Adapting the double-layer equations to include a resistive term

[cannotcomplain]

Hello PyBaMM Team!

We are trying to adapt the PyBaMM double-layer ({'surface from': 'differential'}) equations to mimic those shown in Equation 1 and Table VII of D. Lu, M. Scott Trimboli, G. Fan, Y. Wang, and G. L. Plett, J. Electrochem. Soc. 169, 080504 (2022).. I've repeated the equation below.

We would appreicate any guidance on the following two points:

1. To change the RHS to include the resistive term, we would need to add a resistive term and a time-derivative of the double-layer current density $j_{dl}$. Is there an easy way to access the time derivative of $j_{dl}$?

2. To change the LHS, we need to add a resistive term inside of the time-derivative of delta_phi. It is difficult for us to find if it is possible to do this or where that change would need to be made?

Again, any direction on these issues would be greatly appreciated.

Best,
Jay