The 1D "stack" is the structure of a very simple battery - anode, liquid electrolyte, porous cathode terminating in a cathode current collector. The (ionic) current flows through that stack, with the anode grounded (phis = 0)
and a constant current extracted from the collector. One of the output variables is then the potential at the collector, i.e. the battery voltage.
The porosity is initially uniform (P0), but in principle can change as a function of position (x) in the porous cathode due to the deposition
porosity = P0 - Aa*Ldep(x)
where Aa is the active area and Ldep is the local thickness of deposited product.
I hope that is clearer.
and a constant current extracted from the collector. One of the output variables is then the potential at the collector, i.e. the battery voltage.
The porosity is initially uniform (P0), but in principle can change as a function of position (x) in the porous cathode due to the deposition
porosity = P0 - Aa*Ldep(x)
where Aa is the active area and Ldep is the local thickness of deposited product.
I hope that is clearer.