ARR - Annual Report

This is the third annual report of the IFPRI SUSPENSION RHEOLOGY project 1991-1994 at K.U.Leuven(Belgium), As IFPRI decided to continue this project, dealing with the flow of reversibly flocculated suspensions, an annual report was re- quested at this stage rather than a final report. The project deals specifically with understanding and predicting the flow properties of suspensions which are flocculated at rest but can be deflocculated during flow.

During the two previous years rheological and dielectric measurements were performed on suitable dispersions to clarify the relation between flow and flow-induced microstructure in reversibly flocculated dispersions. During the third year the work focused on the rheological measurements, including the collection of data on the sys- tems which have been used earlier for dielectric measurements.

The rheological work has been divided in two parts. A first part deals with the stationary viscosities of well defined model systems. The results should be useful in evaluating theoretical approaches and scaling laws. Earlier, fragmentary, data have now been supplemented with data on two additional particle sizes, with volume fraction and temperature as parameters. The two sizes provide consistent results which, however, deviate from the earlier data as far as temperature effects are concerned. This discrepancy will be investigated further next year.

The second part of the rheological work is concerned with time-dependent phenomena or “thixotropy”, another important but complex feature of reversibly flocculated dispersions. The effect of temperature has been found to be a result of hydrodynamic effects and interparticle forces. Particle concentration increases the rate of both structural breakdown and recovery during flow. This underlines the effect of particle collisions on these rates. This result has been confirmed by a similar incrtzse in the rate of structural changes when the shear rate is increased. The stretched exponentional has been found to describe the data adequately. Some empirical data reduction schemes are suggested and will be investigated further in the coming year.

The silicotungstate anion-- [ SiW 1204OJ ‘4, referred to in this document as “STA”-- has a diameter of 1 nm and is used as a model particle to investigate the role of short range forces in controlling the colloidal stability of metal oxide nuclei formed in the early stages of precipitation reactions.

1) The role of counter ions

has been studied by investigated the interactions of STA in the presence of H+, Li+, and Na+.

2) By measuring the light scattered

from dilute STA suspensions, the second virial coefficient was determined in ranges of 0.3-5 M HCl, LiCl and N&l solutions where it was found to be a decreasing function of ionic strength. Only small differences appear with changes in cation type.

3) Osmotic stress techniques

indicate that the STA anions crystallize from solution at osmotic pressures that are weak functions of cation type. However, the degree of STA hydration is very sensitive to the cation. Osmotic pressures at crystallization lie between (2.5-3.5)x107 Pa. The largest hydrate of H4STA is 31 while for Li4STA and Na4STA, the largest hydrates are 25-26 and 13 waters per STA molecule respectively. With increasing osmotic pressure, the crystals dehydrate in a series of steps with the osmotic pressures required to induce a step change in hydration varying with temperature and cation type. To a first approximation, the pressures required to induce the first dehydration step vary as. Na>Li>=H.

4) By comparing the volume fractions

at crystallization, the osmotic pressures, and the second virial coefficients of STA particles with the values expected for hard spheres, we conclude that at crystallization, the particles have hard cores with diameters of 1.1-1.24 nm and feel an attraction of depth (0.3-0.8) kT,

5) Our analysis indicates

that the interactions of nanometer sized particles are sensitive to electrostatic, van der Waals, and hydration interactions. To a first approximation, hydration interactions screen van der Waals attractions and block aggregation into the primary minimum, However, the hydration interactions may also provide an attractive minimum in pair potential energy which facilitates aggregation of a reversible type. The hydration interactions are controlled by a competition for water by various species in solution. As a result, the degree of aggregation will be controlled by water activity. This conclusion implies that in precipitation reactions, the activity of water (or its chemical potential) will play a significant role in determining the colloidal stability of growing solid particles.

