Eur. Phys. J. B (2017) 90: 108
https://doi.org/10.1140/epjb/e2017-70597-6

Regular Article

The electrical conductance growth of a metallic granular packing

¹ Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Zemun, Belgrade, Serbia
² Faculty of Engineering, Trg D. Obradovića 6, 21000 Novi Sad, Serbia

^a e-mail: vrhovac@ipb.ac.rs

Received: 7 October 2016
Received in final form: 12 March 2017
Published online: 14 June 2017

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) = σ_∞ − ΔσE_α[ − (t/τ)^α ], where E_α 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 g_eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g_eff 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.