ARR - Annual Report

In this IFPRI funded project we investigate the role of short range forces in controlling the morphology of sub-micron precipitates. Our progress can be summarized as:

1. Silicotungstic acid (STA) has been chosen as a model colloidal particle to mimic the properties of primary particles (nuclei) in precipitation reactions involving metal oxides.
2. STA forms crystal hydrates where the number of waters of hydration per STA molecule varies with the relative humidity of the vapor with which it is in equilibrium.
3. The waters of hydration of STA crystals are lost in discrete steps in solid/solid phase transitions involving changes in the crystal lattice.
4. The locations of the phase transitions can be related to the osmotic pressure which would have to be applied to hold the crystal at a particular solid’s volume fraction if it were equilibrated with pure water. These osmotic pressures are large (the highest hydrate is not formed until an osmotic pressure of approximately 300 atmospheres is applied at 25°C).
5. These studies demonstrate that large driving forces must be applied to squeeze solvent from between small metal oxide particles with a strong affinity for the continuous phase. Resulting from the small particle size and the particle/continuous phase affinity is a strong, short range repulsion which will completely dominate over electrostatic and Van der Waals forces.
6. Future studies will involve developing measures of the spatial dependence of the solvation interaction energy and the effects of varying continuous phase/particle affinity.
7. Our findings suggest that for precipitation reactions producing particles with a strong affinity for the continuous phase, classical nucleation events may never occur. The implications of this concept require better understanding of the role or solvent/particle interactions in controlling particle interaction potentials and molecular attachment rates to growing particles.

Summary

A quantitative theory developed herein for the rheology of concentrated colloidal dispersions accounts for the nature and effect of potential, as well as hydrodynamic, interactions. A configuration-space consemation equation for the pair density P2 provides a fundamental basis for calculating the nonequilibrium microstructure under shear, including three-body couplings due to the pairwise additive interparticle potential. The resulting many-body forces depend on the three-particle distribution function, necessitating an additional equation to completely specify P2. A nonequilibrium closure based on the hypernetted chain (HNC) equilibrium closure relates these forces to the interparticle force and pair distribution function completing the formulation. A computational algorithm exploiting Fast Fourier Transforms solves the resulting integro-differential equations for weak flows, yielding the perturbed pair density as a function of the volume fraction o and the inter-particle potential. Calculation of the stresses is then straightforward.

First, we present the low-shear limiting viscosity as a function of o for hard, soft, and charged spheres without hydrodynamic interactions and demonstrate satisfactory agreement with the limited results available from computer simulations and experiment. Second, we incorporate rescaled hydrodynamic mobilities and the viscous stress, based on extant results for the short-time self-diffusion coefficient and the high frequency limiting viscosity, tb account for hydrodynamic interactions. The corresponding predictions of the low shear viscosity for hard spheres lie within 20% of extensive experimental data for 0 < o < 0.60.

ABSTRACT

The effect of solvent surface tension, pH of water and surface chemistry of particles on agglomerate strength was studied using silica and titania agglomerates washed with different solvents. Aprotic solvents of various surface tension and water at various pH (with and without electrolyte) were employed to separate the effects of capillary pressure and particle-particle condensation reactions. The wetting behavior of the solvent was studied using both the imbibition method and the modified wilhelmy plate technique. The two techniques were compared to determine their limitations when applied to spherical particles. Agglomerate strength was determined using a calibrated ultrasonic field, mechanical shear and isostatic compaction. Organic groups present on the particle surface were identified using infra-red adsorption and 13C NMR and the effect of the groups on agglomerate strength was discussed. The strength and strength distribution of the agglomerates formed was found to depend on the solvent surface tension, wetting characteristic, pH and surface chemistry of the particle. The presence of electrolyte in the solvent was found to effect the extent and strength of agglomeration, specially at higher pH. Agglomerate strength was also found to increase with increasing capillary stresses, and pH of water.

Executive Summary

The goal of developing a unified field theory for bubble control in a fluidized bed is reviewed. Included in this unified theory is a single inter-particle force model that will handle the limiting cases of high as well vanishing field frequencies (ic. the ac and dc limits). The electrostatic bubble model utilizes a perturbation theory to relate force relationships at the particle level to the continuum equations of mass and momentum at the bulk bed level. An extension of the Davidson bubble model gives information on the local stresses induced around a bubble in terms of the far distant electric field strength.