6) Working in collaboration

with Dr. F. van Swol, we are investigating the role of solvent chemical potential in controlling the state of aggregation of colloidal particles. The calculations of Frink and van Swol [4] and Kokkoli and van Swol demonstrate that these interactions can be understood in terms of the affinity of the solvent for the solid and the stacking of solvent molecules between the surfaces. As the chemical potential of the solvent is raised, solvent will begin to partition to wetting surfaces and thus force the surfaces apart. When submerged in pure solvent, the only way to increase the chemical potential of the solvent further is to apply a hydrostatic pressure to the liquid. With increasing hydrostatic pressure the clay swelling continues. While the current models deal only with nonionic solvents, extensions to ion containing solvents and charged surfaces are in progress which demonstrate that solvation interactions continue to play a major role when the surfaces are held at separations on the order of a few solvent molecules.

These models indicate that solvent activity plays an important role in determining the state of particle aggregation. With this concept in mind, the experimental portion of this contract is aimed at developing methods of characterizing the nature of solvation interactions and using solvent chemical potential to manipulate the state of aggregation of particles which model primary particles produced in homogeneous precipitation reactions. For this purpose we have chosen to work with silicotungstate anions [SiW 120a]-4 which are spherical and have a crystallographic diameter of 1 nm. These anions are highly soluble, and when they crystallize, the solids have many waters of hydration.

The chemical potential of the continuous phase is manipulated by two methods in these studies. In the first, the osmotic stress technique of Parsegian and coworkers is used [5]. Here STA solutions are equilibrated with a vapor of known humidity (water activity) and the degree of hydration is measured. In these experiments, the chemical potential of the continuous phase is set by the relative humidity of the water above the solution. The water in the solution equilibrates by increasing or decreasing the concentration of the STA particles and their counterions. At equilibrium, the osmotic pressure of the STA liquid or solid is determined from n: = -RT ln(p/po)/v where RT is the product of the ideal gas law constant (R) and absolute temperature (T), p is the vapor pressure of water above the STA, po is the saturated vapor pressure of pure water, and v is the molar volume of water (with p, po and v all at temperature T). The osmotic pressure (7~) is the pressure that would have to be applied to the STA liquid or solid to maintain the solid volume fraction if it were exposed to pure water.

The second method of controlling the activity of the water and the electrostatic screening ability of the continuous phase is by varying the added electrolyte concentration. Currently we have focused on using electrolytes to alter both the ionic strength and solvent activity. The intensities of the light scattered from dilute solutions of STA at fixed electrolyte concentration are used to determine the second virial coefficient in a concentration expansion of the suspension osmotic pressure. In the limit of small particles, the intensity of the light scattered from the suspension is independent of angle and can be written as:

-----------------------, dn/dc = refractive index increment, ho = incident wavelength in vacuum, no = solvent refractive index at h,, N, = Avogadro’s number 3 (6.02 x 1023), c = mass concentration, RQ = Rayleigh scattering intensity at 8,9 = angle, M, = weight-average molecular weight, and A, = second virial coefficient. In these experiments, as the ionic strength of the supporting electrolyte is increased, the electrostatic repulsions between the STA anions are screened. In addition, the activity of the continuous phase is reduced.

In attempts to investigate the role of the counterion in determining the magnitudes of hydration forces, the dehydration of STA crystals and the second virial coefficients of dilute STA suspensions have been measured with counterions of H+, Li’, and Na+. For this purpose, H&TA, LQSTA and Na&TA materials were synthesized and their composition confirmed with NMR and elemental analysis.

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 inter-particle 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 resealings or lubrication approximations incorporating results for the short-time self-diffusion coefficient and the high frequency limiting dynamic viscosity. The primary accomplishments to date include

1. comparison of predictions without hydrodynamic interactions with low shear viscosities and long-time self-diffusion coefficients from Brownian dynamics simulations for soft spheres and
2. comparison of predictions with hydrodynamic interactions low shear viscosities, nonequilibrium structure, and high frequency shear moduli from experiments with hard spheres.

The accumulated results show quantitative or, at least, semi-quantitative agreement with data and simulations, suggesting success for the hydrodynamic closure but some deficiency in the thermodynamic closure at high concentrations. This report focusses on the high frequency shear modulus mentioned in (ii) above, but includes in the appendices complete derivations of the stresses and the conservation equation governing the non-equilibrium structure. The mathematical analysis in the body of the paper establishes that the limiting shear modulus

• does not depend on three-body couplings through the interparticle potential, ?? is sensitive to the detailed two-particle hydrodynamics near contact, and
• is affected only in a mean-field sense by many-body hydrodynamic interactions.

Thus, the predictions solely test the hydrodynamic closures. The close agreement with experimental data for two different hard sphere dispersions with different high frequency asymptotes demonstrates the robustness of our relatively crude hydrodynamic closures and the ability of the non-equilibrium theory to resolve a perplexing, albeit esoteric, dilemma in the literature. In the coming year we intend to

• complete the assessment of the thermodynamic closure through detailed comparisons with results from simulations without hydrodynamic interactions,
• calculate the frequency-dependent viscoelastic moduli and shear rate dependent viscosity for hard spheres,
• extract a more “‘user friendly”, approximate form of the theory that distributes the contribution from the thermodynamic closure between diffusion and inter-particle force terms,
• develop analogous approximations for the hydrodynamics in the presence of grafted polymer layers and short range attractions, and
• calculate the non-equilibrium structure, long-time self-diffusion coefficient, low shear viscosity, and shear modulus for polymerically stabilized spheres.

The last two items will make contact with earlier measurements in Professor Mewis’ laboratory.

To classify the characteristics of Geldart-A powders in bubbling fluidized beds utilizing electric fields, we have developed the electric field operation map for bubble control relating three variables: electric field strength, frequency and superficial velocity. The map includes regions of expanded bubble control, bed freezing, and elutriation control. These deliniations define our goals for the development of a uniBed theory of bubble control for ac and dc fields.

Perturbation theory and interparticle force theory have led to the evaluation of a powder modulus of elasticity. Results for 3 types of FCC and glass powders are reported. Early discrepancies in utilizing perturbation theory appear to have been resolved. Future studies will include the effects of particle diameter, relative humidity, and high temperatures.

In this reprt we continue our development of a unified theory of bubble control utilizing continuum and particle theories. Studies are reported at the frozen bed limits for ac and dc field and for bubble stabilization based on our extension of the Davidson bubble model. Van der Waals forces are now being incorporated in our ac and dc models. Scaling parameters are being developed and reported for our future work with large beds.

Our new high temperature facility is now operational and continues to be developed. A problem remains with the quartz sinter used for gas distribution in the bed. Our preliminary data from this facility indicate that:

• Bubble control remains effective at elevated temperatures depending on the increase in electrical conductivity of the material; for example, fresh Zeolitic FCC was successfully tested up to 465 “C for bubble control.
• The bed modulus of elasticity decreases with increasing temperature for fresh Zcolitic F C C.
• The bed modulus of elasticity increases approximately linearly with electric field strength for 3 kinds of FCC’s tested and for glass.

The strong influence of electric fields in controlling elutriation is now established for both ac and dc fields. This year a specially designed electrode-from-below fluidized bed was developed for these studies that is capable of measuring both particle charge and elutriation constants. Some first results on naturally occurring and induced particle charging within the bed are presented indicating significant particle charging -lOa C/kg for 8.66 pm sand fines. Particle charge remains an important variable for our interparticle force theory relating to elutriation control.

Executive Summary

This report describes the research in the laboratory of Professor Fuller supported by I.F.P.R.I. on the development and application of techniques in optical rheometry to the study of structure and dynamics of dispersions subject to external fields. In the first three year funding period, four projects were completed. These were:

1. the structure of dense suspensions of spheres subject to electric fields,
2. the microstructural basis for shear thickening in dense suspensions,
3. the electro-hydrodynamics of asymmetric particles,
4. the development of oblique angle polarimetry.

This latter project was aimed at devising an experimental capability of examining dense systems that are normally too opaque to test using standard optical flow cells. By using light that is sent through a sample at an oblique angle, the full refractive index tensor can be reconstructed for very thin samples. In this manner, the optical density of the samples can be significantly reduced. In the coming funding period, the technique of oblique angle polarimetry shall be extended and used to consider several dense particulate systems. Two possible systems would include dispersions of soft particles where the optical experiments can yield information concerning deformation by flow, and dispersions of magnetic particles. These latter systems are of interest due to their use in ferrofluid applications.

