Compositional distributions in multicomponent aggregation

Abstract We consider the granulation of two components, a “solute” (the component of interest) and an excipient. We specifically focus on cases such that the aggregation kernel is independent of the composition of the aggregating granules. In this case, theory predicts that the distribution of components is a Gaussian function such that the mean concentration of solute in granules of a given size is equal to the overall mass fraction of solute in the system, and the variance is inversely proportional to the granule size. To study these effects, we perform numerical simulations of the bicomponent population balance equation using a constant aggregation kernel as well as a kernel based on the kinetic theory of granular flow (KTGF). If the solute and excipient are initially present in the same size (monodisperse initial conditions), both kernels produce identical distributions of components. With different initial conditions, the KTGF kernel leads to better mixing of components, manifested in the form of narrower compositional distributions. These behaviors are in agreement with the predictions of the theory of aggregative mixing. We further demonstrate that the overall mixedness of the system is controlled by the initial degree of segregation in the feed and show that the size distribution in the feed can be optimized to produce the narrowest possible distribution of components during granulation.

[1]  Themis Matsoukas,et al.  Dynamics of aerosol agglomerate formation , 1991 .

[2]  Kangtaek Lee,et al.  Solution of the population balance equation using constant-number Monte Carlo , 2002 .

[3]  Ian T. Cameron,et al.  Optimal control and operation of drum granulation processes , 2004 .

[4]  Michael J. Hounslow,et al.  Tracer studies of high‐shear granulation: II. Population balance modeling , 2001 .

[5]  Gabriel I. Tardos,et al.  Computer simulation of wet granulation , 2000 .

[6]  James D. Litster,et al.  Population balance modelling of granulation with a physically based coalescence kernel , 2002 .

[7]  Gérard Thomas,et al.  Modelling to understand porosity and specific surface area changes during tabletting , 1999 .

[8]  Themis Matsoukas,et al.  Constant-number Monte Carlo simulation of population balances , 1998 .

[9]  B. J. Ennis,et al.  Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review , 2001 .

[10]  Anders Rasmuson,et al.  A volume-based multi-dimensional population balance approach for modelling high shear granulation , 2006 .

[11]  Steven A. Cryer,et al.  Modeling agglomeration processes in fluid‐bed granulation , 1999 .

[12]  James D. Litster,et al.  Population balance modelling of drum granulation of materials with wide size distribution , 1995 .

[13]  A. A. Adetayo,et al.  A new approach to modeling granulation processes for simulation and control purposes , 2000 .

[14]  Denis Mangin,et al.  Modelling of agglomeration in suspension: Application to salicylic acid microparticles , 2005 .

[15]  Kalanadh V.S. Sastry,et al.  Similarity size distribution of agglomerates during their growth by coalescence in granulation or green pelletization , 1975 .

[16]  Anders Rasmuson,et al.  High shear wet granulation modelling—a mechanistic approach using population balances , 2005 .

[17]  Ian T. Cameron,et al.  Evaluation of control strategies for fertiliser granulation circuits using dynamic simulation , 2000 .

[18]  A. A Lushnikov,et al.  Evolution of coagulating systems: III. Coagulating mixtures , 1976 .

[19]  P. C. Kapur,et al.  Coalescence Model for Granulation , 1969 .

[20]  Kangtaek Lee,et al.  Mixing of components in two‐component aggregation , 2006 .

[21]  Ian T. Cameron,et al.  Review and future directions in the modelling and control of continuous drum granulation , 2002 .

[22]  S. Friedlander,et al.  Smoke, dust, and haze , 2000 .

[23]  S. Heinrich,et al.  Analysis of the start-up process in continuous fluidized bed spray granulation by population balance modelling , 2002 .

[24]  Sotiris E. Pratsinis,et al.  Time-Lag for Attainment of the Self-Preserving Particle Size Distribution by Coagulation , 1994 .

[25]  M. Goldschmidt,et al.  Hydrodynamic Modelling of Fluidised Bed Spray Granulation , 2001 .

[26]  Stefan Heinrich,et al.  Particle population modeling in fluidized bed-spray granulation—analysis of the steady state and unsteady behavior , 2003 .

[27]  Michael J. Hounslow,et al.  Kinetics of fluidised bed melt granulation: IV. Selecting the breakage model , 2004 .

[28]  Kangtaek Lee,et al.  Simultaneous coagulation and break-up using constant-N Monte Carlo , 2000 .

[29]  Ian T. Cameron,et al.  Process systems modelling and applications in granulation: A review , 2005 .

[30]  H. Vromans,et al.  Experimental and modelistic approach to explain granulate inhomogeneity through preferential growth. , 2003, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[31]  S. Iveson,et al.  Limitations of one-dimensional population balance models of wet granulation processes☆ , 2002 .

[32]  Babatunde A. Ogunnaike,et al.  Model-based control of a granulation system , 2000 .

[33]  Justin A. Gantt,et al.  High-shear granulation modeling using a discrete element simulation approach , 2005 .

[34]  Ananth Annapragada,et al.  On the modelling of granulation processes: A short note , 1996 .

[35]  Francis J. Doyle,et al.  Solution technique for a multi-dimensional population balance model describing granulation processes , 2005 .