On the control of soil heterogeneity, Péclet number and spatially variable diffusion over unsaturated transport

Christopher V. Henri, Efstathios Diamantopoulos

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Physical properties of soils are ubiquitously heterogeneous. This spatial variability has a profound, yet still partially understood, impact on conservative transport. Moreover, molecular diffusion is often a disregarded process that can have an important counter-intuitive effect on transport: diffusion can prevent non-Fickian tailing by mobilizing mass otherwise trapped in low velocity zones. Here, we focus on macroscopically homogeneous soils presenting small scale heterogeneity, as described by the Miller-Miller theory. We then analyze the dynamic control of soil heterogeneity, advection and diffusion on conservative transport. We focus especially on the importance of diffusion and of its tortuosity-dependent spatial variability on the overall transport. Our results confirm previous finding that relatively high Péclet number systems are highly sensitive to the degree of heterogeneity, which promotes non-Fickian transport. Also, diffusion appears to have a profound impact on transport, depending on both the degree of heterogeneity and the Péclet number. For a high Péclet number and a very heterogeneous system, diffusion leads to the counter-intuitive decrease of non-Fickian spreading described previously. This is not observed for a low Péclet number due to the impact of the spatial variability in the diffusion coefficient, which appears to be a significant controlling factor of transport by promoting or preventing the accumulation of mass in low velocity zones. Globally, this work (a) highlights the complex, synergistic effect of soil heterogeneity, advective fluxes and diffusion on transport and (b), alerts on potential upscaling challenges when the spatial variability of such key processes cannot be properly described.

Original languageEnglish
Article numbere2022WR034271
Number of pages18
JournalWater Resources Research
Issue number8
Publication statusPublished - Aug 2023


  • diffusion
  • Peclet number
  • small scale soil heterogeneity

Programme Area

  • Programme Area 2: Water Resources


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