Computer simulation of wet granulation

Ilkay Talu, Gabriel I. Tardos , M. Irfan Khan
Department of Chemical Engineering
City College of City University of New York, Steinman Hall,
Convent Ave. and 140 Street, New York, NY 10031,
USA
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Abstract

Agglomeration of fine particles in wet granulation is achieved by introducing a binder fluid onto a shearing mass of powder. Owing to the viscosity and the surface tension of the fluid, powder particles are bound together to form larger aggregates. Despite its widespread use in the chemical, pharmaceutical and food industries, little effort has gone into comprehensive modeling of the overall process from first principles. Modeling is important however, if one needs to estimate a-priori agglomerated granule characteristics such as size, shape and density, from knowledge of operating conditions and powder and binder physical and chemical properties. In this work, we present a model of wet granulation that is essentially a computer simulation of shear flows of solid particles, some of which are wet covered by binder and therefore sticky. while the rest are dry. While simulations of shear flows of dry solid particles have earlier been reported in the literature, present work takes this simulation a step further and introduces a liquid surface layer to some particles in the domain. The additional force experienced by two relatively moving particles interacting via their binder-covered layers is modeled by using results from lubrication theory and Stokesian dynamics. The numerical simulations reflect two distinct regimes of agglomeration: that of granule growth and that of granule breakup. The granule growth regime takes place in all granulators including low and high shear machines while granule break-up is mainly characteristic of medium and high-shear devices in which agitation as generated by some mechanical means. During granule growth-simulations, the movement of sticky binder covered. particles is studied in a constant shear, rapid granular flow regime. From these simulations, final granule size, shape and size distributions were obtained using a pattern-recognition technique. A second kind of simulation, also using rapid granular flow modeling, follows the deformation and break-up of an agglomerate made from particles held together by a liquid, viscous binder. Results from these simulations yield critical values of a dimensionless parameter that contains inertial and viscous dissipation effects the so-called Stokes number.. Below a critical value of the Stokes number, agglomerates are stable and only rotate in response to shear while above the critical value they break into several pieces. Around the critical value, they attain a steady elongation. These simulations allow one to obtain correlations between critical sizes, i.e., granules that deform somewhat but do not break, and different parameters of the problem. 2000 Elsevier Science S.A. All rights reserved.

Introduction

The simulations presented in this work are based on the discrete element approach widely used in the literature to predict flows of solid-particulate materials. This method in turn is rooted in the analogy between the character of dry-granular flows with that of the flow of gas molecules and is a generalization of the so-called ‘‘molecular dynamics simulation’’ or MDS. Instead of point particles and force potentials, however, rapid granular flow simulations or RGFS, use actual expressions for the magnitude of forces to describe interactions between finite size particles. During this kind of simulations, Newton’s equation Fexts m dUrdt. is solved for pair-wise interactions between a large number of particles starting from an initial condition, until steady state is achieved. Several of these kinds of calculations have been performed lately and a summary of some results is presented in Hopkins and Louge w8x. Interactions between particles in these works are restricted to frictional effects and elastic, and sometimes, plastic deformations of the surface. It is this restriction that limits the applicability of these models to dry powder flows. During recent work of the present authors w11x, the above RGFS were extended to include viscous interactions between solid particles. The most important addition to the original RGFS simulation was the inclusion of viscous forces into the force balance used to solve for inter-particle interactions. These forces were added vectorially to supplement frictional and elastic forces, used in previous simulation. While the addition of viscous forces, looks like a simple extension of previous work, it is, in fact, a very serious complication. This is due to their complicated dependence on the spatial arrangement of particles, and the fact that they become very large when particles come into close proximity and become unbounded when particles touch.. The goal in our previous work w11x was to study the deformation and breakup of wet agglomerates suspended in a simple shear field of dry powder. The internal pores between particles in the agglomerates, were assumed to be saturated with binder while the effect of surface tension acting on the outer surface of the aggregate was neglected. The ‘‘granule’’ was then treated as a drop of fluid completely filled with solid particles that behaved as one entity in an otherwise dry shear flow of identical small particles. The viscous forces acting upon the individual particles in the granule were computed from their relative velocity with respect to the motion of the agglomerate as a whole. The overall motion of the wet agglomerate was computed by evaluating the net force and torque acting on it as a result of the contribution from individual particles situated outside the agglomerate. This approach, although quite useful and relatively simple, was criticized as being inconsistent with the central philosophy of RGFS, since it did not evaluate the trajectories of individual particles inside the wet agglomerate. from only their binary interactions with neighboring particles. A further drawback of the method was that, since the whole particle-filled drop was treated as one body, it was not possible to follow each binder-coated particle once the original granule broke into pieces. Even the loss of one particle from the initial granule due to excessive deformation. invalidated the original assumption and rendered the granule ‘‘broken’’. In the present work, all particle trajectories are computed by considering only binary interactions between neighboring particles. The trajectory evaluation of each particle, wet or dry, hence follows a uniform and consistent approach. In addition, each particle can be followed independently whether part of an agglomerate or moving just by itself. Aggregates or ‘‘granules’’ in this case, are simply identified as entities composed of several wet binder-covered. particles that are spatially close enough to be inter-connected by their liquid layers. A pattern-recognition image-analysis routine is used to identify agglomerates of this type and determine their size and shape. One of the basic assumptions of the model presented here is the ‘‘constant shear’’ concept taken over from RGFS that assumes all particles, agglomerated or not, to be situated in a constant shear field generated by a special arrangement of periodic boundaries. Dimensionless quantities defined based on this unique, constant-shear value only apply therefore to these simple cases. Clearly, industrial granulators differ from this purely theoretical picture in that shear is variable: larger around moving tools and walls and smaller in the space between them. It is this simplification of the model that renders the results somewhat generic and restricts the results from being used to predict the outcome of granulations in specific industrial machines. The other major assumption of the model is that only two kinds of agglomerations are considered during this work: one in which the binder-covered particles are initially randomly distributed between dry particles and are subsequently led to agglomerate or cluster in the shear field. This process models incipient granule growth in an industrial granulator. In simulations of the second kind, large, wet agglomerates are present in the domain and are subsequently deformed and eventually broken under shear. This process models granule breakup in a granulator as a result of excessive wetting andror growth and determines the size of the largest granule that can form and survive under a set of given conditions. This clearly neglects such important mechanisms of growth as layering and coating, filling of binder droplets with dry powder and a multitude of other phenomena that had to be excluded to obtain a simple enough model that is tractable within existing computational capabilities. A further assumption of the model is the use of two-dimensional 2D. simulations of a clearly three-dimensional process. This is a drastic simplification required again by limitations in computer capability. There is nothing intrinsic in the model presented below that can not, in principle, be extended to 3D calculations except perhaps the image processing procedure to detect formed granules. While there is much discussion in the open literature regarding the relevance of 2D modeling of 3D processes, it is quite clear that enough useful information can be collected from these simplified models until high powered computation will enable the use of millions of particles in real, three dimensional flows.



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