A Primer on the Dynamical Systems Approach to Transport in Porous Media

Historically, the dominant conceptual paradigm of porous media flow, solute mixing and transport was based on steady two-dimensional flows in heterogeneous media. Although it is now well recognised that novel phenomena can arise unsteady and/or three-dimensional at both pore- or Darcy-scales, appropriate methods for analysis understanding these more complex have not been widely employed. In this primer we advocate borrowed from dynamical systems (chaos) theory, which aim to uncover \emph{Lagrangian kinematics} flows: namely how fluid particle trajectories (which form a system) are organized interact associated impacts mixing. This approach inherently Lagrangian, Lagrangian kinematics coherent structures (LCSs), special sets divide frame into chaotic regions, poorly hold-up regions (and some cases non-mixing ``islands'') barriers organise regions. Hence provides insights may exhibit chaotic, regular (non-chaotic) mixed kinematics, also LCSs organize Novel experimental only recently permitting visualization flows. review flow connect tools techniques with latest research findings pore Darcy scales. an introduction theory. Once familiar approaches, researchers will be better positioned know when expect understand their ...