UC San Diego

This dissertation deals with multi-scale, multi-physics descriptions of flow and transport in crowded environments forming porous media. Such phenomena can be described by employing either pore-scale or continuum-scale (Darcy- scale) models. Continuum-scale formulations are largely phenomenological, but often provide accurate and efficient representations of flow and transport. In the first part of the dissertation, we employ such a model to describe fluid flow through carbon nanotube (CNT) forests placed in a turbulent ambient environment of a microscopic wind tunnel. This analysis leads to closed-form analytical formulae that enable one to predict elastic response of CNT forests to aerodynamic loading and to estimate elastic properties of individual CNTs, both of which were found to be in a close agreement with experimental data. The second part of this work explores the applicability range of continuum-scale models of transport of chemically active solutes undergoing nonlinear homogeneous and heterogeneous reactions with the porous matrix. We use two upscaling techniques (the volume averaging method and multiple-scale expansions) to formulate sufficient conditions for the validity of continuum-scale models in terms of dimensionless numbers characterizing key pore-scale transport mechanisms (e.g. Péclet and Damköhler numbers). When these conditions are not satisfied, standard continuum-scale models have to be replaced with upscaled equations that are nonlocal in space and time, effective parameters (e.g. dispersion tensors, effective reaction rates) do not generally exist, and pore- and continuum- scales cannot be decoupled. Such transport regimes necessitate the development of hybrid numerical methods that couple the pore- and continuum-scale models solved in different regions of the computational domain. Hybrid methods aim to combine the physical rigor of pore-scale modeling with the computational efficiency of its continuum-scale counterpart. In the third and final part of this dissertation, we use the volume averaging method to construct two hybrid algorithms, one intrusive and the other non-intrusive, that facilitate the coupling of pore- and continuum-scale models in a computationally efficient manner