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https://hdl.handle.net/2142/19022
Description
Title
Periodic cell models of flow through porous media
Author(s)
Larson, Robert Earl
Issue Date
1989
Department of Study
Chemical and Biomolecular Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Chemical Engineering
Language
eng
Abstract
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.
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