Object surfaces such as semiconductor wafers which are suspended in a rinsing fluid may be dried by replacing the rinsing fluid, such as water, with a drying vapor by directly displacing the water from the surfaces at such a rate that substantially no liquid droplets are left on the surfaces after replacement of the water with drying vapor. Preferably, the drying vapor is miscible with water and forms a minimum-boiling azeotrope with water, such as isopropanol. The drying vapor is then purged with a stream of dry, inert, non-condensable gas such as nitrogen. A vaporizer with automatic refill mechanism produces saturated drying vapor which may then be flashed to a superheated vapor prior to contacting the surfaces, which preferably are at the same temperature as the vapor. Preferably, no liquid is removed by evaporation, and the drying takes place in an enclosed, hydraulically full system which does not require movement or handling of the surfaces between rinsing and drying steps.