Question about the symbol in the DFN model charge conservation equation

[wangatang3]

Just want to know if a symbol in charge conservation law for the DFN model in https://docs.pybamm.org/en/stable/source/examples/notebooks/models/DFN.html is correct or not.

From my point of view, in the third equation, the denominator (the partial derivative) should be with respect to the solid-phase potential \phi_{s,k}, not the electrolyte potential \phi_{e,k}, as you can find in the figure below. I carefully checked this issue and it seems my idea is supported by other works such as "An asymptotic derivation of a single particle model with electrolyte" by Marquis et al. Can anyone help me with this issue and see if I am wrong?