scholarly journals (ECS 236th) Multiphysics Modeling of the Tertiary Current Distribution in Pulse/Pulse-Reverse Electrochemical Processing of Microstructured Workpieces

2020 ◽  
Author(s):  
Brian Skinn ◽  
Alan C West
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Current Distribution ◽  
Surface Finishing ◽  
Workpiece Surface ◽  
Structured Surfaces ◽  
Electrochemical Processes ◽  
Pulse Reverse ◽  
Primary Current ◽  
Primary Current Distribution

The physical phenomena governing the current distribution on an electrode of arbitrary shape are typically categorized as falling into primary, secondary, and/or tertiary effects. Primary current distribution effects are defined by the geometry of the system and the electrical properties of the relevant materials, whereas secondary and tertiary effects incorporate additional position-dependent polarizations that respectively arise from electrochemical-kinetic and mass-transfer/concentration physics. In industrial electrochemical processes, the uniformity of the current distribution across a workpiece is of vital concern. In electrodeposition processes, for example, it is usually desirable for the deposited metal to be as uniformly distributed as possible, regardless of the form of the workpiece. Conversely, in electropolishing processes, it is critical to focus the current density onto the tops of asperities on the workpiece surface, in a highly non-uniform fashion, in order to minimize material removal irrelevant to the goal of decreased surface roughness. In general, the primary current distribution leads to the most non-uniform current distribution possible for a given geometry, from which the secondary and tertiary effects tend to have varying degrees of a “leveling” effect, leading to a comparative increase in processing uniformity.In electrodissolution processes, saturation of the dissolved metal at the workpiece surface is an important mechanism by which the tertiary current distribution effects influence practical electrochemical processes. This saturation phenomenon leads both to an increase in the local overpotential, via concentration polarization, and also has the potential to occlude locally a fraction of the workpiece exposed area due to the formation of insoluble precipitates. As noted, both of these effects tend to increase the uniformity of the resulting overall current distribution, and thus it is important to be able to predict, even if approximately, when a given process will be operating in this regime and to what extent the uniformity of the current distribution might be affected.This talk will summarize results from multiphysics simulations developed to represent this occluded-surface aspect of the tertiary current distribution, in addition to primary and secondary current distribution effects. These simulations incorporate pulse/pulse-reverse waveforms applied to workpieces with structured surfaces, in an attempt to approximate a surface finishing application of industrial relevance. In particular, focus was placed on simulating a “microprofile,” the scenario where surface structures have characteristic dimensions much smaller than the hydrodynamic boundary layer for mass transfer—this choice simplifies the modeling by obviating consideration of the macroscopic fluid dynamics of the system. The effect of pulse waveform parameters on the uniformity of the overall current distribution will be discussed, and simulation results will be shown illustrating the tendency of suitably-chosen waveform parameters to “collapse” toward the workpiece surface the subdomain of the boundary layer in which the local concentration of dissolved material oscillates significantly in response to the applied electric field.

scholarly journals (ECS 233rd) Multiphysics Modeling of Surface Finishing Performance in Pulsed-Waveform Electrochemical Machining

2018 ◽  
Author(s):  
Brian Skinn ◽  
Tim Hall ◽  
Jennings E. Taylor
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Layer Thickness ◽  
Current Distribution ◽  
Surface Finish ◽  
Boundary Layer Thickness ◽  
Electrochemical Machining ◽  
Pulse Plating ◽  
Surface Finishing ◽  
Local Surface

