A method and a device for the continuous purification of a domestic or industrial water stream. After passing through a biological reactor to obtain a sludge of between 4 and 12 g/l of Dry Solids, the method involves feeding a series of chambers separated by restrictions at a flow rate q, injecting air into a second chamber at a flow rate Q>q, in order to obtain an emulsion, injecting a flocculant into a third chamber, and recovering the degassed emulsion in a drain pan. Flocculated and aerated sludge floats on top, such that the remaining liquid centrate has a Dry Solids content less than 100 mg/l and has a positive redox potential >50 mV and a value greater than 100 mV relative to the redox potential of the sludge at the inlet of the chambers, and is reinjected upstream from or into the biological reactor.