A review of applications of fractional calculus in Earth system dynamics

Y Zhang, HG Sun, HH Stowell, M Zayernouri… - Chaos, Solitons & …, 2017 - Elsevier
Fractional calculus has been used to model various hydrologic processes for 15 years. Yet,
there are still major gaps between real-world hydrologic dynamics and fractional-order …

Mixing versus stirring

E Villermaux - Annual Review of Fluid Mechanics, 2019 - annualreviews.org
Mixing is the operation by which a system evolves under stirring from one state of simplicity—
the initial segregation of the constituents—to another state of simplicity—their complete …

Mixing in porous media: concepts and approaches across scales

M Dentz, JJ Hidalgo, D Lester - Transport in Porous Media, 2023 - Springer
This review provides an overview of concepts and approaches for the quantification of
passive, non-reactive solute mixing in steady uniform porous media flows across scales …

Random walk methods for modeling hydrodynamic transport in porous and fractured media from pore to reservoir scale

B Noetinger, D Roubinet, A Russian… - Transport in Porous …, 2016 - Springer
Random walk (RW) methods are recurring Monte Carlo methods used to model convective
and diffusive transport in complex heterogeneous media. Many applications can be found …

Velocity distributions, dispersion and stretching in three-dimensional porous media

M Souzy, H Lhuissier, Y Méheust… - Journal of Fluid …, 2020 - cambridge.org
Using index matching and particle tracking, we measure the three-dimensional velocity field
in an isotropic porous medium composed of randomly packed solid spheres. This high …

Mixing and reactive fronts in the subsurface

M Rolle, T Le Borgne - Reviews in Mineralogy and …, 2019 - pubs.geoscienceworld.org
The interplay between mixing and reactive processes plays a pivotal role in a range of
biogeochemical processes controlling the transport, transformation and turnover of chemical …

Prediction of the low-velocity distribution from the pore structure in simple porous media

P de Anna, B Quaife, G Biros, R Juanes - Physical Review Fluids, 2017 - APS
The macroscopic properties of fluid flow and transport through porous media are a direct
consequence of the underlying pore structure. However, precise relations that characterize …

Harnessing elastic instabilities for enhanced mixing and reaction kinetics in porous media

CA Browne, SS Datta - Proceedings of the National Academy of Sciences, 2024 - pnas.org
Turbulent flows have been used for millennia to mix solutes; a familiar example is stirring
cream into coffee. However, many energy, environmental, and industrial processes rely on …

Stretching and folding sustain microscale chemical gradients in porous media

J Heyman, DR Lester, R Turuban… - Proceedings of the …, 2020 - National Acad Sciences
Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles,
and microorganisms across a wide spectrum of natural and industrial processes. Current …

Impact of saturation on dispersion and mixing in porous media: Photobleaching pulse injection experiments and shear‐enhanced mixing model

J Jiménez‐Martínez, T Le Borgne… - Water Resources …, 2017 - Wiley Online Library
The dynamics of solute dispersion and mixing in unsaturated flows is analyzed from
photobleaching experiments in two‐dimensional porous micromodels. This technique …