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Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

Nariaki Sakaï, Sébastien Moulinet, Frédéric Lechenault, and Mokhtar Adda-Bedia
Phys. Rev. Lett. 122, 168001 – Published 23 April 2019
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Abstract

We experimentally investigate the statistical behavior of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in a liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned from fully dispersed to crystallized as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behavior, where the granular pressure and the packing fraction are related through an equation of state. We obtain an expression of the equation of state allowing us to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behavior of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.

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  • Received 4 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.168001

© 2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Equations of stateFluid-particle interactionsGranular mixingNonequilibrium statistical mechanics
  1. Physical Systems
Granular fluidsSuspensions
Polymers & Soft MatterStatistical Physics & ThermodynamicsNonlinear Dynamics

Authors & Affiliations

Nariaki Sakaï1,*, Sébastien Moulinet1, Frédéric Lechenault1, and Mokhtar Adda-Bedia2

  • 1Laboratoire de Physique de l’Ecole Normale Supérieure, PSL Research University, Sorbonne University, CNRS, F-75231 Paris, France
  • 2Université de Lyon, Ecole Normale Supérieure de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France

  • *nariaki.sakai@lps.ens.fr

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Vol. 122, Iss. 16 — 26 April 2019

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Images

  • Figure 1
    Figure 1

    (a) Schematics of the experimental setup. (b)–(d) Snapshot of the system for a relative density contrast of Δρ/ρ=5.4% at rotation frequencies 0.2 Hz (b), 0.4 Hz (c), and 0.6 Hz (d).

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  • Figure 2
    Figure 2

    (a) Radial packing fraction for selected rotation frequencies 0.17  Hz<f<0.8  Hz at Δρ/ρ=5.4%. The horizontal line locates the maximum fully crystalline packing fraction ϕc. (b) Corresponding rescaled packing fraction profiles using the fitting function given by Eq. (3). (c) The fitting parameter λ as a function of ω=2πf and for different density contrasts. (d) Plot of λ rescaled using Eq. (5).

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  • Figure 3
    Figure 3

    Normalized granular pressure obtained from the mixture model for a range of frequencies and density contrasts. Black dotted line corresponds to the analytical expression for the pressure as given by Eq. (8). The inset shows the nonnormalized pressure in semilog scale.

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