Particle Formation

This report introduces a quasicontinuum formulation for heterogeneous granular systems. The description assumes that the relative displacements between particles are described by a constrained field while the interparticle forces are resolved locally. Equilibrium is enforced weakly by virtue of the principle of virtual displacement. The methodology accounts for particles of variable size and different species. Interaction forces between particles in different cells are computed using a rule which allows for local operations and renders symmetric tangent operators. Energy relaxation from static condensation of an internal node is proposed as an indicator for adaptive meshing. Simulations of uniaxial densification show the robustness and versatility of the formulation for heterogeneous granular beds. The numerical tests also recover the general trends observed in compaction experiments.

Executive Summary

The major objective of our IFPRI project, which started in 1998, is to develop a comprehensive mathematical model of the extrusion process for “concentrated” dense suspensions using the Finite Element Method. The results of the numerical analysis need to be verified through experimental studies carried-out on industrial-scale and well-instrumented extruders. Other objectives include the development of various methods and apparati to probe the rheological behavior and microstructural characteristics of concentrated suspensions (“dense suspensions”) especially in the confines of the extrusion process. Single and twin screw extrusion processes (including co-rotating and counter-rotating twin screw extruders) and flow through dies are included in the scope of the project. The ability to determine the distributions of the pressure, stress, velocity and temperature which develop during the course of the extrusion process is the minimum information wherewithal necessary to understand the development of the structure and the ultimate properties of the processed suspensions. The project is carried out with massive support from other sources also including te US Army, Naval Surface Warfare Center and various corporations.

The major tasks of Year #2 were the modification of our FEM based source codes to accommodate the wall slip behavior of dense suspensions in 3-D, the initiation of the experimental studies of dense suspensions using a well-instrumented and industrial-size co-rotating twin screw extruder and the comparisons of the experimental and simulation results on various isolated sections of the twin screw extruder. The coupled flow occurring at a slit die and the exit section of the twin screw extruder was focused upon using a model suspension, which was well characterized. The experimental results (pressure and temperature distributions) agreed well with the results of our numerical simulation using 3-D FEM. During the next year we intend to expand our mathematical analysis to multiple sections of the extruder simultaneously on the single screw extruder, carry-out detailed experimental studies with realistic suspensions using again a well-instrumented single screw extruder with a complex shaping die and compare the experimental results with the numerical results.

The process of disintegration of liquid/solid suspension sheets and jets is analysed in a fundamental manner and visualized by suitable measurement method which allow qualitative and quantitative evaluation of the process. Supporting numerical analysis and theoretical derivations will contribute to basic understanding and control of the suspension atomization process. Model suspensions based on water and water/glycerol mixture with various suspended particles will be atomized by means of conventional and specifically designed atomizers.

The second year activities which are reported here include:

• Experimental investigations of suspension rheology
• Stability analysis of twin fluid suspension atomization
• Experimental investigations of suspension atomization in twin-fluid atomizer

Model suspensions based on distilled water with neutrally buoyant polymer particles have been studied.

The co-processing of fine-particle agglomerates and liquids is common in industrial practice. In many applications, the processing goal is the reduction of the agglomerate size (or possibly complete breakage of the agglomerate into its constituent particles) and distribution of the fragments throughout the liquid medium. To accomplish this, hydrodynamic shear can be applied to the suspension by various mechanical means. The underlying motivation for this research is to obtain a fundamental understanding of the various factors that influence the dispersion behavior of agglomerates. Attainment of such an understanding may facilitate the development of interfacial engineering strategies aimed at improving the outcome of dispersion processes or to the design of more efficient dispersion equipment.

Our basic approach is to study the dispersion behavior of well-characterized single agglomerates in controlled flow fields. This allows us to establish the links between the fundamental properties of an agglomerate and dispersion characteristics such as critical shear stress for dispersion, mode and kinetics of fragmentation, and the evolution of the fragment size distribution.

The specific emphasis of the work supported under this IFPRI grant involves investigation of how certain time-dependent (dynamic) phenomena affect the outcome of dispersion processes. Such time-dependent effects are inherent in several aspects of the dispersion process. For instance, in practical processing equipment, the agglomerates are subject to complex shear histories. The contacting of particles and agglomerates with processing liquids leads to wetting and spreading phenomena that change over the course of time. Also, for soluble materials, dissolution is a time-dependent effect.

In the first year of this IFPRI grant, the bulk of the research effort was devoted to the development of a new experimental approach for the investigation of the influence of dynamic effects on dispersion behavior. This entailed the design (and redesign) of a dynamic dispersion chamber, and construction of it and the ancillary equipment. Preliminary experiments were done to validate the experimental techniques and to refine the analytical procedures. In the second year, we performed additional modifications to the experimental device and refined our experimental procedures. This allowed us to complete additional experimental studies that highlight the dramatic influence of time-dependent effects on the outcome of dispersion. In addition, we performed a thorough modeling study of the flow and shear fields present within our experimental device. This modeling enables us to analyze the results of our experiments, and to understand the limitations of our dispersion chamber.

