I'm having a tremendously hard time understanding the connection between macro and micro scale electrostatics and how (if?) they're described EQS boundary conditions. I understand that in a medium with mobile ions, an applied current or field will lead to the establishment of an electric double layer with thickness on the order of a debye length, and this explains the micro scale side of EQS and why we see that the boundary conditions are violated since potential is not continuous across a DL. But does this mean that the boundary condition given by the conservation of charge is not very meaningful when you are trying to consider the micro scale? If we consider the interface between an insulator and a conducting electrolyte, where the system is experiencing a DC potential drop, you necessarily have no electric field in the conducting medium, and your conductivity in the insulator is zero. But this clearly has to be describing the macro scale electric field, correct? Because there is still an field due to the DL at the interface. But it doesn't seem like there's any equations that allow Laplace's equation to describe the field due to the DL. I'm also really confused about what AC current does when introduced to these systems. It seems like if the characteristic time of the current is much greater than the characteristic time of charge relaxation you can treat it as a DC current, but does this mean the exact same DL will form in your conducting media as when you were using DC? Or does this mean that your DL will form but will switch interfaces over time? If anyone at all is knowledgable I would really appreciate any clarification you could offer, I've been scouring the internet for hours on end every day for the past week trying to understand this material and haven't gotten anywhere.