This report largely concerns new work using a computer simulation of solid fracture. The details of the simulation technique were described in previous reports. For this model, rigid elements ace assembled into a simulated solid by “gluing” the elements together with compliant boundaries. The joints fracture 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 by available test materials. Consequently, a computer simulation offers the ability to make investigations with a detail that is unthinkable to duplicate experimentally. As such simulation techniques are valuable is areas such as coxnminution 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 report begins with an update on our three-dimensional extension of the model. The extension was described in last year’s report. Unfortunately though, that model had proven to be much too computationally inefficient to be put to much use. We spent quite some time this year in examining the sources of the inefficiency and discovered the culprit to be the algorithm for computing the volumetric overlap of elements undergoing collisional contacts. We realized there were many conditions for which such a general algorithm was unnecessary and a more efficient, specialized approach could be employed. This created as much as an order of magnitude speed improvement and has allowed us to make simulations of single particle fracture consisting of up to 12,000 elements. About this time, we were contacted by Albert van den Bos, a student of BrianScaclett’s who was at that time performing part of his research in Reg Davies laboratory at DuPont. His topic was the jet-milling of plastics. Some of the experimental portion of his work was being performed by Professor Guigon and he wanted to know if we would be interesting in providing a simulation component and was particularly interested in polystyrene. Given the vast IFPRI involvement in the project, we agreed to participate even though it tested the limits of the simulation technique. On the down side, the simulations we performed predicted that no large scale breakage would occur. On the up side however, that prediction was borne out by the experiments which showed that only practical cracking and chipping events were observed. Perhaps the most important result of this exercise is that it pointed out the difficulty in comparing simulations of single particle events against the product of experiments whose output is a mix of the fragments produced by many impacts from a feed stock of many particle sizes. After that experience, we searched the literature for single particle events against which we could compare the simulation results and ran a simulation of one of Arbiter’s experiments of the rapid compression of soda-lime glass spheres. We were very surprised at how accurately the simulation predicted the experiment al out come nearly exactly.

The first scientific problem we considered was the effect of impact velocity on the general pattern of particle breakage. In last year’s report, we had confirmed experimental observations that showed various changes in breakage behavior that were associated with high speed impacts - among them a change in the slope of the size distribution. A two-dimensional simulation of the impact process between round particles and a rigid plate has demonstrated that there are two modes of impact i rstoccurs between the time the particle contacts the plate and the time that the contact force brings its motion to a halt (i.e. the point of maximum compression). Such a contact induces internal tensile stresses that generate a fanlike distribution of cracks that extend radially outward from the contact point. The magnitude of the energy contained by the tensile stresses and consequently the degree of breakage ca4 be related to the degree of particle deformation. Now in last year’s report, we showed that the ratio of the impact velocity to the sound speed V,/C, could be interpreted as a characteristic particle strain. Consequently, the larger the impact velocity, the larger the particle deformation and the larger the degree of Mode I breakage. Mode II breakage occurs as the particle rebounds from the plate. The relaxation of the internal stresses both extends the fanlike cracks begun under Mode I and induces azimuthal cracks that are oriented perpendicular to the original Mode I cracks. These latter Mode II cracks were concentrated near the impact points. It turns out that the induced breakage is nearly independent of impact velocity and depends only on the impact energy. Consequently, the impact velocity determines the balance between the cracks generated by Mode I breakage and those induced by Mode II. All of the observations associated with the high speed impacts can be attributed to a tilting of the balance towards Mode I breakage. We derived a dimensionless parameter that accurately describes the degree- of Mode I breakage in terms of the impact energy, velocity and Poison’s ratio.

