Chaotic Advection, Transport and Mixing in Homogeneous Porous Media (Invited)

All porous media, whether heterogeneous or homogeneous, including granular and packed media, fractured and open networks, are typified by the inherent topographical complexity of the pore-space. Such geometric complexities render exact modelling of fluid flow and transport an intractable problem, hence averaging methods are required for upscaling to the Darcy scale. Although successful transport theories have been developed via averaging techniques, it is also possible to eliminate important flow phenomena during the upscaling process. In general, the detailed flow structure and Lagrangian dynamics of fluid flows can have significant impacts upon a range of fluid-borne processes. In the context of turbulent flow, it is well known that such structure can fundamentally alter processes such as transport, mixing, chemical reactions and biological activity across a wide range of length scales. More recently, it has been established that similar impacts also occur for laminar flows which exhibit chaotic Lagrangian dynamics, commonly known as chaotic advection. In the context of porous media flows, an important question is whether steady Stokes flow at the pore scale can admit chaotic advection, and what are the impacts upon fluid transport, mixing, chemical reaction and biological activity? Conversely, due to limitations of the flow topology, steady Darcy flow cannot admit chaotic advection, and so the impacts of chaotic advection are neglected during the upscaling process. For transport and mixing, chaotic advection imparts strongly anomalous transport for passive tracer particles, whereas diffusive particles exhibit significantly accelerated dispersion even in the limit of vanishing diffusivity. Chemically or biologically active chaotic flows have been shown to generate singularly-enhanced reaction kinetics in autocatalytic, bistable and combustion reactions, and fundamentally alter the stability of a wide variety of reactive processes. An important question is whether homogeneous porous media gives rise to Fickian dispersion, as this assumption forms the kernel of upscaling methods for transport models in heterogeneous media. There currently exists some controversy as to the validity of this assumption, with several experimental and numerical investigations observing persistent non-Fickian transport. This behaviour is often attributed to hold-up dispersion from dead-end pores and/or recirculation zones. Pore-scale chaotic advection provides an alternate mechanism by which non-Fickian transport may occur in homogeneous porous media. It is well-established that chaotic advection can generate strongly anomalous transport within steady flows at low Reynolds numbers typical of pore-scale fluid mechanics. Although this transport mechanism has been identified by several workers as a means of generating anomalous transport in homogeneous porous media, the propensity and impacts of chaotic advection in porous media has received scant attention. We consider the mechanisms by which chaotic advection arise at the pore-scale, and demonstrate that chaotic advection is inherent to flow through all porous media with even the smallest amount of randomness in the pore network. The impacts of chaotic advection upon transport, mixing and chemical reactions in porous media are considered across a range of scales from the pore-scale to the Darcy scale.