I am building a (1D) model of a battery in which an insoluble, insulating product is deposited in the pores of a porous cathode. It uses tertiary currents, with a PDE to give the deposition rate. The capacity of the battery will presumably depend on loss of active area in the cathode, reduction of the exchange current due to the insulating deposit, and loss of porosity. I have successfully modeled the first two, separately, but there is a problem with the third.
Clearly the volume available for the electrolyte is reduced during discharge. So I added Darcy flow with various BCs at the "free" end of the cathode, such as constant pressure, and outlet velocity. At best, the cation concentration increases throughout the electrolyte and cathode domains which is unphysical because it violates charge neutrality. At worst, it fails to converge for any reasonable setting of step-size, damping and tolerance.
How should I describe the flow of electrolyte that results from the reduction of available volume?
With thanks, Campbell
Clearly the volume available for the electrolyte is reduced during discharge. So I added Darcy flow with various BCs at the "free" end of the cathode, such as constant pressure, and outlet velocity. At best, the cation concentration increases throughout the electrolyte and cathode domains which is unphysical because it violates charge neutrality. At worst, it fails to converge for any reasonable setting of step-size, damping and tolerance.
How should I describe the flow of electrolyte that results from the reduction of available volume?
With thanks, Campbell