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  • 1.
    Bark, Fritz H.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes.
    Vynnycky, M.
    A note on electrolysis with forced convection at large peclet number in a channel and an excess of supporting electrolyte2008In: Russian journal of electrochemistry, ISSN 1023-1935, E-ISSN 1608-3342, Vol. 44, no 4, p. 470-478Article in journal (Refereed)
    Abstract [en]

    Electrolysis of an aqueous solution of a metal salt with an excess of supporting electrolyte flowing in a two-dimensional channel is considered. The reaction kinetics is modeled by a Butler - Volmer law. The metal electrodes are symmetrically flush mounted in the channel walls, which are otherwise electrically insulating. Using the perturbation scheme originally proposed by Levich for electrolytes with an excess of supporting electrolyte, a solution in closed form, involving the root of a transcendental algebraic equation, is obtained for the polarization curve. For small and large values of the potential difference between the electrodes, explicit expressions for the polarization curve and the distributions of electric current and concentration on the electrodes are obtained. Particular attention is given to the conditions prevailing during the asymptotic approach to the limiting current.

  • 2. Borg, K. I.
    et al.
    Birgersson, K. E.
    Bark, Fritz H.
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes.
    Effects of non-linear kinetics on free convection in an electrochemical cell with a porous separator2007In: Journal of Applied Electrochemistry, ISSN 0021-891X, E-ISSN 1572-8838, Vol. 37, no 11, p. 1287-1302Article in journal (Refereed)
    Abstract [en]

    The spatial evolution of the ionic concentration of an electrolyte in an isothermal electrochemical cell with a porous separator between the electrodes was investigated for large values of Rayleigh number. The reaction kinetics were described by the Butler-Volmer equation. The full problem, involving the coupled partial differential equations describing the velocity field, the ionic concentration, and the electric potential, was reduced by means of regular and singular perturbation theory, to a simplified evolution equation, coupled with a transcendental function for the ionic concentration and electric potential; the solution was found to agree well with the numerical solution of the full problem. In the limit of large and small cell voltages, closed analytical solutions were secured for the concentration, potential, and overall current density.

  • 3. Fukagata, K.
    et al.
    Zahrai, S.
    Bark, Fritz H.
    KTH, Superseded Departments, Mechanics.
    Dynamics of Brownian particles in a turbulent channel flow2004In: Heat and Mass Transfer, ISSN 0947-7411, E-ISSN 1432-1181, Vol. 40, no 9, p. 715-726Article in journal (Refereed)
    Abstract [en]

    Turbulent channel flows with suspended particles are investigated by means of numerical simulations. The fluid velocity is computed by large eddy simulation. Motion of small graphite particles with diameter of 0.01-10 mum, corresponding to the Schmidt number, Sc, of 2.87 x 10(2)-6.22 x 10(6) and the particle relaxation time in wall unit, tau(p)(+), of 9.79 x 10(-5)-4.51, is computed by Lagrangian particle tracking. Relation between the particle relaxation time and the computed deposition velocity is found to be in good agreement with an empirical relation. The statistics of the particle motion in the vicinity of the wall are studied. Clear differences are found in dynamical behavior of particles with different sizes. Medium size particles show a strong dependence on the structure of the fluid flow, while small and large particles are considerably less sensitive.

  • 4. Fukagata, K.
    et al.
    Zahrai, S.
    Kondo, S.
    Bark, Fritz H.
    KTH, Superseded Departments, Mechanics.
    Anomalous velocity fluctuations in particulate turbulent channel flow2001In: International Journal of Multiphase Flow, ISSN 0301-9322, E-ISSN 1879-3533, Vol. 27, no 4, p. 701-719Article in journal (Refereed)
    Abstract [en]

    Gas-particle turbulent channel flow at Re-tau = 644, loaded with copper particles at a mass flow ratio of 2%, is studied numerically by large eddy simulation (LES) coupled with Lagrangian particle tracking (LPT), Inter-particle collisions and correction of drag force in the vicinity of walls are accounted for. Focus is made on the influence of particle wall boundary conditions and their influence on the statistical structure of the flow, It is shown that accordance with experimental data can be improved if a mechanism which can suppress the direct re-entrainment of particles after the impact at the wall is present. Present result shows that inter-particle collisions may play an important role in the re-distribution of particle momentum among different components even at low mass loading conditions,

  • 5. Gurniki, F.
    et al.
    Fukagata, K.
    Zahrai, S.
    Bark, Fritz H.
    KTH, Superseded Departments, Mechanics.
    LES of turbulent channel flow of a binary electrolyte2000In: Journal of Applied Electrochemistry, ISSN 0021-891X, E-ISSN 1572-8838, Vol. 30, no 12, p. 1335-1343Article in journal (Refereed)
    Abstract [en]

    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.

