The kinetics of liquid-liquid extraction of metals in a rotating diffusion cell. A rotating diffusion cell is used to study the rates of extraction of divalent transition metals by di-(2-ethylhexyl)-phosphoric acid and a sulphur analogue. A chemical-diffusion model describes the rate curves.
AuthorPatel, Hamantkumar Vasudev
Rights© 1988 Patel, H. V. This work is licensed under a Creative Commons Attribution-Non-Commercial-Share-Alike License (http://creativecommons.org/licenses/by-nc-nd/2.0/uk).
InstitutionUniversity of Bradford
DepartmentPostgraduate School of Studies in Chemical Engineering,
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AbstractA rotating diffusion cell (RDC) has been used to study the kinetics of extraction of the transition metals cobalt (II), nickel (II), copper (II) and zinc (II) from sulphate solutions into either of two extractants held in n-heptane; di-(2-ethylhexyl) phosphoric acid (D2EHPA) or di-(2- ethylhexyl) dithiophosphoric acid (D2EHDTPA). The metal concentration was 10 mM and the aqueous pH was held at 4.5. The extractant concentration was varied between 0.015 to 0.4 M. In the case of cobalt extraction by D2EHPA, the metal concentration and the pH were varied Different diluents and modifiers were also studied.The rate of extraction by D2EHDTPA was found to be faster than D2EHPA. A comprehensive mathematical model, based upon established two film theory, was developed and used to describe the above experimental results. The model was also used to predict values of the important parameters. ... These values compared well with those found by other authors but using quite different experimental techniques. OS4 In the case of cobalt extraction by D2EHPA, the more polar diluents lowered the initial rate. The overall model predicts such behaviour where the rate is also dependent on the partition coefficients of the extractant. Finally, the theory of the RDC allows the prediction of the diffusion layer thicknesses, this information together with the reaction zone thickness is used to explore the influences of diffusion and chemical reaction on the overall transfer process. The diffusion processes are calculated to be the most important of the two. This is especially so for the D2EHDTPA systems.
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Numerical modelling of solute transport processes using higher order accurate finite difference schemes. Numerical treatment of flooding and drying in tidal flow simulations and higher order accurate finite difference modelling of the advection diffusion equation for solute transport predictions.Chen, Yiping (University of BradfordDepartment of Civil Engineering, 2010-06-23)The modelling of the processes of advection and dispersion-diffusion is the most crucial factor in solute transport simulations. It is generally appreciated that the first order upwind difference scheme gives rise to excessive numerical diffusion, whereas the conventional second order central difference scheme exhibits severe oscillations for advection dominated transport, especially in regions of high solute gradients or discontinuities. Higher order schemes have therefore become increasingly used for improved accuracy and for reducing grid scale oscillations. Two such schemes are the QUICK (Quadratic Upwind Interpolation for Convective Kinematics) and TOASOD (Third Order Advection Second Order Diffusion) schemes, which are similar in formulation but different in accuracy, with the two schemes being second and third order accurate in space respectively for finite difference models. These two schemes can be written in various finite difference forms for transient solute transport models, with the different representations having different numerical properties and computational efficiencies. Although these two schemes are advectively (or convectively) stable, it has been shown that the originally proposed explicit QUICK and TOASOD schemes become numerically unstable for the case of pure advection. The stability constraints have been established for each scheme representation based upon the von Neumann stability analysis. All the derived schemes have been tested for various initial solute distributions and for a number of continuous discharge cases, with both constant and time varying velocity fields. The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is third order accurate both in time and space. It has been shown analytically and numerically that a previously derived quasi 2-D explicit QUICKEST scheme, with a reduced accuracy in time, is unstable for the case of pure advection. The modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further tested for a number of 2-D continuous discharge cases, with the corresponding exact solutions having also been derived herein. All the numerical tests in both the 1-D and 2-D cases were compared with the corresponding exact solutions and the results obtained using various other difference schemes, with the higher order schemes generally producing more accurate predictions, except for the characteristic based schemes which failed to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme has also been applied to two water quality studies in the U. K., simulating nitrate and faecal coliform distributions respectively, with the results showing a marked improvement in comparison with the results obtained by the second order central difference scheme. Details are also given of a refined numerical representation of flooding and drying of tidal flood plains for hydrodynamic modelling, with the results showing considerable improvements in comparison with a number of existing models and in good agreement with the field measured data in a natural harbour study.
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