ARR - Annual Report

Our objective is a robust and fundamental theory to predict the structure and dynamics of concentrated colloidal dispersions, including the shear viscosity, linear viscoelastic properties, and self diffusion coefficients. To achieve such the approach must handle three-body couplings that arise with pairwise additive interparticle potentials and many-body hydrodynamics. Our treatment is based on the classical configuration space, or Smoluchoski, approach which comprises a rigorous description of dynamics on the diffusion time scale. The couplings through the interparticle potential are approximated via nonequilibrium closures based on diagrammatic expansions and analogous to well-established equilibrium closures. Hydrodynamic interactions are embedded in mean-field approximations that interpolate between physically valid near- and far- field limits, incorporating results for the short-time self-diffusion coefficient and the high frequency limiting dynamic viscosity, In particular, the theory calculates the non-equilibrium structure from a two-particle Smoluchoski equation with a hypemetted chain closure to account for three-body couplings through a pairwise additive potential and three different mean-field approximations for the hydrodynamics. Substitution of the structure into conventional expressions for the stresses and fluxes determines the transport coefficients.

The accomplishments to date include

• extensive comparison of predictions without hydrodynamic interactions with results for the low shear viscosity and long-time self-diffusion coefficient from Brownian dynamics simulations for soft spheres;
• comparison of predictions with hydrodynamic interactions with experimental data for the low shear viscosity, nonequilibrium structure, long-time self-diffusion coefficient, and high frequency shear modulus for hard spheres;
• calculations of the linear viscoelastic spectra of concentrated dispersions of hard and soft spheres with and without hydrodynamic interactions; and
• calculations for shear thinning in the dilute limit for hard spheres. The accumulated results show quantitative or, at least, semi-quantitative agreement with data and simulations, suggesting success for the mean-field hydrodynamics but a tendency of the thermodynamic closure to over-estimate the total interparticle force attempting to restore equilibrium at high concentrations. The sensitivity of the response of hard spheres to the magnitude of the perturbation near contact implies that improvements in the hydrodynamics and the thermodynamic closures must be closely coupled. This work comprises the PhD dissertation which Robert A. Lionberger defended in December and is reported in this and pas1 Annual Reports as well as the papers listed below.

In addition we have either completed or made significant progress toward

• extracting a more “user friendly”, approximate form of the theory that distributes the contribution from the thermodynamic closure between diffusion and interparticle force terms,
• developing analogous approximations for the hydrodynamics in the presence of grafted polymer layers and short range attractions,
• implementing Monte Carlo simulations to generate accurate equilibrium structures as the input for calculations with more complex pair potentials, and
• calculating the non-equilibrium structure, long-time self-diffusion coefficient, low shear viscosity, and shear modulus for polymerically stabilized spheres. These objectives are being pursued by Stacey L. Elliott, with initial results to be reported at the International Congress on Rheology in August and in the next Annual Report, Our further goals of calculating the non-equilibrium structure, long-time self-diffusion coefficient, low shear viscosity, and shear modulus for adhesive hard spheres and addressing polydispersity through selected calculations for binary mixtures and appropriate pre-averaging (over the size distribution) of the conservation equation governing the non-equilibrium structure will be undertaken after establishing a simpler approximate form of the theory.

This and the 1994 Progress Report focus on comparisons of the predictions with experimental data from hard sphere colloidal dispersions, which reveal the following: finite ------- with the lubrication approximation and --------- with the discontinuous approximation, with both in agreement with definitive sets of experimental data, ------ with either the lubrication or discontinuous approximation that conform within 20-30s with the body of experimental data and qualitatively captures the divergence as ----------- with the lubrication or discontinuous approximations that conform to the body of data for 4 I 0.45 and qualitatively captures the zero as ---------- non-equilibrium static structure factors, i.e. Fourier transforms of the non-equilibrium structure, for weak steady shear that exhibit the proper dependence on wave number but too small a magnitude with the lubrication or discontinuous approximations, and stress-optical coefficients in the low shear limit with the proper dependence on volume fraction and roughly the right magnitude but a size dependence inconsistent with the only set of data.

