The vast majority (>70%) of pharmaceutical products produced are solid oral dosages made through the processing and mixing of granular solids. In the pharmaceutical industry, mixing is generally treated as an individual unit operation where granular excipients, lubricants and active pharmaceutical ingredients are mixed into a single blended product. In order to ensure product quality, the individual materials need to be homogenously mixed in the final product. Thus mixing of granular solids is of particular interest to the pharmaceutical industry. Experiments and simulations have been conducted to both qualitatively and quantitatively evaluate mixing of granular materials. Some standard simulation tools for modeling granular solids mixing include Discrete Element Method (DEM) and Finite Element Analysis [1, 2]. DEM has been extensively used in the study of granular solids processing. Pharmaceutical processes that have been modeled using DEM include granular mixing in V-blenders, tote blenders, and rotating drums among others [3-6]. Most of these case studies were performed using cohesionless (i.e. free flowing) powders with relatively large particle sizes and bulk densities. However, many active pharmaceutical ingredients and excipients exhibit cohesive (i.e. non-free flowing) properties that play a significant role in powder mixing behavior.
Cohesion is defined as the shear stress of a powder when no normal stress is applied to the plane of shear. Given the difficulty associated with evaluating this parameter for pharmaceutical powders, substantially less effort has been put into simulating the mixing of cohesive granular solids. Most research in the field has been qualitative, aiming at visually matching experimentally observed behavior with simulation outcomes [6, 7]. Quantitative comparisons between experimental and simulation results have not, to the best of our knowledge, been performed due to the lack of correlation between simulation parameters and measured powder properties. Cohesive particle forces, often measured as pressure (N/ m2) in a laboratory setting, are treated as a function of a surface energy (J/m2) parameter whose effect on the system vary depending on the model used for the simulation of particle interactions .
The objective of this study was to evaluate the effect of cohesion parameters and particle property parameters used in DEM simulations have on the simulated mixing in rotating cylinder. The system was maintained at constant fill level and angular velocity. A quantitative relationship between particle properties (e.g. surface energy, particle density, and particle size) and simulated mixing behavior was developed. Mixing behavior was quantified using the axial dispersion and variance decay rate constant coefficients. Results indicated cohesive forces (i.e., surface energy) are negatively correlated with the axial dispersion and variance decay rate constant coefficients, pointing to an increase in mixing time. A statistical model based on the findings was developed to correlated the particle properties to mixing coefficients. A linear relationship between the relative standard deviation decay constant and axial dispersion coefficient was observed. This relationship was also found to be independent of the particle properties (particle size, bulk density, and surface energy). Evaluation of the DEM model with respect to similar previously performed experimental designs yielded comparable results for the principal components affecting mixing.
1. Nguyen, T., et al., FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations. Acta Geophysica, 2014. 62(5): p. 1109-1126.
2. Imole, O.I., et al., Experiments and Discrete Element Simulation of the Dosing of Cohesive Powders in a Simplified Geometry. Powder Technology, 2014. Pre-print.
3. Arntz, M.M.H.D., et al., Granular mixing and segregation in a horizontal rotating drum: A simulation study on the impact of rotational speed and fill level. AIChE Journal, 2008. 54(12): p. 3133-3146.
4. Lemieux, M., et al., Large-scale numerical investigation of solids mixing in a V-blender using the discrete element method. Powder Technology, 2008. 181(2): p. 205-216.
5. Sudah, O.S., et al., Simulation and experiments of mixing and segregation in a tote blender. AIChE Journal, 2005. 51(3): p. 836-844.
6. Bertrand, F., L.A. Leclaire, and G. Levecque, DEM-based models for the mixing of granular materials. Chemical Engineering Science, 2005. 60(8–9): p. 2517-2531.
7. Alexander, A.W., et al., Avalanching flow of cohesive powders. Powder Technology, 2006. 164(1): p. 13-21.