We also began an investigation of the effect of particle shape on the induced breakage. As a first stab at this problem, we investigated the breakage of regular polygons for which the area is held fixed as the number of sides varies. Surprisingly, we discovered that particles with odd numbers of sides break more readily than those with even numbers of sides; this effect is especially pronounced for low velocity impacts. Consequently, we began an investigation into this phenomenon and discovered a partial solution that the problem lay in the energy ~scaling. Previously, we had found that the major factor in determining the level of particle breakage was the ratio of the kinetic energy of impact to the energy required to propagate a crack across the particle, Ekin/Ecr. This investigation proved that it is critical to correctly choose the “distance” across the particle used to compute E,,. That length scale appears to be most strongly related to Mode I cracks and is thus strongly affected by the impact velocity. For very small V,/C collisions, the dominant Mode I breakage results in a single vertical crack that spans the particle. Consequently, the appropriate length scale is the vertical span of the particle. For very large VJC impacts, the Mode I cracks propagate in all directions away from the point of contact and an averaged particle dimension works quite well.

In our original proposal for the first three years of funding, we had promised to perform two-dimensional simulations of hopper flows, but had largely dropped that phase of the project and devoted most of our time to the fracture work. We decided to finish the hopper project this year and the results are given in the fourth section of this report. Originally, we were interested by experimental observations of an asymmetric unsteadiness in the flow from a hopper: i.e. the flow was observed to move alternately down either side of the hopper. We found that we could reproduce this effect for monodispersed particle sizes, but also could eliminate it by by adding a small amount of polydispersity. From this observation, we were able to understand that the unsteadiness was a result of the strong packings that monodispersed disks are prone to fall into; a small amount of polydispersity is sufficient to disrupt these packing, weaken the material and eliminate the unsteadiness. In the experiments however, we suspect that the strong packings are a result, not of monodispersity, but of that fact that the studies were performed on angular sands which tend to likewise form strong packings. This implies that this unsteadiness is a result of the non-continuum nature of granular ii breakage. The fi materials as the particle packing, shape and size distribution are non-continuum quantities. From there, we went on to examine the stress state internal to the hopper. This permitted us to evaluate common methods of mode& granular materials. In particular, we measured the internal friction coefficient and discovered that it is far from a constant. Consequently, we conclude that models based on plasticity theory that assume that the material is always at the point of imminent yield (and thus should have a constant internal friction coefficient), are questionable at best. Furthermore, we demonstrate that rapid granular flow theory, the other common modeling technique these days, is as should be expected completely inapplicable to this problem. We conclude that hopper flows (and really almost all other granular flows of industrial interest) inhabit the relatively unexplored region between these two limiting flow regimes. That is the area that granular flow research should explore in the future.

Executive Summary

A first order model of the dynamics of pyrogenous fumes, based upon experimental and theoretical studies of the kinetics of particle growth and the structural rearrangements that occur following coagulation, suggests that the growth of nonagglomerated particles in aerosol reactors is best accomplished by dropping the temperature rapidly to quench coalescence before significant agglomeration occurs. Because of their larger collision cross sections, agglomerate particles coagulate more rapidly than do spheres of equal mass. As a result, once agglomerates begin to form, particle growth accelerates dramatically. Although agglomerate particles can be densified, the temperature would have to be increased significantly to do this, instead of decreasing continuously as occurs in most practical reactors.

Notably, the model predictions suggest that, for a given cooling rate, a high initial temperature will more effectively limit neck growth than will a lower one. The rate of decrease of the coalescence rate following the onset of agglomeration depends on the cooling rate and on the initial growth temperature. If the initial operating temperature is low enough that the coalescence time is comparable to the coagulation time, the coalescence time will increase only slightly faster than that for coagulation. Strong neck formation and hard agglomerates can then be expected. On the other hand, if the initial operating temperature is much higher so that coalescence is initially very rapid, the transition will occur much more abruptly. Neck growth within the first agglomerates to form will be reduced, and agglomerates will be more amenable to dispersion. These inferences require experimental testing. The proposed continuation of this project will focus on experimental definition of the bound between dense particle growth and agglomerate formation, and on quantifying the quench rate that is required to inhibit the formation of sintered agglomerates.