Electrochemical machining (ECM) is a manufacturing technology that allows metal to be precisely removed by electrochemical oxidation and dissolution into an electrolyte solution. ECM is suited for machining parts fabricated from “difficult to cut” materials and/or parts with complicated and intricate geometries. In ECM, the workpiece is the anode and the tool is the cathode in an electrochemical cell; by relative movement of the shaped tool into the workpiece, the mirror image of the tool is “copied” or machined into the workpiece. One notable difficulty with ECM is an inability to predict a priori the tool and process parameters required in order to satisfy the final specifications of the fabricated part [[1]]. Accordingly, there is potential value in development of a physical phenomenon-based design platform to predict optimal ECM tool shape. Such a capability is anticipated to dramatically shorten the process/tooling development cycle.A further goal of ECM is to simultaneously achieve a target surface finish on the machined part. It is thus of interest to develop the capability also to predict the distribution of local surface finish resulting from ECM processing. Modeling of the changes in local surface finish intrinsically operates on a different length scale from that of bulk material removal (μm, versus mm or cm), and thus is most easily treated separately. The physicochemical phenomena involved in the evolution of surface finish during ECM processing are strongly coupled, and include the electric field itself (primary current distribution), surface polarization and electrochemical kinetics (secondary current distribution), and fluid flow and mass transfer (tertiary current distribution). Of particular interest is modeling of pulsed-waveform ECM, for which significant practical advantages have been demonstrated [[2],[3],[4]]. While an extensive body of literature exists analyzing pulsed electrodeposition [[5],[6],[7]], comparatively little work has been published to date on pulsed ECM [[8],[9]].This talk will discuss recent modeling work seeking to develop a solid foundation for a predictive understanding of the surface finishing aspects of ECM processes. The work described herein encompasses time-dependent modeling of one-dimensional concentration profiles under the application of pulsed current ECM waveforms, providing a foundation for future development of quantitative descriptions of the transient and steady-periodic behavior on structured substrates. Prior work (see, e.g., Ref. 3) has demonstrated the value in differential pulsed-ECM processing of surfaces with features of size comparable to or larger than the hydrodynamic boundary layer thickness (“macroprofiles”) versus surfaces with features much smaller than the boundary layer thickness (“microprofiles”). Methods are discussed for accurate estimation of a quantity termed the “transition time,” which is the value for the pulse on-time for which the metal concentration at the surface rises exactly to saturation at the end of the forward pulse. Extending the pulse duration beyond this value thus introduces mass transfer limitations to the electrochemistry occurring at the surface.References[1]. Rajurkar, K.P. et al. Annals of the CIRP 82(2), 1999.[2]. Taylor, E.J. et al. “Breaking the Chemical Paradigm in Electrochemical Engineering: Case Studies and Lessons Learned from Plating to Polishing,” in Advances in Electrochemical Science & Engineering: The Path from Discovery to Product, x, y Eds. In press.[3]. Taylor, E.J. and M. Inman. “Electrochemical Surface Finishing.” ECS Interface, Fall 2014: 57-61.[4]. Taylor, E.J. et al. U.S. Patent 9,006,147, 14 Apr 2015.[5]. Puippe, J.C. and F. Leaman, eds. “Theory and Practice of Pulse Plating.” Orlando, FL: AESF, 1986.[6]. Hansel, W.E.G. and S. Roy. “Pulse Plating.” Bad Saulgau, Germany: Leuze Verlag KG, 2012.[7]. Ibl, N. “Some Theoretical Aspects of Pulse Electrolysis.” Surface Technology 10: 81 (1980).[8]. Sautebin, R. et al. J Electrochem Soc 127(5): 1096, 1980.[9]. Sautebin, R. and D. Landolt. J Electrochem Soc 129(5): 946, 1982.

scholarly journals (ECS 235th) Estimation of the Onset of Mass Transfer Limitations in Pulsed Electrochemical Processes

2019 ◽  
Author(s):  
Brian Skinn
Keyword(s):  
Mass Transfer ◽  
Current Distribution ◽  
Current Density ◽  
Electrode Surface ◽  
Electrochemical Process ◽  
Transition Time ◽  
Workpiece Surface ◽  
Electrochemical Processes ◽  
Simplifying Assumptions ◽  
Transition Times

