ARR - Annual Report
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.
Introduction
In many studies of precipitation, the length of the nucleation period is commonly invoked as the primary control parameter for forming uniform particles in a reaction involving homogeneous nucleation and growth (l-3). In the model originally proposed by LaMer and Dinegar (14) for the mechanism of formation of sulfur sols, uniform size distributions result if all the particles are formed in a short burst of nucleation, and then particle growth occurs by a mechanism where large particles increase in diameter slower than smaller particles (as occurs when growth is limited by diffusion to the particle surface). Despite the influence this model has had on studies of inorganic particle precipitation chemistry, the model has seen little corroboration and indeed has been brought into question for the sulfur sol for which it was developed (15). While the LaMer mechanism would undoubtedly result in uniform particles, finding systems meeting the conditions required for the model to hold has been elusive.
In recent years studies on the formation of polymer latex particles have provided an alternative mechanism whereby uniform particles can result from a homogeneous nucleation, precipitation reaction. In emulsion polymerization, an insoluble monomer is mixed with water and a water soluble free radical initiator added. Final particle size depends on reaction temperature, reagent concentration and parameters controlling the colloidal stability of the growing particles (i.e., ionic strength and pH). The initial locus of the reaction is in the aqueous phase. Oligimers grow to a size where they become insoluble and undergo a sol to gel transition. Due to their relatively low concentration, this transition involves only few polymer molecules and the gel phase grows by aggregation. The charge on the primary particles is small but as the aggregation process proceeds, the charge per particle grows. As a consequence, aggregation rates between particles of equal size decrease but the rate of aggregation of particles of dramatically different size increases. The result is a bimodal particle (or gel phase) size distribution with one peak located at the primary particle size and the second peak containing particles that are stable to mutual coagulation and grow by scavenging smaller particles. Upon aggregation, the gel phase particles coalesce and thus the particles are able to retain a spherical shape. As the reaction proceeds the growing particles reach a constant number density. These colloidally stable particles swell with monomer and the locus of the reaction is transferred from the aqueous phase to the inside of the particle phase. Uniformity is achieved through control of the colloidal stability of the primary particles and aggregates of these particles (6-8).
A second organic analogy to the precipitation of inorganic particles occurs in dispersion polymerization. Here a solvent is chosen where the monomer is soluble but the polymer is not. The reaction is initiated and proceeds through polymerization until the oligimers grow to a size where they undergo a phase transition and precipitate to form polymer and solvent rich phases. Uniform particles are achieved through the addition of steric stabilizers that control the aggregation of the growing gel phase (9).
The major distinction between the model of kMer and that developed for uniform latex particles lies in the incorporation of colloidal stability of small particles. The LaMer model assumes that each nucleus is colloidally stable and survives at the end of the reaction at the center of a particle. The aggregation models argue that while stabilizing such small particles is difficult, aggregation does not necessarily result in a broad particle size distribution. In developing schemes for control of particle size distribution, the result of accepting that colloidal stability can play an important role is that rather than focussing attention on the length of the nucleation period, one becomes very concerned about the colloidal properties of the growing particles.
In this paper we review our studies on the formation of uniform precipitates through the hydrolysis and condensation of titanium and silicon alkoxides. Our work has been aimed at elucidating whether uniformity is the result of the details of the chemistry or if particle size distributions can be controlled by physico-chetnical means. In particular we focus on experiments probing the length of the nucleation period in these systems and the effects of parameters controlling particle interaction potentials. We find that for the systems studied, the nucleation period appears to be a substantial fraction of the entire reaction period and that particle size is largely controlled by parameters related to particle interaction potentials. These results suggest that there are strong links between the physical chemistry underlying the formation of uniform latex particles and that controlling particle size distributions of hydrous metal oxide precipitates (10-14).
Summary
The object of this work is to develop methods for the quantitative prediction of all the major features of flow of a gas, together with solid particulate material, through a duct of arbitrary size and inclination. Flows of this sort are of great technical importance in pneumatic transport of particulate material, and in the circulation of particulate materials within chemical processes. Examples of the latter type include the riser reactors and standpipes which form components of the catalyst circulation loop in catalytic crackers, used in the refining of oil, and the long standpipes used in certain coal liquefaction plants. In all these systems the particles tend to distribute themselves over the cross section of the duct in a markedly non-uniform way, making it very difficult to predict the hold up of solid material and the pressure drop along the duct, or even to extrapolate these quantities from measurements made with the same materials in ducts of other sizes. In addition, the crowding of the particles into limited parts of the cross section can lead to undesirable effects, such as recirculation of the solid material against the direction of the main flow.
