Rounding of the localization transition in model porous media

Schnyder, Simon K.; Spanner, Markus; Höfling, Felix; Franosch, Thomas; Horbach, Jürgen

doi:10.1039/c4sm02334j

Cited by 37 publications

(46 citation statements)

References 56 publications

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“…Above a critical obstacle density, the test particle can no longer explore the whole environment but stays trapped and long-range transport is effectively suppressed. Höfling et al have observed that in two dimensions and close to the critical density diffusive and ballistic particles show the same subdiffusive motion in a random Lorentz gas [44,[47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Active Brownian particles moving in a random Lorentz gas

2017

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Abstract. Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study noninteracting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density η c the ABPs are trapped, their long-time diffusion below ηc is strongly influenced by the propulsion speed v 0. With increasing v0, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.

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Section: Introductionmentioning

confidence: 99%

Active Brownian particles moving in a random Lorentz gas

2017

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“…η = 0. Upon increasing the packing fraction the critical obstacle density decreases, and as a peculiarity in 2D systems a minimum emerges at η ≈ 0.5 and increases again for even higher packing fractions [76]. This feature is not present in the corresponding 3D analog [55].…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 76%

“…An equilibrated sample is quenched and acts as host structure for soft noninteracting tracer particles, see Figure 4. The first observation is that for an ideal gas of tracers in the canonical ensemble the localization transition is replaced by a rapid but smooth crossover [76]. This can be easily rationalized since for soft interactions the barriers introduced by the host structures are finite, therefore the question if a tracer meanders through the entire system or not is strongly energy-dependent.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%

“…In computer simulations the simplifying assumptions of independently distributed obstacles can be easily relaxed and the scenario of the transition can be compared to the scaling predictions as obtained for the idealized Lorentz model. In a recent case study [76] for 2D the overlapping hard obstacles were replaced first by a quenched hard-disk liquid and second by a quenched polydisperse matrix interacting via a Weeks-Chandler-Andersen potential. Figure 4 illustrates the three different cases as a tracer explores a frozen host structure.…”

Section: Quenched Host Structuresmentioning

confidence: 99%

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Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

Mandal

Spanner-Denzer

Leitmann

et al. 2017

Eur. Phys. J. Spec. Top.

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Abstract. We provide an overview of recent advances of the complex dynamics of particles in strong confinements. The first paradigm is the Lorentz model where tracers explore a quenched disordered host structure. Such systems naturally occur as limiting cases of binary glassforming systems if the dynamics of one component is much faster than the other. For a certain critical density of the host structure the tracers undergo a localization transition which constitutes a critical phenomenon. A series of predictions in the vicinity of the transition have been elaborated and tested versus computer simulations. Analytical progress is achieved for small obstacle densities. The second paradigm is a dense strongly interacting liquid confined to a narrow slab. Then the glass transition depends nonmonotonically on the separation of the plates due to an interplay of local packing and layering. Very small slab widths allow to address certain features of the statics and dynamics analytically.

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“…Boolean Models are well established models for porous materials from stochastic geometry [39][40][41]. There, porous structures are composed of overlapping grains with random position and orientation (i.e., points in a plane are chosen randomly in a Poisson point process).…”

Section: Boolean Modelsmentioning

confidence: 99%

Direct relations between morphology and transport in Boolean models

et al. 2015

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We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte-Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.

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Rounding of the localization transition in model porous media

Cited by 37 publications

References 56 publications

Active Brownian particles moving in a random Lorentz gas

Active Brownian particles moving in a random Lorentz gas

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

Direct relations between morphology and transport in Boolean models

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