Fluidized bed layering granulation is frequently used to formulate particles of high quality. From previous studies, it is well known that the dynamic behavior of the process, as well as the product properties depend on operating parameters. The process is characterized by heat and mass transfer between fluidized particles and the surrounding fluidization medium. To investigate the mutual influence between particle phase and fluidization medium, a dynamic model is introduced. The model comprises two parts: a population balance model to describe the evolution of the particle sizes and a system of ordinary differential equations to account for thermal conditions. For the first time, the dynamic model considers the bidirectional coupling of particles and fluidization medium in fluidized bed layering granulation. By means of simulations, it is shown that the derived model is capable of reproducing the experimental findings.

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $\beta$ (from series expansion) and $\eta$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.