FRR - Final Report

Executive Summary

This is the final report of the 1994-1997 IFPRI Project on “Reversibly Flocculated Suspensions” at the K.U.Leuven, Belgium. It is an extension of an earlier project of the period 1991-1994. It aims at understanding the flow properties of collodial suspensions that are flocculated at rest but can be deflocculated during flow. This should provide support for predicting properties and formulating colloidal suspensions with controlled flow properties.

Two parts can be distinguished in this project. The first deals with the analysis of the steady state viscosities of weakly flocculated suspensions with controlled stability parameters. Reversibly flocculated suspensions often display a time-dependent vis-cosi ty, a phenomenon called “thixotropy”. This phenomenon is poorly understood, It is the purpose of the second part of this project to attempt to identify and possibly quantify the role of the major factors governing thixotropy.

For the first part suitable model suspensions have been developed by starting from sterically stabilized systems in which the stability is gradually reduced. This can be done by using media that are poorer solvents for the stabilizer molecules or by changing the temperature. Also particles of different sizes have been used. Measurements were performed during steady state shear flow and during oscillatory flow. As often in real systems the stability parameters of the present materials were not known. Viscosity measurements on dilute systems have been used to deduce these parameters. This turns out to be a possible route but the accuracy of the results is limited.

With the available stability parameters it was attempted to correlate the viscosity curves. Qualitative relations could be obtained but no quantitative predictions. It is however very difficult to obtain reliable steady state date on the systems under consideration. Lacking suitable predictions the possibility of using scaling and data reduction schemes was investigated. For systems with a yield stress, common in case of flocculation, such a scheme was found for superimposing data from different temperatures. Also a scaling for concentration was found, using the storage modulus as a scaling parameter for the stress. It turns out that this relation works because of a quite general relation between storage moduli and yield stress.

Flocculated suspensions become gel-like at relatively small particle concentrations. This gel point can easily be measured and can be related to material and structural parameters. Some general theories about gelation can be applied to flocculated suspensions. An interesting model from the literature, developed for suspensions, is applied to the data. It is based on a two-level structure, each with its own fractal structure. Further investigations have to verify the general usefulness of this approach or alternatively the need to develop more complex models for the microstructure in order to predict flow properties on the basis of colloidal parameters.

It turns out that there is no suitable general theoretical framework for thixotropy, the subject of the second part of the project. None of the existing models was found to describe adequately any detailed set of experimental results. Therefore it was decided to concentrate on detecting general patterns in real thixotropic systems. These could then be used to guide further theoretical work. Various suspensions of carbon black and fumed silica were used for this purpose. They were submitted to stepwise changes in shear rate of shear stress to analyse the resulting transient response. In this manner some general trends could be identified.

A stepwise decrease in shear rate has been used to probe the structural recovery or build-up of the samples. The resulting viscosity-time curves could all be fitted by two expressions. They provide means to express thixotropic experiments in a compact manner. The build-up rate changes with shear rate in such a manner that the curves nearly superpose when plotted versus strain. The initial rate of change of the viscosity is proportional to that viscosity. Breakdown experiments follow a somewhat different pattern, the viscosity change with time should be substituted by that with strain.

The rate characteristics derived from fitting the transients to a suitable equation, e.g. a stretched exponential, obey a general scaling procedure that has been empirically derived. This seems to be applicable over a wide range of materials. Detailed thixotropy models are still lacking. Comparing rheological and dielectric transient responses indicate the complexity of the underlying structural changes. These can be qualitatively explained but quantitative solutions are still lacking. This could be the subject of future work. As in the case of the steady state behaviour of weakly flocculated systems, it might be necessary to investigate first in more detail the complex nature of the flow-induced microstructure.