For the first time in this IFPRI work we introduce a relationship between bubble control and elutriation control through an understanding of the various interparticle forces. Two mechanisms relating to electrostatics effects in elutriation are postulated by which the entrainment of fine particles can be diminished with electric fields:

• that bubble formation is inhibited with the application of electric fields, and
• that the bonding strength of fine particles to bulk bed particles is increased with electric fields.

To elaborate on these two mechanisms, various permanent and electrostatic interparticle forces are evaluated. For the electrical forces, current constriction is shown to be the dominating cohesion force that influences both bubble control and elutriation control, with the force of induction charging found to be less important. For the permanent forces, van der Walls and triboelectric particle forces contribute over different size ranges of fine particles depending on the surface roughness of the particle. Gravitational forces affect mainly bubble action through the larger bulk bed particles.

In a separate experiment it is now confirmed that elutriation control with electric fields is a consequence of field action within the bed and not simply a precipitator effect in the bed freeboard. The test was carried out on a specially designed fluidized bed in which the high voltage electrode entered through the bottom of the bed rather than from above so that the possibility of precipitator action was largely reduced or eliminated.

Our present correlations now include bed expansion, superficial velocity, particle diameter, and electric field strength for glass spheres. Previously, particle diameter had not been included in these correlations. The new results should be useful in helping to predict scale-up of beds as well as for predicting the delay of minimum bubbling conditions with fields.

The future plans for this research call for scale-up studies utilizing a larger bed experiment for bubble control and for developing a new high temperature facility. Numerical modeling studies will also be introduced. Our present facility has provided data up to 500 degrees C.

ABSTRACT

An experimental rig has been built to investigate breakage phenomena similar to that encountered in air jet milling. Particles of alumina hydragillite are accelerated by air in a nozzle and impacted on a target. Energy loss during impact is evaluated by measuring particle velocities before and after impact using two different methods: one based on observation with a high speed shutter video camera, the other based on cross-correlation of signals from an emitter-receptor optical fibre system. The particle size shape and distribution of the particle fragments from the apparatus are determined as a function of: solids loading, air flow rate, orientation and the material used for the target.

More detailed structural analysis of the debris is made by morphological characterisation based on fractal dimension. The basic hypothesis is that the breakage mechanism and kinetics depend on the initial fault network in the original particles. This is used to establish a fragmentation scheme for alumina hydragillite. Initial experiments with particles produced as a function of time in a batch operated air jet mill confirm the possibilities of the method of analysis.

Executive Summary

The goals of this research program for the period 1991 through 1994 are:

1. to identify the fundamental mechanisms responsible for effervescent atomization,
2. to quantify the impact that variations in the two-phase flow pattern at the nozzle exit have on the mechanisms responsible for effervescent atomization,
3. to formulate a theoretical model for the transition from a dispersed gas in liquid system, i.e. bubbly or slug flow in the nozzle, to a dispersed liquid in gas system, i.e. spray,
4. to develop a model describing the evolution of droplets as they propagate through a series of shock and expansion fronts.

Work during 1992-1993 focused mainly on identification of the fundamental mechanisms responsible for effervescent atomization, and on the relationship between internal two-phase flow and the mechanisms responsible for effervescent atomization. Both Newtonian and non-Newtonian fluids were considered.

For the Newtonian fluids, we were able to show that spray mean drop sizes decreases rapidly & lower air-liquid ratios because the near nozzle spray structure evolves from a sequence of single bubbles undergoing rapid expansion to an annular tree as air-liquid ratio is increased. The latter results in large caps of liquid which do not break up into small drops. We were also able to show that increasing air-liquid ratio above about 10% (on a mass basis) will lead to only a slight increase in nozzle performance because no further evolution of the annular tree structure is accomplished.

For the non-Newtonian fluids, we have shown that it is the presence of fluid viscoelasticity that degrades atomizer performance and have provided a preliminary correlation between viscoelasticity and atomization. We have also developed a performance map relating polymer molecular weight, polymer concentration, and mean drop size to serve as a rough guideline when applying effervescent atomizer to non-Newtonian systems.

