Abstract
This chapter deals with flow, transport and reaction processes in porous and heterogeneous media characterised by multiple spatial scales. Although the governing equations, at the micro-scale, are simple (and often linear), complex upscaled (effective macro-scale) phenomena can emerge, due to the averaging process. After introducing some general concepts related to multiscale porous media, we present the Darcy’s equation and its assumptions and extensions. A more detailed analysis of dispersion theories for pore-scale and continuum-scale (with Darcy’s flow) solute transport is then carried out, presenting the classical results as well as the most recent research in the field. We then focus on the interaction between dispersion and reaction, through mixing, as well as more complex processes like particle deposition and multiphase flows.
Highlights
Countless environmental, industrial and biological applications involve fluids flowing through complex media or heterogeneous environments
The concept of upscaling and averaging is present in many fluid dynamics problems, relevant to many applications is the understanding of the emerging dynamics of fluid flowing through multiscale materials
In the assumption of stationary profiles and local equilibrium, the periodic cell represents the geometric representative elementary volume (REV) and the right REV for all processes. Relaxing these periodicity assumptions means allowing random “perturbation” in the material that results in a larger geometrical REV, and, possibly, in perturbation in the solution persisting over bigger scales
Summary
Industrial and biological applications involve fluids flowing through complex media or heterogeneous environments. The main difference between flows through porous media and turbulent flows lies in the fact that the latter is an emerging phenomena purely due to the nonlinearity of the Navier–Stokes equations, while the former inherits its multiscale complexity directly from the geometrical and physical properties of the material. This means that, even starting from linearised or simplified flow regimes (e.g., Stokes), interesting emergent macro-scale dynamics can appear due to these properties. A wide range of these emerging dynamics are more observed and studied than the turbulent structures
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