This report summarises progress in IFPRl project 37 in 1999/2000. Karen Hapgood has completed her PhD (November, 2000) and much of this report summarises the significant results of her research on wetting and nucleation. Some very interesting in progress results on the dynamic mechanical properties of wet granules are also included.

A new model for predicting drop penetration time from powder and liquid binder properties is presented. This model takes account of the presence of macrovoids in loosely packed powder beds and introduces the concept of an effective porosity and effective pore size seen by liquid drops penetrating into the bed by capillary action. The effective pore size is smaller than the Kozeny model capillary size by 2 to 4 times for lactose powders and an order of magnitude for very fine zinc oxide and titanium dioxide powders. Model predicted penetration times are compared with experimental data for a wide range of binder and powder properties. Predictions are within an order of magnitude for all powders with good agreement for lactose and glass ballotini. This is much better than the existing literature models.

A simple model to predict the fraction of agglomerates formed in the spray zone as a dictionof dimensionless spray flux is developed using spatial statistics:

The equation is in very good agreement with both Monte Carlo simulations of drop coverage on a powder surface and experimental nucleation experiments.

The conceptual nucleation regime presented in report 37-02 is extended and compared with results From granulation experiments in 1 litre and 25 litre laboratory mixer granulators. Experiments confirm that the narrowest granule size distributions are produced in the drop controlled regime where there is both low dimensionless spray flux and short drop penetration time. The implications for granulator design and scale up are discussed.

The first set of results from detailed measurement of the dynamic mechanical properties of wet mass pellets are presented. Experiments with glass ballotini powders and a wide range of liquid binders confirm that peak flow stress is a strong function strain rate. All results can be collapsed onto a single correlation between dimensionless stress and capillary number. Similar results are shown for crushed silica powders. This work is the first step to develop a generalised correlation that relates wet mass constitutive properties to the formulation properties.

The main research goals for years 4 to 6 of the project are briefly discussed.

In this research, we successfully implemented feedback control of particle shape in a semi-batch crystallization. The overall goal of this research was to measure and regulate the shape and size of particles created by nucleation and growth processes in crystallizers. The state of the art in this field up to 1993 is summarized in the review article [12]. At that time, control of crystal size and crystal size distribution was just becoming possible using simple on-line slurry measurements such as light transmittance or small angle forward light scattering. The challenge undertaken in this research was to go to the next level and attempt direct control of crystal shape. It was felt that demonstration of online shape measurement and control would require the development of entirely new measurement technology compared to what was being used for size control.

The measurement technology we developed for this purpose was direct digital imaging of a sample stream. As discussed in the report, the key to extracting useful particle shape information from the digital images requires the user to monitor two key variables. We chose boxed area and aspect ratio of the identified particle images to infer the shape of the crystals.

We developed the following crystallization system to demonstrate the result. An impurity free stream flowed through the crystallizer and we regulated the flowrate of a habit modifier stream in order to maintain the desired shape. At the 2000 IFPRI Annual meeting, we showed our first results in which, without any prior knowledge of model parameters, a simple proportional-integral control algorithm is able to maintain a desired crystal shape and in doing so, determines the critical concentration of habit modifier required to maintain this shape.

The prototypical system and process we selected is semi-batch crystallization of sodium chlorate (NaClO3 ). Sodium dithionate (Na2 S2 O6 ) is a habit modifier that influences the relative growth rates of 100 and 1 ̄1 ̄1 ̄ faces of the crystal. In the presence of at least 50 ppm sodium dithionate the growth of the 1 ̄1 ̄1 ̄ faces is blocked by the impurity and the crystal shape changes from cubic to tetrahedral. Without impurity present, the 100 faces grow slower than the 1 ̄1 ̄1 ̄ faces and the crystal shape changes from tetrahedral to cubic. The shape change is easy to detect with video images alone, though there are limitations with extracting useful quantitative information from images for use as a signal for feedback control.

This prototypical process displays the following industrially relevant characteristics.

1. Particle shape is affected by unmeasured disturbance variables.
2. Online sensing is available in the form of video images. The images are replete with bad data. Some particles are fused or broken; it is difficult to obtain representative samples; particle boundaries overlap each other; there are significant levels of process noise; and it is difficult to sample enough images to remove the effects of this noise through averaging. The standard image analysis software provides simple measures such as particle boxed area and aspect ratio; as we show later, these simple measures are inadequate signals for feedback control.
3. We can manipulate a process variable that also influences particle shape. Through this feedback policy, we maintain the desired shape in the face of the unmeasured disturbances. The video images are processed in real time to produce the feedback signal that is used for control.

