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

Wirner, Frank; Scholz, Christian; Bechinger, Clemens

doi:10.1103/physreve.90.013025

Cited by 13 publications

(11 citation statements)

References 30 publications

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“…Many of these studies involved no quenched disorder so that the system can be described as containing only particle-particle interactions. It is also possible for the particle motion to be stopped by some form of external constraints, such as flow through bottlenecks or funnels [12][13][14][15][16][17] , motion through a mesh [18][19][20][21][22] , flow over a disordered substrate [23][24][25] , or flow in porous media [26][27][28][29][30][31][32] . The particle flow stops when the combination of the particle density and the obstacle density is high enough.…”

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confidence: 99%

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

Reichhardt

2021

Soft Matter

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confidence: 99%

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

Reichhardt

2021

Soft Matter

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“…At finite drive angles we observe a novel size-dependent clogging effect in which the smaller disks become completely jammed while a portion of the larger disks continue to flow. This work is relevant for filtration processes [14][15][16] , the flow of discrete particles in porous media 17,18 , and the flow and separation of of colloids on periodic substrates [19][20][21][22] Model and Method-We consider a 2D square system of size L × L where L = 60 with periodic boundary conditions in the x and y-directions. The sample contains N l disks of diameter σ l = 0.7 and N s = N l disks of diameter σ s = 0.5, giving a size ratio of 1 : 1.4.…”

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Clogging and jamming transitions in periodic obstacle arrays

Nguyen

Reichhardt

2017

Phys. Rev. E

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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.A loose collection of particles such as grains or bubbles can exhibit a transition from a flowing liquidlike state to a non-flowing or jammed state as a function of increasing density, where the density φ j at which the system jams is referred to as Point J 1-3 . One system in which jamming has been extensively studied is a bidisperse twodimensional (2D) packing of frictionless disks, where the area faction covered by the disks at Point J is approximately φ = 0.84, and where the system density is uniform at the jamming transition 1,2,4 . Related to jamming is the phenomenon of clogging, as observed in the flow of grains 5-8 or bubbles 9 through an aperture at the tip of a hopper. The clogging transition is a probabilistic process in which, for a fixed grain size, the probability of a clogging event occurring during a fixed time interval increases with decreasing aperture size. A general question is whether there are systems that can exhibit features of both jamming and clogging. For example, such combined effects could appear in a system containing quenched disorder such as pinning or obstacles where jammed or clogged configurations can be created by a combination of particles that are directly immobilized in a pinning site as well as other particles that are indirectly immobilized through contact with obstacles or pinned particles. In many systems where pinning effects arise, such as for superconducting vortices or charged particles, the particle-particle interactions are long range, meaning that there is no well defined areal coverage density 10 at which the system can be said to jam, so a more ideal system to study is an assembly of hard disks with strictly short range particle-particle interactions. Previous studies have considered the effect of a random pinning landscape on transport in a 2D sample of bidisperse hard disks 11 , while in other work on the effect of obstacles, the density at which jamming occurs decreases when the number of pinning sites or obstacles increases 12,13 .Here we examine a 2D system of bidisperse frictionless disks flowing through a square periodic obstacle array composed of immobile disks with an obstacle lattice constant of a. The total disk density, defined as the area coverage of the mobile disks and the obstacl...

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“…In contrast to periodic structures, random porous media typically also possess stagnant parts where the flow almost vanishes. Such stagnant parts are known to strongly influence the particle transport and dispersion [37][38][39]. Moreover, it has been observed that stagnant parts lead to the formation of vortices in viscoelastic fluids [40].…”

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Enhanced dispersion by elastic turbulence in porous media

Scholz¹,

Wirner²,

Gomez-Solano³

et al. 2014

EPL

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-We experimentally investigate hydrodynamic dispersion in elastic turbulent flows of a semi-dilute aqueous polymer solution within a periodic porous structure at ultra-low Reynolds numbers < 10 −3 by particle tracking velocimetry. Our results indicate that elastic turbulence can be characterized by an effective dispersion coefficient which exceeds that of Newtonian liquids by several orders of magnitude and grows non-linearly with the Weissenberg number Wi. Contrary to laminar flow conditions, the velocity field, and thus the shear rate, is not proportional to the flow rate and becomes asymmetric at high Wi.Introduction. -Turbulent flow is characterized by unsteady velocity fields which suddenly vary in space and time. For Newtonian liquids, this regime is reached for high Reynolds numbers Re, where inertial effects dominate over viscous forces. In contrast, for viscoelastic fluids, turbulent flow at arbitrarily small Re numbers, usually referred to as elastic turbulence [1], can be observed. Such fluids are characterized by an elastic response, e.g. due to the entanglement and the dynamics of polymer chains [2]. The degree of elastic effects can be described by the dimensionless Weissenberg number Wi = λ ·γ, which quantifies the anisotropic polymer alignment in the presence of shear [3]. Here, λ is the equilibrium polymer relaxation time andγ the shear rate of the flow. Accordingly, for Wi → 0 the response of the fluid to a sudden stress is purely viscous while for Wi > 0 an elastic short-time response is obtained. Since the polymer alignment not only depends on the instantaneous but also on the previous shear, this explains why a highly non-linear flow dependence on the shear strength is observed [2]. It has been experimentally demonstrated that above a critical Weissenberg number Wi c 1, elastic turbulence occurs [4]. Similar to inertial turbulence, this regime is characterized by an enhanced flow resistance and a power-law decay of the spectral power density [1,5,6]. This effect can be exploited to dramatically increase the mixing efficiency at small length scales and small Reynolds numbers (Re < 10 −4 ) in microfluidic devices [7,8].

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

Cited by 13 publications

References 30 publications

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

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

Clogging and jamming transitions in periodic obstacle arrays

Enhanced dispersion by elastic turbulence in porous media

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