ENH: New suite for electrostatic deposition applications

Summary

• New suite for electrostatic deposition applications
  • Solver function object: electricPotential​: Computes the steady-state equation of charge conservation to obtain the electric potential by strictly assuming a quasi-static electrostatic field for single-phase and multiphase applications.
  • Finite-volume boundary condition: electrostaticDeposition​: A boundary condition to calculate electric potential (V) on a given boundary based on film thickness (h) and film resistance (R) fields which are updated based on a given patch-normal current density field (jn), Coulombic efficiency and film resistivity.
    • Allowing to set:
      • Minimum current density for deposition onset
      • Minimum accumulative specific charge for deposition onset
      • Resistance due to main body and/or pretreatment layers
      • Initial electric potential

Resolved bugs

N/A

Details of new models (If applicable)

A showcase illustrating the verification of the electricPotential function object. Right: dielectric-dielectric water-air; left: conductive-dielectric water-air mixture (López-Herrera et al., 2011).

A showcase illustrating the electrostaticDeposition​ BC: pending

Risks

• No changes in existing output.

Constraints

• Depletion or abrasion of material due to negative current is not allowed.​
• Boundary-condition updates are not allowed during outer corrections to prevent spurious accumulation of film thickness.​
• resistivity, jMin, qMin and Rbody are always non-negative.
• Quasi steady​
  • No electrolyte/ionic transport​
  • Quiescent​
• Sufficiently mixed​
• No magnetic field​
• No electrolyte and electric field interaction​
• Isotropic material and electrolyte​
• No film-flow interactions​
• No finite-area numerics​

Remaining issues

• Micro/nano current densities/potential differences cause numerical instabilities.
• Small diffs in patch-normal current-density values of cathode faces can lead to small diffs in incremental film thickness (Delta_h) on those faces. With the very high value of 'resistivity', the small diffs in 'Delta_h' can then lead to comparable diffs in incremental electric potential differences across patch faces.​
  • These differences can then be accumulated throughout a simulation, causing non-zero potential difference gradients across faces of the cathode.​
  • Our workaround was to round the floating-point numbers of operand variables to a given number of decimal points (default: 8 decimals) - disallow micro/nano volts, so that such accumulation could be avoided.​
  • However, this issue may cause numerical instabilities in more complex cases.​
  • Therefore, the original expressions of the formulation may need to be revisited.​
• Advanced electrodeposition applications using OpenFOAM can be visited as well:
  • Kauffman et al., 2020
  • López-Herrera et al., 2011
  • Roghair et al., 2013
  • Takayama et al., 2013, Implementation of a Model for Electroplating in OpenFOAM.
  • Kashir et al., 2019
  • EHDIonFOAM