The role of the transport equation in the grinding and fragmentation of solid objects

Abstract

The Boltzmann transport equation is employed to describe the time dependent evolution of two physical processes. (1) The grinding of solid particles and their subsequent size distribution and (2) the fragmentation of man-made satellites in earth orbit. It is shown how, by making rational assumptions about the break-up process, the Boltzmann equation provides a convenient framework in which to describe the mass and velocity distributions as a function of time. An equation is derived for the number of particles of a given size present in a homogeneous mixture after a specified grinding time. Also the number and mass of fragments in earth orbit due to satellite break-up by collisions is derived and some useful practical results obtained for finding the average lifetime of a satellite against collision.