solid potential in electrolyte current formulation

[dion-w]

Hello everyone,
i have a question concerning the equation for the electrolyte current in the submodel {"electrolyte conductivity": "full", "surface form": "differential"}. The equation for electrolyte current in get_coupled_variables in the file pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py (line 59) reads like this:

i_e = conductivity * (
                ((1 + param.Theta * T) * param.chi(c_e, T) / c_e) * pybamm.grad(c_e)
                + pybamm.grad(delta_phi)
                + i_boundary_cc / sigma_eff
            )

My question now is: Why do you use delta_phi in this equation? Normally for conduction in the electrolyte you would use the electrolyte potential phi_e and not delta_phi when treating a capacitor-like double layer (as seen here and here). I sort of get, that you want to use delta_phi, so you only need to solve the model for c_s, c_e and delta_phi but i don't get the physical motivation, or does the "i_boundary_cc/sigma_eff" in the i_e equation above somehow cancel out the contribution of grad(phi_s)? I see some stuff in the boundary conditions, but i gues it would cancel stuff out only on the boundaries and not in between?

Thanks in advance for your help.

[dion-w]

By doing a comparison between the i_e from the double layer fromulation and the i_e without a double layer i found out that by comparison both equations differ in a term of . This means when including this term in the formulaton with double layer one gets the equation without double layer. So to use the double layer in dependence of there needs to be an additional term as well as an updated prefactor (which includes the conductivities). Can anybody confirm or deny this? Is there any publication about this? I found nothing else than the usual papers when using pybamm.print_citations at the end of my script.

[valentinsulzer]

This is the paper: https://iopscience.iop.org/article/10.1149/2.0301910jes/pdf
See equations 47 and 48. The variable in the time derivative is delta phi

[dion-w]

Thanks a lot!