Non-linear effects in momentum transport (i.e., flow) equations can arise from a variety of physical mechanisms, such as inertial effects or non-Newtonian rheological behaviors. For instance, inertia terms in the Navier-Stokes equations are important in various applications such as flows in highly permeable media, fractured rocks, canopies, urban canyons or near well injections. Non- Newtonian rheologies feature non-linear or history-dependent relationships between stress and shear rate, and/or yield stresses, and are commonly encountered in a number of varieties: polymer slugs for the remediation of NAPL-polluted aquifers, enhanced oil recovery (EOR), or to investigate subsurface properties; foams for the remediation of vadose zone environments; clay-based drilling muds; suspensions of solid particles for soil remediation or fracking.
The non-linear effects associated with such flows, combined with the complexity of the multi-scale heterogeneous structure of the subsurface, make it extremely challenging to model them accurately at the macro-scale. On the other hand, understanding pore-scale flows and the relationship between the various scales of the problem requires accurate simulations (molecular or quasi-molecular, meso-scale approaches, effective boundary conditions such as slip conditions for polymer flows, continuum approaches) performed in realistic structures. Advances in the field further require the development of experiments at the corresponding scales (pore, Darcy, field), along with novel visualization and imaging techniques (e.g. PIV, photon microscopy, tomography). Finally, the interpretation of pore/fracture scale results in terms of macro-scale models and effective properties challenges all upscaling techniques and homogenization paradigms, which must be adapted and improved. Consequently, how non-linear effects impact the flow in porous/fractured media, and how it is beneficial to applications, are still open questions.
We welcome contributions addressing the impact of non-linearities in the flow equations on single- or multiphase flows in porous media, based on theoretical/numerical studies, laboratory experiments, or macro-scale/field investigations, and over a broad range of scales and applications. Topics may include, among others, rheological studies, characterization of flow behavior through porous and fractured media, impact of the rheology on solute transport, estimation of medium properties through upscaling procedures, and field applications such as aquifer/soil/vadose zone remediation, EOR, and fracking. Discussions on improved modeling and investigation strategies are also encouraged.