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Ben-Zeev S, Goren L, Toussaint R, Aharonov E. Drainage explains soil liquefaction beyond the earthquake near-field. Nat Commun 2023; 14:5791. [PMID: 37758695 PMCID: PMC10533503 DOI: 10.1038/s41467-023-41405-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 09/04/2023] [Indexed: 09/29/2023] Open
Abstract
Earthquake-induced soil-liquefaction is a devastating phenomenon associated with loss of soil rigidity due to seismic shaking, resulting in catastrophic liquid-like soil deformation. Traditionally, liquefaction is viewed as an effectively undrained process. However, since undrained liquefaction only initiates under high energy density, most earthquake liquefaction events remain unexplained, since they initiate far from the earthquake epicenter, under low energy density. Here we show that liquefaction can occur under drained conditions at remarkably low seismic-energy density, offering a general explanation for earthquake far-field liquefaction. Drained conditions promote interstitial fluid flow across the soil during earthquakes, leading to excess pore pressure gradients and loss of soil strength. Drained liquefaction is triggered rapidly and controlled by a propagating compaction front, whose velocity depends on the seismic-energy injection rate. Our findings highlight the importance of considering soil liquefaction under a spectrum of drainage conditions, with critical implications for liquefaction potential assessments and hazards.
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Affiliation(s)
- Shahar Ben-Zeev
- Institute of Earth Sciences, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel.
- University of Strasbourg, CNRS, ENGEES, Institut Terre & Environnement de Strasbourg, UMR7063, F-67000, Strasbourg, France.
| | - Liran Goren
- The Department of Earth and Environmental Sciences, Ben-Gurion University of the Negev, 84105, Negev, Israel
| | - Renaud Toussaint
- University of Strasbourg, CNRS, ENGEES, Institut Terre & Environnement de Strasbourg, UMR7063, F-67000, Strasbourg, France
- PoreLab, the Njord Centre, Department of Physics, University of Oslo, P.O. Box 1048 Blindern, NO-0316, Oslo, Norway
| | - Einat Aharonov
- Institute of Earth Sciences, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel
- Departments of Geosciences and Physics, The Njord Centre, University of Oslo, Oslo, Norway
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2
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Maier ML, Patel RA, Prasianakis NI, Churakov SV, Nirschl H, Krause MJ. Coupling of multiscale lattice Boltzmann discrete-element method for reactive particle fluid flows. Phys Rev E 2021; 103:033306. [PMID: 33862794 DOI: 10.1103/physreve.103.033306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 03/04/2021] [Indexed: 11/07/2022]
Abstract
Reactive particulate systems are of prime importance in varieties of practical applications in process engineering. As an example this study considers extraction of phosphorous from waste water by calcium silicate hydrate particles in the P-RoC process. For such systems modeling has a large potential to help to optimize process conditions, e.g., particle-size distributions or volume flows. The goal of this study is to present a new generic modeling framework to capture relevant aspects of reactive particle fluid flows using combined lattice Boltzmann method and discrete-element method. The model developed is Euler-Lagrange scheme which consist of three-components viz., a fluid phase, a dissolved reactive substance, and suspended particles. The fluid flow and reactive mass transport are described in a continuum framework using volume-averaged Navier-Stokes and volume-averaged advection-diffusion-reaction equations, respectively, and solved using lattice Boltzmann methods. The volume-averaging procedure ensures correctness in coupling between fluid flow, reactive mass transport, and particle motion. The developed model is validated through series of well-defined benchmarks. The benchmarks include the validation of the model with experimental data for the settling of a single particle in a cavity filled with water. The benchmark to validate the multi-scale reactive transport involves comparing the results with a resolved numerical simulation. These benchmarks also prove that the proposed model is grid convergent which has previously not been established for such coupled models. Finally, we demonstrate the applicability of our model by simulating a suspension of multiple particles in fluid with a dissolved reactive substance. Comparison of this coupled model is made with a one-way coupled simulation where the influence of particles on the fluid flow and the reactive solution transport is not considered. This elucidates the need for the two-way coupled model.
