Perspective on theories of non-Fickian transport in heterogeneous media

By Shlomo P. Neuman, Daniel M. Tartakovsky. 2009

402 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/0682daf83c25044a6ecac702e57a8a58c744603a

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Citations in the corpus

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, background): “It is well understood that that Fick’s first law, which is a constitutive relation for diffusive fluxes, is a questionable model for numerous phenomena; see [11, 43, 44] for discussions and numerous citations to the literature.”
FracFit: A robust parameter estimation tool for fractional calculus models (2017, background): “Anomalous transport cannot be adequately described with classical Fickian advection-dispersion equations (ADE) with constant coefficients [Metzler and Klafter, 2004; Neuman and Tartakovsky, 2009].”
The lamellar description of mixing in porous media (2015, background): “…and its relation to the medium heterogeneity, the inﬂuence of the possible presence of traps and dead zones for the transported substances, as well as the validity of the advection-dispersion equation to describe large scale solute transport (e.g. Berkowitz et al. 2006; Neuman & Tartakovsky 2009).”
Expanding the role of reactive transport models in critical zone processes (2017, methodology): “Effective, upscaled models were developed to capture anomalous behavior (Neuman and Tartakovsky, 2009), including the dual porosity model (Gerke and Van Genuchten, 1993), multirate mass transfer model (Haggerty and Gorelick, 1995), non-local methods including Continuous Time Random Walk (Berkowitz…”
Solute transport in low‐heterogeneity sandboxes: The role of correlation length and permeability variance (2014, background): “It has been argued that may be non-local models both in time and space are needed to fully capture non-Fickian transport [Neuman and Tartakovsky, 2009].”
Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, methodology): “The SA-ADE model is attractive in many ways, as reviewed recently by Neuman and Tartakovsky [113].”
Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column (2009, methodology): “Using CDE at local scale, many upscaling methods such as volume averaging and stochastic approaches were proposed to describe solute transport in heterogeneous porous media at large scales (Berkowitz et al., 2006; Frippiat and Holeyman, 2008; Neuman and Tartakovsky, 2008).”
Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions? (2008, background): “[11] Despite the above nice properties, non local formulations have been subject to criticism [Neuman and Tartakovsky, 2009].”
Use of a variable-index fractional-derivative model to capture transient dispersion in heterogeneous media. (2014, methodology): “For example, Brownianmotion is assumed for tracer particles moving in a Darcy-scale homogeneous medium (Neuman and Tartakovsky, 2009), or at a long travel distance much larger than the maximum correlation scale of heterogeneity in a stationary medium (due to the central limit theory).”