Mathematical Modeling of Electrolyte Circulation in Cells with Planar Vertical Electrodes: II . Electrowinning Cells

Abstract

A mathematical model has been developed to predict the electrolyte velocity field, bubble distribution, current distribution: and mass-transfer rates in cells with vertical planar electrodes, one of which evolves gases. The mathematical model employed either the k-e or the k-l representation of turbulence. The predictions of the model were compared with experimental velocity measurements, carried out using a laser-Doppler velocimeter, on a laboratory cell; semi-quantitative agreement was obtained in the case of the k-l model when the bubble size was used as an adjustable parameter.Crude comparisons could be made between mass-transfer predictions and measurements of others.As described in Part I of this two-part paper, electrolyte flow has an effect on the performance of the cells employed in electrometallurgy. The effect is first on mass transfer (and thereby on limiting current and deposit morphology) and particle suspension. In the case of electrorefining cells, flow can be natural convection, driven b:~ solute concentration gradients. Such natural convection can also occur in electrowinning cells, as will be seen below, but a much stronger effect is circulation driven by gas bubbles evolved at an electrode. The bubbles evolved (see Fig. 1) at an anode rise through the electrolyte and by a "gas lift" effect (a reduction in effective electrolyte density in the region of high gas fraction resulting in a buoyancy of this region); upfiow of electrolyte occurs near the anode. Most of the gas bubbles disengage from the electrolyte at the electrolyte surface, and the electrolyte returns downward, sweeping with it some of the bubbles, particularly smaller ones.The bubble distribution, therefore, affects the flow field and is, in turn, itself a function of the flow, since the rise velocity of bubbles encountered in aqueous electrometallurgy is typically small, and, to a first approximation, the bubbles are carried along with the electrolyte. Furthermore, the bubble distribution has an effect on the effective conductivity of the electrolyte, which, in turn, leads to a nonuniform current distribution in the cell. The nonuniformity in the current results in nonuniform metal deposition at the cathode and also in nonuniformity in gas generation at the anode. The latter has an effect on the bubble distribution.The phenomena occurring in the cell are seen to be complex and interacting. This paper describes an attempt at mathematically simulating such phenomena. The results of such predictions are compared with experimental measurements of electrolyte velocities carried out on a laboratory cell. Finally, some predictions are made of the effect of varying cell parameters. Previous InvestigationsPart I of this two-part paper reviewed the topics of fluid flow and mass transfer in electrorefining cells. In the case of cells where gas is evolved at one (or both) electrodes, i.e., electrowinning cells, the bubbles can affect

Dynamic modelling of hydrogen evolution effects in the all-vanadium redox flow battery

“…A wide range of diameter values has been reported [14,15,47], and the full range is considered in this work: 25-100 m.…”

“…The formation and effects of gas bubble evolution on planar electrodes, particularly from H 2 evolution, has been investigated fairly extensively [14][15][16][17][18]. Analytical and numerical models have been developed, notably by Dahlkild and co-workers [19,20], Ziegler and Evans [15] and Mat and co-workers [21,22], all based on the multi-phase mixture (or 'drift-diffusion') model [23,24]. The same approach towards bubble formation and gas/liquid transport is adopted in this paper.…”

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“…The bubble diameter depends on various factors, including the electrolyte composition, current density and flow rate. A wide range of diameter values has been reported [19,33,34], from 25 to 100 m. In this work, a range of bubble diameter is considered.…”

“…The average (equivalent) diameter of the bubbles formed from gas evolution can range from 25 to 100 m, depending on the operating conditions [19,33,34]. Simulations were performed using values of d g = 25 m and d g = 100 m (to an equivalent SOC) with other parameter values as in the base case in which d g = 50 m (Figs.…”

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