A pseudo-similarity solution to the integro-differential equation of batch grinding

A solution to the integro-differential equation of batch grinding has been presented which maps the trajectory of particle size spectra of continuous size and time domains. The solution, which is the most general analytical closed form expression available at present, employs Kapur's similarity solution to the grinding equation along with standard transformation techniques. The resulting size spectra, a modified form of the generalized gamma distribution, is not self-preserving and the energy—size reduction relationship does not conform to Walker's power law. These aspects have been illustrated by simulation studies.