We present nonlinear breakage models to explain various observations reported in the literature based on the rational physics following the earlier work of Bilgili and Scarlett (2005). We show that the dynamics of the particle size distribution resulting due to certain nonlinear milling models also exhibits self-similarity that can very well be harnessed to extract models for both the breakage rates and daughter particle size distributions using the inverse problem approach developed by Sathyagal et al. (1994).
We show some interesting simulation results and validation of the adopted inverse problem approach for some model breakage rates and the daughter size distributions. It is also of interest to propose the methodology to relate the extracted breakage functions to the physics of the process and the operating parameters for two-stage hammer mill operated with screens in place that is a part of continuous tablet press.
1. Sathyagal, A. N.; Ramkrishna, D.; Narsimhan, G. Solutions of Inverse Problems in Population Balances II. Particle Break-Up. Comput. Chem. Eng. 19, (1995), 437.
2. Bilgili, E., Scarlett, B. Population balance modeling of non-linear effects in milling processes, Powder Technology 153, (2005), 59– 71.