Magnetic field effects on electrochemical metal depositions

Abstract

This paper discusses recent experimental and numerical results from the authors' labs on the effects of moderate magnetic (B) fields in electrochemical reactions. The probably best understood effect of B fields during electrochemical reactions is the magnetohydrodynamic (MHD) effect. In the majority of cases it manifests itself in increased mass transport rates which are a direct consequence of Lorentz forces in the bulk of the electrolyte. This enhanced mass transport can directly affect the electrocrystallization. The partial currents for the nucleation of nickel in magnetic fields were determined using an in situ micro-gravimetric technique and are discussed on the basis of the nucleation model of Heerman and Tarallo. Another focus of the paper is the numerical simulation of MHD effects on electrochemical metal depositions. A careful analysis of the governing equations shows that many MHD problems must be treated in a 3D geometry. In most cases there is a complex interplay of natural and magnetically driven convection.     

Use of paired, bonded NdFeB magnets in redox magnetohydrodynamics

Bonded neodymium-iron-boron (NdFeB) permanent magnets in a paired configuration were successfully used to control mass transport in redox-based, magnetohydrodynamics (MHD). Control of fluid flow based on magnetic fields has potential for use in portable lab-on-a-chip (LOAC) and analytical devices. Bonded magnets, composed of magnetic powder and organic binder materials, are less expensive and easier to fabricate and pattern than electromagnets and sintered permanent magnets, which have been previously used in MHD studies on electrochemical systems. The ability to pattern bonded magnets near and around the electrodes is expected to allow for better control over the magnetic field distribution and solution flow. Current was generated at an 800-microm-radius platinum disk electrode in a solution of 0.06 M nitrobenzene and 0.5 M tetra-n-butylammonium hexafluorophosphate in acetonitrile. Increases in limiting current in the presence of the magnetic field, which indicate enhancement in mass transport, for sintered (210+/-14%, N = 4, where B(r) = 1.23 T and magnetic field strength is 0.55 T) and bonded (94+/-8%, N = 4, where B(r) = 0.41 T and magnetic field strength is 0.20 T) magnets, were similar to those obtained using an electromagnet with the same magnetic flux densities. The magnetic field strength and not the magnet type is important in controlling fluid flow, which is encouraging for integration of bonded permanent magnets into LOAC devices.     

Hall effect on MHD flow and heat transfer over a stretching sheet with variable thickness

We investigate the MHD flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness. The wall temperature and the wall velocity are assumed to vary. The effects of external magnetic field along the sheet and the Hall currents are considered. The governing equations are solved numerically using an implicit finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in very good agreement. The effects of the physical parameters on the velocity and temperature fields are presented graphically and analyzed. The effect of the Hall current gives rise to a cross flow. Moreover, the Hall current and the magnetic field have strong effect on the flow and heat transfer characteristics, i.e., shear stress and the Nusselt number.     

A flux‐limited numerical method for solving the MHD equations to simulate propulsive plasma flows

For numerical simulations to be effective tools in plasma propulsion research, a high‐order accurate solver that captures MHD shocks monotonically and works reliably for strong magnetic fields is needed. For this purpose, a characteristics‐based scheme for the MHD equations, with flux limiters to improve spatial accuracy, has been developed. In this method, the symmetric form of the MHD equations, accounting for waves propagating in all directions, are solved. The required eigensystem of axisymmetric MHD equations, with appropriate normalization, is presented. This scheme was validated with unsteady (Riemann problem) and force‐free equilibrium (Taylor state) test cases, as well as with measured current density patterns in a magnetoplasmadynamic thruster. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element modeling of contaminant transport in soils including the effect of chemical reactions

