An integrated chemicalelectrochemical method for the recovery of copper from dilute solutions

The addition of reducing agents such as hydrazine or sodium sulphite to buffered dilute copper solutions containing chloride ions reduces cupric ions to cuprous ions chemically, thus by-passing this rate-determining electrochemical step. The subsequent electro-deposition of cuprous ions can then proceed readily and the overall faradaic efficiency, based on a 2 electron process, may reach 141%.     

A comparison of the performance of electrochemical reactor designs in the treatment of dilute solutions

The performance and efficiency of five different types of electrochemical reactors were compared, using the test reaction: Cu²⁺Cu ? 2e. The cell types used comprised parallel plate with forced flow, the same design packed with Netlon® and glass beads respectively between the parallel plates, a cell using mesh electrodes and lastly a packed bed type reactor. The experimentally obtained limiting current densities are compared with predicted values and cell performances is discussed in terms of these and other parameters such as pressure-drop across the cells.     

An investigation of the spouted bed electrode cell for the electrowinning of metal from dilute solutions

The depletion process of copper ions from dilute solutions has been used as a model system to investigate the spouted bed cell with a three-dimensional electrode of conducting particles. Experiments under potentiostatic and galvanostatic conditions have been carried out. Results obtained indicate that the spouted bed cell has several favourable characteristics for application in metal recovery. The potentiostatic mode of operation appears to be superior to the galvanostatic mode for electrowinning.     

Thermomechanics of dilute polymer solutions: multiple bead-spring model

Using the Rouse—Zimm model of the marcomolecule, the stress constitutive equation of dilute polymer solutions is derived in the form of a functional of temperature and deformation histories.The non-equilibrium thermodynamics of the system is also considered by relating excess free-energy, entropy and dissipation first to the distribution function and then to the histories of temperature and deformation. Similarly to the case of the stress, the excess internal energy functional can be derived without explicit knowledge of the distribution function.     

Critical temperature of the site dilute model by the approximate RG approach

The equation for the temperature of ferroelectric (ferromagnetic) phase transition is obtained within the renormalization group method. In the case of the site dilute model the bounderies of the concentration region, where the phase transition exists are discussed.     

Indirect electrochemical synthesis of active oxygen in dilute sulfate solutions

Anodic oxidation of dilute solutions of sodium sulfate was developed to generate oxidants into aqueous solutions with a diaphragm electrolyzer, which consisted of titanium anodes covered with mixed oxides of iridium, ruthenium and tin, a titanium cathode, and Teflon cation-exchange membrane. An electronic device was created for continuous self-purification of cathode surface from hardness salt deposits. The anodic products of electrolysis were molecular oxygen and sodium persulfate. It should be noted that sodium persulfate was the only active oxidant. The synthesized anolyte was tested for its oxidizing activity towards certain metabolites and toxicants. Disinfecting properties of anolyte were detected towards gram-positive and gram-negative bacteria. The comparison of redox potentials of commercial samples of persulfate and the synthesized anolyte showed that the redox potential value for the anolyte is much higher than for solutions with the same concentration of commercial persulfate.     

Copper recovery from dilute solutions in the Falling-Film cell

The removal of copper from dilute solutions is examined in electrochemical reactors where the electrolyte flows as a thin film in an inclined channel between a plane plate and a sheet of expanded metal (Falling-Film cell). Copper is recovered as a thin sheet from the plane plate. The results are compared with a known simplified model and the variations of the faradaic yield with the operating conditions are discussed.Nomenclature A _e electrode surface area - b width of inclined channel - C(t) copper concentration at timet - C ₀ initial copper concentration - d interelectrode distance - overall current density - overall limiting current density - overall mass transfer coefficient - L length of the channel - Q _v volumetric flow rate - Q _vl volumetric flow rate per unit of channel width (=Q _v/b) - t time - t _s residence time in the reactor, defined by Equation 1 - mean flow velocity of the liquid film, defined by Equation 2 - V volume of electrolyte in the circuit - V _R reactor volume - v _sn normalized space velocity, defined by Equation 9 - inclination angle with respect to the horizontal - instantaneous faradaic yield - time-averaged faradaic yield - v _e number of electrons exchanged in the electrochemical reaction     

The performance of a forced-flow parallel plate electrochemical reactor with dilute solutions

Experimental data relating to the performance of a fast flow parallel plate electrochemical reactor are reported, using very dilute reactant solutions. The results are shown to conform to the Chilton-Colburn analogy. The significance of such reactors, in terms of both electrochemical processing and treatment of dilute aqueous effluents, is discussed.     

