The work performed during the first 8 months of the project concerned the first work package (WP1), as planned in the project proposal. WP1 is dedicated to fulfilling the specific objective SO1 (see the paragraph on the objectives, above), while WP2, planned to be started 15 months after the initiation of the project, was dedicated to fulfilling the specific objective SO2 (see the paragraph on the objectives, above). Since the contract was terminated a little more than 8 months after initiation, due to the ER having been hired on an academic (permanent) position in his home country, WP2 could not be addressed.
To achieve the objective stated in WP1, the ER has primarily worked on two relevant problems:
1) Geo-electrical Signatures of Reactive Mixing:
In this work, the ER considered a special class of reactions where the products have significantly larger electrical mobility as compared to the reactants, and computed the variations in the effective conductivity resulting from reactive mixing occurring in a simple shear flow (see figure). He showed that the changes in effective conductivity are dependent on the local rate of stretching as well as on the orientation of the reaction front with respect to the flow of the electrical current. The evolution in time of the effective conductivity through the medium was studied as a function of the Péclet number, which quantifies the ratio of advection to diffusion strength, and the Damköhler number, which quantifies the ratio of the typical diffusion time to the typical reaction time. Power law scalings were observed depending on the values of these numbers and the time range considered. These power law could be explained theoretically.
This work has recently been resubmitted to the Geophysical Research Letters after minor revision. We expect the manuscript to be accepted for publication soon. The study has also be presented at three international conferences.
2) Coupled Electrohydrodynamic Transport in fractures:
This work was carried out in an effort to understand the flow dynamics in geological fractures and other subsurface features in presence of external or naturally-occurring solute concentration field, electrical potential on the solid surfaces, as well as pressure gradients across the medium. So far, only pressure driven flows through rough fractures have been studied by the concerned scientific community. The ER has applied the classical techniques of the lubrication theory to analyze the transport equations governing net charge, concentration and the fluid momentum (i.e. Poisson-Nernst-Planck and Navier-Stokes-Continuity equations) in the fracture, and derive a set of coupled equations describing the temporal evolution of the spatial distribution of these quantities. These theoretical developments were then applied to weakly charged 2-D fractures, and the coupled equations were solved numerically.
This work will be presented at two international conferences in the spring of 2018.
