Journal
GEOPHYSICAL RESEARCH LETTERS
Volume 33, Issue 16, Pages -Publisher
AMER GEOPHYSICAL UNION
DOI: 10.1029/2006GL027054
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Fickian models of diffusion often fail to describe transport phenomena in heterogeneous environments due to their inability to capture the sub-scale fluctuations. We present an effective description of non-Fickian behavior that reflects the dichotomy between the continuum nature of Fick's law and the finite ( effective) observation scale associated with experimental studies of transport phenomena in heterogeneous systems. This dichotomy gives rise to a time delay between the cause and effect, i.e. between the concentration gradient and the mass flux. Evolving scales of heterogeneity induce a spectrum of such delay times that can lead to anomalous behavior. The presented model is a direct generalization of Fick's law and the well-established delay diffusion model. It complements effective modeling frameworks based on stochastic non-local theories and continuous time random walks.
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