Periodic cell models of flow through porous media

Model problems are analyzed to study the microscopic flow within porous media. In Part 1, the primary focus is on the flow near the surface of a porous body. The idealized system consists of two-dimensional media of infinite and semi-infinite periodic lattices of cylindrical inclusions. The solution of Stokes flow in these complicated geometries is accomplished through the boundary-integral method. Results are discussed in the context of macroscopic approaches such as slip coefficients and Brinkman's equation. In Part 2, calculations are presented for a periodic three-dimensional model of porous media consisting of consolidated grains. The model is an extension of previous works on lattices of spheres. In this work, the radius of the spheres is allowed to increase past the point of close touching to form a consolidated media. A collocation method is used for the solution of Stokes flow in terms of Lamb's general solution in spherical coordinates. Results are presented for drag coefficients and permeability for the full range of void fraction.U of I OnlyETDs are only available to UIUC Users without author permissio