Cubic autocatalysis with Michaelis-Menten kinetics: semi-analytical solutions for the reaction-diffusion cell

Cubic-autocatalysis with Michaelis-Menten decay is considered in a one-dimensional reaction-diffusion cell. The boundaries of the reactor allow diffusion into the cell from external reservoirs, which contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to obtain a semi-analytical model consisting of ordinary differential equations. This involves using trial functions to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. The semi-analytical model is then obtained from the governing partial differential equations by averaging. The semi-analytical model allows steady-state concentration profiles and bifurcation diagrams to be obtained as the solution to sets of transcendental equations. Singularity theory is then used to determine the regions of parameter space in which the four main types of bifurcation diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found by a local stability analysis of the semi-analytical model. An example of a stable limit-cycle is also considered. Comparison with numerical solutions of the governing partial differential equations shows that the semi-analytical solutions are very accurate.     

An approximate model for binary azeotropic distillation design

A simple analytical model has been developed for representing vapor-liquid equilibrium data in binary azeotropic mixtures. The method treats the azeotrope as a new pure component and considers the mixture to be composed of two independent binary subsystems; component 1 + azeotrope and azeotrope + component 2. After suitable variable transformations, each subsystem can then be represented by a constant relative volatility type model. The resulting vapor-liquid equilibrium models have been used to derive design equations for binary azeotropic distillation columns.     

Development of separation sharpness model for hydrocyclone

Hydrocyclones are mechanical devices used in classifying and separating many different types of materials. A classification function of the hydrocyclone has been continually developed for solid–liquid separation. In the classification process of solids from liquids, it is desirable to reduce the amount of misplaced material; therefore, the separation sharpness, α(alpha), is a parameter that helps in evaluating misplaced material and has been developed as a model to help the designer predict the performance of the classification. However, the problem with the separation sharpness model is that it cannot be used outside the range of conditions under which it was developed. Therefore, this research aimed to develop the separation sharpness model to predict more accurately and cover a wide range of conditions using the multiple linear regression method. The new regression model of separation sharpness was based on a wide range of both experimental and industrial data-sets of 431 tests collaborating with the additional experiments of 117 tests that were obtained from a total of 548 tests. The new model of separation sharpness can be used in the range of 30–762 mm hydrocyclone body diameters and feed solid concentrations in the range of 0.5 wt%–80 wt%. When compared with the experimental separation sharpness, the accuracy of the separation sharpness model prediction has an error of 4.53% and ~ of 0.973.     

An approximate analytical model for electrolyzers with axial dispersion

The steady state and transient behaviour of electrolyzers with axial dispersion is described in terms of an approximate mathematical model.     

A mathematical model of the viscosity of dilute solutions of rigid-chain polymers

Conclusions A procedure has been developed for identifying and discriminating between competing viscosity models from experimental data, plus a complex of programs for identifying models and discriminating between competing hypotheses.For the systems poly-p-phenyleneterephthalmaide-sulfuric acid (96.3 or 99.3%), the best results in prediction were given by the Martin model [K₅=0.435 (0.36)] and the Budatov model [K₇=0.16 (0.21)]; the temperature for both of the investigated systems was 274.25°K.In the investigated concentration region, a linear dependence is observed between sp and [], which is convenient for transition from specific viscosity to inherent viscosity. Adequate equations for expressing this relationship have been obtained from the experimental data.Translated from Khimicheskie Volokna, No. 2, pp. 20–24, March–April, 1985.     

