Mass transfer in a rotating cylinder cell—I. Laminar flow

The relationship between mass transfer and rotation rate for a concentric cylinder cell, in which the inner cylinder rotates and the outer cylinder remains stationary, has been derived for a simple model assuming linear velocity gradients near the rotating cylinder surface. A previous treatment by Kimla and > Stráfelda has been shown to be in error, but when corrected it takes essentially the same form as that derived in this paper.     

Effect of electrolysis parameters on the morphologies of copper powder obtained in a rotating cylinder electrode cell

In this paper, electrolysis method was used to produce copper powder particulates. The effects of parametric values, such as current density, concentration of copper ions, electrolyte temperature and rotation speed of cathode, on the morphologies and on the apparent densities of copper powders were examined. These parameters were evaluated by the current efficiency of hydrogen evolution. In addition, scanning electron microscopy (SEM) was used for analyzing the morphology of the copper powders. It was found that the increasing of the current density or the electrolyte temperature decreased the size of the powder particles promoting their morphology into dendritic structure. In contrast, the increase of copper ion concentration or rotation speed of cathode also increased the size of the particles resulting in a cauliflower-like morphology. All powder particles obtained were consisted of agglomerated copper grains. The most important difference was the size and the shape of the copper grains which were notably influenced by the electrolysis parameters. The apparent density values of copper powders were found to be suitable for many powder metallurgical applications. Attempts were also made in the later part of the paper to determine optimum process parameters for the production of electrolytic copper powders.     

Mass transfer modeling and simulation at a rotating cylinder electrode (RCE) reactor under turbulent flow for copper recovery

This work presents the numerical simulation of a laboratory reactor with rotating cylinder electrode (RCE) and a six-plate counter electrode that is used in studies on heavy metal recovery. The rate of electrode rotation and the potential applied are of such magnitude that the electrochemical reactor works in conditions of mass transport control under turbulent flow to obtain high recovery rates and formation of dendritic metal deposits. For hydrodynamics, the Reynolds averaged Navier–Stokes (RANS) equations were solved using the standard k–ε turbulence model, as well as wall functions based on the universal velocity distribution in the near-wall region. Results of 3-D simulations of the velocity field show clearly the formation of the turbulence Taylor vortex flow. For mass transfer, convection–diffusion equation was solved using the Kays–Crawford model for turbulent Schmidt number and Launder–Spalding wall functions adapted for mass transfer. Kinetics of copper recovery from aqueous solutions containing 0.019 M CuSO₄ and 1 M H₂SO₄, in the range of rotation speed of 400–1100 rpm, was adequately fit (error <8%) during the electrolysis time to achieve a final recovery of 85% for potentiostatic and 60% for galvanostatic experiments. The fitting parameter of the concentration wall function used in all experiments was A=2.9.     

Primary current distribution in a two-dimensional model cell composed of an electrode with an open part

A two-dimensional model for industrial production-type cells in which electrodes have holes for releasing gas bubbles to the back side of the electrodes and a separator located between the working- and counter-electrodes is proposed in conjunction with some geometrical parameters of the electrode and the cell. The primary current distribution in this model was calculated for a series of values of the parameters by the finite element method. The current distribution in the cell with the separator is quite different from that without the separator. Variations of the ohmic potential drop with the parameters reveal that the cell resistance is determined not only by the interelectrode distance but also by the per cent open area and in some cases by the superficial surface area. The partitions of the total current into the currents on the front, the back and the intermediate sides of the working-electrode are obtained as functions of the per cent open area and the superficial surface area. These results may be useful for estimating the performance of the electrode.Nomenclature b distance from the back wall to the back side of the working-electrode - d ₁ distance between the front side of the working-electrode and the separator (or the counter electrode when cell has no separator) - d ₂ width of the separator - I total current per half pitch - L length of a real electrolysis cell - n coordinate perpendicular to the boundary of the model cell - o _p per cent open area, given by Equation 1 for the present model - p pitch, i.e. twice the length of the unit cell - R equivalent unit-cell resistance defined by Equation 13 - R _t total cell resistance - r ratio of the average current density on each side of the working-electrode to that of the counter-electrode - s superficial surface area, given by Equation 2 for the present model - t thickness of the working electrode - u _k function defined by Equation 10 - test function - w width of the working electrode - x abscissa located on the cell model - y ordinate located on the cell model - d infinitesimal length on the boundary - ₁ resistivity of the solution phase - ₂ resistivity of the separator - potential - ^* potential at the working electrode - linear integration contour along I0, AH or EFDH - double integration space in the solution or the separator phase     