The movement of chemicals through soils to the groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. Recent studies have shown that the current models and methods are not able to adequately describe the leaching of nutrients through soils, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. Furthermore, the effect of chemical reactions on the fate and transport of contaminants is not included in many of the existing numerical models for contaminant transport. In this paper a numerical model is presented for simulation of the flow of water and air and contaminant transport through unsaturated soils with the main focus being on the effects of chemical reactions. The governing equations of miscible contaminant transport including advection, dispersion-diffusion and adsorption effects together with the effect of chemical reactions are presented. The mathematical framework and the numerical implementation of the model are described in detail. The model is validated by application to a number of test cases from the literature and is then applied to the simulation of a physical model test involving transport of contaminants in a block of soil with particular reference to the effects of chemical reactions. Comparison of the results of the numerical model with the experimental results shows that the model is capable of predicting the effects of chemical reactions with very high accuracy. The importance of consideration of the effects of chemical reactions is highlighted.     

Influence of variable permeability on the dispersion of a chemically reacting solute in porous media

In this paper in the first part, the influence of variable permeability on the two MHD basic flows in porous media is studied numerically. It is seen that the variable permeability due to random packing causes the hydromagnetic channelling in both the flows. Further, it is also observed that the flow in both the cases is retarded for any increase in the magnetic parameter.

In the second part, the influence of variable permeability and the effects of homogeneous and heterogeneous reactions on the dispersion of a solute in the above two basic flows are investigated. In the case of diffusion with a first order homogeneous reaction, in both the flows, the variation of permeability increases the effective dispersion coefficient while it decreases with increase in the magnetic parameter. In the case of diffusion combined with homogeneous and heterogeneous chemical reactions, the variation in permeability again increases the effective dispersion coefficient while with increase in magnetic parameter causes a decrease in the effective dispersion coefficient. Several earlier results follow as particular cases of the present study.     

A study of the lead dioxide electrocrystallization mechanism on glassy carbon electrodes. Part I: Experimental conditions for kinetic control

The dependence on chemical and electrochemical variables of lead dioxide electrodeposition on a glassy carbon electrode from Pb(II) aqueous solutions has been studied. Depending on the experimental conditions, the mechanism of lead dioxide electrodeposition may involve kinetic or mass transport control. Both modeling and morphological studies of the nucleation and growth process have been carried out. The analysis of the chronoamperometric curves obtained from potential step experiments required a previous study regarding (i) the experimental solution conditions (pH, Pb(II) concentration), (ii) range of the final step potential to be used, and (iii) the choice of theoretical models used to obtain the kinetic parameters. Direct microscopic observation of the electrode through the initial stages of oxide phase formation has provided independent values of nucleation kinetics parameters (N₀A), growth constants (k), induction time (t₀) and their dependence on the electrochemical variables. The fitting of the experimental curves using some of these independent values allowed other ones, with more realistic values, to be obtained. Further discussion on the mechanistic details of the lead dioxide electrodeposition is presented.     

Effect of magnetic fields on solid-melt phase transformation in pure bismuth

The differential thermal analysis (DTA) apparatus has been designed in order to investigate the effect of magnetic fields on solid-melt phase transformation in pure bismuth. The endothermic peaks of DTA curves show that melting is insensitive to magnetic fields, which can be verified from thermodynamics. However, the exothermic peak obviously shifts to higher temperature as the magnetic field strength increases, from which the magnetic field does not affect the crystal growth but nucleation. On the basis of the assumption that there is an intermediate state between a crystal nucleus and a liquid atom, one possible reason for the shift of exothermic peaks is that kinetic barrier of nucleation is lowered and nucleation is activated by magnetic fields.     

MHD flow in conducting circular expansions with strong transverse magnetic fields

This paper treats the steady, inertialess flow of an incompressible, electrically conducting fluid through perfectly conducting, variable-area ducts of circular cross section in the presence of strong transverse magnetic fields. The problem is of fundamental importance in the design of liquid-lithium cooling systems for fusion reactors, of liquid-metal MHD generators and of MHD machinery in metallurgy. First we find that, if a straight pipe of radius r is joined to an expansion or contraction, then the disturbance of the fully developed flow in the pipe dies out like exp ($\text{? 12.16¦x¦r}{}^{\mathrm{?1}}$), where x is distance from the join. Next we consider the flow in conical expansions with end effects neglected; and find that the flow becomes concentrated near the plane of symmetry as the divergence increases. Finally numerical schemes for determining the flow in more general expansions and contractions are outlined. Extension of the present analysis to non-circular sections is also discussed.     