Executive Summary

The general objective of our IFPRI project was to develop various methods and apparati to probe the rheological behavior and microstructural characteristics of concentrated suspensions (“dense suspensions”) for which the solid concentration approaches the maximum packing fraction of the solid phase, and the mathematical modeling of the extrusion process for such dense suspensions. The validation of the numerical analysis results generated using FEM through experimental studies (carried-out on industrial-scale and well-instrumented extruders) and development of methods and materials to simulate the interrelationships between the processing history and the microstructure on one hand and the ultimate properties of the suspensions on the other hand were additional objectives.

Major Accomplishments

1. Development of comprehensive mathematical models of the single and twin screw extrusion processes which incorporate the specific flow and deformation behavior of dense pastes including their complicated wall slip and viscoplasticity. The mathematical models numerically solved the three dimensional conservation equations without the necessity to simplify the geometry of the extruder and dies which are attached to the extruder.
2. Retrofitting of a 50.8 mm twin screw extruder with a programmable logic controller, multiple sensors for pressure and temperature, an Inframetrics thermal-imaging camera, an x-ray system and an adjustable gap in-line rheometer for validation of the predictions of the mathematical model.
3. Rheological characterization of a series of polymers and suspensions and the mathematical modeling of their single and twin screw extrusion behavior and comparisons with the experimental results from our well-instrumented experimental systems.
4. Development of a specific conductive composite paste to facilitate the linking of the rheological behavior and the electrical conductivity of the paste to the specific energy input during the mixing process and the degree of mixedness of the suspension ingredients as characterized by wide-angle x-ray diffraction.
5. Development and application of a wide-angle x-ray diffraction technique to the determination of the degree of mixedness of the conductive composite quantitatively.
6. Upon receiving information from the sponsors that the wet systems (systems which contain water) are of interest setting up a shear roll mill extruder which allowed the recording of the thermal history of the wet cellulosic system being processed and the development of preliminary mathematical models of the processing of a wet system (outside of the initial scope of the project) to determine what is important in the processing of such systems and what the challenges are. Experimental and theoretical results are included here to aid IFPRI’s future research in this area.

According to the proposal there were the three following aims we wanted to achieve in the first year of the project extension:

1. Extension of the co-current experimental rig to a co- and counter-current spray drying system
2. Design, construction and testing of a small-scale device for determination of drying kinetics parameters
3. Elaborating of CFD model for scaling-up of spray drying process

The process of disintegration of liquid/solid suspension jets and sheets by atomization is analysed in a fundamental manner and visualized by suitable measurement method which allow qualitative and quantitative evaluation of the process. Supporting numerical analysis and theoretical derivations will contribute to basic understanding and control of the suspension atomization process. Model suspensions will be atomized by means of conventional and specifically designed atomizers.

The third year activities which are reported here include:

• Extending the stability analysis to predict the primary droplet break-up
• Experimental investigations of suspension atomization in twin-fluid atomizer
• Performing experiments with a new rotary-atomizer

Model suspensions based on water, water/glycerol mixture and water/CMC- (carboxymetylcellulose) mixture with suspended glass particles have been atomized.

Executive Summary

Uniform anatase-type TiO2 nanoparticles of different shapes have been formed by phase transformation of Ti(OH)4 gel matrix in the presence of shape controllers. For example, triethanolamine (TEOA) was found to change the morphology of TiO2 particles from cuboidal to ellipsoidal at pH above 11. The shape control can be explained in terms of the specific adsorption of TEOA to the crystal planes parallel to the c-axis of the tetragonal system in the alkaline range, as supported by the observation of preferential adsorption of TEOA to the crystal planes parallel to the c-axis at pH 11.5 and by the pH dependence of the adsorption to ellipsoidal particles. Diethylenetriamine (DETA) also modified the particle shape to ellipsoidal above pH 9.5 and the aspect ratio was much higher than with TEOA. The mechanism of the shape control could be explained in the same way as with TEOA, since analogous specific adsorption was observed with DETA as well. Similar shape control to yield ellipsoidal particles of a high aspect ratio was also achieved with other primary amines, such as ethylenediamine (ED), trimethylenediamine (TMD), and triethylenetetramine (TETA). However, secondary amines, such as diethylamine, and tertiary amines, such as trimethylamine and triethylamine, acted as a complexing agent of Ti(IV) ion to promote the growth of ellipsoidal particles of a low aspect ratio, rather than a shape controller to produce ellipsoids of a high aspect ratio. Sodium oleate and sodium stearate were found to modify the particle shape from round-cornered cubes to sharp-edged cubes. The mechanism was explained in terms of the reduction of the specific surface energies of the {001} and {100} planes of the tetragonal crystal system by the preferential adsorption of oleate or stearate ion to these planes, based on the adsorption experiment using ellipsoidal and cubic particles.