Analysis Based on Boundary Layer Theory of Natural Convection near Electrodes

In an electrolysis tank where electrorefining or electrowinning is performed, differences in the local density of the electrolyte due to variations in ion concentration bring about natural convection near each electrode. This natural convection affects the supply of metal ions from the bulk solution to the cathode surface and the movement of ionic species generated at the anode surface. This paper describes calculation methods that are based on boundary layer theory and have been proposed in the past to analyze natural convection caused by the ion concentration distribution in an electrolyte. The boundary layer theory makes it possible to understand the diffusion-limited current density at the cathode by linking it to the concentration of metal ions in the electrolytic bath and the physical properties of the electrolyte. First, we introduce a method of converting the boundary layer equations from partial differential equations into ordinary differential equations using similarity variables, and then derive theoretical formula for the flow velocity of natural convection and the diffusion-limited current density at the cathode with the help of numerical calculations. Furthermore, we derive a formula for estimating the diffusion-limiting current density from the size of the electrode and the physical properties of the electrolyte using dimensional analysis, which is widely used in fluid mechanics. Next, we will explain the von Kármán-Pohlhausen integration method as another approach for analyzing the flow velocity of natural convection and current density distribution. Experimental methods for observing the boundary layer and a calculation model improved for application to electrolysis at current densities below the diffusion limit are also presented.