ARR - Annual Report
Abstract
Coagulation in a flowing suspension is governed by the colloidal and hydrodynamic interactions between the aggregating particles and flocs. Beyond the initial particle-particle coagulation step, these interactions determine the structure of a floe being formed, and at the same time they depend on the structure of the aggregating floes. To develop a better understanding of the coagulation process, we have examined both the internal structure and growth rate of floes formed by rapid shear coagulation of dilute suspensions. Floe sizes were measured by dynamic light scattering, and structure information was extracted from static light scattering spectra covering the domain 0.18<q.a<1.7, where q is the scattering wavenumber and a is the individual particle radius. Interestingly, comparison of the sheared suspension results with results for floes formed by Brownian coagulation reveals a similar structure for the two modes, indicating similar aggregation mechanisms act in both cases. In contrast, the growth kinetics for these two modes are inherently different, as expected. To model the growth behavior in a shear flow, we treat a porous floe as a body with a hydrodynamic radius which is less than the capture radius corresponding to floc-floc contact, and we compare predicted kinetics based on this model with data at several shear rates.
A theory is presented for the fully-developed flow of gas and particles in a vertical pipe. The relation between gas pressure gradient and the flow rates of the two phases is predicted, over the whole range of cocurrent and countercurrent flows, together with velocity profiles for both phases and the radial concentration profile for the particles. The gas and the particles interact through a drag force depending on their relative velocity, and there are mutual interactions between pairs of particles through inelastic collisions. This model is shown to account for marked segregation of gas and particles in the radial direction, and the predicted relation between the pressure gradient and the flow rates of the two phases is surprisingly complex.
Introduction
There are many important problems on the conduction of heat in granular powder beds, i.e. silo beds, coal beds, high furnace in steel making, compaction of powder in ceramics industry, etc. The mathematical treatise on these problems, however, is not necessarily clear, because the correct physical model is not considered. In this report it is theoretically considered.
Summary
Polymers are used in a number of industries to improve solid-liquid separation. While polymer conformation has been considered to be an important parameter in determining the flocculation/dispersion characteristics of fines, no experimental study that correlates the conformation to flocculation/dispersion in terms of the important flocculation/dispersion responses such as sediment characteristics, sediment volume and supernatant clarity has been reported in the literature. We have developed a multi-pronged approach involving a study of polymer conformation on solids using fluorescence along with adsorption density and zeta potential in order to understand the behavior of various sedimentation characteristics mentioned above. We are currently extending this study to include relevant filtration parameters. Information obtained from these studies should prove useful in identifying conditions under which enhanced solid-liquid separation by either sedimentation or filtration can be achieved using polymer flocculation.
Summary
This report describes the work carried out in the year 1989 on the project ‘Impact Attrition of Particulate Solids’ supported by a grant from IFPRI. It contains a brief summary of our previous work outlining the features which require further investigation, a literature survey on the relation between fracture mechanics and attrition, and some preliminary work on the effect of hardness on the formation of cracks by quasi-static compression of a corner of cubic particles.
The main objective of this work is to investigate the mechanisms of attrition of particulate solids, and therefore particular attention is paid to the initiation and propagation of cracks and their morphology. Ionic crystals with cubic habit such as NaCl, KC1 and MgO have been used so far as model granular materials because their physical and structural properties are well-characterised. It has been shown previously that the impact attrition of these crystals takes place mainly through localised loading on the corners and edges. This leads to plastic deformation of the impact site, followed by the formation of diagonal cracks, and detachment of platelets from the face adjacent the impact site. It is the last feature which is particularly responsible for the formation of debris in the attrition process, and whose mechanism is under investigation in the current work.
To ascertain whether the formation of platelets in impact attrition of particulate solids is due to strain rate hardening, single melt-grown crystals of KCl, NaCl and MgO were subjected to quasi-static compression of their corners against a hard flat surface. These crystals have different values of hardness, so that the effect of hardness can be investigated independent of dynamic effects which may be present under High strain rates.
The results show that in all cases the material response is elastic/plastic; compression of a corner leads to plastic deformation followed by initiation and propagation of cracks from the plastic zone. The deformation stress is found to be lower than the Vickers hardness.
