Phase Saturation Control on Mixing-Driven Reactions in 3D Porous Media

Transported chemical reactions in unsaturated porous media are relevant to environmental and industrial applications. Continuum scale models are based on equivalent parameters derived from analogy with saturated conditions and cannot appropriately account for incomplete mixing. It is also unclear how the third dimension controls mixing and reactions. We obtain three-dimensional (3D) images by magnetic resonance imaging using an immiscible nonwetting liquid as a second phase and a fast irreversible bimolecular reaction. We study the impact of phase saturation on the dynamics of mixing and the reaction front. We quantify the temporally resolved effective reaction rate and describe it using the lamellar theory of mixing, which explains faster than Fickian (t^0.5) rate of product formation by accounting for the deformation of the mixing interface between the two reacting fluids. For a given Péclet, although stretching and folding of the reactive front enhance as saturation decreases, enhancing the product formation, the product formation is larger as saturation increases. After breakthrough, the extinction of the reaction takes longer as saturation decreases because of the larger nonmixed volume behind the front. These results are the basis for a general model to better predict reactive transport in unsaturated porous media not achievable by the current continuum paradigm.