|Gabriel I. Tardos|
Powder Science and Technology; Granulation (size increase) of fine powders; Theory and practice of powder flows; Caking of powders; Fluid-particle systems.
The goal of this work is to develop a general theoretical and practical framework of binder granulation (particle size increase) which takes an agglomeration process from binder selection and testing, to granule formation, growth and consolidation, to granule deformation and break-up and finally to the scale-up of the process. Binder selection and testing are crucial steps in granulation and special instrumentation and procedures have been developed during the present work to find the appropriate binder agent. In such granulation processes as detergents and pharmaceutical products, both the powders to be agglomerated and the binders are defined by the formulation and, in general, little liberty is given to alter the chemistry. Binder “selection” in this case is essentially reduced to adjusting the properties of the binder using small amounts of additives such as surfactant, polymeric compounds and small amount of liquids and, tailor the binder to exhibit specific properties. This allows fine-tuning of solid-binder properties that include surface wetting, spreading, adsorption, binder strengthening and final solid bridge strength to determine final granule attributes.
Most of the present work is dedicated to the theory of growth kinetics during granulation and the prediction of critical sizes that delimitate different regimes of granulation[1-5]. Several dimensionless parameters based on energy dissipation principles were developed and examples of how these can be used to predict the outcome of granulation and the scale-up of the process, are given. 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.
Granulation scale-up  is addressed next and is based on the dimensionless parameters defined during constant shear granulation. We found that stresses in a granulating mass can be determined directly using calibrated particles of known yield strength and that using the condition of “equal stress” in the small, laboratory, and large, industrial, machines, yields granules of similar attributes. Additional parameters that reflect the distribution of key variables of the process such as the distribution of shear and of liquid binder in a real, industrial granulator, are defined and tested at different scales in drum, fluidized bed and high shear granulators. The construction and testing of a new mixer granulators is in progress to check the developed scale-up criteria.
Bleeding of liquid species and/or adsorption of moisture from the surrounding atmosphere usually results in caking of powders stored in hoppers and containers. The main mechanism by which agglomeration takes place is the formation of liquid bridges between particles that subsequently solidify. In addition to the formation of solid bonds this also results, in the case of crystalline materials, in compression of the powder due to "swelling" of the bond during crystallization . Our present work is a study of the caking behavior of fine, bulk powders composed of crystalline chemical compounds while exposed to a humid atmosphere. A typical example, characteristic of detergents, is the formation of crystalline bridges of sodium carbonate as it hydrates by absorption of moisture from the surrounding gas or from the other components of the powder.
Our present study includes computations and measurements of the rate at which atmospheric moisture penetrates into bulk powders  as well as experiments when, due to hydration, crystalline water is retained in the powder. Methods to measure the liquid bridge , the solid neck  as well as the powder's isotherm are described. The application to powder flow and fluidization  is undertaken. A review of the more widely used methods in the field are presented in .
It was found during this research that large changes in bulk volume occur at the relative humidity where hydrates form in the crystal and this is associated with agglomerate formation and powder caking. A direct relation between powder swelling due to the formation of the hydrates and caking propensity was found for the case of the sodium carbonate and other crystalline powders. Caking of powder mixtures could be directly related to the relative humidity where a large amount of moisture was taken up by the powder.
Chemical and Mechanical engineers are quite familiar with concepts of flow of a Newtonian fluid 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 that have to be solved to obtain details of the flow field; a large number of analytical solutions of these equations exist. Somewhat similar equations were 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 flow of small elastic (or elasto-plastic) particles and resemble, for certain limiting cases, the fluid flow equations.
Slow, frictional (generally referred as Coulomb) flows of powders are different in that particles are in contact for long times and friction is the overwhelming interaction. The same mass and momentum balances govern flow in this regime but the constitutive equations are different. The equations developed for slow powder flows are usually presented in a mixed format i.e. they retain both velocity and stress components in their general formulation. They contain special conditions such as yield or rupture criteria that are well known in solid mechanics and plasticity theory but are generally not familiar to Fluid Mechanists. Furthermore, these equations were only lately the subject of rigorous mathematical scrutiny such as for example stability analysis [1,2]. We found that the time dependant equations for incompressible powder flows are unstable for most cases, i.e. exponential solutions are amplified beyond control. This situation is not common in fluid mechanics but has enormous implications for powder flows; one of the more disturbing ones is that even if a solution is found to the general equations of motion this may have little resemblance to the actual motion of the powder. We also found that allowing for compressibility of the media, leads to regularization of the equations that are therefore more stable and should be used to solve actual powder flows.
The goal of our present work is to develop general equations of motion for bulk powder flows in the slow regime using a fluid mechanics approach. The method used is to apply the concept of constitutive equations to describe the correlation between stresses and velocity fields and to employ these in the conservation of momentum equation. It is thus possible to eliminate the mixed character and to put the general equations of motion in a more transparent, homogeneous format that only contains velocities and pressure. This approach holds the advantage of being more familiar to a larger segment of the engineering community and especially to students of chemical and mechanical engineering who apply similar concepts to solve equations for fluid flow. This format is also more amenable to stability studies that become essential in obtaining numerical solutions for more complex geometries that were not attempted in the past.
It is also the goal of our present work to recast some known analytical solutions for slow powder flows in the new format and to provide examples to the applicability of the equations of motion to concrete problems to calculate simultaneously both stress and velocity distributions in the powder . In addition, a set of constitutive equations for compressible slow and rapid granular flows is also shown and comparisons between these and Newtonian fluids are made. Finally, in a more recent effort , we introduce the concept of powder flows in the “intermediate” regime spanning between the slow, quasi-static and rapid granular flows. The flowing powder exhibits some kind of “fluid like” behavior in that the constitutive equations contain a viscosity-like term and a powder-low index. This is index is related in turn to the velocity (and /or stress fluctuations in the flow), and provide a connection between them. Both experimental and theoretical studies are being performed to elucidate this dependence further.
Many industrial operations with powders result in particle surface melting, sintering, deformation (flow) and reaction at the inter-particle contact points. This is mainly due to high temperatures, compression forces, the presence of moisture and/or liquid formation, the formation of different chemical species or the condensation of vapors. These processes are associated with a relative volume change of the powder and usually result in agglomeration and caking. In the majority of cases, caking and agglomeration must be avoided although some agglomeration is sometimes acceptable.
The dilatometer is an instrument that allows one to measure small volume changes and is used routinely to measure the expansion coefficient of solid materials. During the present research, a dilatometer was modified to be used with powders and procedures were developed to employ it as a tool to detect the above phenomena. Examples were developed to show the application of the method to different powder processing unit operations such as for example fluidization  and storage of powders at high temperature as well as production of powders such as for example the production of aluminum nitride  in a high temperature fluidized bed. The detection of sintering, agglomeration and caking was subsequently studied in high and low temperature fluidized beds and a correlation between the sintering point detected in the dilatometer and the de-fluidization point in the fluidized bed was demonstrated. Applications of this work to solid-gas and solid-solid reactions in a powder bed are being studied.
The emphasis was placed in more recent work [4-7] on the evolution of drying liquid bridges between two particles that form an agglomerate. Both, microscopic studies to determine the shape and crystallography of the forming bridges as well as the strength and forces exerted by the forming bridge on the adjacent particles, were studied in detail. X-ray tomography  was also used to shed light on the process of bridge formation.