Gabriel I. Tardos

Critical parameters and limiting conditions in binder granulation of fine powders

Abstract The goal of this work is to present a general theoretical and practical framework of binder granulation that takes an agglomeration process from binder selection and testing to granule formation, growth and consolidation and finally to granule deformation and breakup. For agglomeration and granule growth to commence at all, a certain minimum amount of binder has to be introduced in the granulator and this has to be determined carefully. This paper presents special instrumentation and procedures for binder selection. In granulation processes such as detergents and pharmaceutical products, both the powders to be agglomerated and the binders are defined by the formulation and, usually, little liberty is given to alter the chemistry. Binder ‘selection’ in this case is practically reduced to adjusting the properties of the binder using small amounts of additives such as surfactants, polymeric compounds and small amounts of liquids and tailoring the binder to exhibit specific behavior. This allows fine-tuning of binder properties that include surface wetting, spreading, adsorption, binder strengthening and solid bridge strength. The bulk of the present work is dedicated to the theory of growth kinetics during granulation and the prediction of critical sizes which delimit different regimes of granulation. Several dimensionless parameters based on energy dissipation principles are presented and examples given about how these parameters and the critical sizes they define can be used to predict the outcome of granulation and the scale-up of the process. The above theoretical framework is then tested with experimental data from the literature and with granulation results obtained by the present authors using a specially constructed constant-shear granulator based on the principles of a Couette viscometer. A theory of consolidation of formed granules is also given and additional experimental support from the literature is presented.

Use of X-ray tomography to study the porosity and morphology of granules

Abstract X-ray computed tomography (XRCT) is a technique that uses X-ray images to reconstruct the internal microstructure of objects. Known as a CAT scan in medicine, it has found wide application for whole-body and partial-body imaging of hard tissues (e.g., bone). A modern tabletop XRCT system with a resolution of about 4 μm was used to characterize some pharmaceutical granules. Total porosity, pore size distribution, and geometric structure of pores in granules produced using different conditions and materials were studied. The results were compared to data obtained from mercury porosimetry. It was found that while XRCT is less precise in the determination of total porosity in comparison to mercury porosimetry, it provides detailed morphological information such as pore shape, spatial distribution, and connectivity. The method is nondestructive and accurate down to the resolution of the instrument. Tomographic images show that the pore network of individual granules comprises relatively large cavities connected by narrow pore necks. The major structural difference between granules produced at different conditions of compaction and shear is a reduction in the pore neck diameter; the cavity size is relatively insensitive to these conditions. Comparison of pore size distributions determined from tomographic images and mercury porosimetry indicates that mercury intrusion measures the pore neck size distribution, while tomography measures the true size distribution of pores ca. 4 μm or larger (the instrument resolution).

Slow and intermediate flow of a frictional bulk powder in the Couette geometry

Most current research in the field of dry, non-aerated powder flows is directed toward rapid granular flows of large particles. Slow, frictional, dense flows of powders in the so-called quasi-static regime were also studied extensively using Soil Mechanics principles. The present paper describes the rheological behavior of powders in the “intermediate” regime lying between the slow and rapid flow regimes. Flows in this regime have direct industrial relevance. Such flows occur when powders move relative to solid walls in hoppers, bins and around inserts or are mixed in high and low shear mixers using moving paddles. A simple geometry that of a Couette device is used as a benchmark of more complicated flows. The constitutive equations derived by Schaeffer [J. Differ. Equ. 66 (1987) 19] for slow, incompressible powder flows were used in a new approach proposed by Savage [J. Fluid Mech. 377 (1998) 1] to describe flows in the intermediate regime. The theory is based on the assumption that both stress and strain-rate fluctuations are present in the powder. Using Savages approach, we derive an expression for the average stress that reduces to the quasi-static flow limit when fluctuations go to zero while, in the limit of large fluctuations, a “liquid-like”, “viscous” character is manifested by the bulk powder. An analytical solution of the averaged equations for the specific geometry of the Couette device is presented. We calculate both the velocity profile in the powder and the shear stress in the sheared layer and compare these results to experimental data. We show that normal stresses in the sheared layer depend linearly on depth (somewhat like in a fluid) and that the shear stress in the powder is shear rate dependent. We also find that the velocity of the powder in the vicinity of a rough, moving boundary, decays exponentially so that the flow is restricted to a small area adjacent to the wall. The width of this area is of the order of 10–13 particle diameters. In the limit of very small particles, this is tantamount to a shear band-type behavior near the wall.

