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A D Davydov - One of the best experts on this subject based on the ideXlab platform.
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mass transfer during metal electrodeposition into the pores of anodic aluminum oxide from a Binary Electrolyte under the potentiostatic and galvanostatic conditions
Electrochimica Acta, 2016Co-Authors: D A Bograchev, V M Volgin, A D DavydovAbstract:Abstract The mass transfer during the nanowire formation by the metal electrodeposition into the pores with a high aspect ratio from a Binary Electrolyte is studied theoretically. The application of quasi-steady-state approximation is justified. The equations for the ion concentration and electric potential at the bottom and in the mouth of the pores, the reaction overpotential, and the variation of the current density with time are obtained. The problem of time dependence of unfilled pore part length is solved numerically. The distinctions between the results obtained under the potentiostatic and galvanostatic conditions are demonstrated.
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linear analysis of the free convective stability of a Binary Electrolyte solution in an electrochemical cell with horizontal electrodes
Journal of Engineering Physics, 2010Co-Authors: V M Volgin, A D Davydov, A V ZhukovAbstract:The influence of the electrode reaction kinetics on the critical Rayleigh number for a Binary Electrolyte solution situated between flat horizontal electrodes has been investigated. The equations of motion of an incompressible viscous fluid in the Boussinesq approximation and the material balance equations with the electrical neutrality condition have been used as a mathematical model. Analytical and numerical solutions of the linear stability problem have been obtained. The influence of the kinetic parameters of the electrode reaction (exchange current density, transport number of cations) and the transport properties of the solution on the critical value of the Rayleigh number has been investigated.
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mass transfer in the rotating electrochemical cell with vertical cylindrical electrodes the effect of rotational rate and cell geometry on the limiting current density
Russian Journal of Electrochemistry, 2010Co-Authors: V M Volgin, A D DavydovAbstract:The mass transfer in the rotating electrochemical cell with vertical cylindrical electrodes containing a Binary Electrolyte is theoretically studied. The Navier-Stokes equations in the rotating system of coordinates, the equations of ionic transfer of Electrolyte components, which is caused by diffusion, convection, and migration, and the condition of electroneutrality are used as the mathematic model of the process. The effects of centrifugal force and Coriolis force are studied by using the numerical simulation; the effect of geometry of electrochemical cell on the limiting mass transfer rate is determined.
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the limiting current of electrochemical reaction in the Binary Electrolyte in the rotating electrochemical cell
Russian Journal of Electrochemistry, 2008Co-Authors: D A Bograchev, A D DavydovAbstract:A rotating cylindrical electrochemical cell with a plane ring electrode on its cover containing a Binary Electrolyte was considered. The equation for the diffusion limiting current density on the ring electrode was derived ignoring the effect of Coriolis force. The solution of transfer equations by the Karman method at the limiting current in the cell allowed us to analyze the effect of Coriolis force on the boundary layer thickness and to determine the conditions, under which the Coriolis force may be ignored.
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monotonic and oscillatory free convective instability of solution in the space between two plane horizontal electrodes solutions containing three types of ions
Journal of Electroanalytical Chemistry, 2006Co-Authors: V M Volgin, A D DavydovAbstract:The conditions for the onset of natural convection (convective instability) in the electrochemical system consisting of two plane horizontal electrodes and solution containing three types of ions between them were analyzed theoretically. The equations of flow of incompressible viscous liquid to the Boussinesq approximation and the equations of material balance with the electroneutrality condition were used as the mathematical model. The set of equations for amplitudes of perturbations was solved using the Galerkin method. The dependences of critical Rayleigh number on the system parameters are obtained for monotonic and oscillatory instabilities in the case that the electrochemical reaction proceeds under the conditions of limiting current. The examples of instability diagrams are presented. In contrast to the Binary Electrolyte, for a solution containing three types of ions, the critical Rayleigh number depends on the charges of ions and the ratio between the diffusion coefficients of ions in the solution.
