Tangential Velocities at the Intersection Between a Depositing and a Noncorroding Boundary

Shared points (in 2D) or edges (in 3D) between corroding and noncorroding boundaries are handled specifically in the Corrosion, Deformed Geometry interfaces.

The deformation in the normal direction of a noncorroding boundary is set to zero at all times. However, for the deformation velocity of the shared points/boundaries in the tangential direction of the noncorroding boundary, special conditions apply. These conditions can be derived expressions by assuming growth/dissolution to occur only in the normal direction of the corroding boundary by addition or removal of spherical particles (for example metal atoms), see Figure 4-1 below.

Figure 4-1: Gray/black arrows in whole stroke indicate the tangential electrode growth/dissolution velocities, vt, point, at the three-phase intersections between an electrolyte, a deposition/dissolution electrode and a noncorroding material. Dashed arrows are the growth/dissolution velocities, vcorr, based on the corrosion rate expressions. Note that the tangential velocities depend on both the angle between the corroding surface and the noncorroding surface, as well as the direction of the normal velocity.

In the following, the boundary tangents are denoted by t (pointing from electrolyte to electrode) and the normal by n (pointing in the direction out from the electrolyte domain).

If the angle between the corroding boundary and the noncorroding boundary is larger than π, the tangential velocity is set to zero:

(4-3)

Otherwise, (that is, if the angle between the corroding boundary and the noncorroding boundary is less than π), the following expressions are used:

(4-4)

Note that Case 2 above results in a lower velocity in the normal direction of the corroding surface than the corrosion velocity, and that this will act toward forming a π/2 angle between the dissolving and the noncorroding boundary, a phenomena observed in experiments (Ref. 1).

On shared points (2D) and edges (3D) between a Non-Deforming Boundary and an Deforming Electrode Surface, the velocity of the corroding boundary is set according to the expressions above.

Reference

1. J. Deconinck, “Mathematical Modeling of Electrode Growth,” J. Applied Electrochemistry, vol. 24, 212–218, 1994.