A fluid mechanistic approach to slow, frictional flow of powders

Chemical and mechanical engineers are quite familiar with concepts of fluid flow which include mass and momentum balances and constitutive equations which contain such material characteristics as viscosity and density. Combination of the above correlations yields the well-known Navier-Stokes equations which have to be solved to obtain details of the flow field; a large number of analytical solutions of these equations exist. Somewhat similar equations have been developed for granular materials moving in the rapid granular flow regime, i.e. in the regime in which particle-particle contacts are not very extensive and hence friction is not prevalent. These equations result from a similarity between the movement of molecules and the flow of small elastic (or elasto-plastic) particles and resemble, for certain limiting cases, the fluid flow equations. Slow, frictional flows of powders are different in that particles are in contact for extended periods of time and friction is the overwhelming interaction. Flow in this regime is governed by the same mass and momentum balances but the constitutive equations are different. Only very recently have some of these equations been combined to yield a set of differential equations which take the place of the Navier-Stokes equations; only very few solutions of these equations exist. The present paper describes common features and major dissimilarities between different equations of motion for the above systems and some of their solutions and presents examples and comparisons of powder and fluid flows in identical geometries. Furthermore, general equations of motion for compressible powders in slow flow are developed and an example of an analytical solution is given.

The behavior of liquid bridges between two relatively moving particles

Abstract The strength and rupture point of a liquid phase between two moving spherical particles in air were studied experimentally and theoretically. The liquid forms an axisymmetrical bridge when the particles are in close proximity which subsequently elongates and finally ruptures as the spheres are moved away from each other in an axial direction. The resistance of the liquid to the movement of the spheres (bridge strength) was measured using a strain gauge and high-speed photography. It was found that dynamic bridges are much stronger than geometrically identical static bridges where the attraction force is due to surface tension only. The force required to separate two moving particles is sometimes orders of magnitude higher than that required in static systems because the viscosity of the fluid resists the motion in the dynamic case. These findings explain why in fluidized beds, for example, where either high temperatures create sticky granules by surface softening (melting) or an added liquid creates a viscous surface coating, quenching or collapsing of the bed is such a catastrophic phenomenon. It also explains why in other systems such as coating and drying devices and wet powder processing, small amounts of fluid drastically change the properties and the behavior of the system.

The effect of gravity on the shape and strength of a liquid bridge between two spheres

Etudes de la force et des criteres de rupture du pont liquide entre 2 spheres, dans un champ gravitationnel

Forces on a slowly rotating, rough cylinder in a Couette device containing a dry, frictional powder

In the present work, a fine, dry powder was sheared in a Couette device: i.e., sheared between concentric vertical cylinders. The torque generated on the rough, inner cylinder was measured as this inner wall was rotated. Our experiments provided evidence that, in a column of granular material undergoing continuous shearing, normal and shear stresses increase linearly with depth. In other words, Janssen’s analysis ceases to apply if granular material is continuously sheared.

Chemical reaction induced agglomeration and defluidization of fluidized beds

Abstract Industrial fluidized beds are operated with particles that usually contain impurities or are themselves a mixture of many components (for example, ores). Upon heating to high temperatures, some of these components soften, melt or react with each other, generating stickiness. In fluid bed reactors, the fluidizing gas can also react chemically with the solids producing new components and during this process particle cohesion and stickiness can occur. In all these cases, the fluidization behavior of the particles changes dramatically as temperature is increased, agglomerates form and such characteristics as the minimum fluidization and bubling velocity, the bubble size and bubble frequency, etc., all change significantly. It has been demonstrated in earlier work by the present authors and also by others that above a certain temperature (the so-called sintering point), fluidization is not possible at all unless special precautions are taken and the gas velocity is increased significantly. The goal of the present research is to determine the sintering or ‘sticking’ temperature in these more complicated cases when the particles are chemically complex and/or when chemical reactions take place. It is shown during the present work that even under these conditions, sintering temperatures can be measured using the dilatometer technique developed earlier for inert gases and pure materials assuming that such conditions as gaseous atmosphere and temperature can be reproduced in the instrument. A special class of agglomeration due exclusively to the formation of new species during a chemical reaction which occurs on the surface of the solid particle is also presented in this paper. It is shown that at temperatures well below the softening (sintering) points of both the reactants and the products, particle agglomeration can occur during the process of product formation: examples such as the oxidation of coke and magnesium powders, the reduction of calcium sulfate and the production of aluminum nitride are given.

Computer simulation of wet granulation

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.

Minimum sintering temperatures and defluidization characteristics of fluidizable particles

Abstract It has been demonstrated that the minimum sintering temperature of a fluidizable particle can be determined simply and reliably using pushrod dilatometry. The minimum sintering temperature is an important physical property of the particle in the process of high-temperature fluidization, and is defined as that temperature at which thermally induced surface softening and sintering begins. In addition, at temperatures above the minimum sintering temperature, there is a relationship between the dilatation-temperature curve and the excess gas velocity-temperature curve (the defluidization limit). The experimental work performed is in two parts. In the first, dilatometry curves are presented showing the minimum sintering temperature for a number of inorganic salts as well as a complex titanium dioxide ore and coal ash. The second consists of defluidization curves for both amorphous and crystalline materials obtained using a 7.6 cm-diam. high-temperature fluidized bed capable of attaining 1150°C. The results of both sets of experiments are compared and discussed.