Pseudo two-dimensional finite element models were developed to predict the hypochlorite (chloric(I)) (HOCl + OCl À ) production by electrolysis of near-neutral aqueous sodium chloride solution, in reactors with (a) an anode and cathode in the form of plates, and (b) a lead dioxide-coated graphite felt anode and titanium plate cathode. The model was used to investigate the feasibility of using a porous anode to achieve high single pass conversions in oxidising chloride ions. For the model reactor with planar anode, the effects of diffusion, migration and convection on the mass transport of the reacting species were considered, whereas with the porous anode, a supporting electrolyte (Na 2 SO 4 ) was notionally present to eliminate the migrational contribution to reactant transport. For an electrolyte flow rate of 10 À6 m 3 s À1 (Re = 10 for plate electrodes, Re porous = 0.76 for porous anode), a cell voltage of 3.0 V and an inlet NaCl of 100 mol m À3 , the single-pass conversion of Cl À was predicted to increase from 0.45 for the reactor with a planar anode to 0.81 for the reactor with a porous anode. For the same operating conditions, the overall current efficiency was also predicted to increase from 0.71 to 0.77 by replacing the plate with the porous anode. Keywords Hypochlorite Á Chloric(I) Á Chloride Á Modelling Á Porous electrode Notation A Specific surface area of porous electrode (m 2 m À3 ) C i Concentration of species i (mol m À3 ) C i,in Inlet concentration of species i (mol m À3 ) D i Diffusion coefficient of species i (m 2 s À1 ) d Distance between the planar anode and cathode (m) d f Fibre diameter (m) d h Hydraulic diameter of felt fibre (m) E k Equilibrium electrode potential of reaction k versus reference electrode (SHE) (V) F Faraday constant (C mol À1 ) j k Current density of reaction k (A m À2 ) j L Limiting current density (A m À2 ) j 0 Exchange current density (A m À2 ) k Standard heterogeneous rate constant coefficient (m s À1 ) k m Mass transport rate coefficient (m s À1 ) K Equilibrium constant (mol À1 dm 3 ) N i Superficial flux of species i (mol m À2 s À1 ) n Number of electrons involved in a reaction (-) R Universal gas constant (J mol À1 K À1 ) Re Reynolds number for reactor with planar electrodes (vd/m) (-) Re porous Reynolds number for porous electrode (v eff d h /m) r k Rate of homogeneous reaction k (mol m 3Linear electrolyte velocity (m s À1 ) v eff Solution velocity in the empty cross-section area (m s À1 ) z i Number of charge on species i (-) iSubscript i refers to reacting species (-) kSubscript k refers to reactions (-)
A film model is presented for the analysis of mass transfer to a rotating hemispherical electrode when sinusoidal alternating current (AC) together with direct current (DC) are flowing across the electrode surface. The concentration of a diffusing ion is separated into two independent components: a constant DC component and a periodic AC component. The DC concentration is obtained by solving the steady‐state convective mass transport equation with the perturbation method. The periodic AC concentration distribution is analyzed by the solution to the one‐dimensional transient diffusion equation based on the concept of Nernst diffusion layer. The limiting AC current densities corresponding to a zero surface concentration of a reactive ion are investigated for various DC current densities and AC frequencies. The resulting periodic concentration overpotential wave and its phase shift with respect to the applied AC are examined. A comparison with a previous rigorous model indicates that the film model is a good approximation to the mass transfer calculation in the regimes of a dimensionless AC frequency K = (ω/Ω)Sc1/3 greater than 2 and less than 0.01.
One-dimensional steady-state models have been developed for the recovery of Pb(II) ions from lead-acid battery recycling plant effluent by simultaneous lead and lead dioxide deposition, including oxygen evolution/reduction and hydrogen evolution as loss reactions. Both monopolar and bipolar reactor with porous graphite electrodes were modelled, as a design aid for predicting spatial distributions of potentials, concentrations, current densities and efficiencies, as well as specific electrical energy consumptions and by-pass currents. Since the industrial effluent contains a large excess of supporting electrolyte (Na2SO4), the electrical migrational contribution to reactant transport rates was neglected and the current density-potential relationship was described by the Butler-Volmer equation, allowing for both kinetic and mass transport control. The models were implemented and the governing equations solved using commercial finite element software (FEMLAB). The effects were investigated of electrolyte velocity, applied cathode potential, dissolved oxygen concentration and inlet Pb(II) ion concentration on single-pass conversion, current efficiency and specific electrical energy consumptions. According to model predictions, de-oxygenation of the inlet process stream was found to be crucial to achieving acceptable (i.e. > 0.8) current efficiencies. Bipolar porous electrodes were also determined to be inappropriate for the recovery of Pb(II) from effluents, as the low concentration involved resulted in the predicted fraction of current lost as by-pass current, i.e. current not flowing in and out of the bipolar electrode, to be greater than 90% for the ranges of the variables studied
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