Secondary current distribution in a two-dimensional model cell composed of an electrode with an open part

On the assumption that the relation between the overpotential and the current density is expressed by linear and Butler-Volmer equations, secondary current distributions were obtained in a two-dimensional model cell in which a working electrode with an open part serving to release gas bubbles to the back side of the electrode is located parallel to a counter electrode or a separator. Cell resistances or cell voltage in the model cell were evaluated for various combinations of geometrical parameters and heterogeneous kinetic parameters by means of the finite element method. As a result, when the kinetic equation was the linear approximation, the cell resistance or cell voltage varied mainly with two geometrical parameters (the interelectrode distance and the electrode surface ratio) and the kinetic parameters. On the other hand, when the kinetic equation was of the Butler-Volmer type the cell voltage varied with the kinetic parameters and the percentage of open area instead of the electrode surface ratio. In order to facilitate estimation of cell voltage for an industrial productiontype cell composed of electrodes with voids or holes, the computed cell voltages were expressed as functions of these parameters in simple approximate equations. A criterion for estimating whether the cell voltage is controlled by the overpotential or the ohmic drop is presented.     

超重力法臭氧处理三硝基甲苯碱性废水传质模型

在前期试验研究的基础上建立了超重机中硫酸水溶液物理吸收臭氧的体积传质模型和三硝基甲苯(TNT)碱性废水化学吸收臭氧的体积传质模型。模型计算表明:硫酸水溶液物理吸收臭氧的体积传质系数为0.0191 s-1;臭氧氧化TNT碱性废水的体积传质系数在反应初始达到0.258 s-1,臭氧利用率达到93%,远高于鼓泡塔中臭氧氧化硝基苯类化合物的化学体积传质系数(0.005 88—0.017 s-1),模型的建立为以后的工业放大提供了理论依据。     

Mass transfer from crystalline surfaces in a turbulent impinging jet part I. Transfer by erosion

Mechanical erosion from two crystalline coating materials, naphthalene and trans-cinnamic acid, in submerged turbulent impinging jets of water has been studied. In the absence of diffusion, the observed erosion rates in the wall jet region vary linearly with wall shear stress. Threshold shear stress values below which erosion may be neglected have been defined for both coating materials. Erosion rates in the impingement region also depend on the shear stress which, depending on the crystalline grain size, may interact with pressure forces.     

Reduction of metal ions in dilute solutions using a GBC-reactor Part II: Theoretical model for the hydrogen oxidation in a gas diffusion electrode at relatively low current densities

The GBC-reactor is based on the combination of a gas diffusion anode and a porous cathode. A theoretical model for gas diffusion electrode, valid at relatively low current densities, is derived. This is based on the pseudohomogeneous film model including an approximation of the Volmer–Tafel mechanism for the hydrogen oxidation kinetics. Results show a severe mass transfer limitation of the hydrogen oxidation reaction inside the active layer of the gas diffusion electrode, even at low current densities. Empirical formulae are given to estimate whether leakage of dissolved hydrogen gas into the bulk electrolyte occurs at specific process conditions. A simplified version of the model, the reactive plane approximation, is presented.     

The effect of benzotriazole on mass transfer in the corrosion of a copper rotating disk electrode

The effect of benzotriazole, BTA, on mass transfer in dissolution-corrosion of the copper rotating disk electrode in 0.02 M Fe(III)–0.5 M H₂SO₄ has been studied by means of atomic absorption spectrometry. The mass transfer coefficient, K, was determined from the slope of ln(C ₀/C)_Fe(III) vs. time plots. In the absence of BTA the corrosion process can be described by the correlation Sh = KR/D = 4.47Re ^0.5. The difference in values between Sh and Sh _Levich, and the change in slope in the Arrenhius plot points to mixed control for the cathodic process Fe³⁺ + 1e^– Fe ²⁺ and charge transfer control for the anodic process, Cu Cu²⁺ + 2e. The average activation energies were 7.7 kJ mol^–1 and 19.5 kJ mol^–1 at (500–1500) and (2000–3000) rpm, respectively. At low concentration of BTA the inhibiting action of BTA increases with concentration and with rotation speed. For [BTA] 5 × 10^–3 M, the K value, 10^–4 cm s^–1, remains constant and is independent of rotation rate. The morphology of the copper rotating disk after corrosion in the absence and presence of BTA was examined using scanning electron microscopy (SEM).     

