New discretization procedure for the breakage equation



A new discretization method, applicable for both batch and continuous systems, is developed for the breakage equation. The problem of intrainterval interactions due to discretization is accounted for by matching the zeroth and first moments of the continuous population balance equation with the corresponding moments of the discretized equation, thereby guaranteeing conservation of mass and total number of particles. Without loss of generality, the use of this method is demonstrated with a power law form of the specific rate of breakage, and with both theoretical and empirical breakage functions. The systematic method requires minimum computational efforts by allowing the user to choose either geometric size intervals with any geometric ratio or equal-size intervals for the particle size range. Simulation results show that the new method significantly improves predictions of the particle size distribution over the discretization method currently in use.