Mechanism behind Erosive Bursts In Porous Media

Temporal Evolution of Erosion in Pore Networks: From Homogenization to Instability

We study the dynamics of flow networks in porous media using two and three dimensional pore-network models. We consider a class of erosion dynamics for a single phase flow with no deposition, chemical reactions, or topology changes assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.

Soil granular dynamics on-a-chip: fluidization inception under scrutiny

Predicting soil evolution remains a scientific challenge. This process involves poorly understood aspects of disordered granular matter and dense suspension dynamics. This study presents a novel two-dimensional experiment on a small-scale chip structure; this allows the observation of the deformation at the particle scale of a large-grained sediment bed, under conditions where friction dominates over cohesive and thermal forces, and with an imposed fluid flow. Experiments are performed under conditions which span the particle resuspension criterion, and particle motion is detected and analyzed. The void size population and statistics of particle trajectories bring insight into the sediment dynamics near fluidization conditions. Specifically, particle rearrangement and net bed compaction are observed at flow rates significantly below the criterion for instability growth. Above a threshold flowrate, a channel forms and grows in the vertical direction; and eventually it crosses the entire bed. In the range of flow rates where channelization can occur, the coexistence of compacting and dilating bed scenarios is observed. The results of the study enhance our capacity for modeling of both slow dynamics and eventual rapid destabilization of sediment beds. Microfluidic channel soil-on-a-chip studies open avenues to new investigations including dissolution-precipitation, fine particle transport, or micro-organism swimming and population growth, which may depend on the mechanics of the porous medium itself.

Fluid flow through packings of elastic shells

Fluid transport in porous materials is commonly studied in geological samples (soil, sediments, etc.) or idealized systems, but the fluid flow through compacted granular materials, consisting of substantially strained granules, remains relatively unexplored. As a step toward filling this gap, we study a model of liquid transport in packings of deformable elastic shells using finite-element and lattice-Boltzmann methods. We find that the fluid flow abruptly vanishes as the porosity of the material falls below a critical value, and the flow obstruction exhibits features of a percolation transition. We further show that the fluid flow can be captured by a simplified permeability model in which the complex porous material is replaced by a collection of disordered capillaries, which are distributed and shaped by the percolation transition. To that end, we numerically explore the divergence of hydraulic tortuosity τ_{H} and the decrease of a hydraulic radius R_{h} as the percolation threshold is approached. We interpret our results in terms of scaling predictions derived from the percolation theory applied to random packings of spheres.

Critical Bursts in Filtration

Particle detachment bursts during the flow of suspensions through porous media are a phenomenon that can severely affect the efficiency of deep bed filters. Despite the relevance in several industrial fields, little is known about the statistical properties and the temporal organization of these events. We present experiments of suspensions of deionized water carrying quartz particles pushed with a peristaltic pump through a filter of glass beads measuring simultaneously the pressure drop, flux, and suspension solid fraction. We find that the burst size distribution scales consistently with a power law, suggesting that we are in the presence of a novel experimental realization of a self-organized critical system. Temporal correlations are present in the time series, like in other phenomena such as earthquakes or neuronal activity bursts, and also an analog to Omori's law can be shown. The understanding of burst statistics could provide novel insights in different fields, e.g., in the filter and petroleum industries.