Topological mixing in three-dimensional porous media

The topological complexity inherent to all porous media can impart complicated transport dynamics under steady flow conditions. Recently, it has been established [2] that such topological complexity imparts ubiquitous and persistent chaotic advection via a 3D fluid mechanical analogue of the baker's map. In the presence of molecular diffusion, chaotic Lagrangian dynamics are well-known to impart anomalous transport and rapidly accelerated mixing, however this phenomenon has received little attention in the context of porous media flow. In this paper we consider the impact of chaotic advection upon transport and mixing of a continuously injected dye plume in a model 3D porous network which consists of randomly connected pore branches and mergers. Punctuated stretching of fluid elements during advection through the random network is described by a novel stretching continuous time random walk (CTRW) which captures fluid deformation and scalar dispersion in the model network. This model indicates that chaotic mixing in 3D topologically complex media exponentially accelerates mixing and scalar dissipation across all Peclet numbers, from diffusion-dominated (Pe=10-0) to advection-dominated (Pe=10-8) transport. Whilst the CTRW model is highly idealised, the critical features of this model (no-slip boundary condition, topological complexity) are inherent to almost all porous media