A new time-dependent rate constant of the coalescence kernel for the modelling of fluidised bed granulation

This paper presents a novel approach to the determination of the coalescence kernel for population balance modelling of a general class of batch fluidised bed aggregation systems, using a continuous sprayed-in liquid binder. Coalescence requires inter-particle collisions, the wetting of the contact surfaces and the dissipation of particle kinetic energy by the viscous squeezing of the binder film. These three sub-processes in principle depend both on the size of the contacting particles and on time. A new time-dependent aggregation rate constant of the coalescence kernel has been formulated by considering the general evolution of inter-particle collision behaviour with time. The model is implemented in MATLAB and its numerical output compared to two sets of experimental data: the granulation of glass beads with polyethylene glycol as a binder and the granulation of semolina with water. The evolution of mean and standard deviation in diameter versus time are examined as is the state of the size distribution at different stages in the process. The time-averaged aggregation rate for the glass beads evaluated as 7.59 × 10−9 m-0.5 s−1 while for the semolina it was 3.86 × 10−9 m-0.5 s−1. The agreement between numerical predictions and experiment is shown to be good, demonstrating the validity of the approach. Whilst conceptually simple, the model generates realistic output and provides a powerful insight into the underlying mechanisms of granulation. [Display omitted] •A new time-dependent rate constant of the coalescence kernel has been derived from inter-particle collision behaviour.•The novel approach is applied to model batch fluidised bed granulation and requires only one adjustable parameter.•The model is integrated with an existing size-dependency methodology using a discrete PBM form.•The agreement between model (solved by MATLAB) and two experimental case-studies is good.•Output from the model reveals and helps explains underlying trends in batch FBG systems.