Minerals Beneficiation - A Physical Explanation of the Empirical Laws of Comminution

The laws of Kick and Rittinger are explained as functions of particle size with metal cutting theory. Comminution is shown to be basically the same process as metal grinding. The machine shop type of grinding operation is used to study mineral crushing. Evidence indicates that plastic flow occurs in comminution. THE laws of comminution of Kick and Rittinger have been debated for many years. Certain data obtained from ball mill and drop tests are found to be in approximate agreement with Rittinger's law while other data would seem to support Kick's law. In all these tests the energy required to produce a wide variety of particle sizes has been studied. Surface area has also been measured with considerable difficulty, at first because it was thought that the energy associated with crushing was that required to create new surface, later because of precedent and because a more fundamental variable was unknown. Tests made with the machine shop type of grinding process show that normally brittle materials that are usually crushed can behave like the more ductile metals. Brittleness is then a relative prop- erty largely dependent on specimen size and stress state. The machine grinding operation offers a convenient means for studying the comminution of materials in which the important size variable retains its identity. The energy required to grind a certain volume of material is shown to be strongly dependent on size. Kick's law is found to hold very well for particles below 1 micron in size, while Rittinger's law holds approximately in the comminution of larger particles. While a physical origin of Kick's law is established in terms of the theoretical strength of materials having a perfect lattice structure, there is found to be no physical basis for Rittinger's law. Because of its industrial importance, comminution has commanded considerable technical attention and has been the subject of continuous study for nearly a century. A number of empirical rules have been proposed to make it possible for grinding energies to be predicted. Of these so-called laws of comminution those bearing the names of Kick and Rittinger have been most widely applied and debated.