Before revision: We analyze steady interface shapes in zero gravity in rotating right circular cylindrical containers under rigid body rotation  . Predictions are made near criticality, in which the interface, or part thereof, becomes straight and parallel to the axis of rotation.
After revision: We analyze steady interface shapes in rotating right-circular cylindrical containers under rigid body rotation . Predictions are made near criticality, in which the interface, or part thereof, becomes straight and parallel to the axis of rotation.