An electrochemical model of the induced‐polarization phenomenon in disseminated sulfide ores

Abstract

A disseminated sulfide ore is idealized by a system of electronically conducting metallic spheres randomly dispersed in an electrolytically conducting host medium. When an external electric field is applied, the transport of cations and anions in the interphase region near the metal‐electrolyte interface will involve both drift and diffusion flux densities. The flow of ions to or from the metal‐electrolyte interface causes an excess or deficit of inactive ions to accumulate there, since the metal is neither a source nor sink for these ions. These inactive ions are loosely held to the metallic particles by image forces, and concentration gradients build up which oppose the migration of these ions due to electric fields. In addition to the inactive anions and cations, a minor concentration of active cations is assumed to exist in the electrolytic medium, and the electric fields at the electrolyte‐metal interface cause these to engage in electrochemical reactions making possible charge transfer across the interface. Under these conditions, coupled partial differential equations describing the temporal and spatial variations in the concentrations of active and inactive ions can be derived by considering the net flux of cations and anions into a small test volume of the host medium. The variations are expressed as perturbations on the background concentrations and are found when the partial differential equations are solved using the Laplace transformation and separation of variables in spherical coordinates. The perturbation concentrations are Gouy‐Chapman types of diffuse distributions localized near the metal‐electrolyte interface with thickness on the order of the Debye screening length. The cloud of loosely held ions surrounding each metallic particle and the diffusion‐controlled charge transfer reaction at the interface are responsible for inducing a time‐ or frequency‐dependent electric dipole moment on each particle. With the assumption that no mutual interactions exist between these dipoles, the effective conductivity (in frequency domain) of an assemblage of metallic spheres residing in an electrolytic host medium can be found by using Maxwell’s formula. The resulting frequency dispersion in the effective conductivity is the basis of the induced‐polarization (IP) effect. Conductivity and resistivity spectra calculated from this electrochemical model are compared to laboratory measurements on synthetic metalliferous ores, and good fits with the experimental data are obtained by using physically reasonable values for the various parameters in the model.