V M Volgin - One of the best experts on this subject based on the ideXlab platform.
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mass transfer during metal electrodeposition into the pores of anodic aluminum oxide from a Binary Electrolyte under the potentiostatic and galvanostatic conditions
Electrochimica Acta, 2016Co-Authors: D A Bograchev, V M Volgin, A D DavydovAbstract:Abstract The mass transfer during the nanowire formation by the metal electrodeposition into the pores with a high aspect ratio from a Binary Electrolyte is studied theoretically. The application of quasi-steady-state approximation is justified. The equations for the ion concentration and electric potential at the bottom and in the mouth of the pores, the reaction overpotential, and the variation of the current density with time are obtained. The problem of time dependence of unfilled pore part length is solved numerically. The distinctions between the results obtained under the potentiostatic and galvanostatic conditions are demonstrated.
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linear analysis of the free convective stability of a Binary Electrolyte solution in an electrochemical cell with horizontal electrodes
Journal of Engineering Physics, 2010Co-Authors: V M Volgin, A D Davydov, A V ZhukovAbstract:The influence of the electrode reaction kinetics on the critical Rayleigh number for a Binary Electrolyte solution situated between flat horizontal electrodes has been investigated. The equations of motion of an incompressible viscous fluid in the Boussinesq approximation and the material balance equations with the electrical neutrality condition have been used as a mathematical model. Analytical and numerical solutions of the linear stability problem have been obtained. The influence of the kinetic parameters of the electrode reaction (exchange current density, transport number of cations) and the transport properties of the solution on the critical value of the Rayleigh number has been investigated.
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mass transfer in the rotating electrochemical cell with vertical cylindrical electrodes the effect of rotational rate and cell geometry on the limiting current density
Russian Journal of Electrochemistry, 2010Co-Authors: V M Volgin, A D DavydovAbstract:The mass transfer in the rotating electrochemical cell with vertical cylindrical electrodes containing a Binary Electrolyte is theoretically studied. The Navier-Stokes equations in the rotating system of coordinates, the equations of ionic transfer of Electrolyte components, which is caused by diffusion, convection, and migration, and the condition of electroneutrality are used as the mathematic model of the process. The effects of centrifugal force and Coriolis force are studied by using the numerical simulation; the effect of geometry of electrochemical cell on the limiting mass transfer rate is determined.
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monotonic and oscillatory free convective instability of solution in the space between two plane horizontal electrodes solutions containing three types of ions
Journal of Electroanalytical Chemistry, 2006Co-Authors: V M Volgin, A D DavydovAbstract:The conditions for the onset of natural convection (convective instability) in the electrochemical system consisting of two plane horizontal electrodes and solution containing three types of ions between them were analyzed theoretically. The equations of flow of incompressible viscous liquid to the Boussinesq approximation and the equations of material balance with the electroneutrality condition were used as the mathematical model. The set of equations for amplitudes of perturbations was solved using the Galerkin method. The dependences of critical Rayleigh number on the system parameters are obtained for monotonic and oscillatory instabilities in the case that the electrochemical reaction proceeds under the conditions of limiting current. The examples of instability diagrams are presented. In contrast to the Binary Electrolyte, for a solution containing three types of ions, the critical Rayleigh number depends on the charges of ions and the ratio between the diffusion coefficients of ions in the solution.
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effect of uniform magnetic field on the stability of the rayleigh benard convection in a Binary Electrolyte a theoretical analysis
Russian Journal of Electrochemistry, 2005Co-Authors: V M Volgin, A D Davydov, D A BograchevAbstract:The Rayleigh-Benard stability in an electrochemical cell with a Binary Electrolyte in a uniform magnetic field is studied theoretically. The mathematical model is based on equations describing the motion of incompressible viscous liquid in the Boussinesq approximation, which account for the Archimedean buoyancy force and the Lorentz force, and equations of material balance with the electroneutrality condition. The set of equations for perturbation amplitudes is solved analytically by the Galerkin method and numerically, by the Runge-Kutta method. Dependences of the critical value of the Rayleigh number on the Hartmann number, which expresses the ratio between magnetic and viscous forces, are obtained for monotonic instability of limiting current at liquid and solid electrodes. The effect the variations in the Electrolyte's electroconductance, which are caused by concentration variations, exert on the instability emergence is analyzed.
