  We study the electro-hydrodynamics of the Debye screening layer that arises
in an aqueous binary solution near a planar insulating wall when applying a
spatially modulated AC-voltage. Combining this with first order perturbation
theory we establish the governing equations for the full non-equilibrium
problem and obtain analytic solutions in the bulk for the pressure and velocity
fields of the electrolyte and for the electric potential. We find good
agreement between the numerics of the full problem and the analytics of the
linear theory. Our work provides the theoretical foundations of circuit models
discussed in the literature. The non-equilibrium approach also reveals
unexpected high-frequency dynamics not predicted by circuit models.
