Colloidal Transport in Porous Media - Modeling and Analysis

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The scope of this thesis is the mathematical investigation and analysis of fluid flow and transport processes in porous media. In detail, the following aspects will be examined and incorporated in a mathematical model: 1) the heterogeneous spatial structure of the porous medium and 2) the interplay and coupling of processes between fluid flow, charged colloidal particles, their transport and the porous matrix. The main aim of this thesis is to achieve a deeper understanding of the most significa aspects and relevant physical processes, which influence the colloidal dynamics with a porous medium on different spatial scales. Since the spatial structure of the high heterogeneous porous medium cannot be resolved exactly on reasonable spatial an temporal scales, a direct numerical approach is unfeasible. For this reason, the ma focus of this thesis is on deriving meaningful mathematical models that describe flu flow and transport on a macroscopic, averaged scale. Main parts of the work are concentrated on electric interactions, which significantly influence the transport of charged colloidal particles. Another question that is addressed in this thesis is the extension to a mathematical model that is capable of changes in porosity together with the back coupling to fluid flow and the change of transport properties of the porous medium.