Ali Haghtalab - One of the best experts on this subject based on the ideXlab platform.
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An Electrolyte Non-random-UNIQUAC Model for Thermodynamic Modeling of Binary and Multicomponent Aqueous Electrolyte Systems
Journal of Solution Chemistry, 2019Co-Authors: Seyed Mohammad Razavi, Ali Haghtalab, Ali Reza KhanchiAbstract:An Electrolyte non-random-UNIQUAC (NR-UNIQUAC) local composition model is developed for calculation of the excess Gibbs energy and activity coefficients for Binary and the multicomponent Electrolyte solutions. A new expression for the energies of the reference cells in the random state is used and a modified version of the UNIQUAC model is provided. The high efficiency of the presented model is demonstrated through the correlation of the available experimental data for various Electrolyte solutions. Obtained results are compared with those of Electrolyte-UNIQUAC-NRF model. The correlation of data was carried out using two different approaches, the single system correlation and the global optimization of the interaction parameters. In the single fitting approach, two adjustable Binary interaction parameters of the model are regressed using the experimental mean activity coefficient data of Binary solutions. In the global approach, the anion-water and cation–anion interaction energy parameters of different ions are calculated via simultaneous correlation of the mean activity coefficient data of the forty-nine Binary Electrolyte solutions. In both approaches, the adjustable parameters are calculated in a wide range of Electrolyte concentrations and at different temperatures, so that these parameters can be used to predict the osmotic coefficient data of many Binary systems. Moreover, the solubility and osmotic coefficient data of ternary Electrolyte solutions were predicted using the previously obtained Binary parameters. Using the present model, the predicted data for the Binary and multicomponent Electrolyte solutions are in good agreement with the experimental data. When compared to Electrolyte-UNIQUAC-NRF model, the present model is more accurate. Additionally, the presence of salt–salt interaction parameters in the Electrolyte-NR-UNIQUAC model can further improve its efficiency when experimental data for a ternary system is available.
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Electrolyte uniquac nrf model for the correlation of the mean activity coefficient of Electrolyte solutions
Fluid Phase Equilibria, 2009Co-Authors: Ali Haghtalab, Kiana PeyvandiAbstract:Abstract The new Electrolyte-UNIQUAC-NRF excess Gibbs function is obtained for calculation of the activity coefficient of the Binary Electrolyte solutions. The excess Gibbs energy of the model consists of the Pitzer–Debye–Huckel equation, describing the long-range electrostatic contribution and the Electrolyte-UNIQUAC-NRF model to account for the short-range contributions. With two adjustable parameters per Electrolyte, the new model is applied to correlation of the mean activity coefficients of more than 130 Binary aqueous Electrolyte solutions at 25 °C. Also the Binary parameters, obtaining from regression of mean activity data, are used for prediction of osmotic coefficient data for the same Electrolytes. The results are compared with various local composition models such as the Electrolyte-NRTL, Electrolyte NRF-Wilson, Electrolyte-NRTL-NRF, N-Wilson-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental activity coefficient data and predict the osmotic coefficient data of Binary Electrolytes accurately.
