Transport phenomena in porous media
Non-Newtonian flow in heterogeneous media is of enormous theoretical and industrial importance. This phenomenon is studied to reveal macroscopic effects that arise due to the interaction between the non-linear flow behaviour and the spatial variation of the medium through which it is forced to move. The heterogeneity is achieved by using porous granular media, which is naturally non-homogeneous. The non-Newtonian properties of the fluid may have many causes and is an intrinsic property of the fluid that is used: One way of achieving it is by studying dense slurries of neutral particles or naturally occurring magmatic flows. Another way is to study the case where the flow is dominated by its ionic content and where the double layer thickness (the effective size of the ionic entities) is of the order of magnitude of the pore size. All cases studied in this thesis pertain to slow flow (low Reynolds number), though the fluid may be compressible. The variations in the flow are calculated in first order and these turn out to be coupled to the spatial variations in the porous medium. In this way structure formation is predicted. The structures may be either aligned with or may be perpendicular to the mean flow direction. 'Experiments to decide on which regime is relevant have been conducted. The genesis of structure formation is studied as a temporal development by considering a compressible flow. The constitutive equation that is required to couple the compressibility to the flow parameters is investigated. Two possible mechanisms have been identified: compressibility coupled to the pressure field and compressibility associated with the fluctuations in the flow. Using linear analysis the structure formation patterns associated with these two mechanisms are established for the steady state. Flow of ionically laden fluids has also been studied. Experiments done at Loughborough University (Department of Chemical Engineering) on electrowashing of filter cakes has been used to prove a major macroscopic effect. This effect takes place when the ionic diameter (which is approximately twice the double layer thickness) is of the order of magnitude of the pore size. A phenomenological set of transport equations has been set up. These contain coefficients, such as transition probabilities and mean ionic flow rates, that can be obtained from experiments by doing a first order solution of the equations for short times. A more involved numerical solution is also supplied and confirms the initial analytical estimates.