The electrical conductance growth of a metallic granular packing

  • Zorica M. Jakšić
  • Milica Cvetković
  • Julija R. Šćepanović
  • Ivana Lončarević
  • Ljuba Budinski-Petković
  • Slobodan B. Vrhovac
Regular Article
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Abstract

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σΔσEα[ − (t/τ)α ], where Eα denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration geff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity geff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Zorica M. Jakšić
    • 1
  • Milica Cvetković
    • 1
  • Julija R. Šćepanović
    • 1
  • Ivana Lončarević
    • 2
  • Ljuba Budinski-Petković
    • 2
  • Slobodan B. Vrhovac
    • 1
  1. 1.Institute of Physics Belgrade, University of BelgradeBelgradeSerbia
  2. 2.Faculty of EngineeringNovi SadSerbia

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