Hydrodynamic study of a rotating MHD flow in a cylindrical cavity by ultrasound Doppler shift method

An experimental study of a steady laminar magnetohydrodynamic (MHD) flow driven by a rotating disk at the top of a cylindrical cavity filled with water or mercury is presented. The velocity distributions were analysed using the ultrasound velocity (UVP) measuring technique. The uniform and constant applied magnetic field is directed along the axis of the cavity. The measurements were compared with results obtained from a numerical model based on a finite volume computational fluid dynamics (CFD) model. The effects of the magnetic field, the fluid and wall electrical conductivities, and the wall thickness are investigated through the conductance ratio k which characterises the influence of the wall on the closure of the electric current distribution. The other relevant parameters are the Hartmann number M, and the Reynolds number Re. The study was performed essentially for different values of Re ? 30,000 and M ? 260. There were close agreement between numerical results, the present ultrasonic measurements and other reported experimental and numerical works. The experiments have revealed something that has not been predicted numerically, the sidewall layer is unstable for special conditions of Hartmann and Reynolds numbers.     

Application of the “K-ε” model to open channel flows in a magnetic field

In magnetohydrodynamic (MHD) flows turbulence reduction occurs due to the Joule dissipation. It results in heat transfer degradation. In open channel flows, heat transfer degradation is also caused by the turbulence redistribution near the free surface. Both effects can be significant in fusion applications with low-conductivity fluids such as molten salts. In the present study, the “K-ε” model equations for turbulent flows and the free surface boundary condition are adjusted with taking into account MHD effects. Different orientations of the magnetic field, perpendicular and parallel to the main flow, have been considered. The model coefficients have been tuned by a computer optimization using available experimental data for the friction factor. The effect of free surface heat transfer degradation due to the turbulence redistribution has been implemented through the variation of the turbulent Prandtl number. As an example, the model is used for the analysis of a turbulent MHD flow down an inclined chute with the heat flux applied to the free surface.     

Factors influencing the kinetics of electrochemical reactions in milling

Input of mechanical energy at a high rate can drive a system and induce phase transformations and chemical reactions away from equilibrium. The evolution of such a change depends on both thermodynamic as well as kinetic factors. Besides the microstructural changes like attainment of nanostructure, which alters the overall free energy, the high rate of mechanical energy input also changes the kinetics by influencing the mass transport and related processes. In order to understand these factors, we have recently started a programme of looking at the influence of mechanical energy on driving simple chemical reactions in solid state. In this presentation we shall present and discuss the results of two kinds of situation that we have studied. The first one is simple electrochemical replacement reactions between metals and metal sulphates in solid state. We show that the mechanical milling alters the kinetics of these reactions, which can be rationalized by considering the phenomena taking place at the microscopic level. For example we will show that the crystal structure of the sulphate and the nature of the reaction product at the interface influence the mechanochemistry significantly. It is even possible in some special cases to alter the direction of the chemical reaction. In the second set of results we shall present the effect of mechanical milling on the site occupancy in ferrites, which can lead to a significant change in magnetic behaviour.     