Underprediction of the non-equilibrium structure for hard spheres with hydrodynamic interactions and the low shear viscosities for soft spheres without hydrodynamic interactions suggests that the HNC closure over-estimates the interparticle forces driving the structure towards equilibrium. If corrected, the viscosities/self-diffusion coefficients predicted for hard spheres with the discontinuous and lubrication approximations for the hydrodynamic interactions would undoubtedly be too large/small. However, the physically more reasonable interpolation constructed with the ADA then might prove more accurate. The predictions of the high frequency limiting viscosities lend considerable credibility to the simple, mean-field hydrodynamic approximations. None the less, deficiencies in the hydrodynamic models undoubtedly still exist, e.g. direct interactions with a third particle neglected in the conservation equation itself and the approximation of the conditionally averaged divergence of the relative velocity in the Brownian stress. These neglected terms could be estimated through Stokesian dynamics simulations.

Though imperfect the theory clearly provides robust semi-quantitative predictions for the structure and dynamics of concentrated dispersions with a variety of repulsive interparticle potentials. At present the only alternative is Brady’s approach, Though based on more serious, ad hat approximations, his theory is appealingly simple and, thus far, provides comparably accurate predictions for the transport coefficients, despite erring qualitatively and quantitatively on the non-equilibrium structure. We proceed now with reasonable confidence that the current formulation and, perhaps, that of Brady’s should suffice for mechanistic studies involving complexities such as polydispersity, adsorbed or grafted polymer, or attractive interactions.

Publications R.A. Lionberger and W.B. Russel, “High frequency modulus of hard sphere colloids”, J. Rheology 38 1885 1908 ( 1994). R.A, Lionberger and W.B. Russel, “Effectiveness of closures for many-body forces in concentrated colloidal dispersions”, J. Chem. Phys, (submitted). R.A. Lionberger, Rheology, Structure, and Diffusion in Concentrated Colloidal Dispersions, PhD Dissertation, Department of Chemical Engineering, Princeton University, December 1995. A.A. Potanin and W.B. Russel, “Hydrodynamic interaction of particles with grafted polymer brushes and applications to rheology of colloidal dispersions”, Phys. Rev. E 52 730-7 (1995).

This report presents the work on cornmunition under the IFPRI grant since 1993. A literature review has already been produced together with a detailed presentation of the experimental methods used (see report AR 27.02). Complementary references can be obtained from the literature review on communition research at the university of Karlsruhe (report SAR 012-06).

The objective of this research is to advance understanding of the fundamentals of fragmentation behaviour and develop experimental techniques to predict communition behaviour from a universal test. An experimental rig has been built to reproduce single particle impacts on a target and study the influence of the material properties on breakdown in ultra-fme grinding. Another experimental rig has also been constructed to study the impact of two jets of particles, as in an air-jet mill. Further experiments concern grinding experiments in laboratory scale equipment in particular wet grinding with a stirred bead mill and dry grinding with an air jet mill. The develoment of methods for characterizing debris from fragmentation forms a link between these two experimental studies.

Part A

Part A of this report presents the results of the experiments performed with the single jet apparatus. Seven kinds of particles have been used showing different behaviour depending on the type material and the processing involved in its manufacture.

Part B

Part B gives the results of the study with the opposed jet rig. Three diffent powders have been used so far.

Part C

Part C presents the methods being developped for morphological analysis.

Part D

Part D describes a method developed for analysing fine grinding kinetics for determining breakage and selection functions.

Executive Summary

The primary project aims are to develop relationships which predict the wet massing behaviour of particulate solids granulated with binders by mechanical agitation, and to apply such findings in probing scale-up factors.

Work with model substrates: polymer binder systems has previously shown the critical estimate from surface free energy measurements, in determining the wet-massing and rheological character of the role of solid:liquid interfacial phenomena, particulate systems during granulation. This approach has been employed to predict the wet-massing behaviour of four representative powder substrates - two microcrystalline celluloses, calcium carbonate and griseofulvin - granulated with two aqueous polymer binders - polyvinylpyrrolidone and hydroxypropylmethylcellulose. The findings have been tested with a new mixer torque rheometer, which has been shown to provide data which can be directly related to the theological terms yield stress (T), kinematic viscosity (7) and degree of non-Newtonian rheological behaviour (n).

In general, the rheological behaviour of the various substrate:binder systems was consistent with the predictions made from surface free energy calculations, and followed similar patterns to those observed for model substrates. The spreading of substrate and binder components were critical factors in influencing the stability of the wet masses in the domains where, in industrial processes, many granules are prepared. Preliminary observations with mixed powder substrates suggest that topographical features of particulates also play an important role in determining rheological behaviour during granulation.

In the scale-up studies, a modified power number/Reynolds number relationship has been developed and successfully applied to large scale (up to 600L) mixer granulators. This approach has shown that, via measurements of wet mass rheology by mixer torque rheometry, a master surve for a specific formulation can be prepared using laboratory scale equipment which allows prediction of optimal granulation end-point conditions for large scale production equipment.

This report concerns new work using a computer simulation of solid fracture. The details of the simulation technique were described in previous reports and wiIl not be repeated in detail here. For this model, rigid elements are assembled into a simulated elastic solid by “gluing” the elements together with compliant boundaries. The joints ticture when the tensile strength of the glued joints is exceeded, permitting a crack to propagate across the simulated solid. The great value of a computer simulation is that literally everything is known about the simulated system and is accessible to the computer experimenter. In addition the simulation allows the independent variation of material properties such as Young’s modulus, Poisson’s ratio and work of fracture - flexibility, that in the laboratory, is limited to the properties of available test materials. Consequently, a computer simulation offers the abiity to make investigations with a detail that is unthinkable to duplicate experimentally. As such simulation techniques are valuable is areas such as comminution and attrition, for which the actual problem is so complicated and so many events happen in so short a time, that experiments are historically limited to performing post-mortems on the fragments.

The first topic to be addresses in this year’s report finishes an investigation started in last year’s report. There we identified two breakage mechanisms that are responsible for the 16nal crack patterns observed in impact breakage. The frrst mechanism (Mechanism I) can be attributed to the stresses that develop in unbroken particles. These stresses are oriented azimuthally about the contact point and produces a series of fanlike cracks issuing outwards from the contact point. This is the only type of breakage occurs between the time that the particle fist makes contact with the wall and the time that the contact force has brought the center of mass to a halt (which is also roughly the point of maximum compression at the contact point). This type of cracking will continue as the particle rebounds, but will also develop cracks that are oriented perpendicular to the fanlike cracks. Such cracking cannot be accounted for by the stresses that develop within an unbroken particle and must be attributed to some other mechanism (Mechanism II) that in turn must be a byproduct of the Mechanism I cracks that have already developed in the particle. Making full use of the powers of a computer simulation, we were able to determine that buckling of the Mechanism I fragments was ultimately responsible for the Mechanism II breakage. From the way that this investigation utilizes the abilities of a computer simulation to control the simulated system and thus reveal the bending stresses that bring about the Mechanism II breakage, this investigation is an unusually good example of the utility of a computer simulation for studying this type of problem.

For the next topic, we returned to the Ball Drop simulations that were created long ago as examples of the simulation in action. These simulations were based on the IFPFU supported Ultra-Fast Load Cell experiments performed at the University of Utah. These are approximate experiments related to ball-milling that are tractable (i.e. involve relatively few particles) by the simulation (i.e. involve relatively few particles). Essentially they are 2-D simulations of a single large grinding ball dropped onto a static bed of breakable particles. As a result the particles in the bed are broken and/or scattered away from the grinding ball as it falls. Simulations were performed for 4 different bed depths and 3 diierent frictions. Generally, the deeper the bed, the less the total amount of breakage. The results show also show the dual role that friction plays in the breakage process. On the one hand, the majority of the grinding ball’s energy is lost to friction so that increasing the friction increases this energy loss. On the other hand, the friction holds the bed together and the larger the friction, i the longer the bed stays in place for the grinding ball to do its work. It appears that this latter effect is the stronger of the two in that increasing the particles’ coefficients of surface friction greatly increases the amount of breakage; that extra energy for breakage appears to come from a reduced kinetic energy of the scattered fragments.

Fiiy, to help address the interest expressed in the breakage of porous particles, we have performed some simulations of the effect of internal defects in the form of circular holes. The simulations show that the holes have two effects. First of all, they concentrate stress internally and are thus become the source of many of the cracks that form. Secondly, they act as internal free surfaces and thus attract propagating cracks. As a result, if the internal holes are regularly spaced the particle will break with a large number of fragments with sizes of the order of the hole spacing. Consequently, it were possible to create particles containing such holes, it would be possible to gain some control on the particle sizes generated by impact (and, as the mechanisms are much the same, presumably by crushing as well).

Executive Summary

Although compaction has been the object of considerable study, questions remain about compaction. These questions exist due to the difficulties with obtaining in-situ information about powder rearrangement/breakage during compaction. In general, compaction work has primarily studied stress-strain curves. Depending upon the relative density and the change of density with pressure, one tries to infer the mechanism(s) of compaction.

In this work, we address the development of in-situ techniques to tlrobe comtlaction mechanisms. Instead of simply measuring density variation and attempting to infer compaction mechanisms, we employ scattering to study compaction. In order to demonstrate the utility of these in-situ techniques, we have:

1. performed preliminary experiments to demonstrate the sensitivity of the technique to a dilute second phase (sensitive to l-5% depending upon the powder size, morphology, and electron density),
2. used compaction with ex-situ scattering to demonstrate how compaction mechanisms can be directly observed and
3. employed fluids with electron density matched to that of the solid phase (or one powder if a mixture) to selectively study the second powder.

In one example, we studied changes of a silica compact as it was compacted isostatically or by drying capillary pressure. By assessing the variation in the scattering intensity associated with different length scales as well as the change in the hydraulic radius with pressure/density, pores around the agglomerates were observed to disappear due to agglomerate breakage and compaction. This result could not have been obtained by simply measuring the stress-strain of the compact as is normally done in compaction studies. For another example, dibromomethane was impreganted into a silica-titania mixture and scattering was performed. This shows that contrast matching and small-angle x-ray scattering may be employed to selectively “illuminate” a few hard aggiomerates of a second material type during compaction.

Optical rheometric methods are being used in this project to characterize the structure and dynamics of suspensions during flow. The methods being employed are primarily scattering methods: scattering dichroism and small angle light scattering. These are being applied to a wide range of problems that include:

1. determinations of the aspect ratio of colloidal particles,
2. flow induced structure in strongly flocculated suspensions,
3. orientation dynamics of a concentrated nematic suspension, and
4. the influence of interparticle interactions on the microrheology of dense suspensions.

The platform for these measurements is a newly developed facility based upon the principle of light transmission at oblique angles of incidence within a commercial stress rheometer.

A numerical simulation is presented of the FflteringIdewatering of structured suspensions. III the model the constitutive properties that are needed include:

1. the membrane permeability as a function of the solidosity of the deposited particulates (this is obtained by analysing the experimental data of the initial stages of the flow for a wide range of solids concentrations);
2. the effective drag coefficient which is found as a function of the solidosity from a least squares cell model; and
3. the stiffness of the solids matrix due to the inter-particle repulsion. For this the double layer interaction is used, combined with recent advances in techniques of micromechanics, as well as improved estimates for the inter-particle distance in dense suspensions. The resulting stiffness function is valid over a wide range of solidosities and contains two easily measurable parameters.

Experimental data are presented for tests on anatase at initial solidosities in the range 0.07 < $u < 0.3. The filtrate collected from the slurry as a function of time is recorded and used for analysis of the initial stage of the experiment to obtain the membrane permeability as a function of solidosity. Then a nonlinear numerical simulation is presented using the aforementioned constitutive relations and the results of this are compared to the Volume vs Time curves. The comparison shows that alI experiments can be adequately described with the same set of constants for the suspension flow. Only two parameters need to be introduced: the effective thickness of the double layer (related to the <-potential) and one phenomenological constant that describes the effective inter-particle potential strength in a suspension.

With the aid of the simulation cake formation is studied; the evolution of various internal parameters, such as the solidosity, pressure, skeletal stress and tluid and particle velocities is presented.

