We study the electrohydrodynamics 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 nonequilibrium 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 nonequilibrium approach also reveals unexpected high-frequency dynamics not predicted by circuit models.