Growth of Nodules in Copper Electrorefining: Numerical Simulation of Natural Convection
Authors: Miyamoto Masayuki , Kitada Atsushi , Fukami Kazuhiro , Murase Kuniaki 
Published: December 2020

It is well known that copper can be electrodeposited with 100 % current efficiency without hydrogen evolution. In modern copper electrorefining process, however, the current utilization rate for copper electrorefining is generally 93-98 %. This is because nodulation occurs on cathode to cause short circuits and lose currents [1]. In other words, when nodules on the cathode grow to reach anode, current can flow but electrochemical reaction can not occur. There are various studies on the mechanism of nodule formation [2], and it is considered that suspended particles (e.g. floating slime) adhering to the cathode are an origin of nodule formation or nodule outbreak (see Fig. 1a).
Previously we investigated the effect of current concentration on a nodule by experiments and numerical simulations [3-5]. Based on the secondary current distribution model, i.e. without considering the effect of natural convection, it was found that the experimental growth rate cannot be explained by the effect of current concentration on nodules only.
Upward and downward natural convection occurs near the cathode and anode, respectively, as the density of the electrolyte solution near the electrode changes due to electrolysis (see Fig. 1a). Although natural convection can affect mass transfer, its contribution to the nodule formation has not been clarified. In this study, we focused on the natural convection as a factor for nodule growth in the early stages of nodule formation or after nodule outbreak.
We performed numerical simulations based on the tertiary current distribution model. Using the FEM simulation software COMSOL Multiphysics®, we calculated the natural convection behavior and the cupric ion concentration distribution. Cylindrical protrusions were considered to mimic the nodules. The partially simplified governing equations for electrochemical model, mass transfer and computed fluid dynamics (CFD) were solved simultaneously (see Fig. 2). In CFD, laminar flow was assumed. The calculation was performed in 3D area of the electrolyte solution between the single pair of vertical anode and cathode plates.
Figures 1b and 1c confirmed that the flow behaviors changed as a function of the protrusion length. When the protrusion length was 0.2 mm or less, natural convection along the cathode surface flowed over the protrusion. By contrast, when it was about 0.5 mm or more, the flow was divided into both sides of the protrusion, implying that natural convection is weakened at the protrusion tip. It is also notable that the simulated thickness of the diffusion layer at the protrusion tip decreased as the protrusion length increased. Thus, as the protrusion length increases, more Cu2+ ions are supplied by diffusion at the protrusion tip. This effect may promote the nodule growth above a certain size under natural convection.
[1] M. E. Schlesinger, M. J. King, K. C. Sole and W. G. Davenport, Extractive metallurgy of copper 5th, Elsevier (2011), pp. 251-279.
[2] T. N. Andersen, C. H. Pitt and L. S. Livingston, J. Appl. Electrochem., 13(4), 429 (1983).
[3] K. Adachi, Y. Nakai, A. Kitada, K. Fukami and K. Murase, TMS Annual Meeting & Exhibition, Springer, Cham (2018), pp. 215-222.
[4] Y. Nakai, K. Adachi, A. Kitada, K. Fukami and K. Murase, TMS Annual Meeting & Exhibition, Springer, Cham (2018), pp. 319-323.
[5] K. Adachi, Y. Nakai, S. Mitsuno, M. Miyamoto, A. Kitada, K. Fukami and K. Murase, Journal of MMIJ (in Japanese), 136(2), 8 (2020).

Figure 1