An equation suitable for describing the viscosity of dilute to moderately concentrated polymer solutions

It is shown that an equation first derived for describing the Newtonian viscosity of suspensions of rigid spheres is also applicable for describing the Newtonian viscosity of dilute to moderately concentrated polymer solutions. The equation is applicable for relative viscosities from 1 to about 100. In addition, it is possible to rearrange the equation so that the intrinsic viscosity is expressible as an explicit function of the other variables. This leads to a very convenient method of calculating the intrinsic viscosity from a determination of the relative viscosity at a single polymer concentration.     

A mechanistic model of a packed-bed electrode cell to remove metal ions from dilute effluent solutions

A mathematical model of a porous cathode cell is derived in terms of fundamental kinetic parameters for the deposition of metals from dilute solutions. The model is used to design a pilot plant to treat electroplating waste effluents. Experimental results show that the plant can reduce the concentration of copper, nickel, chromium and zinc by at least 90% at acceptable current efficiencies.     

An approximate integral model for the burning rate of a thermoplastic-like material

An approximate integral model is formulated and solved to describe the pyrolysis or burning rate of a thermoplastic-like material. A constant temperature gasification process is assumed to occur at the solid–atmosphere interface. The preheating ignition problem is also solved by a matching integral method. The ignition problem leads to a solution involving a non-linear algebraic equation, but the gasification problem yields an exact solution provided the convective heat transfer coefficient is unaffected by the fuel mass loss or blowing effect. The results are compared to numerical solution in the literature and show good agreement. Comparisons with experimental data for PMMA are limited.     

An electrochemical study of the dissolution of gold in thiosulfate solutions Part I: Alkaline solutions

The anodic dissolution of gold in alkaline thiosulfate solutions has been studied by using a rotating gold disc. Experimental results have shown that the gold dissolves at measurable rates in thiosulfate solutions at potentials above 0.2 V. It has been confirmed that dissolution occurs in parallel with oxidation of thiosulfate with a dissolution current efficiency that varies with time and with the experimental conditions and which is generally in the range of 0.3 to 0.6. Although oxygen could be used as an oxidant for gold in the thiosulfate system, the rate of the cathodic reduction of oxygen in the relevant potential region is too slow for practical purposes. It was found that in the potential region investigated, thiosulfate ions undergo oxidative decomposition leaving a sulfur-like film on the surface of gold, which inhibits the rate of dissolution of gold and results in a low anodic current efficiency for the dissolution of gold. The factors (temperature, pH, thiosulfate concentration and ammonia) have been found to have positive effects on the kinetics of gold dissolution. The rates of gold dissolution in oxygenated alkaline thiosulfate solutions have been estimated to be much lower than in the copper–ammonia–thiosulfate and cyanide systems.     

Removal of zinc from dilute aqueous solutions by galvanochemical treatment

The possibility of zinc removal, a common toxic metal, from simulated liquid effluents by the application of a novel treatment method, termed galvanochemical, was investigated. The galvanochemical process is considered as a simple, economic, friendly to the environment, method, which does not create harmful end‐products. Synthetic wastewaters were examined, these contained concentrations of zinc commonly found in real wastewaters from small‐to‐medium size industrial units, such as metal‐plating or metal‐treatment plants. These liquid wastes pose an important environmental problem, due to the content of heavy metals. The optimization of the main operating parameters was the objective of the study. The galvanic pair scrap ratio iron:coke was used for these investigations. It was found that the use of the galvanic pair mixture of 80 g dm^?3 (weight per solution volume ratio), agitated at 160 rpm for 5 h, removed more than 90% of zinc from the initial solution, containing initially 50 mg dm^?3 of zinc. The scanning electron microscopy/energy disperse spectrometry (SEM/EDS) analysis performed on the products showed that zinc was adsorbed onto the coke to a small extent and that the zinc removal was mainly based on the adsorption of zinc onto the surface of active iron oxides formed as a result of galvanochemical reactions. Copyright © 2005 Society of Chemical Industry     

Mathematical model for choosing the preferable range of concentrations of ligands as components of solutions for alloy electrodeposition

Based on a statistical analysis of the information on the composition of solutions for the electrodeposition of A-B alloys, a mathematical model is proposed that makes it possible to choose the preferable range of the total concentrations of ligands in solutions for alloy electrodeposition. The prediction by the model is verified by known and new experimental data.