Pressure wave propagation in a granular bed

Hostler, Stephen R.; Brennen, Christopher E.

doi:10.1103/physreve.72.031303

Cited by 48 publications

(43 citation statements)

References 24 publications

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“…This observation that particle contacts can change during sound propagation violates the well-bonded assumption of effective medium theory [1] because the connectivity of the network transiently changes due to the passage of the wave. Similar, but permanent, changes to the force network were presumably at work in experiments where minute thermal expansion [24] or consolidation of loose packs [25] modified the signal coda. In spite of the inherent nonlinearity of such events, we nonetheless observe an approximately linear response in the average propagation amplitude of the system.…”

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confidence: 99%

Sound propagation and force chains in granular materials

Owens

Daniels

2011

EPL

106

113

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Abstract. -Granular materials are inherently heterogeneous, leading to challenges in formulating accurate models of sound propagation. In order to quantify acoustic responses in space and time, we perform experiments in a photoelastic granular material in which the internal stress pattern (in the form of force chains) is visible. We utilize two complementary methods, high-speed imaging and piezoelectric transduction, to provide particle-scale measurements of both the amplitude and speed of an acoustic wave in the near-field regime. We observe that the wave amplitude is on average largest within particles experiencing the largest forces, particularly in those chains radiating away from the source, with the force-dependence of this amplitude in qualitative agreement with a simple Hertzian-like model of particle contact area. In addition, we are able to directly observe rare transient force chains formed by the opening and closing of contacts during propagation. The speed of the leading edge of the pulse is in quantitative agreement with predictions for onedimensional chains, while the slower speed of the peak response suggests that it contains waves which have travelled over multiple paths even within just this near-field region. These effects highlight the importance of particle-scale behaviors in determining the acoustical properties of granular materials.Introduction. -Sound propagation in granular materials differs from propagation in ordinary elastic materials in that there is a poor separation of length scales, particularly manifest in the branching networks of force chains which transmit stresses between particles. Continuum models [1][2][3], including effective medium theory (EMT), have failed to quantitatively describe important features such as the dependence of the sound speed on pressure [4][5][6]. Particle-scale changes in the coordination number and force chains are likely responsible for important deviations from these models, and have been the focus of numerical simulations on model amorphous systems near jamming, where soft modes are important [7][8][9].Hertzian contact theory underlines models of sound propagation, whether as the interaction potential between particles in discrete element simulations [10] or in the calculation of an effective bulk modulus in EMT [1]. The contact force f between two particles is given by an equation of the form f ∝ δ β , where δ is the distance each particle is compressed and the exponent β depends on the particle geometry. Two common idealized situations are β = 3/2 for spheres and β = 1 for cylinders. The contact area a between the particles, which in EMT are permanently bonded, has a force dependence given by a ∝ f

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confidence: 99%

Sound propagation and force chains in granular materials

Owens

Daniels

2011

EPL

106

113

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“…Liu [12] interpret this as evidence that a small number of force chains carry most of the vibration. In agitated beds, Hostler and Brennen [13] reach a similar conclusion that pressure waves and stress are propagated along ephemeral chains of particles.…”

Section: Introductionmentioning

confidence: 82%

“…If a granular chain subject to an impact at one end remains connected on a time scale greater than the binary collision time, we expect Eq. (13) to capture the propagation of energy on wavelengths > d. …”

Section: Kinematic Restitutionmentioning

confidence: 99%

“Phonon” conductivity along a column of spheres in contact

Louge

2011

Granular Matter

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We calculate energy conduction and dissipation along a column of spheres linked with linear springs and dashpots to illustrate how grains in simultaneous contact may produce a constant "phonon" conductivity of granular fluctuation kinetic energy. In the core of dense unconfined granular flows down bumpy inclines, we show that phonon conductivity dominates its counterpart calculated from gas kinetic theory. However, the volume dissipation rate of phonon fluctuation energy is of the same order as the kinetic theory prediction.

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“…This small disturbance was observed to create large variations in the tail of the transmitted sound pulse, likely due to having altered the force chain network. Similarly, Hostler and Brennen [5] argue, based on experiments in three-dimensional systems, that the specific arrangement of force chains affects sound propagation. Their system was either prepared in a loose, unconsolidated state, or shaken to consolidate the system.…”

Section: Introductionmentioning

confidence: 99%

“…Two sets of prior experiments [4,5] have inferred their importance even though the chains themselves were not visible. Liu and Nagel [4] placed a resistor within a granular pack and disturbed the configuration by thermally expanding the resistor.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporally Resolved Acoustics in a Photoelastic Granular Material

Owens¹,

Couvreur²,

Daniels³

2009

AIP Conference Proceedings

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Abstract. The effect of the force chain network on sound propagation in a granular material is poorly understood. To quantitatively study these effects, we perform acoustics experiments in a two dimensional photoelastic granular material in which force chains are visible. We send acoustic pulses into the material from a point source and measure the effects of this pulse via two methods: accelerometers within individual grains and movies which produce spatiotemporally resolved measurements of the acoustic propagation.

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Pressure wave propagation in a granular bed

Cited by 48 publications

References 24 publications

Sound propagation and force chains in granular materials

Sound propagation and force chains in granular materials

“Phonon” conductivity along a column of spheres in contact

Spatiotemporally Resolved Acoustics in a Photoelastic Granular Material

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