Granule Growth Kinetics

It will be assumed for the present considerations that sufficient binder is present in the granulator as determined by the binder/powder ratio and that the binder is appropriately spread on enough granular surfaces so as to ensure that most random collisions between particles will occur on binder-covered areas. It will also be assumed that the particles are more or less spherical having a characteristic dimension, a. The simplified system of two colliding particles is schematically shown in Fig. 21. The thickness of the liquid layer is taken to be h, while the liquid is characterized by its surface tension yand its viscosity /x. The relative velocity U0 is taken to be only the normal component between particles while the tangential component is neglected. 

As the two particles approach each other, the first contact will be made by the outer binder layers the liquid will subsequently be squeezed out from the space between the particles to the point where the two solid surfaces will touch. A solid rebound will occur based on the elasticity of the surface 

It is important to note that the viscous force is singular in the separation distance h and hence will predict infinite large forces at contact. Since this is physically impossible, a certain surface roughness has to be assigned to the granular surface as is shown in Fig. 21 where this parameter is assigned the value ha this prevents particles from touching.  

Conditions of Coalescence. The outcome of the collision of two binder-covered particles is determined by the ratio of the initial kinetic energy of the system and the energy dissipated in the liquid bridge and in the particles. This can be expressed analytically by the definition of a so called Stokes number, St 

The trajectory calculations mentioned above also yield analytical expressions for the critical Stokes number 

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Tattiyakul, J. 1997. Studies on granule growth kinetics and characteristics of tapioca starch dispersions using particle size analysis and Aeological methods. M. S. Thesis, Cornell University, Ithaca, NY. 

X. Hu, J.C. Cunningham and D. Winstead, Study growth kinetics in fluidized bed granulation with at-line FBRM, Int. J. Pharm., 347, 54-61 (2008). 

Hemati, M., Cherif, R., Saleh, K., and Pont, V., Fluidized bed coating and granulation Influence of process-related variables and physicochemical properties on the growth kinetics. Powder TechnoL, 2003,130,18-34. 

Each of the mentioned main constmctive elements of spray fluidized bed equipment can be used to manipulate product properties in the desired direction. For example, droplet size and spray pattern have an influence on the particle wetting and on the local liquid distribution in the fluidized bed - thus also on particle growth kinetics, the type of particle size enlargement (agglomeration in comparison to granulation and coating) and product properties (e.g., particle porosity and density, and surface morphology). 

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