Fluid-driven deformation of a soft granular material
CW MacMinn, ER Dufresne, and JS Wettlaufer, Physical Review X, 5:011020, 2015. doi:10.1103/PhysRevX.5.011020
Most biological and geological materials are porous and filled with fluid. For example, human bones and tissues are saturated with water, and so are rocks and soils (below the water table). Compressing one of these materials will drive fluid out of the pore space, as when squeezing water out of a kitchen sponge. Inversely, injecting additional fluid into one of these materials can deform the solid structure, as when recovering natural gas from a shale via hydraulic fracturing.
These poromechanical interactions are important for a wide variety of real-world problems, from traumatic brain injury (concussion) to the geological storage of carbon dioxide (carbon sequestration), but they are notoriously difficult to study in the laboratory. This is mainly because most porous materials are not transparent, so it is very hard to see and measure the flow and deformation. This is even more difficult in geophysical systems because they require working with very large fluid pressures.
We have developed a new model system for studying poromechanical deformation: A saturated packing of soft particles. We drive deformation by injecting fluid into the packing at a constant rate, and then we use high-resolution imaging and particle tracking to measure the full, dynamic deformation field. We use this system here to study the interplay between grain-scale rearrangements and the macroscopic poroelastic response.
Video 0. A soft particle similar to those used in our experiments. They are extremely soft, elastic, and slippery. This one has a disameter of about 2.5 mm.
The next three videos show the experiment. The flow cell has a diameter of 210 mm and the particles have a mean diameter of 1.2 mm. We inject fluid at a constant volume rate of 16 mL/min for about 130 s and then allow the packing to relax, and we repeat this injection-relaxation cycle two more times in the same packing.
Each injection-relaxation cycle lasts for about 3 minutes in realtime and plays back in about 14 seconds. The speedup factor changes during the video from about 10x immediately after the pump turns on or off (when the dynamics are fast) to about 30x at other times, when the dynamics are slower.
Video 1. The experiment in grayscale.
Video 2. We overlay colored dots on a subset of the particles for a qualitative, visual assessment of the deformation. The deformation is long-range and roughly axially symmetric, but features complex heterogeneity and irreversibility at the grain scale.
Video 3. The radial displacement field on a color scale of dark blue (less than about 8 particle diameters) through off-white (zero) to dark red (greater than 8 diameters). The displacement field is characterized by a striking, petal-like mesoscale structure that has its origins in spiral bands of shear failure (see the paper).