Mass transfer from crystalline surfaces in a turbulent impinging jet. part 2: Erosion and diffusional transfer

Simultaneous erosion and diffusional transfer from transcinnamic acid coatings in submerged, axisymmetric, impinging jets of water has been studied at a Reynolds number of 100,000 and a nozzle height of 8 diameters. The concentration driving force was varied from zero to the acid solubility value. For low transfer rates roughness development was small and the two transfer modes were additive. At higher dissolution rates, however, diffusion enhanced erosion by loosening surface grains. This loosening action was largest in the impingement region where large surface roughness developed and further enhanced the high dissolution rates and subsequent interactions.     

Mass transfer in fluidized beds of inert particles. Part I: The role of collision currents in mass transfer to the electrode

The effect of particle-wall collision on the mass transfer rate mechanism in liquid fluidized bed electrochemical cells was studied. Collision frequencies and currents were measured at microelectrodes set in the bed wall. It is postulated that, at each particle–electrode collision, a specific microvolume of bulk concentration electrolyte is introduced into the near-electrode diffusion layer during particle movement towards the electrode causing an enhancement of the limiting diffusion current. Based on measurements made at microelectrodes calculations of the contribution of the particle collision mechanism to total mass transfer to a planar electrode are attempted and are in good agreement with experimental values.     

Mass transfer study in a pulsed bed electrode - application to the electrodeposition of a poly(dibenzo-18-crown-6) film

The polymerization of dibenzo-18-crown-6 has been carried out in an electrochemical reactor containing a granular electrode percolated by a pulsed solution. The influence of different parameters (pulse frequency, permanent flow velocity of the electrolytic solution, particle diameter and bed height) on the mass transfer has been studied. A correlation between the reduced mass transfer coefficient and the Strouhal number has been established. The maximum mass transfer coefficient and the maximum Strouhal number have been determined as a function of the Galilee number. The correlation predicts well the mass transfer coefficient over a larger range of the variables than previously achieved.     

Current-time behaviour for copper electrodeposition. I. Theoretical analysis based on a surface diffusion model

The form of the current-time transients for copper electrodeposition from copper sulphate solutions have been calculated based on a surface diffusion model. The transient was greatly affected by whether the ad-species diffusing across the surface was ad-atom Cu⁰ or ad-ion Cu⁺, and by the surface coverage by the ad-species. The results imply that it is possible to experimentally test the applicability of the surface diffusion model to copper electrodeposition, to identify the ad-species (Cu⁰ or Cu⁺), to estimate the surface coverage and to calculate the parameters related to surface diffusion,D/l ² andi ₀/c ₀.     

Shear-thinning film on a porous substrate: Stability analysis of a one-sided model

The temporal stability of a Carreau fluid flowing down an inclined porous substrate is considered. A reduced model is derived under the assumption of small permeability which decouples the flow in the liquid layer from the filtration flow in the porous medium and incorporates the effect of the porous medium by means of an effective slip condition at the liquid–solid interface. The slip coefficient in the effective slip condition is a function of the structure, permeability of the porous medium and the rheology of the fluid saturating the porous medium. The effects of shear-thinning rheology and permeability of the substrate on the stability of the film flow system are investigated. This problem gives rise to a generalized eigenvalue formulation which is solved through two approaches. The problem is solved analytically for long waves in the limiting cases of weakly and strongly non-Newtonian behaviors (power-law limit). A numerical investigation is carried out in the general case. The results are shown to agree well for the weakly non-Newtonian limit. Further, the power-law model and the Carreau model agree on a wide range of shear-thinning parameter values for a thin film over a rigid substrate. However, when considering a porous medium, this trend is not observed. The Carreau model gives valid results for the entire range of shear-thinning parameter values for a film over a rigid/porous substrate. The novelty of the present investigation lies in the inclusion of both the effects of bottom permeability and shear-thinning rheology. Both permeability and shear-thinning rheology have a destabilizing effect on the film flow system. The numerical results indicate the correlation between the effects due to shear-thinning properties and permeability. An energy balance analysis performed on the perturbation fields shows that destabilization induced by both shear-thinning and permeability is linked to the viscous shear work rate on the free surface.     

