Non-dimensionalisation of quadrature method of moments for wet granulation

Wet granulation is a multiphase process utilised to produce aggregate particles with defined properties from very fine powders. Simulating this process on the microscale is challenging because of the large number of particles involved, which differ widely in both size and material properties. Macroscale methods, which track only the particle bulk properties, are efficient but do not resolve disperse particle properties such as the particle size distribution (PSD), which is key information for downstream processing. These deficiencies are addressed by mesoscale methods like population balance (PB) models, which track distributed properties such as the particle size by adding them as internal variables to the macroscale (CFD) model. However, most mesoscale methods are either inaccurate (method of moments when cutting off moments) or computationally expensive (Monte Carlo, class methods). Recently a new closure for the method of moments, the quadrature method of moments (QMOM), was introduced to allow accurate moment tracking of a PSD with low computational effort. Disadvantages of this method, e.g., it can suffer from instabilities, can be overcome by non-dimensionalization. In this study we show our insights gained by non-dimensionalizing the QMOM equations for wet granulation processes, which model the PSD via growth, aggregation and breakage kernels. Relevant theoretical and numerical issues as well as limitations are discussed.