Multiphysics Modeling of the Tertiary Current Distribution in Pulse/Pulse-Reverse Electrochemical Processing of Microstructured Workpieces

Abstract

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 polarization that respectively arises 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 (indicated by δ in Figure 1)—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 (δp in Figure 1) the subdomain of the boundary layer in which the local concentration of dissolved material oscillates significantly in response to the applied electric field. Figure 1. Schematic of the hydrodynamic boundary layer above a structured workpiece (δ), and a “collapsed” pulsating boundary layer (δp) arising from the use of a pulsed electric waveform. Figure 1