Erosion in extruder flows: Analytical and numerical study

We consider the erosion of particles (e.g. carbonblack agglomerates) advected by the polymeric flow in a single screw extruder. We assume a particle to be made of primary fragments bound together. In the erosion process a primary fragment breaks out of a given particle. Particles disperse because of the shear stresses imparted by the fluid. The time evolution of the numbers of particles of different sizes is described by the Bateman coupled differential equations developed a century ago to model radioactivity. Using the particle size distribution we compute an entropic fragmentation index which varies from 0 for a monodisperse system to 1 for an extreme poly-disperse system. The time dependence of the index exhibits a maximum at some intermediate time as the system starts monodisperse (large size particle) and evolves through a poly-disperse regime at intermediate times to a monodisperse (small size particle) at late times.