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

Electrokinetics of Erosive Seepage through Deformable Porous Media

Channelization and branching patterns frequently appear in porous structures as a result of fluid-flow-mediated erosion, which causes spatiotemporal changes in the medium. However, most studies on electrokinetic effects in porous media focus on the overall impact of the electric field on electrical double-layer formation in micropores and its influence on ionic transport, without addressing the spatiotemporal erosive characteristics and resulting porosity distribution. In this study, we explore the interplay between flow-induced shear stress and an external electric field on the dynamic evolution of porosity in deformable porous media using semi-analytical modeling. Our numerical simulations accurately predict the differences in porosity and erosive development when the electric field aligns with or opposes the flow, highlighting the importance of the direction of the external stimulus and not just its magnitude. Our findings establish a foundation for electric-field-mediated control of porous media properties and explain electrokinetic transport by considering dynamic porosity variations as a result of erosive deformation, an aspect previously unaddressed.

Emergence of preferential flow paths and intermittent dynamics in emulsion transport in porous media

We investigate the dynamics of emulsions within a two-dimensional porous medium using an integrated experimental approach that combines pore-level dynamics of single emulsions and bulk transport properties of the medium. Using an on-chip microfluidic drop-maker, we precisely control the concentration and sizes of emulsions injected into the medium. The dynamics of emulsion droplets are highly intermittent despite a small average velocity over the trajectory of an individual emulsion. At low concentrations, emulsions predominantly flow through pores with higher local velocities including pores smaller than the size of emulsion droplets, leading to trapping of emulsions and a decrease in medium porosity. Preferential pathways for the emulsions emerge within the medium once the porosity of the medium decreases significantly, from 55% to 36%. At constant injection flow rates and low concentrations of monodisperse emulsions, these pathways remain the only paths of transport of emulsions within the medium. Introducing a slight polydispersity in emulsion sizes unveiled additional transport pathways. Our pore-level measurements reveal that the average velocity of emulsions scales with the inverse residence time of an emulsion, and this scaling separates the emulsions into distinct groups along the emergent preferential pathways.

Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads

We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments. We explore the deposition profile over a two-dimensional phase diagram defined in terms of the pressure and shear stress threshold, and show that two distinct phases exist. We explain this apparent phase transition by drawing an analogy to simple one-dimensional mass-aggregation models in which the phase transition is calculated analytically.

Dispersive transport dynamics in porous media emerge from local correlations

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.

Dispersive transport through complex media, relevant for semiconductors, liquid crystals, and biological soft matter, is influenced by their microscopic, porous structure. The authors consider the statistics of pore-junction units, in contrast to individual pores, to link morphology and macroscopic transport characteristics.