Here we employ statistical mechanics for predicting the nonequilibrium structure and rheology of concentrated colloidal dispersions, with particular attention to the interparticle potential and polymeric additives. The outcome is a hicrsrchical theory for spherical particles characterized by radius, number density, pair potential, and thickness and density of any adsorbed polymer layer. From that the equilibrium dynamics and pair hydrodynamic functions are constructed. These, along with the applied shear field, enter the conservation equation governing the nonequilibrium pair probability. To approximate the effect of pairwise additive coupling with a third particle, we implement a series of increasingly sophisticated closures. The conservation equation is solved numerically by perturbing from the equilibrium fluid state to determine the nonequilibrium structure and linear viscoelastic properties.

For the present, comparison of extensive calculations for a variety of interaction potentials and hydrodynamic conditions establishes quantitative accuracy in the high frequency limit and qualitatively correct results for steady shear. For the latter the error with the most sophisticated closure is systematic and can be normalized by examining ratios of properties or trends. We demonstralc this with a variety of repulsive interparticle potentials and complications such as adsorbed or grafted polymer layers and polydispersity. The current formulation is especially useful for mechanistic studies of changes in dispersion behavior with modifications to either the interparticle potential or the size distribution. We also have confidence in the applicability of the. theory to systems with attractive interactions as long as the dispersion remains fluid (i.e. lacks a yield stress).

Calculations at the lowest or pair level yield semiquantitative results for rel- atively short range potentials and monodispersions. More accurate closures that account explicitly for many body couplings are required to capture the effects of polydispersity and longer range interactions.

This final report covers research funded by IFPRI arising out of a French national research effort on fine grinding. Three relatively independent teams were involved in separate projects which were to be combined to give an overall view of fine grinding in air jet mills. The teams are:

• Pierre Guigon (Compiegne) Individual High Velocity Particle Impacts.
• Alain Thomas, succeeded by Marie-Noelle Pons (Nancy), Morphological Description of Debris.
• John Dodds (Nancy then Albi) Modelling Fine Grinding Processes.

Whilst much progress has been made in each of the separate investigations the ambitious objective of combining the three projects has not been fully achieved.

We describe specific progress in our understanding of granular segregation in granular and powder processing equipment of industrial importance. We have found several new results of apparent practical importance for the blending of solids.

We have:

• Established that in some applications segregation patterns shut down above a specific particle size ratio. Velocimetry measurements indicate that this cut-off occurs when larger particles sink into the cascading layer, at which point they become unable to overtake their smaller neighbors.
• Determined that segregation in tumbling blenders scales according to two distinct scaling relations depending on tumbling regime.
• Confirmed that small amounts of cohesion are sufficient to significantly inhibit segregation. When cohesion is introduced by increasing the moisture content of a blend, the amount of moisture needed to effectively mitigate segregation decreases with particle size.
• Quantitatively evaluated the effects of intensifier bars on preblending of cohesive blends of common industrial powders.
• Determined that there exist a robust and reproducible set of segregation patterns that can be found across a wide range of blender sizes and geometries and across a wide scale of particle sizes.

These segregational states can actually be accentuated by traditional strategies for improving mixing by introducing cross-flows. Moreover, the dominant segregation pattern seen at high fill levels and tumbling speeds is the pattern exhibiting the most extreme segregation throughout the highest volume of the blend.

• Developed accurate models for the development of segregation patterns based on velocity histories of cascading particles that successfully predict segregation outcomes in a several different classes of 3D blenders. These results are of direct practical importance and call for validation at all feasible scales.

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.

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.

The aim of this Lancaster University-Bradford University collaborative project was to understand the forces between a variety of dry materials at the single-particle level, to relate these to complementary bulk powder flow measurements, and hence to assess how far such-single particle data are able to predict flow behaviour of real value to chemical engineers. In particular, the objectives may be summarised as follows:

• At Lancaster, to investigate the forces acting between single dry particles in simple model systems, using atomic force microscope technology;
• to acquire a force-curve data bank, using mostly materials already well studied in bulk cohesion testers or of particular interest to IFPRI members;
• at Bradford and elsewhere, to standardise the bulk cohesion measurements in an annular shear cell, and to compare the results with those obtained using a variety of other testers;
• at Bradford and Lancaster, to clarify the role of particle size and morphology, relative humidity and powder-wall adhesion effects, in the bulk flow behaviour of cohesive powders.

