenomena in fractures [50], porous media [51] and compact clays [52,53]. As well known the linear approximation is strictly valid for low zeta potentials ζ whose absolute value is smaller than 25 mV [54,55].…”

“…Only a few results with relatively coarse spatial discretiztation steps have been found to reach reasonable computation times [29,[50][51][52][53][54]56]. Kang et al [58] introduced the interval functions approximation [59] into the Poisson-Boltzmann equation to simplify the solution process and to improve the efficiency.…”