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a nonElectrolyte local composition model and its application in the correlation of the mean activity coefficient of aqueous Electrolyte solutions
Fluid Phase Equilibria, 2009Co-Authors: Ali Haghtalab, Seyed Hossein MazloumiAbstract:Abstract The local composition models have been widely used for the correlation of activity coefficient of nonElectrolyte and Electrolyte solutions. A new equation for the excess Gibbs energy function is developed based on the local composition expression of Wilson and the random reference state. This new function, the nonElectrolyte Wilson nonrandom factor (N-Wilson-NRF) model, is presented in the form of a molecular framework so that it can be used for both nonElectrolyte and Electrolyte solutions. Without any particular assumptions for ionic solutions, the new function is used to described the short-range contribution of the excess Gibbs energy of Electrolyte solutions. The long-range contribution is represented by Pitzer–Debye–Huckel model. With two adjustable parameters per Electrolyte, the new model is applied to correlate the mean activity coefficients of more than 150 Binary aqueous Electrolyte solutions at 25 °C. The results are compared with various local composition models such as the Electrolyte-NRTL, Electrolyte NRF-Wilson and Electrolyte-NRTL-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental data accurately. Moreover, the model shows high precision of predictability for the osmotic coefficient of Binary Electrolyte solutions.
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g ex model using local area fraction for Binary Electrolyte systems
International Journal of Thermophysics, 2007Co-Authors: Ali Haghtalab, Marzieh JodaAbstract:The correlation and prediction of phase equilibria of Electrolyte systems are essential in the design and operation of many industrial processes such as downstream processing in biotechnology, desalination, hydrometallurgy, etc. In this research, the local composition non-random two liquid-nonrandom factor (NRTL-NRF) model of Haghtalab and Vera was extended for uni-univalent aqueous Electrolyte solutions. Based on the assumptions of the NRTL-NRF model, excess Gibbs free energy (g E) functions were derived for Binary Electrolyte systems. In this work, the local area fraction was applied and the modified model of NRTL-NRF was developed with either an equal or unequal surface area of an anion to the surface area of a cation. The modified NRTL-NRF models consist of two contributions, one due to long-range forces represented by the Debye–Huckel theory, and the other due to short-range forces, represented by local area fractions of species through nonrandom factors. Each model contains only two adjustable parameters per Electrolyte. In addition, the model with unequal surface area of ionic species gives better results in comparison with the second new model with equal surface area of ions. The results for the mean activity coefficients for aqueous solutions of uni-univalent Electrolytes at 298.15 K showed that the present model is more accurate than the original NRTL-NRF model.
Henrik Bruus - One of the best experts on this subject based on the ideXlab platform.
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numerical analysis of finite debye length effects in induced charge electro osmosis
Physical Review E, 2009Co-Authors: Misha Marie Gregersen, Gaurav Soni, Carl D. Meinhart, Mathias B Andersen, Henrik BruusAbstract:: For a microchamber filled with a Binary Electrolyte and containing a flat unbiased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that, compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e., for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.
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frequency response in surface potential driven electrohydrodynamics
Physical Review E, 2006Co-Authors: Louise Ejsing, Kristian Smistrup, C M Pedersen, Niels Asger Mortensen, Henrik BruusAbstract:Using a Fourier approach we offer a general solution to calculations of slip velocity within the circuit description of the electrohydrodynamics in a Binary Electrolyte confined by a plane surface with a modulated surface potential. We consider the case with a spatially constant intrinsic surface capacitance where the net flow rate is, in general, zero while harmonic rolls as well as time-averaged vortexlike components may exist depending on the spatial symmetry and extension of the surface potential. In general, the system displays a resonance behavior at a frequency corresponding to the inverse $RC$ time of the system. Different surface potentials share the common feature that the resonance frequency is inversely proportional to the characteristic length scale of the surface potential. For the asymptotic frequency dependence above resonance we find a ${\ensuremath{\omega}}^{\ensuremath{-}2}$ power law for surface potentials with either an even or an odd symmetry. Below resonance we also find a power law ${\ensuremath{\omega}}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}$ being positive and dependent of the properties of the surface potential. Comparing a tanh potential and a sech potential we qualitatively find the same slip velocity, but for the below-resonance frequency response the two potentials display different power-law asymptotics with $\ensuremath{\alpha}=1$ and $\ensuremath{\alpha}\ensuremath{\sim}2$, respectively.
