A rotary vacuum-chuck mounts a substrate such as a silicon wafer for rotation. The vacuum-chuck includes a hollow rotary shaft and a chuck mounted on the hollow rotary shaft and having a surface adapted to support a substrate, the surface having one or more openings in fluid communication with the hollow rotary shaft. A vacuum generator evacuates the hollow rotary shaft and the one or more openings so as to vacuum chuck a substrate to the chuck surface. A labyrinthine gap is defined between a first member that rotates with the hollow rotary shaft and a second member that is stationary. A fluid in the labyrinthine gap provides a gas-tight seal between the first and second members.