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Affiliation(s)
- Marie-Luise Maier
- Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.,Lattice Boltzmann Research Group, KIT, Karlsruhe, Germany
| | - Ravi A Patel
- Institute for Concrete Structures and Building Materials and materials testing laboratory (IMB/MPA), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.,formerly at Laboratory for Waste Management, Paul Scherrer Institute, Villigen, Switzerland
| | | | - Sergey V Churakov
- Laboratory for Waste Management, Paul Scherrer Institute, Villigen, Switzerland.,Institute of Geological Sciences, University of Berne, Switzerland
| | - Hermann Nirschl
- Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Mathias J Krause
- Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.,Lattice Boltzmann Research Group, KIT, Karlsruhe, Germany.,Institute for Applied and Numerical Mathematics, KIT, Karlsruhe, Germany
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3
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Eriksen FK, Toussaint R, Turquet AL, Måløy KJ, Flekkøy EG. Pressure evolution and deformation of confined granular media during pneumatic fracturing. Phys Rev E 2018; 97:012908. [PMID: 29448387 DOI: 10.1103/physreve.97.012908] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Indexed: 06/08/2023]
Abstract
By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity μ_{B} and displacement thresholds ∇[over ⃗]P_{c} evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η=2, where fractal dimensions are found between 1.5 and 1.6 for the patterns.
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Affiliation(s)
- Fredrik K Eriksen
- Institut de Physique du Globe de Strasbourg, Université de Strasbourg, EOST, Centre National de la Recherche Scientifique, 67084 Strasbourg, France
| | - Renaud Toussaint
- Institut de Physique du Globe de Strasbourg, Université de Strasbourg, EOST, Centre National de la Recherche Scientifique, 67084 Strasbourg, France
| | - Antoine Léo Turquet
- Institut de Physique du Globe de Strasbourg, Université de Strasbourg, EOST, Centre National de la Recherche Scientifique, 67084 Strasbourg, France
| | - Knut J Måløy
- PoreLab, Department of Physics, University of Oslo, P.O. Box 1074 Blindern, 0316 Oslo, Norway
| | - Eirik G Flekkøy
- PoreLab, Department of Physics, University of Oslo, P.O. Box 1074 Blindern, 0316 Oslo, Norway
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4
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Niebling MJ, Toussaint R, Flekkøy EG, Måløy KJ. Dynamic aerofracture of dense granular packings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061315. [PMID: 23367940 DOI: 10.1103/physreve.86.061315] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2011] [Revised: 09/28/2012] [Indexed: 06/01/2023]
Abstract
A transition in hydraulically induced granular displacement patterns is studied by means of discrete numerical molecular dynamics simulations. During this transition the patterns change from fractures and fingers to finely dispersed bubbles. The dynamics of the displacement patterns are studied in a rectangular Hele-Shaw cell filled with a dense but permeable two-dimensional granular layer. At one side of the cell the pressure of the compressible interstitial gas is increased. At the opposite side from the inlet of the cell a semipermeable boundary is located. This boundary is only permeable towards the gas phase while preventing grains from leaving the cell. The imposed pressure gradient compacts the grains. In the process we can identify and describe a mechanism that controls the transition of the emerging displacement patterns from fractures and fingers to finely dispersed bubbles as a function of the interstitial gas's properties and the characteristics of the granular phase.
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Affiliation(s)
- Michael J Niebling
- Department of Physics, University of Oslo, PO Box 1048, 0316 Oslo, Norway
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5
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Idler V, Sánchez I, Paredes R, Botet R. Reverse buoyancy in a vibrated granular bed: Computer simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:106. [PMID: 23096151 DOI: 10.1140/epje/i2012-12106-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2012] [Revised: 09/11/2012] [Accepted: 10/05/2012] [Indexed: 06/01/2023]
Abstract
We have performed molecular dynamics simulations of an intruder in a vibrated granular bed including interstitial fluid effects to account for the phenomenon of reverse buoyancy. We show that our model is able to reproduce the overall behaviour observed by previous experimental works and is the first finite-elements simulation to show the sinking of intruders lighter than the granular bed. To further advance our comprehension of this phenomenon, we studied the motion of the intruders in a single vibration cycle with respect to the bottom of the granular column, finding a substantial qualitative difference for heavy and light intruders and we compare these results with experiments using fine-sized glass beads. We show that, though heavy intruders seem unaffected by the force due to the fluid, the effect on light intruders is remarkable.
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Affiliation(s)
- Vladimir Idler
- Departamento de Física, Universidad Simón Bolívar, Apartado 89000, Caracas 1080-A, Venezuela.
