Embodiments of the invention provide systems and methods for water purification. Embodiments can generally be applied to demister cyclones (6). Some embodiments allow for more of the pressure change which occurs in demister cyclones to occur in the separating chamber (19) of the demister cyclone. Some embodiments include a demister cyclone having an internal perforated wall (52). Some embodiments include a groove (103) or a baffle (102) on the underside of a boiler cover.