Two types of crack morphology are observed: {110190 and subsurface lateral cracks. UO)90 cracks are found on all the three crystal types. These cracks are similar to both the quasi-static indentation fracture by a sharp indenter and impact fracture. This is expected as these cracks are formed by dislocation activity on {110145 slip planes, a common feature in all the three materials. Subsurface lateral cracks are found in MgO crystals only, i.e. in the hardest of the three materials tested. This supports the idea that the strain-rate hardening mechanism is responsible for the formation of the platelets as observed previously in the impact fracture of the softer NaCl crystals. It is therefore necessary to investigate the stress field in the region of the plastically deformed zone, with particular attention to the role of hoop tensile stresses in initiating the cracks. The most appropriate way to analyse the stress field in view of the anisotropy of the material is by Finite Element Analysis. Therefore our plan for the current year includes a theoretical analysis of the stress/strain state by the above numerical technique. This will be complemented by experimental work on quasi-static indentation, and on impact by a hard projectile in order to validate the theoretical work.
The Ultrafast Load Cell Device at the Comminution Center of the University of Utah was used for experiments on quartz (1400 pm - 1700 pm) with the density of 2.65 g/cm? The sieves used for preparing the sample were A.S.T.M.E square hole sieves of 12 and 10 mesh respectively.
The Ultrafast Load Cell Device (ULCD) has been used for impact comminution of defined particle beds. The energy consumed by the particles, the force applied to the particles and the deformation of the particle bed is being determined.
After the comminution test the broken mass as well as the particle size distribution are determined by sieve analysis.
The impact test parameters varied are:
- Number of particle layers (pl)
- Drop height of ball (h)
- Anvil geometry of ULCD so that a ball-flat anvil and
- ball-curved anvil (called ball-ball) impact can be simulated.
ABSTRACT
This study examines the transition from fluid behavior to solid behavior that too often occurs in granular flow and brings with it such unwelcome events as funnel flows in hoppers and other clogging of material handling devices. This situation is studied using a discrete particle computer simulation of a Couette flow with gravity. This simulation exhibits the full range of granular flow behavior, from a stagnant solid-like material, through a quasistatic transition zone, to a rapid granular flow. The most important result is that the first motion in the material just above the static bed, occurs in a quasistatic mode at a fixed value of the stress ratio rxy/ryy. Thus it appears that the location of the transition from solid to fluid behavior can indeed be described by a Mohr-Coulomb failure criterion.
Agglomeration naturally occurs in today's industrially important powders due to adhesion forces between fine particles. The characterization of these powder agglomerates, especially the determination of the strength of these agglomerates and the nature of effective bonding forces is critical for a series of industries. The successful dispersion of powders reproducibly often necessitates the elimination of agglomerates totally. This objective can only be accomplished by a careful characterization of agglomerates, the strength of bonds in between the primary units forming them in relation to the powder processing technique used for their generation.
Although it is known that the presence of strong agglomerates in powders is the main reason for a series of undesirable phenomena in post processing, there are no known techniques for the quantitative determination of the strength of agglomerates. Most prior studies employ models assuming monosize spherical particles forming the pellets or sizeable granules which are held together by relatively weaker Van-der Waals forces or liquid bridges. Generally the most common and adverse affects are due to solid bridging generated during sintering or dissolution/precipitation rather than these relatively weaker bonding mechanisms. Because it would be very hard to detect the presence of small fractions of strong agglomerates in such pellets, development of a characterization technique which focusses on single agglomerates in a powder would be very helpful. It has been shown that these types of bonding mechanisms effective in forming ceramic powder agglomerates are very critical in determining the powder's sintering behaviour (1,2). In those studies ultrasonic forces were utilized to break dispersed suspended agglomerates in solutions. These forces which are a result of the cavitation phenomena are able to break most agglomerates and have been utilized in powder dispersion for a long time.
