An air vortex mill (1) mill dries a flowable product in a gas-/air flow-through grinding chamber (3) with several grinding stages arranged in the grinding chamber. The grinding stages are formed by a rotor (4) with a multitude of grinding plates (9) and a stator housing. A device (12, 13) delivers preferably heated carrier gases, as a device (6, 15, 16, 18) delivers the product into the grinding chamber (3). In order to improve the product delivery to the mill (1), one component of the delivery device is a supply line (6) which encircles at least part the circumference of the grinding chamber (3). The supply line (6) is equipped with an inflow (15) for the product to be treated and a plurality of outlet apertures (18) distributed over the circumference of the grinding chamber, for delivering the product into the grinding chamber.