A liquid electrolyte can be desalinated and purified using a system that includes a first electrode and a configuration selected from (a) a second electrode and at least one distinct ion-selective boundary and (b) a second electrode that also serves as the ion-selective boundary. The ion-selective boundary is contained in the liquid conduit adjacent to a porous medium that defines pore channels filled with the liquid and that have a surface charge, and the charge of the ion-selective boundary and the surface charge of the pore channels share the same sign. A liquid including at least one charged species flows through the pore channels, forming a thin diffuse electrochemical double layer at an interface of the liquid and the charged surface of the pore channels. A voltage differential is applied between the electrodes across the porous medium to draw ions in the liquid to the electrodes to produce brine at the electrodes and to create a shock in the dissolved-ion concentration in the bulk volume of the liquid within the pore channels, wherein a depleted zone with a substantially reduced concentration of dissolved ions forms in the liquid bulk volume between the shock and the ion-selective boundary.