Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium’s length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

Mixing controls the fate of any solute entering porous media. Hence, an understanding of the involved processes is essential for assessing subsurface contamination and planning for its protection. However, the three-dimensional mechanisms dominating solute mixing in the presence of several fluid phases in the pore space, and their dependency on phase saturation degree (fraction of the pore volume occupied by a phase) are unknown. Here, we analyze solute mixing in unsaturated porous media at the pore scale using X-ray micro-tomography performed with synchrotron radiation at unprecedented temporal and spatial resolutions for such an investigation. Transport experiments through a synthetic, sand-like porous medium, followed in 4D using a contrast solution, are performed at different liquid phase saturation degrees. The results reveal larger solute's front deformation at lower saturation, which translates into an enhanced mixing with time. Using different topological indexes, defined based on a description of the liquid phase geometry and of the resulting hydrodynamics, we show an increase in the spatial convergence of flow streamlines at lower saturation, which, in turn, leads to a strengthened helical flow inside the liquid phase. Consequently, this increases the number of shear- and vorticity-dominated deformation regions, as characterized by larger negative and positive Q-criterion values, respectively. These findings represent a major step toward understanding the control of both saturation and the system's heterogeneity on solute mixing, essential, among others, to assess reactivity in porous media.

The unsaturated zone, located between the soil surface and the phreatic level, plays an important role in defining the fate of any substance entering the subsoil. In addition to the processes of flow and transport taking place in the liquid phase, surface reactions such as adsorption to the solid phase may occur and increase the residence time of the substance entering the system. In this study, we aim to understand the pore-scale mechanisms that control adsorption in unsaturated systems. We combine 2D pore-scale experimental images with numerical simulations to analyze flow, transport, and adsorption under different liquid saturation degrees. We demonstrate the role of mixing on adsorption at the liquid-solid interfaces by analyzing the deformation in time of a pulse-injected surfactant. We also analyze the impact of the isotherm functional shape and the inclusion of the liquid-gas interfaces as adsorption sites on this surface reaction. The enhancement of mixing as saturation decreases is accompanied by a reduction in the amount of adsorbed mass, located mainly along preferential flow paths, where the solute is primarily transported. For the same isotherm, a nonlinear behavior of adsorption as a function of liquid saturation has been observed. This is explained by the nonlinear variation of the volume fraction of liquid behaving as preferential path or stagnation zone as liquid saturation decreases, despite the linear decrease in the surface area of solids accessible for adsorption.

Space-Lagrangian random walk models conceptualize advective transport in terms of collections of particles undergoing fixed-length steps along flow streamlines. The statistics and correlation structure of the underlying flow velocity statistics determine the transit times of particles undergoing advective transport. Broad velocity distributions lead to broadly distributed step transit times, reproducing commonly observed anomalous transport features such as superdiffusive plume growth, which are not captured by classical Fickian theories. Early space-Lagrangian models considered uncorrelated velocities across steps. These approaches were later extended to account for correlations through a spatial-Markov process. Here, we compare longitudinal dispersion dynamics in an uncorrelated continuous-time random walk with fixed-space steps to a Bernoulli relaxation spatial-Markov model exhibiting exponential decay of spatial velocity correlations along streamlines. We provide rigorous theoretical derivations, validated against numerical simulations. We find that, although the scaling forms of asymptotic dispersion agree between the two models, exact asymptotic equivalence requires employing different correlation lengths, which depend on the underlying Eulerian velocity statistics. The two models become equivalent in the limit of very broad velocity distributions, corresponding to a new quasiballistic regime recently identified in unsaturated porous media, which we rigorously characterize here.

The simultaneous presence of liquid and gas in porous media increases flow heterogeneity compared to saturated flows. However, the impact of saturation on flow and transport has so far remained unclear. The presence of gas in the pore space leads to flow reorganization. We develop a theoretical framework that captures the impact of that reorganization on pore-scale fluid velocities. Preferential flow is distributed spatially through a backbone, and flow recirculation occurs in flow dead-ends. We observe, and predict theoretically, that this previously identified flow structure induces a marked change in the scaling of the velocity probability density function compared to the saturated configuration and a sharp transition to strongly anomalous transport. We develop a transport model using the continuous time random walk theory that predicts advective transport dynamics for all saturation degrees. Our results provide a new modeling framework linking phase heterogeneity to flow heterogeneity in unsaturated porous media.

X-ray tomographic microscopy is a well-established analysis technique in different fields of the Earth Sciences to access volumetric information of the internal microstructure of a large variety of opaque materials with high-spatial resolution and in a non-destructive manner. Synchrotron radiation, with its coherence and high flux, is required for pushing the temporal resolution into the second and sub-second regime and beyond, and therefore moving from the investigation of static samples to the study of fast dynamic processes as they happen in 3D. Over the past few years, several hardware and software developments at the TOMCAT beamline at the Swiss Light Source contributed to establishing its highly flexible and user-friendly fast tomography endstation, making a large variety of new dynamic in situ and operando investigations possible. Here we present an overview of the different devices, including an in-house developed detector, a new highly efficient macroscope and a programmable fast rotation stage. Their tight interplay and synchronization are key for lifting experimental design compromises and follow dynamic processes with high spatial and temporal resolution unfolding over prolonged periods of time, as often required by many applications. We showcase these new capabilities for the Earth Sciences community by presenting three different geological studies, which make use of different sample environments. With a tri-axial deformation rig, chemo-mechanical-hydraulic feedbacks between gypsum dehydration and halite deformation have been studied, while the spatio-temporal evolution of a solute plume has been investigated for the first time in 3D with a flow cell. A laser-based heating system available at the beamline provides access to the high temperatures required to address bubble growth and collapse as well as bubble-bubble interaction and coalescence in volcanological material. With the integration of a rheometer, information on bubble deformation could also be gained. In the near future, upgrades of most large-scale synchrotron radiation facilities to diffraction-limited storage rings will create new opportunities, for instance through sub-second tomographic imaging capabilities at sub-micron length scales.