Fritz H Bark - One of the best experts on this subject based on the ideXlab platform.
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LES of turbulent channel flow of a Binary Electrolyte
Journal of Applied Electrochemistry, 2000Co-Authors: F. Gurniki, Koji Fukagata, S. Zahrai, Fritz H BarkAbstract:The turbulent diffusion boundary layer in a Binary Electrolyte was considered at Schmidt numbers of 1, 10 and 100 and exchange current densities between 10−4 A m−2 and 10−2 A m−2. A numerical scheme was developed for efficient investigation of the dynamics by means of large eddy simulations. The methodology was examined by detailed comparisons with documented data from earlier large eddy and direct numerical simulations and good agreement was found. Application of the methodology to electrochemical mass transfer indicated that the exchange current density seems to have negligible effect on the mean concentration profile but it influences the structure of the fluctuating field in a visible manner.
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turbulent free convection in large electrochemical cells with a Binary Electrolyte
Journal of Applied Electrochemistry, 1999Co-Authors: F. Gurniki, Fritz H Bark, Said ZahraiAbstract:A mathematical model proposed by Bark and Alavyoon for modelling laminar natural convection in electrochemical cells, with Binary Electrolytes, is extended to simulation of two-dimensional turbulent flows. The turbulence was modelled by a standard k–π model. The constants used in the model are the same as those used by Henkes and Hoogendoorn. Steady state calculations were carried out in a square, differentially heated enclosure for Gr=7×1010 and Pr=0.71. The turbulence model used could not predict the transition effect on the Nusselt number along the hot wall. Transient calculations performed in an enclosure with an aspect ratio of 35, for Gr=6.4×1011 and Sc=2763, revealed large scale fluctuations in the boundary layers near the vertical walls. The model was able to predict qualitatively the velocity field for transitional flow for air induced by buoyancy at Grh=8100 and Grh=22 500. The correlation between the Sherwood and Rayleigh numbers was studied by modelling the mass transfer at the electrodes using a Butler–Volmer law. The computed Sherwood number was found to be approximately proportional to the Rayleigh number to the power of 0.2 in the range of Rah between 5×108 and 1010, and with an order of magnitude of 105.
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electrolysis of a Binary Electrolyte in two dimensional channel flow
Electrochimica Acta, 1996Co-Authors: Fredrik C Wallgren, Fritz H Bark, Bengtjoel AnderssonAbstract:Abstract Numerical simulations have been performed to analyze the electric current density in an aqueous solution of CuSO4, flowing in a two-dimensional channel with finite electrodes placed symmetrically on opposite sides. A Butler-Volmer law is chosen as a boundary condition on the electrodes for current densities below the limiting current. At limiting current density, two modified boundary conditions at the cathode are derived. For 0 ⩽ Pe ⩽ 25 000, comparisons are made with results of other studies, and the agreement is excellent for large values of Pe but differ for Pe ~ 1. For small values of the applied voltage and large values of Pe, a semi-analytic solution of the electric potential is derived.
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on morphological instability during electrodeposition with a stagnant Binary Electrolyte
Electrochimica Acta, 1995Co-Authors: Larsgoran Sundstrom, Fritz H BarkAbstract:Abstract For a metal deposition problem with a stagnant Binary Electrolyte a study is made of how low amplitude irregularities in the electrode surfaces evolve with time. The linear stability problem is solved numerically as an eigenvalue problem. Analytical solutions for three different limits are obtained and found to agree with the numerical solution. In contrast to previous work simultaneous perturbations to both electrodes are treated and the full equation for the electric potential is solved. Also, the common assumption of neglecting the time derivative in the equation for concentration perturbation is not made use of. As a result, the growth rate for very large wavelengths is found to approach a finite value rather than decreasing to zero. Non-dimensional parameters are identified and their influence is studied. As in most previous results growing modes are found for each value of the applied current.