For the single-particle work it was necessary to design and construct the required humidity control system within which the atomic force microscope could be operated. Much of the data took the form of normal force as a function of separation between the two surfaces. In addition we broke new ground in devising a reliable method of measuring lateral force (friction) at the single-particle level. To help confirm the basis of theoretical interpretation, simple model systems were studied first, followed by cohesive powders of current interest. Values of pull-off force were surprisingly similar for a range of materials, and strong humidity-dependence was the exception rather than the rule. In the case of alumina, no particle size effects were apparent, in contrast with cohesion test results. Surface treatments of glass or silica-based materials produced clear differences, but not in the case of titania. Clear increases in adhesion were seen for particle-wall contacts in alumina and limestone (in agreement with suggestions from cohesion test results), but not with most of the other materials studied.

The data obtained by means of our new single-particle friction technique gave a wealth of information on linear and non-linear load-dependence, the nature of the inter-particle contact (single- or multi-asperity), the occurrence of stick-slip behaviour, and the relevance or otherwise of adhesion in determining friction. In general, the friction technique was considerably more effective in detecting differences in the behaviour of different materials than the normal force curve technique.

The Warren Spring-Bradford Cohesion Tester – an annular shear tester - was selected to measure the bulk cohesion of the selected powders. Further study of the topic of bulk powder testers, however, revealed not only that many shear testers are available today but also that the design, measurement procedure and interpretation are topics of great discussion and controversy. For this reason, the programme of bulk powder measurement (unconfined yield strength versus major consolidation stress) were extended to form an experimental study of three different shear testers for measuring the flow properties of bulk solids. A large amount of flowability and cohesion data has enabled us to present a rigorous qualitative comparison of five different types of testing device.

We have attempted a quantitative, if somewhat over-simplified, link between the single-particle and bulk studies. This involves, in the first instance, the simulation of yield loci, making allowance for particle size effects in any approximation of average force per particle in the bulk cohesion experiments. Thus, we have attempted to predict, from single particle normal and friction forces, the results of bulk experiments by suitable scaling, and compare them with the actual bulk data. This has involved deriving a suitable model, and has enabled us to determine the limitations and advantages of the two contrasting testing techniques (atomic force microscope-based and bulk). The single-particle AFM technique is good for the rapid screening of many powders for sensitivity to humidity, and appears to be well suited to studying particle-wall friction: this is important in powder flow where the internal cohesion of the powder is high in comparison with its adhesion to walls (leading to “plug flow”). The roughness studies possible with the AFM are also highly relevant to wall friction and the internal cohesion of powders. However, with the bulk cohesion, particle size effects and consolidation effects, the AFM fails to see many phenomena of interest to chemical engineers simply because they appear to be controlled overwhelmingly by particle geometry rather than the adhesion of single contacts. The single-particle type of experiment is found to explore only the first part of the corresponding bulk experiment, near the origin of the data plots. By plotting the bulk cohesion data as average force/particle rather than as force/unit area, most of the differences between the two types of data disappear. For the finest particles (e.g. 2-4 µm limestone), the average forces per particle coincide between the two types of experiment. Fortunately, many fine powders of interest have particle sizes in the range where overlap occurs and interesting comparisons can be made. Thus, the two experimental approaches appear to be converging at small particle sizes and low consolidation loads, just where we might expect the contacts between individual particles in both studies to be single- or few-asperity contacts.

