Self-similarity law of particle size distribution and energy law in size reduction of solids

The concept of fractal dimension and scaling is used to determine the particle size distribution for ground powder and a generalized energy law for size reduction of solids. Based on the theory of stochastic processes, a master equation for the size distribution under a sieve is introduced. For the case that the functional forms of the transition probabilities are given, the solution is analutically obtained. Introducing a scaling concept and a characteristic size constant which measures the particle size distribution of the ground product, we present a power law for the distribution function. We, furthermore, present a generalized fractal energy law which has an intimate relation to the size distribution through a fractal specific surface area.