Machines and methods adapted to process, for example, to reduce the size of, disperse, or homogenize, a variety of materials and compositions. Such methods and machines are capable of reducing the size of a material and dispersing the material in a liquid by cutting the material with knives located along a perimeter of an annular-shaped cutting head, causing the cut material to flow radially outward from the cutting head through gaps between the knives, and flowing a liquid through passages in the cutting head that cause the liquid to cascade around the knives of the cutting head in an axial direction of the cutting head.