The classical model of neck development during sintering has been extended beyond the early stage of neck growth. Neck growth predicted using our model deviates significantly from that of the early-stage sintering model, raising serious questions about efforts to model the evolution of particle structure with sintering rates based on the classical model. Although this means that the model developed in this report can only be assumed to provide a qualitative picture of the transition, importance of the coupling of coagulation with coalescence is clear. Attempts at quantitative prediction of the structural evolution of pyrogenous fumes based upon the classical sintering time scales are, however, premature. Trace oxygen contamination of the silicon we have studied led to anomalous sintering behavior. Oxidation of the silicon surface would be expected to dramatically reduce the rate of surface diffusion. Neck growth predictions based upon the transport properties of pure silicon, but with surface diffusion eliminated, agree well with experimental observations. Thus, future work on the structural evolution of pyrogenous fumes must take the reaction atmosphere into account.

This report focuses on the theoretical interpretation of the results of our experimental program, and on defining the direction for future work. Experimental investigations aimed at obtaining quantitative measurements of the sintering of model agglomerates and at validating the models of the coagulation kinetics of agglomerate particles are near completion, and analysis of those experimental results is underway.

The work performed by our group during the previous IFPRI contract period focussed on fully developed, turbulent flow of gas-particle mixtures in vertical pipes, A K-E model for the fully developed flow was formulated and used to explain the mechanism responsible for the nonuniform distribution of particles over the pipe cross section (please refer to last year’s annual report, FRR 09-15, for a detailed description). In the present contract period is work will be extended to developing flow problems in an effort to understand (1994-97), th’ how the flow evolves in risers and standpipes, and get an appreciation for the length scales associated with various regimes of flow development.

We first derive the time-smoothed equations for a 2D, developing, turbulent gas- particle flow. The coordinate system used for this purpose is shown in Figure 1: x and y denote the axial and transverse coordinates, respectively. A Cartesian coordinate system is used rather than a cylindrical one so that asymmetric inlet conditions can eventually be analyzed. The vertically upward flow in a slit (Figure la) should have characteristics similar to those of flow in a riser so, henceforth, this geometry will be referred to as riser flow. By a similar token, the flow corresponding to Figure lb will be called a standpipe flow. The equations take the form of eight coupled partial differential equations ‘representing two mass balances, four momentum balances (two axial, two transverse) and balances for turbulent kinetic energy and its dissipation rate per unit volume of suspension. As in the case of the fully developed flow equations derived in FRR 09-15, separate transport equations for K and E are not required for the two phases, since, for the solid mass fluxes being considered, the inertia associated with the gas is negligible when compared to that of the solids. A full fledged analysis of developing flow in vertical ducts on the basis of this K-E model, taking into account the entrance and exit effects and the possibility of internal recirculation of particles and gas, is a very large-scale computational problem.

The axial development of the flow of gas-particle suspension in vertical ducts is characterized by a number of distinct zones. The pariticles are initially accelerated by a high-velocity gas stream (acceleration zone), where large changes in the particle concentration, pressure gradient, etc. take place over very small axial distances. Accurate numerical computations in this zone will necessarily require a very fibe axial mesh. Following the acceleration, the particle concentration and velocity fields slowly evolve to their fully developed states over a relatively larger distances (transition zone). This is followed by a fully-developed zone, after which is an end zone where the flow patterns change again to conform to the exit geometry. If the riser is not “sufficiently tall,” the fully developed zone may be absent and exit and entrance zones will interact strongly. A general purpose computational code that allows for all these regions will require large computer resources. It is therefore of interest to identify simplifications which will make the problem computationally more tractable.

In the present annual report, we have derived the time-averaged equations of motion for steady developing flow and simplified the resulting system of equations through a scaling 1 analysis (see Section 2). This analysis led to a system of equations containing only the first derivatives of dependent variables in the axial (vertical) direction, and the first and second derivatives in the transverse direction, This form allows us to view the developing flow problem as an initial value problem (as opposed to a boundary value problem) and compute the solution by marching form the inlet to the exit. It should be noted that the existence of a solution for such an initial value problem is not guaranteed. For example, when the flow develops an internal recirculation, such an approach will necessarily fail; however, in case no recirculation develops, this approach will yield the entire solution. Nevertheless, it is useful to solve the initial value problem and get a feel for the developing flow, largely because of the tremendous computational advantages it offers over the boundary value problem. With this in mind, we performed a number of calculations and these are described in Sections 3 and 4.

