A method for continuous water desalination, ion separation and selective ion removal and concentration by capacitive deionization using an apparatus, comprising: a first current collector, a first compartment for a flow electrode, a first ion exchange membrane (AEM, CEM), a first liquid-permeable channel 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, a second liquid-permeable channel 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, a second compartment for a flow electrode, and a second current collector, wherein a fluid 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 is provided in the first and second compartments (1', 2'), acting as the flow electrode, the method comprising the steps of: applying a voltage or a current between the first and second current collectors (1, 2), continuously supplying feed water containing ionic components to the first and second liquid-permeable channels (6a, 6b), supplying said fluid into the first and second compartments (1', 2') for a flow electrode, wherein the fluid is continuously circulated in the first and second compartments (1', 2') for a flow electrode such that the fluid leaving the first compartment for a flow electrode is introduced in the second compartment for a flow electrode, and the fluid leaving the second compartment for a flow electrode is introduced in the first compartment for a flow electrode, continuously discharging from the first liquid permeable channel a water having a lower concentration of the ionic components compared to the water introduced in the first liquid permeable channel, and continuously discharging from the second liquid permeable channel a water having an increased concentration of the ionic components compared to the water introduced in the second liquid-permeable channel. a first current collector, a first compartment for a flow electrode, a first ion exchange membrane (AEM, CEM), a first liquid-permeable channel 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, a second liquid-permeable channel 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, a second compartment for a flow electrode, and a second current collector, wherein a fluid 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 is provided in the first and second compartments (1', 2'), acting as the flow electrode, the method comprising the steps of: applying a voltage or a current between the first and second current collectors (1, 2), continuously supplying feed water containing ionic components to the first and second liquid-permeable channels (6a, 6b), supplying said fluid into the first and second compartments (1', 2') for a flow electrode, wherein the fluid is continuously circulated in the first and second compartments (1', 2') for a flow electrode such that the fluid leaving the first compartment for a flow electrode is introduced in the second compartment for a flow electrode, and the fluid leaving the second compartment for a flow electrode is introduced in the first compartment for a flow electrode, continuously discharging from the first liquid permeable channel a water having a lower concentration of the ionic components compared to the water introduced in the first liquid permeable channel, and continuously discharging from the second liquid permeable channel a water having an increased concentration of the ionic components compared to the water introduced in the second liquid-permeable channel. applying a voltage or a current between the first and second current collectors (1, 2), continuously supplying feed water containing ionic components to the first and second liquid-permeable channels (6a, 6b), supplying said fluid into the first and second compartments (1', 2') for a flow electrode, wherein the fluid is continuously circulated in the first and second compartments (1', 2') for a flow electrode such that the fluid leaving the first compartment for a flow electrode is introduced in the second compartment for a flow electrode, and the fluid leaving the second compartment for a flow electrode is introduced in the first compartment for a flow electrode, continuously discharging from the first liquid permeable channel a water having a lower concentration of the ionic components compared to the water introduced in the first liquid permeable channel, and continuously discharging from the second liquid permeable channel a water having an increased concentration of the ionic components compared to the water introduced in the second liquid-permeable channel.