Nonlinear effects in particulate processes

The nonlinear effects in various particulate processes are analyzed within the context of population balance modeling. Our main objective is to indicate the origin of the nonlinear effects and to categorize them in a systematic manner. To illustrate the importance of the nonlinear effects, a continuous milling process is considered, which has been analyzed in the literature with linear population balance models only. A continuous stirred tank mill (CSTM) and a plug-flow tube mill (PFTM) of identical volume were numerically simulated. It is well known that the accumulation of fine particles has a slowing-down effect on the breakage kinetics, which leads to non-intuitive results in terms of the produced particle size distribution. A nonlinear population balance theory is presented to account for these effects, and numerical simulations indicate the enormous potential of the new theory.