An appliance comprises a power base 3 having an electrical connector 4 providing power to a detachable cordless portion (2, fig.1) of the appliance. The base has an air flow generator 6 (fan or electrostatic fluid accelerator) supplying air through an outlet (5, fig. 2) to the cordless portion when mounted on the base. A low voltage power source (5 to 12V) may be connected to the electrical connector and housed in the base. The cordless portion may be a humidifier having a reservoir 11 for containing water and a transducer 10 generates water vapour, and receives the air flow from the base to provide a humidified air flow from an outlet 1. The appliance may be a vaporizer, a cooling fan, an air filtration device or a dehumidifier. The cordless portion may include one or more passages for carrying the air flow from a base of the cordless portion to an upper part of the reservoir. The electrical connectors may allow connection through a range of relative rotation. Since electrical components are housed in the power base and water sealed in a compartment 17 of the cordless portion, the cordless portion may be removed to be cleaned easily.