Determining the thickness of liquid film in laminar condition on a rotating drum surface using CFD

This is a pioneering paper that deals with the semi-steady-state liquid film thickness on a rotating drum partially submerged in liquid using CFD. The CFD predictions have been compared with both experimental results and analytical solutions. The liquid film thickness and the film rising on a circular curved wall were monitored for various rpm of the rotating drum. The 2D simulations were performed neglecting the end effects (assuming the rotating drum is very long). As the rotating drum speed was increased, the film thickness was found to increase at the film rising side and at the minimum film thickness point (top of the rotating drum). There was never been a steady-state condition reached, the opposite was expected as a wiper is used in the CFD calculation (same as the experimental investigation). The liquid that leaves the domain by the wiper (as outflow boundary condition) is forced to enter to the domain from far end to keep the level of the free surface constant.     

Enhanced mass transfer at the rotating cylinder electrode. I. Characterization of a smooth cylinder and roughness development in solutions of constant concentration

A versatile rotating cylinder electrode (RCE) assembly has been constructed in order to study the development of surface roughness during the prolonged cathodic deposition of metal at high overpotential. The initial smooth cylindrical surface and its behaviour have been characterized and the onset of rough deposits is described by an empirical power law (based on the mass transfer correlation)I _L= (constant)U ^x where x～-0.74 for a smooth surface and x～-0.90 for a roughened surface. The uses and limitations of this power law are discussed.     

Direct electron transfer of hemoglobin in a CdS nanorods and Nafion composite film on carbon ionic liquid electrode

In this paper the direct electron transfer of hemoglobin (Hb) was carefully investigated by using a room temperature ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF₆) modified carbon paste electrode (CILE) as the basal working electrode. Hb was immobilized on the surface of CILE with the nanocomposite film composed of Nafion and CdS nanorods by a step-by-step method. UV–vis and FT-IR spectra showed that Hb in the composite film remained its native structure. The direct electrochemical behaviors of Hb in the composite film were further studied in a pH 7.0 phosphate buffer solution (PBS). A pair of well-defined and quasi-reversible cyclic voltammetric peaks of Hb was obtained with the formal potential (E⁰′) at −0.295 V (vs. SCE), which was the characteristic of heme Fe(III)/Fe(II) redox couples. The direct electrochemistry of Hb was achieved on the modified electrode and the apparent heterogeneous electron transfer rate constant (k_s) was calculated to be 0.291 s⁻¹. The formal potentials of Hb Fe(III)/Fe(II) couple shifted negatively with the increase of buffer pH and a slope value of −45.1 mV/pH was got, which indicated that one electron transfer accompanied with one proton transportation. The fabricated Hb sensor showed good electrocatalytic manner to the reduction of trichloroacetic acid (TCA).     

Determination of diffusivity and solubility of oxygen in phosphoric acid using a transit time on a rotating ring-disc electrode

A transit time method on a rotating ring-disc electrode was used to simultaneously determine the diffusivity and solubility of oxygen in phosphoric acid. The method consisted of measuring the limiting current for the diffusion of dissolved oxygen on the central disc electrode, and a transit time for the diffusion of oxygen from the disc to the ring electrode. The diffusivity of oxygen was calculated from the measured transit time, electrode rotational speed and kinematic viscosity of the electrolyte without the need of its bulk concentration and the number of electrons transferred in the electrode reaction. Once the diffusivity was known, the solubility of oxygen in the bulk electrolyte was determined from the limiting current on the disc using the Levich equation. This work has demonstrated that the transit method is a swift and reproducible technique for the diffusivity measurement. The diffusivity and solubility of oxygen in phosphoric acid of a concentration range of 0.79–14.7m were determined at 23° C and an oxygen partial pressure of 1 atm. A set of empirical equations are presented to correlate the Stokes-Einstein constant,Dµ/T, and solubility of oxygen to the phosphoric acid concentration.     

Diffusion model for charge transfer from a photosynthetic reaction center to an electrode in a photovoltaic device

In spite of a high quantum efficiency in the bacterial photosynthetic reaction center (RC) the overall efficiency in a RC-based photovoltaic device is very poor partly because of an inefficient collection of charges by electrodes. To explain charge transport between the RC and an electrode a diffusion model is proposed. The numerical solution of the diffusion process describes the measured photocurrent well. An approximation of the initial condition is also made to obtain analytical expressions for the photocurrent. The model suggests that the slow transient response of the photocurrent is due to the diffusion in a biological photovoltaic device.