  • 6.
    Ipek, Nulifer
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Faxén Laboratory. KTH, Superseded Departments, Mechanics.
    Lior, Noam
    University of Pennsylvania, Dept. Mech. Eng. and Appl. Mechanics.
    Bark, Fritz H.
    KTH, School of Engineering Sciences (SCI), Centres, Faxén Laboratory. KTH, Superseded Departments, Mechanics.
    Eklund, A.
    Avesta Sheffield AB.
    Alemany, Antoine
    Université Joseph Fourier, Lab. des Ecoulements Geophysique, Inst. de Mécan. de Grenoble.
    Simple analytical model predicting some features of the electrolytic steel-pickling process2002In: Russian journal of electrochemistry, ISSN 1023-1935, E-ISSN 1608-3342, Vol. 38, no 3, p. 238-246Article in journal (Refereed)
    Abstract [en]

    Electrolytic pickling of steel with neutral solutions, to remove the surface scale, reduces the need for the use of strong acids as needed in conventional pickling. This study is a step towards a more in-depth understanding of the factors affecting the former process. A theoretical model, sufficiently simplified to allow analytical solution, is developed and evaluated to provide a first approximation of the potential and current distributions in the electrolyte and steel band. To gain knowledge and validate the model, a small electrolytic pickling cell is constructed, and experiments, including bubble generation and motion observation, are conducted. The experimental work has shown the remarkable bubble production and adherence to the surfaces, and its effects on reducing pickling efficiency and uniformity. The pickling efficiency is about 30%, confirming other researchers' results. The analytical model shows trends very similar to those observed in the experiments, and provides very valuable guidance. It shows, for example, that the current efficiency decreases as the electrode-band distance increases, and it increases with the band thickness and the band-to-electrolyte conductivity ratio, The energy efficiency decreases by orders of magnitude faster than the current efficiency with all of the above-mentioned parameters, because of the correspondingly strong drop in the band-surface potential. A large amount of current is lost due to interelectrode short circuiting.

  • 7.
    Ipek, Nulifer
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Faxén Laboratory. KTH, School of Engineering Sciences (SCI), Mechanics.
    Lior, Noam
    University of Pennsylvania, Dept. Mech. Eng. and Appl. Mechanics.
    Vynnycky, Michael
    KTH, School of Engineering Sciences (SCI), Centres, Faxén Laboratory. KTH, School of Engineering Sciences (SCI), Mechanics.
    Bark, Fritz H.
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes.
    Numerical and experimental study of the effect of gas evolution in electrolytic pickling2006In: Journal of Applied Electrochemistry, ISSN 0021-891X, E-ISSN 1572-8838, Vol. 36, no 12, p. 1367-1379Article in journal (Refereed)
    Abstract [en]

    As part of a progressive approach to model the electrolytic pickling process, this paper focuses on the important aspect of hydrogen and oxygen gas evolution on the electrodes and on the steel strip being pickled. The system considered consists of type 316 stainless steel pickled in aqueous sodium sulphate, with lead anodes and stainless steel cathodes. The mathematical model is two-dimensional steady-state, and includes the differential equations describing the effect of migration, giving the potential and current fields, and the Tafel kinetic rate expressions for hydrogen and oxygen gas generation. Experiments were conducted to obtain a better understanding of the process and for model validation. Good agreement between the experimental measurements of the global current efficiency and the model predictions was obtained.

  • 8. Olivas, P.
    et al.
    Alemany, A.
    Bark, Fritz H.
    KTH, Superseded Departments, Mechanics.
    Electromagnetic control of electroplating of a cylinder in forced convection2004In: Journal of Applied Electrochemistry, ISSN 0021-891X, E-ISSN 1572-8838, Vol. 34, no 1, p. 19-30Article in journal (Refereed)
    Abstract [en]

    Continuous electrodeposition on a cylindrical cathode, e. g. electrodeposition of gold on electrical connectors, is usually characterized by an undesirable non- homogeneity of the deposit thickness. This has been observed in industrial applications. Numerical simulations have shown very good agreement with observations. This paper deals with the possibility of improving the homogeneity of the deposit thickness by a magnetic field that is parallel to the axis of the cylinder. The electromagnetic volume force generated by such a magnetic field may set up a swirling motion around the cylinder. By controlling the force density it is possible to control the thickness of the diffusive layer and consequently the mass transfer. The magnetic field can be optimized with respect to strength, spatial extent and variation with time. It is shown that a strong alternating magnetic field of low frequency gives a nearly homogeneous deposit.

  • 9. Widlund, O.
    et al.
    Zahrai, S.
    Bark, Fritz H.
    KTH, Superseded Departments, Mechanics.
    Structure information in rapid distortion analysis and one-point modeling of axisymmetric magnetohydrodynamic turbulence2000In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 12, no 10, p. 2609-2620Article in journal (Refereed)
    Abstract [en]

    It has recently been suggested that dimensionality information, as carried by the Reynolds dimensionality tensor, should be included in an extended Reynolds stress closure for modeling of magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds numbers. This would enable more accurate modeling of the Joule dissipation, and capture the length-scale anisotropies and tendencies towards two-dimensionality characteristic of MHD turbulence. In the present work, an evolution equation for the Reynolds dimensionality tensor is derived, based on the spectral formulation of the Navier-Stokes equations. Most of the terms in the equation require modeling. Rapid distortion theory (RDT) is applied to study the behavior of the different magnetic terms of the dimensionality and Reynolds stress tensor equations; a variety of different anisotropy states could be examined by letting magnetic forcing act on a number of initial spectral energy distributions obtained from axisymmetric strain. The properties and limitations of linear or bilinear invariant tensor models for the magnetic terms are evaluated. In the limit of large interaction numbers (where Joule dissipation dominates), the resulting model equations for the energy decay have analytic solutions. By choosing one model constant appropriately, these are made consistent with the asymptotic energy decay K similar to t(-1/2) predicted earlier by Moffatt. The long-term objective of these efforts is the development of an effective second-moment closure for engineering applications.

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