The contributions of the physical phenomena governing the distribution of current across an electrode in an electrochemical process are conventionally categorized as primary, secondary, and/or tertiary current distribution effects, which respectively embody geometric/ohmic, kinetic polarization, and concentration polarization effects. On virtually all non-trivial workpieces of interest to industrial electrochemical practice, it is important to be able to control the areas affected by the process; viz., preferentially adding or removing material to some regions over others. Two of the most significant phenomena contributing to the tertiary current distribution in electrochemical processes are depletion (for electrodeposition) and saturation (for electrodissolution) of the active soluble metal species at the workpiece surface. Both of these phenomena lead to mass-transfer limitations: taking electrodissolution as an example, if material is being dissolved at a particular point on the electrode surface at a rate greater than diffusion can carry the products away from the surface, then mass-transfer limitations will result. The tertiary current distribution effects arising from these limitations will tend to disfavor further increases in the local electrodissolution current density at that point, thus shifting the current density distribution to other locations on the workpiece surface, to other reactions at the same location, or both. Thus, exerting control over these tertiary current distribution effects can be highly valuable for developing an efficient and accurate electrochemical process.An interesting feature of these mass-transfer-limiting phenomena is that they are almost entirely inactive for a short time (generally < 1 s for processes of practical interest) after the electrical voltage is applied, even if the applied current density is sufficiently high that significant mass transfer limitations will result after this initial interval. Thus, it follows that pulsing the applied potential/current at sufficiently high frequencies has the potential to enable significant control of these tertiary current distribution effects, by allowing the physicochemical conditions contributing to mass-transfer limitations at the electrode surface to “relax” while the potential is turned off. For the purposes of electrochemical process optimization, the ability to estimate the maximum concentration of dissolved species at the electrode surface for a given system and applied waveform would provide guidance as to whether and when a particular mode of mass-transfer limitation is likely to be active. In particular, evaluation of the “transition time,” the value of the waveform on-time above which mass-transfer limitations become appreciable, is of significant practical interest.Methods for transition time estimation based on linearized approximation of the boundary-layer concentration dynamics under a number of simplifying assumptions are available in the literature; e.g., Ref. [1]. However, the transition times calculated using these methods were found to deviate from COMSOL Multiphysics® simulation results by anywhere between –80% to +2780%, depending on the form of the estimation used and the particular waveform under consideration. This talk summarizes a method developed to provide appreciably more accurate predictions of transition times, under a similar set of simplifying assumptions as in Ref. 1. Separate on-time and off-time analytical solutions of the time-dependent steady-periodic mass transport behavior in a one-dimensional boundary layer were developed via the ‘finite Fourier transform’ (FFT) technique [[2]] and used to generate transition time estimates. Optimal values of the FFT model parameters were separately identified for fifty-three pairs of two pulsed-waveform timing parameters, period and duty cycle, spanning substantially the entire parameter space of practical industrial relevance. When compared to COMSOL® simulation results, the deviation of the transition time predictions (equivalently, predictions of the maximum surface concentration, in the electrodissolution paradigm of the model) was within 9% for all of the examined sets of timing parameters, with most deviating less than 5%. This FFT method thus provides a highly accurate method for estimation of transition times, within the approximations made in constructing the model.References[[1]] Ibl, N. “Some Theoretical Aspects of Pulse Electrolysis.” Surface Technology 10: 81-104 (1980).[[2]] Deen, W.M. “Analysis of Transport Phenomena,” 2nd ed., Ch. 5. New York: Oxford University Press, 2012.

Primary current distribution in the Hull cell and related trapezoidal geometries

1992 ◽  
Vol 22 (3) ◽  
pp. 301-303 ◽  
Author(s):  
A. C. West ◽  
M. Matlosz ◽  
D. Landolt
Keyword(s):  
Current Distribution ◽  
Hull Cell ◽  
Primary Current ◽  
Primary Current Distribution

scholarly journals Molten Salt Electrometallurgy

2019 ◽  
Author(s):  
Charles Osarinmwian
Keyword(s):  
Molten Salt ◽  
Current Distribution ◽  
Scale Up ◽  
Rotating Disk ◽  
Comsol Multiphysics ◽  
X Ray ◽  
Disk Electrodes ◽  
Primary Current ◽  
Cell Construction ◽  
Primary Current Distribution

The experimental results are for electro-deoxidation in molten salt and the numerical results are for molten salt processes in electrometallurgy.<div>The internal cathode microstructure is analysed using SEM, Energy dispersive X-ray spectroscopy, and computerised X-ray tomography.<br></div><div>Numerical simulations using COMSOL multiphysics report results for molten salt processes using theory from rotating disk electrodes and multiphase flow. Scale-up of electro-deoxidation is discussed using primary current distribution simulations in various electro-deoxidation cell designs.<br></div><div>Experimental details of electro-deoxidation cell construction is referenced to and outlined in my earlier work: <i>Electrochim. Acta</i> <b>164</b>, 48 (2015)<br></div>

scholarly journals Theoretical and Experimental Study of Copper Electrodeposition in a Modified Hull Cell

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Srinivas Palli ◽  
Suhash R. Dey
Keyword(s):  
Numerical Simulation ◽  
Current Distribution ◽  
Mapping Technique ◽  
Copper Electrodeposition ◽  
Approximate Analytical Expression ◽  
Hull Cell ◽  
Average Current ◽  
Current Densities ◽  
Primary Current ◽  
Primary Current Distribution

The primary current distribution and the resistance of a modified Hull cell are calculated by using conformal mapping technique coupled with numerical evaluation of the resulting integral equations. An approximate analytical expression for the primary current distribution of a modified Hull cell is presented. The primary current distribution along the cathode surface is noticed varying in controlled manner as a function of position on the substrate. The current distributions (primary, secondary, and tertiary) in the cell have also been calculated at different applied average current densities (2, 4.1, and 8.2 mA cm−2) through numerical simulation by using finite element based software. The numerical simulation result of the primary current distribution is then compared with the analytical solution and a good match is found. Experimentally, single Cu metal electrodeposition is carried out at different applied average current densities (2, 4.1, and 8.2 mA cm−2) in a modified Hull. The current distribution (primary, secondary, and tertiary) results obtained from the numerical simulation are compared with the experimental results and a satisfactory match is found. Surface morphology of the Cu deposits is examined using scanning electron microscopy (SEM).

