Geometrical interpretation of long-time tails of first-passage time distributions in porous media with stagnant parts

Structure induced laminar vortices control anomalous dispersion in porous media

Natural porous systems, such as soil, membranes, and biological tissues comprise disordered structures characterized by dead-end pores connected to a network of percolating channels. The release and dispersion of particles, solutes, and microorganisms from such features is key for a broad range of environmental and medical applications including soil remediation, filtration and drug delivery. Yet, owing to the stagnant and opaque nature of these disordered systems, the role of microscopic structure and flow on the dispersion of particles and solutes remains poorly understood. Here, we use a microfluidic model system that features a pore structure characterized by distributed dead-ends to determine how particles are transported, retained and dispersed. We observe strong tailing of arrival time distributions at the outlet of the medium characterized by power-law decay with an exponent of 2/3. Using numerical simulations and an analytical model, we link this behavior to particles initially located within dead-end pores, and explain the tailing exponent with a hopping across and rolling along the streamlines of vortices within dead-end pores. We quantify such anomalous dispersal by a stochastic model that predicts the full evolution of arrival times. Our results demonstrate how microscopic flow structures can impact macroscopic particle transport.

Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays

We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.

Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.

Clogging and jamming transitions in periodic obstacle arrays

We numerically examine clogging transitions for bidisperse disks flowing through a two-dimensional periodic obstacle array. We show that clogging is a probabilistic event that occurs through a transition from a homogeneous flowing state to a heterogeneous or phase-separated jammed state where the disks form dense connected clusters. The probability for clogging to occur during a fixed time increases with increasing particle packing and obstacle number. For driving at different angles with respect to the symmetry direction of the obstacle array, we show that certain directions have a higher clogging susceptibility. It is also possible to have a size-specific clogging transition in which one disk size becomes completely immobile while the other disk size continues to flow.