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 fine powders. Simulating this process on the microscale is challenging because of the substantial 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, which is key information for downstream processing. These deficiencies are addressed by mesoscale methods, like population balance models, which track distributed properties such as the particle size by adding them as internal variables to the macroscale model. However, most mesoscale methods are either inaccurate (method of moments when closed by cutting off moments) or computationally expensive (Monte Carlo, class methods). Recently a new closure for the method of moments, the quadrature method of moments, was introduced to allow accurate moment tracking of a particle size distribution with low computational effort. The drawbacks associated with this method, such as potential instabilities, can be effectively mitigated through non-dimensionalisation. In this study we show our insights gained by non-dimensionalising the quadrature method of moments equations for wet granulation processes, which model the particle size distribution evolution via growth, aggregation and breakage kernels. Relevant theoretical and numerical issues as well as limitations are discussed. Using constant kernels, the non-dimensionalised model is verified and validated thereafter on certain special cases. The effect of non-constant kernels on the non-dimensionalisation is discussed. Furthermore, we show that the non-dimensionalised model fails to accurately predict the moments of an experimental distribution using a volume-based population balance model, whereas a length-based population balance model can successfully predict the moments by setting non-constant kernels to fit the Sauter mean diameter.