Deposition-Dissolution Rates, Growth Velocities, and Thicknesses on an Electrode Surface

The rate of dissolution or deposition on due to an electrode reaction is defined based on the reaction stoichiometry, νi,m, and the local current density, iloc,m, as described in Mass Fluxes and Sources Due to Electrochemical Reactions.

If the reaction rate is known, the total growth vdep, tot (m/s) is defined as the sum of the velocity contributions for all species and electrode reactions according to:

(4-3)

Where Mi (SI unit: kg/mol) is the molar mass and ρi (SI unit: kg/m3) the density of the species. (i is the species index, and m the index of the electrode reaction).

This velocity may be used in deforming geometry models as a boundary condition for the geometry deformation by assuming that dissolution or deposition always occurs in the normal direction to an electrode boundary, with the velocity being directed into the electrolyte domain:

In a time-dependent simulation one may also introduce a surface concentration variable, cs,i (mol/m2) on the boundary and calculate the accumulated surface concentration change by using a local ordinary differential equation (ODE):

The total deposited thickness stot(m) can then be defined as