In the pull-off experiments with the AFM, a particle (or group of particles) is pulled away from another particle or group, so that the results are analogous to experiments in which the tensile strength of the powder is measured or deduced. Analysis of the results suggest that the pull-off force is a material, not a particle, property. To explain why the bulk tensile strength falls much less steeply with particle size than expected by simple scaling arguments, it is necessary to assume that the larger particles exhibit multi-asperity contacts. In general, it may be true that friction is more relevant to the particle-wall interface, and adhesion more relevant to the internal shear or cohesion of powders.

EXECUTIVE SUMMARY

This project’s objective is to bring unique experimental insight to the detailed interactions between a gas and dispersed particles. By informing recent theories for those interactions, this work will benefit a wide array of industrial processes involving gas-solid suspensions.

The research is made possible by our development of an axisymmetric Couette cell producing shearing flows of gas and agitated solids in the absence of gravitational accelerations (Fig. 1). The facility will permit gas-particle interactions to be studied over a range of conditions where the suspension is steady and fully-developed.

Unlike Earth-bound flows where the gas velocity must be set to a value large enough to defeat the weight of particles, the duration and quality of microgravity on the Space Station will permit us to achieve suspensions where the agitation of the particles and the gas flow can be controlled independently by adjusting the gas pressure gradient along the flow and the relative motion of the boundaries.

We will carry out two series of experiments in space, due to take place in 2007. In the first series, which we call “viscous dissipation experiments,” we will characterize the viscous dissipation of the energy of the particle velocity fluctuations, when there is no relative mean velocity between gas and solids. To do so, we will reduce the boundary speed in successive tests until the inertia of the solid particles becomes small enough for the particle motion to be affected by viscous forces in the gas. By evacuating the cell partially, we will also investigate the role of the molecular mean free path in dissipating the particle agitation.

In a second series of tests, which we call “viscous drag experiments,” we will impose a gas pressure gradient on the shearing cell sketched in Fig. 1. The gradient will induce a relative velocity between the two phases, while the shearing will set the solids agitation independently. These Viscous Drag Experiments will be unique in exploring a regime where particle velocity fluctuations are determined by a mechanism other than interactions with the gas. In this regime, we will measure the dependence of the drag coefficient on the solid volume fraction and agitation of the solid particles. Partially evacuation will also allow us to test the effects of particle Reynolds number on the drag coefficient.

In June 2000, this project passed the crucial “Science Concept Review,” where a panel of scientists evaluated the feasibility and importance of our investigation. This significant milestone strengthened NASA’s commitment toward our experiments.

In this final year of the IFPRI grant, we tested the prototype shear cell on the KC-135 microgravity aircraft and on the ground. On the aircraft, we demonstrated the accuracy of our capacitance probe system to record solid volume fractions; we obtained a large data base of digital images with metal and ceramic spheres that will be used to develop further the computer vision software; and we gained confidence in the ability to design the experimental system. The tests on the ground allowed us to demonstrate the measurement of the mean volume flow rate using an isokinetic section of the channel, and their data verified the accuracy of our gas-solid theory. This year, we also continued to support NASA’s development of the granular flow module that will run our experiment on the Space Station. Because the term of this project is longer than the three years of the IFPRI grant, we have not yet completed all experiments, which will await launch to the International Space Station.

However, we have already achieved the following:

• We have specified the conditions of all tests (ARR 30-06).
• We have developed theories to predict their outcome based upon best available knowledge of drag coefficients and constitutive relations (ARR 30-06 and ARR 30-07).
• We have developed computer vision software to measure the velocity of the solids (ARR 30-06); a new capacitance probe system for recording solid volume fractions (ARR 30-07); a new isokinetic technique to evaluate the mean gas flow rates (ARR 30-07); and we have proposed a tracer technique to measure the velocity of the gas (ARR 30-06).
• We have manufactured a prototype of the cell, which we tested this year on the KC-135 microgravity aircraft and in the laboratory, thus demonstrating feasibility of the experiments.

This Final Report summarizes our progress to date, with some detail on this year’s activities, and it includes all papers written on this research during the grant period in the Appendix.