FRR - Final Report

EXECUTIVE SUMMARY

The flow of coarse materials from hoppers is well correlated by the Beverloo correlation. However this over-predicts the flow rate of particles of size less than about 5:00 pm. The purpose of this work was to investigate the hypothesis that the retarded flow is caused by air drag resulting from the dilation of the material as it approaches the orifice.

The work was carried out in Cambridge by T.M.Verghese under the supervision of R.M.Nedderman. This report is a summary of the work presented in Verghese’s Ph.D. Dissertation.

Experimental work was carried out on kale seed and 6 closely-graded sands with mean sixes ranging from 2280 pm to 150 pm. Measurement of the flow rates confirmed the validity of the Beverloo correlation for coarse materials and the existence of related flow for finer materials. Direct measurement of the interstitial pressure profile showed that the immediate cause of retardation was the existence of adverse pressure gradients near the orifice. From this it can be inferred that dilation occurs and direct confirmation of this was obtained using gamma-ray tomography.

We conclude therefore that the work has confirmed the starting hypothesis and this has led to a correlation for the discharge rate of fine sands which shows good agreement with experiment.

A theoretical analysis for the discharge rate of coarse materials from bunkers and hoppers has been undertaken. This analysis differs from all previous analyses in that allowance has been made for the non-uniform velocity distribution in the hopper. For mass flow hoppers the predictions do not differ greatly from those of earlier work. However, the theory also predicts the discharge rate from core flow bunkers and to the best of our knowledge this is the first time that a theoretical prediction has been made for this situation.

Summary

In this research project it was intended to examine the existence of the grinding limit of fineness of product powder mainly by inliquid grinding method using media mills, such as vibration and planetary mills, and to find out the factors which determine this limit, and the laws which govern the rate of grinding to approach to this limit value.

First the results of research works on the limit fineness in dry grinding, mainly about those of the authors, were reviewed and its general tendency was conclusively summarized. And then it was confirmed using a planetary ball mill, which had shown very high grinding rate with high acceleration number, that the equilibrium particle size, or limit fineness, does exist even in &-liquid grinding, when the size is expressed by 50% average diameter, though in some cases the limit fineness has not been found. This equilibrium size reduces with decreasing ball size and is well correlated with the force excerting on a single ball by mill pot. On the other hand, the limit size obtained as specific surface area by BET gas adsorption method is found to be much smaller than the 50% diameter and also independent of the grinding conditions within most of the present experimental range.

The laws to describe the approaching process to the equilibrium state was also examined and it was found that Tanaka’s law which includes the limit specific surface area in the equation as a sort of saturation state, is not valid. More simple relation, which can be approximated to Rittinger’s law is approved as a general law until the limit fineness is attained. That means that the factors which determine the rate of grinding and the limit fineness have no or only little connection each other. This fact was also approved by the simulation calculation of the lshifting process of size distribution of ground product.

It was also found that Rosin-Rammler’s formula is extensively approved to be able to present the size distribution of ground product even in this micron and submicron order size range.

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 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 agglomerate particles and by their collision cross sections. The lower density of agglomerates has competing effects on the coagulation kinetics &s compared with dense particles of equal mass: (i) the aerodynamic drag on the particles is increased due to the larger size of the particle of the same mass; (ii) 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.

The dynamics of aerosol formation and growth is well documented for particles that remain as dense spheres throughout their growth. We have generalized those models to account for aggregate structure, and have developed the first model for the collision frequency function that spans the entire range of particle Knudsen numbers and fractal dimensions. The particle size distribution is shown to approach an asymptotic form when the primary growth mechanism is coagulation, This asymptotic form is the so-called self-preseting particle size distribution. A dynamic exponent is defined that describes the rate of growth of the mean particle size. The dynamic exponent is shown to pass through a minimum in the transition regime, behavior that has not previously been described. Essential features of this asymptotic solution are observed experimentally, although direct comparison between experiment and theory is complicated by the transition between coalescing coagulation and agglomer&ion that took place in our experiments at about the same particle size as the transition between the free molecular and continuum size regimes.

A more complete description of aerosol agglomeration was made in numerical solutions to the coagulation equation using a modified sectional code. Comparison of the collision frequency functions of spheres and agglomerate particles reveals that the predominant effect is the increased collision cross section of the agglomerate, leading to a dramatic increase in the collision frequency of agglomerates as compared to dense particles of the same mass. Simulations that assume that particles coalesce completely up to a limiting size and do not coalesce at all beyond that size exhibit a broadening of the size distribution at that transitional size. Experimental evidence of that broadening is provided. The comparisons at this point can be considered only provisional in as much as direct experimental validation of the collision frequency function is still lacking.

