Mixing in Heterogeneous Media Across Spatial and Temporal Scales: From Local Non-Equilibrium to Anomalous Chemical Transport and Dynamic Uncertainty

The MHetScale team investigates mixing, transport and reaction processes under heterogeneity from the pore to the field scale. Natural and engineered media are inherently heterogeneous, which gives rise to scale effects and process laws that can be very different from what is expected for homogeneous media. Heterogeneity increases the dispersion and thus global segregation of dissolved substances, while it enhances solute mixing locally, as illustrated in Figure 1. Heterogeneity induces a broad spectrum of mass transfer times, which leads to history-dependent transport and reaction dynamics. Our research focuses on the upscaling of transport, mixing and reaction phenomena from pore to Darcy to regional scale.


Figure 1: Concentration distribution in a steady heterogeneous flow (after Dentz and de Barros, J. Fluid. Mech., 2015). Flow heterogeneity enhances dispersion and thus segregation of a dissolved substance within a macroscopic support volume (blockscale). The concurrent creation of local concentration gradients enhances mixing.

Research lines

Transport upscaling

Large scale transport is in general non-Fickian or anomalous. The objective is to understand and quantify the impact of heterogeneity and small scale processes on large scale transport.


Medium characterized by spatially heterogeneous retardation properties, equivalent to the quenched random trap model. Diffusion is non-Fickian and self-averaging is dimension-dependent (Russian et al., Phys. Rev. E 96, 022156, 2017)

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Mixing in heterogeneous media cannot be reduced to the concept of effective dispersion. The objective is to quantify the controls on mixing in terms of the flow and medium properties and cast them into a large scale modeling approach.

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Heterogeneity and fluctuation induced segregation and incomplete mixing lead to chemical reaction dynamics very different from the ones expected for well-mixed environments. The objective is to identify and quantify the large scale reaction dynamics in terms of small scale mass transfer and mixing processes.

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Numerics and data

Detailed numerical simulations and experimental data provide process understanding, guide theory development, and serve for model validation. Effective large scale transport, mixing and reaction models are implemented in numerical toolboxes.

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