It is of course natural that almost all of the powder characteristics can be traced back to the powder processing technique utilized for the preparation of the powder. The powder particles are mostly formed by precipitation of a solute from a liquid or by nucleation and growth in a vapor. A large number of pathways can be utilized for the precipitation of the precursors to the final material. Precipitation involves the phase change of a sparingly soluble solute at high levels of supersaturation where at least initially, high nucleation rates are favored. Techniques used for the transformation of the precipitated precursor to the final form through heat treatment along with various precipitation conditions (reactant concentrations, temperature, pH, surface properties of the new phase, concentration levels of impurities and additives etc.) all may have significant effects on the state of agglomeration of the prepared powder. Agglomeration during the creation of the precursor phase depends on how well the nucleation and growth stages are separated. The way solvents are removed from these precursor precipitates and accompanying events like dissolution/reprecipitation have a determining role on the nature of bonds in the final agglomerates. Thus a study on the powder agglomerate characterization can not be complete without an effort to tie the ultimate properties back to the powder processing technique.
In our three year project, we plan to address the determination of agglomerate strength distributions for hard agglomerates via a three step process. These are:
- The demonstration of the validity of using hollow glass microspheres as a measurement of disruptive forces in an ultrasonic field.
- The synthesis of model hard agglomerates with narrow and well-defined bond strength distribution.
- The study of hard agglomerate formation in commercially significant powder processing schemes.
In the first year of this project, experimental work on the calibration of the effective ultrasonic forces on suspended particles in liquids have been completed. Strength distributions of hollow glass bubbles were determined by using a mercury porosimeter. Samples of these bubbles were suspended in water and ultrasonically treated at different energy output levels. Similar mercury porosimetry tests were done on the recovered treated glass bubbles. The strength distributions of the untreated and treated glass bubbles were compared with each other in order to reach an effective strength value for the specific energy output level. Model agglomerates formed from monosize submicron silica spheres were aged in basic solutions or heat treated at different temperatures to change the nature of bonding between the particles. Suspensions of these powder agglomerates were ultrasonically treated at different energy output settings and the agglomerate breakdown process was followed in situ by sedimentation type particle size analysis. The results of these changes in particle size distributions were combined with the results obtained during calibration studies to obtain strength values for the synthesized model agglomerates. These agglomerates were characterized by a range of methods.
Within the framework of the “SuspensionFlow” Project, the purpose of the present work is to predict the rheological properties of stable colloidal suspensions, in particular, polymerically (sterically) stabilized systems. This kind of stabilization can be used in ayueotis as well as in non-aqueous media.
Investigation of Materials
At this stage three particular items of the said materials are under investigation. Firstly, we try to describe the “softness” effect, caused by the deformability of the stabilizer layer. From earlier work, data on three different particle sizes (i.e. degrees of softness) are already available. They are now being supplemented with data on dispersions with intermediate softness.
This will allow an evaluation and eventually an improvement of the available theoretical approach and the available scaling methods. The experiments include viscosity measurements over a wide range of shear rates. The data support the validity of a theoretical approach used before. In addition, the dynamic moduli are measured at various frequencies to characterize experimentally the particle interaction or the stabilizer layer softness.
Polydispersity
The second item concerns polydispersity. The earlier data have been taken on monodisperse systems. Some data on bimodal systems are available from the previous research period. These have now been supplemented with data on different particle sizes and different diameter ratios. A rule for estimating the mixing ratio at which the viscosity reaches a minimum is suggested. Differences with the behaviour of bimodal systems of non-colloidal particles are demonstrated and simple mixing rules for describing the non-Newtonian flow regime are shown to be inadequate.
Shear Thickening Phenomenon
Finally, the phenomenon of shear thickening or dilatancy (increase in viscosity with shear rate) has been investigated. On shear rate-controlled devices, the sample often fractures at the dilatancy threshold. On a stress controlled device, the shear rate suddenly drops at a critical value of the shear stress to remain constant at still higher shear stresses. In this latter regime, the response is very irregular, indicating structural heterogeneities. Near the critical condition, hysteresis is observed as well as occasional jumps in shear rate between the two extreme values. These are attributed to instabilities in microstructure. Scaling ratios for the onset of dilatancy will be investigated.
Summary
During the first two years of this project, we have developed a scheme for quantitatively measuring the bond strength distribution of agglomerates via the use of a calibrated ultrasonic field and developed a synthesis technique for producing model agglomerates with monosize primary particles and narrow strength distributions which can be varied over a wide strength range. Also, the use of this calibrated ultrasonic field approach as a diagnostic tool was demonstrated during titania processing to show at what points in the process, hard agglomerate formation occurs and identify possible processing changes to eliminate hard agglomerate formation.