The present invention relates to a single module, flow-electrode apparatus for continuous water desalination, ion separation and selective ion removal and concentration by capacitive deionization, comprising: a first current collector (1), a first compartment (1′) for a flow electrode, a first ion exchange membrane (AEM, CEM), a first liquid-permeable channel (6a) next to the first ion exchange membrane (AEM, CEM), a second ion exchange membrane (CEM, AEM) with a fixed charge opposite to that of the first ion exchange membrane (AEM, CEM) next to the first liquid-permeable channel (6a), a second liquid-permeable channel (6b) next to the second ion exchange membrane (CEM, AEM), a third ion exchange membrane (AEM, CEM) having the same fixed charge as the first ion exchange membrane (AEM, CEM) next to the second liquid-permeable channel (6b), a second compartment (2′) for a flow electrode, and a second current collector (2), wherein a fluid (4) containing suspended conductive particles or a mixture of conductive and non-conductive particles or particles made of a mixture of conductive and non-conductive materials (5) is provided in the first and second compartments (1′, 2′), acting as the flow electrode, as well as a corresponding method.