Thermal treatment of polydispersed material in vortex equipment results in uneven heating and drying of particles of different sizes. To overcome these deficiencies and enhance the process economy, the following measures should be effected: combining power-intensive processes like drying and fine grinding in a single unit; classification of the polydispersed mixture within the equipment and return of the oversize for further drying and grinding. To implement these measures, the authors designed a unit for drying and grinding friable materials. It consists of vertical conical drying chamber and cyclone chamber placed in it with annular clearance. The chamber has tangential inlet, charging device, and axial pipe with nozzle, swirler, discharge pipe, cyclone, additional tangential pipe, circulation contour with two-stage impact-ejector mill, and heater. The unit was tested for treating zinc-bearing slimes and granular wastes of magnesium carbonate. The tests demonstrate the capability of the unit for dehydrating highly moist material to yield a product with guaranteed dispersed composition.