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6
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Chareyre B, Cortis A, Catalano E, Barthélemy E. Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings. Transp Porous Media 2012. [DOI: 10.1007/s11242-012-0057-2] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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7
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Chareyre B, Cortis A, Catalano E, Barthélemy E. Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings. Transp Porous Media 2011. [DOI: 10.1007/s11242-011-9915-6] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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8
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Guttenberg N. Approximate hard-sphere method for densely packed granular flows. Phys Rev E 2011; 83:051306. [PMID: 21728524 DOI: 10.1103/physreve.83.051306] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2010] [Revised: 04/18/2011] [Indexed: 11/07/2022]
Abstract
The simulation of granular media is usually done either with event-driven codes that treat collisions as instantaneous but have difficulty with very dense packings, or with molecular dynamics (MD) methods that approximate rigid grains using a stiff viscoelastic spring. There is a little-known method that combines several collision events into a single timestep to retain the instantaneous collisions of event-driven dynamics, but also be able to handle dense packings. However, it is poorly characterized as to its regime of validity and failure modes. We present a modification of this method to reduce the introduction of overlap error, and test it using the problem of two-dimensional (2D) granular Couette flow, a densely packed system that has been well characterized by previous work. We find that this method can successfully replicate the results of previous work up to the point of jamming, and that it can do so a factor of 10 faster than comparable MD methods.
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Affiliation(s)
- Nicholas Guttenberg
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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9
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Burgener T, Kadau D, Herrmann HJ. Simulation of particle mixing in turbulent channel flow due to intrinsic fluid velocity fluctuation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:066301. [PMID: 21797471 DOI: 10.1103/physreve.83.066301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2010] [Indexed: 05/31/2023]
Abstract
We combine a discrete-element-method simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We find a linear increase of the mixing zone with the length of the pipe. Flows at different Reynolds number are studied. Below a critical Reynolds number at the Taylor microscale of around Rc ≈ 300 the mixing rate is strongly dependent on the Reynolds number. Above Rc the mixing rate stays nearly constant.
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Affiliation(s)
- Thomas Burgener
- Computational Physics, IfB, ETH-Hönggerberg, Schafmattstrasse 6, CH-8093 Zürich, Switzerland.
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10
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Niebling MJ, Flekkøy EG, Måløy KJ, Toussaint R. Sedimentation instabilities: impact of the fluid compressibility and viscosity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051302. [PMID: 21230468 DOI: 10.1103/physreve.82.051302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2010] [Indexed: 05/30/2023]
Abstract
The effect of an interstitial fluid on the mixing of sedimenting grains is studied numerically in a closed rectangular Hele-Shaw cell. We investigate the impact of the fluid compressibility and fluid viscosity on the dynamics and structures of the granular Rayleigh-Taylor instability. First we discuss the effect of the fluid compressibility on the initial fluid pressure evolution and on the dynamics of the particles. Here, the emerging patterns do not seem highly affected by the compressibility change studied. To characterize the patterns and motion the combined length of the particle trajectories in relation to the movement of the center of mass is analyzed, and the separation of particle pairs is measured as a function of the fluid viscosity.
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Affiliation(s)
- Michael J Niebling
- Department of Physics, University of Oslo, PO Box 1048, 0316 Oslo, Norway
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11
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Goren L, Aharonov E, Sparks D, Toussaint R. Pore pressure evolution in deforming granular material: A general formulation and the infinitely stiff approximation. ACTA ACUST UNITED AC 2010. [DOI: 10.1029/2009jb007191] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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12
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Niebling MJ, Flekkøy EG, Måløy KJ, Toussaint R. Mixing of a granular layer falling through a fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011301. [PMID: 20866605 DOI: 10.1103/physreve.82.011301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2009] [Revised: 05/18/2010] [Indexed: 05/29/2023]
Abstract
We analyze the granular Rayleigh-Taylor instability of densely packed grains immersed in a compressible or an incompressible fluid using numerical simulations and two types of experiments. The simulations are based on a two-dimensional (2D) molecular dynamics model and the experiments have been carried out in systems of grains immersed in water/glycerol (incompressible fluid) and in air (compressible fluid). The variation of the interstitial fluid is shown to generate different dynamical patterns and mixing properties of the granular systems. The results have been quantified using 2D autocorrelation functions, the power spectrum of the velocity field and velocity field histograms. Excellent agreement is found between the numerical simulations and the experiments.
