High shear wet granulation modelling—a mechanistic approach using population balances

A population balance approach based on splitting the coalescence kernel into two factors, the first describing the collision frequency of particles and the second describing the collision efficiency, is applied to modelling wet granulation in a high shear mixer. Four different expressions for the collision frequency are compared and discussed. The kernels are the size independent kernel, the shear kernel proposed by Smoluchowski [M. Smoluchowski, “Versuch einer matematischen Theorie der Koagulationskinetic kolloider Lösungen”, Z. Physik. Chem. 92, (1917) 129–168.] and the two kernels proposed by Hounslow [M.J. Hounslow, “The population balance as a tool for understanding particle rate processes”, Kona (1998) 179–193.], i.e. the EKE kernel and the less used kernel based on equipartition of fluctuating translational momentum (ETM kernel). Microcrystalline cellulose (mcc) is granulated under different process conditions and it is found that the ETM kernel best describes the granulation at higher impeller speeds, whereas the EKE kernel gives better agreement at lower impeller speeds. The collision efficiency is assumed to be a function of the liquid saturation. By using this assumption, it was possible to detect similar trends for the remaining part of the collision efficiency regardless of process conditions.