This project focuses on the fluid dynamics of vertical gas-solid risers. Its principal objective is to produce data for evaluating theories elaborated by Professors Sundaresan and Jackson at Princeton. Thus in this report, we review Cornell activities in the area of gas-solid suspension flows.

At Cornell, we possess a unique facility with the ability to recycle - rather than discard - fluidization gases of adjustable composition to a vertical riser of 20cm diameter and 7m height. This allows us to simulate the fluid dynamics of industrial units (atmospheric and pressurized coal-burning circulating fluid beds, catalytic crackers) in a cold, atmospheric riser by matching the dimensionless parameters that govern the flow. The facility is equipped with capacitance, optical fiber and pressure instrumentation that records solid concentration profiles in the vertical and radial directions.

In the first year of the award, we have established that, under typical industrial conditions, dense gas-solid flows are nearly independent of gas density in the fully-developed region of the riser. This observation of a viscous flow regime suggests that particle clusters dominate the exchange of momentum between the two phases. It further suggests that extrapolations of flow behavior from atmospheric to pressurized conditions should be more straightforward than previously envisaged.

To inform closure of theories elaborated at Princeton, we have also carried out simultaneous measurements of pressure fluctuations and local wall volume fraction. Here we have shown that, because gas pressure reflects fluctuations originating throughout the vessel, they are not closely correlated with local solid volume fractions.

In addition, we have begun a study of cyclone performance under conditions of high gas density and solid loading, which have not yet received much attention despite their importance for a new generation of high efficiency coal gasifiers and other dense gas-solid processes operating at high pressures.

In 1996, we have also made progress in the area of instrumentation, which is often of interest to industry. In particular, we have designed an uncooled capacitance instrument capable of recording instantaneous solid volume fraction near the wall of an industrial vessel operating up to 950°C and 15 bar. In addition, we have completed a technology review of instrumentation for dense gas-solid suspensions to be presented at an upcoming IFPRI meeting.

This research work addresses the correlation between the material properties and the processing conditions to the final characteristics of powders and granular materials compacted at, low and medium pressures. This correlation is based on the study of the microstructural characteristics and evolution during the compaction process. The materials (powders: granules, binders and lubricants) selected for this study are representative: of those used mostly by pharmaceutical and household consumer companies.

The main objective of this study is focused on providing Guidelines to improve rationally and systematically the current compaction operations by helping in the optimal selection of particles, binder, lubricants as well as compaction pressures and compaction speeds.

Rutgers University offers a unique environment to conduct this investigation. This university provides first hand access to current research on fundamental aspects related to compaction such as granulation, milling, mixing and blending, within a coherent and collaborative effort with concentration on Pharmaceutical Manufacturing. Also, it provides the state-of the-art iii characterization techniques and computational facilities, and ad-hoc testing facilities such as the Compactor Simulator Laboratory.

A sensor with 12 sensing electrodes and 24 driven guard clcctrodes has been constructed. This provides an increase of 80% in the measured capacitances and enables narrower cross sectional slices to be imaged.

A series of experiments on both bubbling and fast fluidization flow regimes were conducted at University of Bradford. The tomographic data were compared with measurements taken with an existing mass flux probe as well as pressure transducer measurements. The results showed that for a bubbling fluidization the data obtained from ECT measurements agreed very well with the data obtained from the pressure drop measurements. A satisfactory correlation of the tomographic data was obtained for a fast fluidization flow regime.

A new method for setting the system measurement range has been incorporated into our Windows software to measure a mean solid concentration in the range 2 to 10%. This method allows more accurate measurement of low solid concentrations (up to 5% by volume).

To order to study the dynamic behaviour of a fluidized bed by using Deterministic Chaos Theory it is necessary to calculate statistical invariants from hundreds of thousands of data points. Our existing software has been modified to carry out such an analysis. The application of a singular value decomposition technique combined with the data from an ECT system is presented (Dyakowski et al, 1996).

AVS software has been used to visualize the movement of a bubble chain through a fluidized bed. In the future we intend to use this software to visualise slugging and turbulent flow regimes.