We also considered spray-surroundings interactions during 1992-1993. In particular, we have measured the rate at which effervescent sprays entrain surrounding air using a direct technique. It was found that the rate of entrainment increases linearly with axial distance and depends strongly on the initial gas-to-liquid mass flow ratio (GLR). Entrainment results were correlated using a dimensionless group based on spray momentum flux. The correlation indicates that spray structure may significantly affect entrainment behavior. The correlation may be used to predict entrainment in effervescent atomization of low viscosity fluids.

Executive Summary

This report describes new size reduction work using a computer simulation of solid fracture. The details of the simulation technique were described in last year’s report. For this model, rigid elements are assembled into a simulated solid by “gluing” the elements together with compliant bouridaries. 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 may be invaluable in areas, such as comminution and attrition, in which the actual problem is so complicated, and for which so many events happen in so short a time, that experiments are historically limited to performing post-mortems on the fragments.

The first detailed application of the simulation was to study the impact of single, disc-shaped, particles on flat plates. Where comparison is possible, the simulation appears to accurately mimic experimental results. This study shows that the size distributions are, as would be expected, most strongly dependent on the collisional energy. Of secondary importance is the ratio of the impact velocity to the sound speed within the solid material; detailed observations, permitted by the simulations, suggest a physical mechanism for this behavior. Finally, the size distributions are nearly independent of Poisson’s ratio as the tensile loads that result in breakage result from the inertia and geometry of the impact and do not depend strongly on the elastic properties.

In the past year we have also developed a 3-D version of the simulation (which to this point has been limited to two-dimensional problems.) This model has proven to be very computationally intensive. As a result, we have only applied it to a handful of impact examples. However, we have recently begun to probe deeply into the source of the problem and have discoverd ways of significantly improving the performance of the simulation. We hope to implement these shortly.

The two-dimensional model has been used to investigate Bridgewater’s IFPRI sponsored shear cell experiments on particle attrition. In one of his experiments, he notices a distinct change in the slope of his Gwyn rate curves when very low normal forces were applied to the sample. An examination of the fragments indicated that this was accompanied by a change in breakage mechanism, from corner chipping to pervasive fracture of the particles. Our simulations, duplicate the change in breakage mechanism, but indicate that the observed change in slope is due to a misinterpretation of the experimental results. In fact, the degree of breakage was observed to be directly proportional to the work performed. We have also extended the two-dimebsional model to cases in which the particle experiences large deformations. The rigid, element simulation was restricted to small deformations as the elements could not change their shapes and, thus, could not conform to any general body shape. The current extension creates a hybrid model by applying portions of the finite element technique to allow changes in the shapes of elements.

This is implemented at the element level and no global stiffness matrix is assembled; instead, the elements interact across the same compliant boundaries used in the rigid element simulation. As a result, there is no need to assemble and invert a global stiffness matrix as in the standard finite element technique. As the elements may deform in response to an elastic/plastic stress-strain law, this allows the inclusion of realistic plasticity into the model. (As discussed in last years report, only approximate plasticity could be incorporated into the rigid element model.) This model also has two unintended but beneficial side effects. The first is that, if the joints are made stiff compared to the elements, then the elastic properties of the body are determined by the elastic properties of the elements themselves; consequently, the elastic properties of the body do not change, even when it is broken into individual elements. (For the rigid element simulation, only bodies eight elements across, retained the elastic properties of the full macroscopic body.) Also, the deformation of the elements is performed in response to the stress state the element experiences. Consequently, the stresses inside the elements are computed as a natural part of this procedure permittin the internal stress state to be determined even down to the the scale of elements. For the rigid (” element model, the stress state would have to be computed by averaging the forces in the compliant contacts of many neighboring elements.) Finally, we have performed some preliminary simulations of the effects of collision geometry on particle fracture. These show that a conforming, or near conforming, impacts generate strong elastic compressive waves that, when reflected from free surfaces as a tensile wave, can generate very fine fracture. This is a completely different mechanism than that which generates breakage in non-conforming collisions such as the single particle impact studies discussed in the frrst section. This was a rather controversial result and one that will probably turn out to have no useful applications (other than increased understanding of breakage processes). However, while we have not been able to fmd experimental observations of this effect, we have been able to successfully address all objections that are raised against it. Along the way, some of the results suggested that there may be an effect of relative particle size in the breakage induced by the impact between two particles. We hope to be able to explore these possibilities in the near future.