Angular Dependence of Transport AC Losses in Superconducting Wire with Position-Dependent Critical Current Density in a DC Magnetic Field

Transport AC losses play a very important role in high temperature superconductors (HTSs), which usually carry AC transport current under applied magnetic field in typical application-like conditions. In this paper, we propose the analytical formula for transport AC losses in HTS wire by considering critical current density of both inhomogeneous and anisotropic field dependent. The angular dependence of critical current density is described by effective mass theory, and the HTS wire has inhomogeneous distribution cross-section of critical current density. We calculate the angular dependence of normalized AC losses under different DC applied magnetic fields. The numerical results of this formula agree well with the experiment data and are better than the results of Norris formula. This analytical formula can explain the deviation of experimental transport current losses from the Norris formula and apply to calculate transport AC losses in realistic practical condition.     

Electrodeposited hydroxyapatite coatings in static magnetic field

Uniform hydroxyapatite (HA) coatings were deposited electrochemically on titanium in magnetic fields. The structure and morphology of the deposited films were investigated by scanning electron microscopy, X-ray diffraction and transmission electron microscopy (SEM, XRD and TEM). It was found that the morphology of HA deposits could be altered by direction and intensity of applied magnetic field. Needle-like crystals formed when magnetic field was applied perpendicularly to electric field (B⊥ J), whereas spherical nanocrystals formed when magnetic and electric fields were in parallel (B||J). In addition, the nucleation rate of the HA crystals was proportional to the magnetic field intensity. Therefore, the resultant crystal size decreased with increasing magnetic field intensity.     

Pseudospectral method for MHD pipe flow

The paper deals with MHD flow in pipes with arbitrary wall conductivity under the influence of a transverse magnetic field. We employ the pseudospectral collocation method for obtaining a numerical solution of the problem. The numerical results are compared with analytical ones in the case of pipe with insulating walls. We notice that the magnetic field is slowing the motion. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of Current and Magnetic Distributions in REBCO Superconducting Coated Conductors in Self- and External Fields

The influence of a self-field on the critical current density J _c for a REBCO superconducting tape is presented in this paper. The distributions of the current density and magnetic field are analyzed in the tape under three kinds of conditions, i.e., applying an external magnetic field only, applying a transport current only, and applying a transport current together with an external magnetic field. In the analysis, the two-dimensional Poisson equation for the vector potential is employed. For the convenience of calculation, that the dependence of critical current versus the perpendicular and parallel fields tested from experiment is substituted for the traditional Kim-type or Bean model. The results show that the distributions of the current density and magnetic field in the REBCO tape change for the different frequencies and amplitudes of the transport current I _a and applied magnetic field B _a.     

Fluid Flow and Solidification Under Combined Action of Magnetic Fields and Microgravity

Mathematical models, both 2-D and 3-D, are developed to represent g-jitter induced fluid flows and their effects on solidification under combined action of magnetic fields and microgravity. The numerical model development is based on the finite element solution of governing equations describing the transient g-jitter driven fluid flows, heat transfer, and solutal transport during crystal growth with and without an applied magnetic field in space vehicles. To validate the model predictions, a ground-based g-jitter simulator is developed using the oscillating wall temperatures where timely oscillating fluid flows are measured using a laser PIV (Particle Image Velocimetry) system. The measurements are compared well with numerical results obtained from the numerical models. Results show that a combined action derived from magnetic damping and microgravity can be an effective means to control the melt flow and solutal transport of single crystal growth in space environment.     

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

Mass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.     

High-Field Electronic Properties of Graphene

We have measured the energy gaps in single-layer and bilayer graphene by means of temperature dependent transport experiments in high magnetic fields up to 33 T. They follow the expected Landau level splitting when a finite level width is taken into account. The quantum Hall effect, hitherto only observed up to 30 K, remains visible up to 200 K in bilayers and even up to room temperature in single-layer graphene. Our experiments in single-layer graphene show that the lowest Landau level, shared equally between electrons and holes at zero energy, becomes extremely narrow in high magnetic fields. It is this narrowing, together with the large Landau level splitting in graphene that leads to an extremely robust localization and makes the quantum Hall effect visible up to room temperature. In high magnetic fields (B>20 T) we observe a strongly increasing resistance with decreasing temperature. These results are explained with field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements.