Yves Méheust

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918)10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Electrical Resistivity Monitoring of Saline Tracer Fingering at Pore Scale under Partially Saturated Conditions

Time-lapse electrical resistivity tomography is a widely used geophysical method to remotely monitor water saturation and the migration of contaminant plumes. The effects of heterogeneous solute concentrations below the resolution limits of the tomogram are commonly ignored. We have adapted an experimental set-up to study the effects of sub-resolution solute heterogeneities on the effective bulk electrical resistivity. We used a 2D analogous porous medium consisting of a Hele-Shaw cell. We monitored simultaneously the bulk electrical resistivity and the spatial distribution of the water/air phases and the saline solute concentration field in the water phase using a fluorescent tracer injected together with the saline solute and a high-resolution camera. We performed saline tracer tests under full and partial water saturations. The bulk electrical conductivity measured at the scale of the medium were confronted to electrical conductivity computed numerically from the measured spatial distributions of the fluid phases and the salinity field. We find that the air distribution, saline tracer fingering, and mixing phenomena all result in large changes in the measured and simulated bulk resistivities by creating preferential flow paths or barriers for electric current at the pore scale.