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 aggre- gate aerosols have been undertaken with IFPRI support. Following on our studies of the properties of agglomerate particles, we have developed models to describe the kinetics of agglomeration. The kinetics of agglomeration are determined by the mobilities of the ag- glomerate particles and by their collision cross sections. The lower density of agglomerates has competing effects on the coagulation kinetics as compared with dense particles of equal mass:

• The aerodynamic drag on the particles is increased due to the larger size of the particle of the same mass;
• The low density tends to increase the collision cross section of the agglomerate over that of the dense sphere.

We have used fractal scaling concepts to evaluate the relationship between these measures of particle size and the particle structure. Our theoretical investigations suggest that the collision frequency of aggregate particles is enhanced over that of dense spheres of equal mass.

This report describes experiments that are being undertaken:

1. To probe the structural rearrangements that take place when aggregate particles sinter;
2. To measure the col- lision frequency for aggregate particles as a function of particle size and structure.

The ex- periments are performed using model particles: bispheres for idealized sintering experiments and aggregates produced by low temperature aerosol coagulation for studies of aggregate sintering and aggregation kinetics.

SUMMARY

A mechanistic model of impact attrition has been developed in the previous IFPRI programme (Ghadiri and Zhang, 1992). The model was tested on ionic crystals that were known to fail under semi-brittle mode, and showed that the theoretical predictions agreed reasonably well with the experimental results. In the current programme the work is extended to glassy polymers since they represent a category of materials that is completely different from ionic crystals. Polymethylmethacrylate (PMMA) was selected as a model material because it is the most common of the glassy polymers, it is readily available, and has a wide variety of applications. The PMMA particles used in the experiments were cubic extrudates, provided by ICI, in the size range 2.36-2.80 mm.

The primary objectives of the work are as follows:

1. To identify the failure mode of PMMA particles under impact loading, by carrying out single particle impact testing, high speed photography of the process of impact, and scanning electron microscopy (SEM) of the impact damage.
2. To determine the velocities at which transitions occur from plastic deformation to chipping and from chipping to fragmentation.
3. To assess the impact attrition propensity of polymethylmethacrylate by evaluating gravimetrically the mass loss per impact as a function of impact velocity.
4. To analyse the data by comparison with the predictions of the model of impact attrition developed previously.

Single particle impact testing and high speed photography of the impact event show that PMMA fails in the semi-brittle mode under the prevailing high strain rates. However, PMMA shows a significant amount of ductility under quasi-static conditions as reflected in the relatively large size of the plastic zone when compared with the dimensions of the specimen.

The results of single particle impact tests reveal two distinct transition velocities. The first marks the onset of chipping and is about 25 m/s, while the second marks the onset of fragmentation and lies around 89 m/s. The above transition velocities apply only to the particle size used, i.e. 2.36-2.80 mm. However, the threshold velocities for other particle sizes have been estimated, based on the minimum load required for initiating various types of crack. For example, when the particle size is around 1 mm, the impact velocities for the onset of chipping and fragmentation are estimated to be approximately IS6 m/s and 556 t/s, respectively. These velocities are more relevant to comminution than attrition processes.

The SEM photographs reveal the occurrence of extensive plastic deformation beneath the impact site. The morphology of the impact site indicates that chipping is responsible for material loss.

The results of the impact attrition experiments show that attrition becomes appreciable only at very high velocities. In the range of impact velocities of interest to attrition, i.e. up to about 30 r&s, the attrition rate is very small. Within the chipping regime, the attrition rate is proportional to the impact velocity to the power of 234. If the fragmentation regime is taken into account, the power of velocity can reach up to 5.69. The attrition behaviour of PMMA does not follow the trends predicted by the model of impact attrition developed previously. The exact reasons are not clear at present, but it is considered that the lateral crack propagation in PMMA may not follow closely the model of lateral crack extension used previously. Formation of subsurface lateral cracks in PMMA requires further detailed investigations. In conclusion, PMMA appears to be an attrition-resistant material at least up to moderately high velocities.

A framework for simulating filter cycles is presented, based on a blend of tested theoretical models and accepted design procedures. Output from the simulator predicts correctly the general effects of process variables. Some sample results are used to illustrate these when it is applied in a general sense to a diaphragm (variable volume) filter press.