Section 3

which is devoted to a laminar flow model, that neglects the effect of tur-bulent fluctuations, shows that the entrance length in two-phase flow is considerably larger than that in a comparable single-phase flow, and this is a consequence of the particle seg- regation in the acceleration zone.

Section 4

results based on laminar and turbulent flow models are compared to demonstrate that the initial segregation of particles to the tube wall in the acceleration zone in purely a continuity effect, and the turbulent fluctuations, which come into play only in the transition zone, are solely responsible for causing segregation of particles in fully developed flow The main findings of the study are summarized in Section 5.

Abstract

Data from a range of filtration experiments on dilute particle fluid mixtures are used to determine the parameters that describe the physics of suspension flow in compaction. The range of solids volume fractions used is 0.00001<~0.1; <-potentials vary between O-50 mV. The relevant physical data are extracted from an analysis of the initial stages of a range of experiments at various - and - Theoretical considerations on suspension flow are presented to argue that the physical character of the flow at relatively dense, strongly interacting conditions is significantly different than that of quite dilute systems. The latter are dominated by fluctuations in the particle velocity near the septum to give gas-type diffusive btthaviour, while in the former the particles are more or less locahzed This observation has implications for the diffusion coefficient, which is predicted to behave quadratic in the filtration pressure for very dilute media and which is roughly independent of this quantity for mixtures containing strongly interacting particles. Experiments are described and analyzed to establish this behaviour and the experimental trends that are obtained bear out the main theoretical insights.

The general aim of the work is to elucidate the mechanisms of attrition of particulate solids. The specific objective of the current work is to investigate various types of damage under impact and sliding conditions. In particular, the transition velocities involved in impact breakage, the relative importance of normal and tangential stresses, the size distribution of the impact product and the effect of load and displacement on the material removal in surface wear have been investigated.

High-speed digital video recording was used to observe fracture patterns of a range of materials with diverse properties and structures as a function of impact velocity. The video recordings clearly show the existence of three identifiable velocity ranges where materials exhibit plastic deformation only, chipping, and a combination of chipping and fragmentation. This information is essential for developing realistic models of particle breakage.

Single particle impact tests of porous silica particles were carried out to investigate the dependence of attrition rate on impact velocity and impact angle. There is a significant increase of the attrition rate with impact velocity, with a maximum level of approximately 4.5% at 20 m s-l, for the size range 2.00-2.36 mm. The attrition behaviour of the samples is relatively insensitive to the impact angle in the range 25”-65’. However, preliminary impact tests with silica particles of different shape and porosities show that there is a dependence of the attrition rate on impact angle, depending on particle structure. Further work is on-going in this area.

A full size analysis of the impact products of PMMA and porous silica particles after a single impact was carried out in order to investigate the change of the size distribution with impact velocity. The Gates-Gaudin-Schumann distribution describes very well the size distributions of the mother particles and debris. The power index of the distribution is nearly constant for PMMA, but it varies significantly for porous silica. The cause of this variation is currently under investigation.

Single particle wear tests were also performed with the aim of elucidating the mechanisms of particle failure under sliding conditions. This occurs by abrasive wear at relatively low loads and long sliding distances, by chipping at slightly higher loads and short sliding distances, and by fragmentation at high loads. The data in the abrasive-wear regime of silica particles with high porosity, and hence low strength, show that the material loss is linearly proportional to the sliding distance and hence corroborate the predictions of the model developed by Ghadiri et al. (1995) for the semi-brittle failure mode. However, the wear test method developed here can provide quantitative information only about the abrasive wear rate, and the impact testing method has to be used for investigating the chipping rate of particulate solids.