Prediction of Multimodal Distributions in Breakage Processes

The prediction of multimodal distributions through the population balance equation (PBE) in breakage processes is addressed. A numerical approach based on physical arguments is suggested and applied. The time-dependent unknown distribution is approximated by a weighted sum of (beta)-subdistributions. The parameters of the (beta)-PDFs and their weights are treated as unknown functions of time. The method allows for the tracking of the evolution of multimodal distributions through few unknown functions, determined by ordinary differential equations. The method is applied here to PBEs for pure breakage processes, although it can be further developed to include growth and coalescence.