The key to making useful predictions for these systems is to understand and quantify the mechanism that determines the distribution of particle concentration over the cross section. In many situations of practical interest the gas flow is highly turbulent, and it is tempting to attribute the observed distribution of the particles to their interaction with turbulent eddies. However, a closer examination shows that this could produce the observed effects only in quite restrictive circumstances, where the particles are almost, but not quite light enough to follow the gas motion exactly. In this work we investigate an alternative mechanism, which attributes the stratification of the concentration distribution to collisions between particles. We have derived a criterion (presented in this report) to judge whether this mechanism is likely to be important in any given system, and have developed a complete mathematical model to predict the distribution of particle concentration and the velocity profiles for both gas and particles in steady flows of this kind. A computer program has been constructed to solve the model equations, and extensive sets of solutions have been found for ducts of different sizes and inclinations.
The solutions obtained appear to simulate most of the characteristic observed properties of flows of this sort, including the undesirable recirculation patterns referred to above. There is a dearth of good quantitative experimental data covering ranges of design and operating conditions broad enough to provide a searching test of the theory, but we intend to seek out what is available for comparison with our predictions. For systems where collisions between particles mediate the pattern of flow our program provides, for the first time, a rational basis for the design of particle-gas transport systems and, perhaps of equal importance, for identifying those circumstances in which their performance is likely to be unsatisfactory. It is not a very large step to extend the method to include developing flows, where the particles are accelerating under the influence of forces exerted on them by the gas stream. To the extent that turbulence can be modelled, it is also possible to introduce into the model some effects of turbulent fluctuations in the gas velocity.
EXECUTIVE SUMMARY
The primary objective of the Caltech program supported by IFPRI is to understand the dynamics of particles which do not coalesce immediately upon coagulation and, through that understanding, to guide the development of processes for production of particles with particular properties. Theoretical and experimental investigations of the dynamics of aggregate aerosols have been undertaken. The factors that must be taken into account in such models were first explored theoretically. Particles are represented as fractal agglomerates. The mobilities and cross sections of such aggregates were examined, and upper and lower bound estimates of the collision frequency function are developed. Predictions of the dynamics of a coagulating aerosol indicate that aggregates coagulate more rapidly than do dense spheres.
In the initial year of the program we have focussed our experimental program on describing the mobility of agglomerates. Agglomerate particles were classified using electrical mobility techniques. The classified particles were collected on electron microscope grids for image analysis of the photographs taken from those samples to estimate fractal structure parameters. The particles studied include titanium dioxide particles produced by pyrolysis of titanium tetraisopropoxide and elemental silicon particles produced by pyrolysis of silane. The former particles are representative of particles of considerable industrial interest. The latter particles are a convenient model system that has been used for initial studies of coalescence of agglomerate particles.
The mobility equivalent size of the free molecular and transition regime aggregates studied to date has been found to correlate well with the projected area of the particles. During the past year we also had an opportunity to study the mass transfer to agglomerate particles using an instrument which was brought to Caltech by Urs Baltensperger, a visitor from ETH in Zurich. The instrument, called an epiphaniometer, is a device for measuring the mass transfer to particles by attachment of radioactive lead atoms. The experiments have been performed using mobility classified particles and, as expected, we find that the mass transfer rate scales directly with the mobility for drag equivalent diameter of the particles. That is, spherical particles and agglomerate particles with the same migration velocity in an electric field exhibit the same mass transfer rates.
Because electrical mobility measurements play a key role in our studies of the dynamics of agglomerate particles, we have also conducted a series of experiments aimed at measuring the charge uptake by these agglomerate particles. These experiments have been conducted using bipolar chargers, that is, radioactive sources that generate both positive and negative ions in the gas that then attach to the particles. The experiments involve taking a neutral aerosol from which all charge particles have been removed with an electrostatic precipitator and exposing it to bipolar ions. The number of neutral particles remaining after exposure to a fixed ion concentration is measured. The neutral fraction scales, once again, directly with the mobility equivalent diameter.
Thus, from each of our studies to date, we find that the mobility equivalent diameter is a very convenient quantity for characterizing the agglomerate particles. During the past year we have also advanced our efforts somewhat in the modeling of the agglomeration process itself. This requires an understanding not only of the mobility or diffusivities of the particles, but also of their collision cross sections. To date, we do not have direct measurements of the collision cross section, so we have been forced to make estimates to provide upper and lower bounds on those cross sections and, hence, on the coagulation rates. Still, the estimates that we have made do provide some insights into the differences between the agglomeration process and coagulation of rapidly coalescing particles.