Unsteady natural convection and mass transfer in copper electrolysis with a supporting electrolyte

Abstract

A two-dimensional mathematical model for buoyancy-driven flow and mass transfer in a rectangular cell for copper electrolysis is proposed. The cell contains an excess of sulfuric acid as a supporting electrolyte. The electrodes are placed vertically and the electric current density along them is assumed to be constant and uniform. Effects of migration are accounted for in the laws for conservation of mass. A set of coupled nonlinear partial differential equations for describing the electrolysis is derived, and solved by numerical methods. It is shown that, after an initial and rather short period of time, the electrolyte becomes vertically stratified, with light electrolyte at the top and heavy electrolyte at the bottom of the enclosure. Thereafter, the system evolves slowly on a long time scale. The concentrations of the cupric and the hydrogen ions decrease in the upward and the downward directions respectively. Strong horizontal gradients of concentration appear in boundary layers adjacent to the electrodes. Electrolyte motion is confined to vertical and horizontal boundary layers on the solid walls of the container. The electrolyte in the core region is practically stagnant. Although Sc ⪢ 1 and D 2 ⪢ D 1, the vertical boundary layers for the velocity and the concentration fields have the same thicknesses. It is also demonstrated that the hydrogen ions carry the major part of the electric current. Moreover, and perhaps somewhat unexpectedly, it is shown that, at least for intermediate values of copper sulfate concentration ( c * 1/ c * 2 ≈ 0.3 as is the case dealt with in this work), migration plays a more important role than diffusion in the transport of the minority ions (Cu 2+).