Introduction

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

“…The above two-scale expansion can be considered as a special case of the general expansions of this type from the monographs by Sanchez-Palencia [72] and Hornung [39]. The differential operators transform as follows…”

“…In connection with the homogenization in porous media, we recommend to the reader the book edited by U. Hornung [39]. It contains number of contributed chapters, and we mention the chapters on the 2-scale convergence and on the derivation of Darcy's law by homogenization by G. Allaire, which we are going to quote frequently in this text.…”

Solvability of the Brinkman-Forchheimer-Darcy Equation

“…We start with the weak formulation of problem (6) and look for its solution in suitable Sobolev spaces that are adjusted to the modified momentum and mass balances in (6) and to the smoothness of the weighting function .…”

“…We will extend this result for the flow component to the case (6) when the variable porosity depends on the location and the convective term is included. The recent existence results for the linear Brinkman problem with spatially varying can be found in [17].…”

“…The model (1)-(2) with the pressure term of the form ∇( ) has been proposed in [3,Section 2.2]. For the derivation of the equations, their limitations, modelling, and homogenization questions in porous media we refer to [4][5][6][7][8][9] and [10,Chapter 1].…”