(Invited) Estimation of the Onset of Mass Transfer Limitations in Pulsed Electrochemical Processes

2019 ◽  
Vol MA2019-01 (20) ◽  
pp. 1100-1100
Author(s):  
Brian Skinn
Keyword(s):  
Mass Transfer ◽  
Current Distribution ◽  
Current Density ◽  
Electrode Surface ◽  
Practical Interest ◽  
Electrochemical Process ◽  
Transition Time ◽  
Workpiece Surface ◽  
Simplifying Assumptions ◽  
Transition Times

The contributions of the physical phenomena governing the distribution of current across an electrode in an electrochemical process are conventionally categorized as primary, secondary, and/or tertiary current distribution effects, which respectively embody geometric/ohmic, kinetic polarization, and concentration polarization effects. On virtually all non-trivial workpieces of interest to industrial electrochemical practice, it is important to be able to control the areas affected by the process; viz., preferentially adding or removing material to some regions over others. Two of the most significant phenomena contributing to the tertiary current distribution in electrochemical processes are depletion (for electrodeposition) and saturation (for electrodissolution) of the active soluble metal species at the workpiece surface. Both of these phenomena lead to mass-transfer limitations: taking electrodissolution as an example, if material is being dissolved at a particular point on the electrode surface at a rate greater than diffusion can carry the products away from the surface, then mass-transfer limitations will result. The tertiary current distribution effects arising from these limitations will tend to disfavor further increases in the local electrodissolution current density at that point, thus shifting the current density distribution to other locations on the workpiece surface, to other reactions at the same location, or both. Thus, exerting control over these tertiary current distribution effects can be highly valuable for developing an efficient and accurate electrochemical process. An interesting feature of these mass-transfer-limiting phenomena is that they are almost entirely inactive for a short time (generally < 1 s for processes of practical interest) after the electrical voltage is applied, even if the applied current density is sufficiently high that significant mass transfer limitations will result after this initial interval. Thus, it follows that pulsing the applied potential/current at sufficiently high frequencies has the potential to enable significant control of these tertiary current distribution effects, by allowing the physicochemical conditions contributing to mass-transfer limitations at the electrode surface to “relax” while the potential is turned off. This “relaxation” behavior is schematized in Figure 1 for a generic pulse-electrodissolution process under steady-periodic conditions, where the orange and blue traces represent the concentration profiles at the end of the on-time and off-time, respectively, under conditions where no mass-transfer limitations are active at any point in time. For the purposes of electrochemical process optimization, the ability to estimate the maximum concentration of dissolved species at the electrode surface for a given system and applied waveform would provide guidance as to whether and when a particular mode of mass-transfer limitation is likely to be active. In particular, evaluation of the “transition time,” the value of the waveform on-time above which mass-transfer limitations become appreciable, is of significant practical interest. Methods for transition time estimation based on linearized approximation of the boundary-layer concentration dynamics under a number of simplifying assumptions are available in the literature; e.g., Ref. [1]. However, the transition times calculated using these methods were found to deviate from COMSOL Multiphysics® simulation results by anywhere between –80% to +2780%, depending on the form of the estimation used and the particular waveform under consideration. This talk summarizes a method developed to provide appreciably more accurate predictions of transition times, under a similar set of simplifying assumptions as in Ref. 1. Separate on-time and off-time analytical solutions of the time-dependent steady-periodic mass transport behavior in a one-dimensional boundary layer were developed via the ‘finite Fourier transform’ (FFT) technique [[2]] and used to generate transition time estimates. Optimal values of the FFT model parameters were separately identified for fifty-three pairs of two pulsed-waveform timing parameters, period and duty cycle, spanning substantially the entire parameter space of practical industrial relevance. When compared to COMSOL® simulation results, the deviation of the transition time predictions (equivalently, predictions of the maximum surface concentration, in the electrodissolution paradigm of the model) was within 9% for all of the examined sets of timing parameters, with most deviating less than 5%. This FFT method thus provides a highly accurate method for estimation of transition times, within the approximations made in constructing the model. References [[1]] Ibl, N. “Some Theoretical Aspects of Pulse Electrolysis.” Surface Technology 10: 81-104 (1980). [[2]] Deen, W.M. “Analysis of Transport Phenomena,” 2nd ed., Ch. 5. New York: Oxford University Press, 2012. Figure 1

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