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Affiliation(s)
- Michael J Niebling
- Department of Physics, University of Oslo, PO Box 1048, 0316 Oslo, Norway
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13
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Vinningland JL, Johnsen Ø, Flekkøy EG, Toussaint R, Måløy KJ. Size invariance of the granular Rayleigh-Taylor instability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041308. [PMID: 20481718 DOI: 10.1103/physreve.81.041308] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2008] [Revised: 02/18/2010] [Indexed: 05/29/2023]
Abstract
The size scaling behavior of the granular Rayleigh-Taylor instability [J. L. Vinningland, Phys. Rev. Lett. 99, 048001 (2007)] is investigated experimentally, numerically, and theoretically. An upper layer of grains displaces a lower gap of air by organizing into dense fingers of falling grains separated by rising bubbles of air. The dependence of these structures on the system and grain sizes is investigated. A spatial measurement of the finger structures is obtained by the Fourier power spectrum of the wave number k. As the size of the grains increases the wave number decreases accordingly which leaves the dimensionless product of wave number and grain diameter, dk, invariant. A theoretical interpretation of the invariance, based on the scaling properties of the model equations, suggests a gradual breakdown of the invariance for grains smaller than approximately 70 microm or greater than approximately 570 microm in diameter.
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Affiliation(s)
- Jan Ludvig Vinningland
- Advanced Materials and Complex Systems, Department of Physics, University of Oslo, P.0. Box 1048, 0316 Oslo, Norway.
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14
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Idler V, Sánchez I, Paredes R, Gutiérrez G, Reyes LI, Botet R. Three-dimensional simulations of a vertically vibrated granular bed including interstitial air. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051301. [PMID: 19518443 DOI: 10.1103/physreve.79.051301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2009] [Indexed: 05/27/2023]
Abstract
We present a numerical study of the effect of interstitial air on a vertically vibrated granular bed within one period of oscillation. We use a three-dimensional molecular-dynamics simulation including air phenomenologically. The simulations are validated with experiments made with spherical glass beads in a rectangular container. After validation, results are reported for a granular column of 9000 grains and approximately 50 layers deep (at rest), agitated with a sinusoidal excitation with maximal acceleration 4.7g at 11.7 Hz. We report the evolution of density, granular temperature, and coordination number within a vibration cycle, and the effect of interstitial air on those parameters. In three-dimensional computer simulations we found that the presence of interstitial air can promote the collective motion of the granular material as a whole.
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Affiliation(s)
- V Idler
- Centro de Física, Instituto Venezolano de Investigaciones Científicas, Apartado Postal 21827, Caracas 1020-A, Venezuela.
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15
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Knudsen HA, Werth JH, Wolf DE. Failure and success of hydrodynamic interaction models. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 27:161-170. [PMID: 18810516 DOI: 10.1140/epje/i2008-10368-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Accepted: 08/07/2008] [Indexed: 05/26/2023]
Abstract
In suspensions with charged particles, electrostatic forces and hydrodynamic interactions are both important to describe the system. We study different models of hydrodynamic interaction for monopolarly charged particles in a non-polar liquid. In this case, there is no screening of the Coulomb repulsion, so the repulsion between all pairs must be taken into account. The particles are expected to drift away from each other, however at a lower rate when hydrodynamic interaction between the particles is taken into account. Existing, frequently used models of hydrodynamic interactions tend to overestimate the slowing down of the charged particles, even to the extent that the particles effectively attract each other. This is demonstrated for some selected particle setups. We find that these anomalies even occur in dilute systems, if they contain sufficiently many particles. We explain why these anomalies can be avoided by an approach, in which the superposition of interactions is done in the friction tensor instead of the mobility tensor.
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Affiliation(s)
- H A Knudsen
- Department of Physics, University of Oslo, P.O. Box 1048, NO-0316, Oslo, Norway
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16
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Royer JR, Corwin EI, Conyers B, Flior A, Rivers ML, Eng PJ, Jaeger HM. Birth and growth of a granular jet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011305. [PMID: 18763946 DOI: 10.1103/physreve.78.011305] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2007] [Indexed: 05/26/2023]
Abstract
The interaction between fine grains and the surrounding interstitial gas in a granular bed can lead to qualitatively new phenomena not captured in a simple, single-fluid model of granular flows. This is demonstrated by the granular jet formed by the impact of a solid sphere into a bed of loose, fine sand. Unlike jets formed by impact in fluids, this jet is actually composed of two separate components, an initial thin jet formed by the collapse of the cavity left by the impacting object stacked on top of a second, thicker jet which depends strongly on the ambient gas pressure. This complex structure is the result of an interplay between ambient gas, bed particles, and impacting sphere. Here we present the results of systematic experiments that combine measurements of the jet above the surface varying the release height, sphere diameter, container size, and bed material with x-ray radiography below the surface to connect the changing response of the bed to the changing structure of the jet. We find that the interstitial gas trapped by the low permeability of a fine-grained bed plays two distinct roles in the formation of the jet. First, gas trapped and compressed between grains prevents compaction, causing the bed to flow like an incompressible fluid and allowing the impacting object to sink deep into the bed. Second, the jet is initiated by the gravity driven collapse of the cavity left by the impacting object. If the cavity is large enough, gas trapped and compressed by the collapsing cavity can amplify the jet by directly pushing bed material upwards and creating the thick jet. As a consequence of these two factors, when the ambient gas pressure is decreased, there is a crossover from a nearly incompressible, fluidlike response of the bed to a highly compressible, dissipative response. Compaction of the bed at reduced pressure reduces the final depth of the impacting object, resulting in a smaller cavity and in the demise of the thick jet.
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Affiliation(s)
- John R Royer
- James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
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17
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Maionchi DO, Morais AF, Costa Filho RN, Andrade JS, Herrmann HJ. Model for erosion-deposition patterns. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061402. [PMID: 18643261 DOI: 10.1103/physreve.77.061402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2007] [Revised: 04/15/2008] [Indexed: 05/26/2023]
Abstract
We investigate through computational simulations with a pore network model the formation of patterns caused by erosion-deposition mechanisms. In this model, the geometry of the pore space changes dynamically as a consequence of the coupling between the fluid flow and the movement of particles due to local drag forces. Our results for this irreversible process show that the model is able to reproduce typical natural patterns caused by well-known erosion processes. Moreover, we observe that, within a certain range of porosity values, the grains form clusters that are tilted with respect to the horizontal with a characteristic angle. We compare our results to recent experiments for granular material in flowing water and show that they present a satisfactory agreement.
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Affiliation(s)
- D O Maionchi
- Departamento de Física, Universidade Federal de Ceará, Fortaleza-Ceará, Brazil
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18
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Johnsen Ø, Toussaint R, Måløy KJ, Flekkøy EG, Schmittbuhl J. Coupled air/granular flow in a linear Hele-Shaw cell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011301. [PMID: 18351844 DOI: 10.1103/physreve.77.011301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2007] [Indexed: 05/26/2023]
Abstract
We investigate experimentally the pattern formation process during injection of air in a noncohesive granular material confined in a linear Hele-Shaw cell. We characterize the features and dynamics of this pattern formation on the basis of fast image analysis and sensitive pressure measurements. Behaviors are classified using two parameters--injection pressure and plate opening--and four hydrodynamic regimes are defined. For some regions of the parameter space, flows of air and grains are shown to be strongly coupled and instable, and lead to channelization within the granular material with obvious large-scale permeability variations.
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Affiliation(s)
- Ø Johnsen
- Department of Physics, University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway
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19
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Vinningland JL, Johnsen O, Flekkøy EG, Toussaint R, Måløy KJ. Experiments and simulations of a gravitational granular flow instability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051306. [PMID: 18233651 DOI: 10.1103/physreve.76.051306] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2006] [Revised: 09/28/2007] [Indexed: 05/25/2023]
Abstract
An instability is observed as a layer of dense granular material positioned above a layer of air falls in a gravitational field [Phys. Rev. Lett. 99, 048001 (2007)]. A characteristic pattern of fingers emerges along the interface defined by the grains, and a transient coarsening of the structure is caused by a coalescence of neighboring fingers. The coarsening is limited by the production of new fingers as the separation of the existing fingers reaches a certain distance. The experiments and simulations presented are shown to be comparable both qualitatively and quantitatively. The characteristic inverse length scale of the structures, obtained as the mean of the solid fraction power spectrum, relaxes toward a stable value shared by the numerical and experimental data. Further, the response of the numerical model to changes in various model parameters is investigated. These parameters include the density of the grains, the shape of the initial air-grain interface, and the dissipation of the granular phase. Also, the growth rates of the bulk solid fraction and the air-grain interface are obtained from Fourier power spectra of the numerical data. This analysis reveals that the instability is never in a linear regime, not even initially.
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20
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Vinningland JL, Johnsen Ø, Flekkøy EG, Toussaint R, Måløy KJ. Granular Rayleigh-Taylor instability: experiments and simulations. PHYSICAL REVIEW LETTERS 2007; 99:048001. [PMID: 17678407 DOI: 10.1103/physrevlett.99.048001] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2006] [Indexed: 05/16/2023]
Abstract
A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.
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Johnsen O, Toussaint R, Måløy KJ, Flekkøy EG. Pattern formation during air injection into granular materials confined in a circular Hele-Shaw cell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011301. [PMID: 16907083 DOI: 10.1103/physreve.74.011301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2005] [Indexed: 05/11/2023]
Abstract
We investigate the dynamics of granular materials confined in a radial Hele-Shaw cell, during central air injection. The behavior of this granular system, driven by its interstitial fluid, is studied both experimentally and numerically. This allows us to explore the associated pattern formation process, characterize its features and dynamics. We classify different hydrodynamic regimes as function of the injection pressure. The numerical model takes into account the interactions between the granular material and the interstitial fluid, as well as the solid-solid interactions between the grains and the confining plates. Numerical and experimental results are comparable, both to reproduce the hydrodynamical regimes experimentally observed, as well as the dynamical features associated to fingering and compacting.
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Affiliation(s)
- O Johnsen
- Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo, Norway
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Milburn RJ, Naylor MA, Smith AJ, Leaper MC, Good K, Swift MR, King PJ. Faraday tilting of water-immersed granular beds. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:011308. [PMID: 15697596 DOI: 10.1103/physreve.71.011308] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2004] [Revised: 11/17/2004] [Indexed: 05/24/2023]
Abstract
Under low-frequency vertical vibration, a system of fine grains within a fluid is observed to tilt or to form piles, an effect studied by Faraday for grains in air. Here, we investigate the physical mechanisms behind Faraday tilting in a bed of vertically vibrated bronze spheres fully immersed in water. Experimental observations of surface tilting and bulk convection are compared with the results of molecular dynamics simulations in which the water is treated as an incompressible fluid. Our simulations reproduce the main features observed experimentally. Most tilt construction is shown to be due to horizontal fluid flow within the bed, principally occurring when the gap between the bed and the supporting platform is close to a maximum. Tilt destruction occurs by granular surface flow and in the bulk of the bed at times during each vibratory cycle close to and just later than bed impact. Destruction becomes more important for higher values of frequency and vibration amplitude, leading to lower tilt angles, partial tilting, or the symmetric domed geometry of Muchowski flow.
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Affiliation(s)
- R J Milburn
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Biswas P, Sánchez P, Swift MR, King PJ. Numerical simulations of air-driven granular separation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:050301. [PMID: 14682780 DOI: 10.1103/physreve.68.050301] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2003] [Revised: 07/31/2003] [Indexed: 05/24/2023]
Abstract
Recently it has been shown that binary mixtures of equal-sized fine granular materials exhibit spontaneous separation under vertical vibration in the presence of air [Science 295, 1877 (2002)]. Here we describe a model of this behavior based on soft-sphere molecular dynamics coupled to the motion of the surrounding air. It exhibits many of the features observed experimentally including almost complete separation of the components into well defined regions with extremely sharp boundaries. The basic separation mechanism is robust and insensitive to many of the model parameters. Our results show that the forced flow of air through the bed, induced by vibration of the container, is responsible for this form of separation.
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Affiliation(s)
- Parthapratim Biswas
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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Burtally N, King PJ, Swift MR. Spontaneous air-driven separation in vertically vibrated fine granular mixtures. Science 2002; 295:1877-9. [PMID: 11884749 DOI: 10.1126/science.1066850] [Citation(s) in RCA: 127] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
We report the observation of the spontaneous separation of vertically vibrated mixtures of fine bronze and glass spheres of similar diameters. At low frequencies and at sufficient vibrational amplitudes, a sharp boundary forms between a lower region of glass and an upper region of the heavier bronze. The boundary undergoes various oscillations, including periodic tilting motion, but remains extremely sharp. At higher frequencies, the bronze separates as a mid-height layer between upper and lower glass regions, and the oscillations are largely absent. The mechanism responsible for the separation can be traced to the effect of air on the granular motion.
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Affiliation(s)
- N Burtally
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
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