Experimental studies have been conducted to explore a number of aspects of the evolution of aggregate aerosols. The structure-drag relationship has been explored by image analysis of transmission electron micrographs of mobility classified aggregate particles. For the low fractal dimensions of the aggregates studied (Df N 1.8), the drag on the particle scales well with the projected area. This result holds through most of the transition regime even though it is expected to be strictly valid only for particles much smaller than the mean free path of the gas molecules.

Structural rearrangements during sintering of aggregates have been explored by heat treating aggregate particles while they are still entrained in the carrier gas. Particles are observed to retain the appearance of fractal clusters of smaller primary particles throughout coalescence that leads to many primary particles from the original particle being incorporated into a single primary particle in the sintered agglomerate. This observation raises serious questions about the inference of mechanisms of particle growth from structure measurements alone.

EXECUTIVE SUMMARY

The formation mechanisms of uniform, submicron, inorganic particles were explored in this three year study. This project was initiated after a detailed literature review demonstrated that insufficient data was available to provide the basis on which to test various growth models. A research program was developed to explore growth mechanisms of a variety of systems such that common themes resulting in narrow size distributions could be extracted. This program sought to determine if uniformity is the result of details of bond breaking and making during the chemical reaction or if there is an underlying physical chemistry which must be satisfied for uniform precipitates to be formed. Following a general summary and summaries from each material studied, a detailed discussion is presented.

1. In conjunction with US Department of Energy supported research, three experimental systems were investigated; i) silica from hydrolysis and condensation of tetraethylortho-silicate, ii) titania from hydrolysis and condensation of tetraethylortho-titanite and iii) gold from the reduction of auric acid with sodium citrate.

2. In each system, particle growth rates, rates of loss of solution phase metal containing species and colloidal properties of the growing particles were characterized. Particular attention was paid to developing methods of distinguishing between growth by molecular addition and growth by aggregation of smaller particles. Kinetic models were developed which linked particle growth with rates of reaction in solution and the effects of variables such as precursor concentration; ionic strength and pH.

3. This research program demonstrated that the LaMer model for the formation of uniform particles is rarely, if ever, followed. Indeed, developing reactor schemes based on the LaMer model can result in focusing on the wrong control variables.

4. The central result of this research program is that uniformity is a consequence of particle interaction potentials which act to generate a constant number density of colloidally stable particles early in the precipitation reaction. This result suggests that in the development of reactor conditions resulting in uniform precipitates, the correct control variable set must include factors which influence colloidal stability.

5. This research program demonstrates the importance of understanding size dependency of heterocoagulation and the interaction potentials of sub-10 nm particles. In particular, the ability of small adsorbed molecules to provide a steak barrier which prevents aggregation into the primary van der Waals minimum has been demonstrated: a result of tremendous technological significance.

Executive Summary

Many industries produce, or encounter during processing, dry powders having mean sizes in the range 20-150pm; others, notably the petroleum and petrochemical industries, deliberately choose such powders as catalysts for use in fluided bed reactors. These Group A powders, as they are known, are, on the whole, aeratable; that is, they retain gas in the interparticle voids, and this property gives them to a greater or lesser extent good flowability. However, flowability and other related properties are influenced by interparticle forces (IPFs) and hydrodynamic forces (HDFs) which in turn are affected by the physical and physico-chemical properties of the gas and particles. It is believed that it is the balance of these which determines the behaviour of fine powders in a fluidized bed and in powder flow and handling operations.

The overall objectives of this research programme were to understand better (a) the nature of these forces and their relative importance and, in particular (b) the influence which temperature, addition of fine particles, and the gas itself have on them.

Experiments were carried out in 152 mm diameter columns with cracking catalyst (a spherical alumino-silicate) to which much finer catalyst particles were added. These were fluidized at temperatures up to SOOC with air, argon, neon, carbon dioxide, and freon-12. Measurements were made of bubble sizes, bed expansion, and collapse times using specially developed purged pressure probes.

The results show that the behaviour of Group A powders is caused by a combination of IPFs and HDFs, and that their relative magnitudes change with mean particle size. For cracking catalyst HDFs dominate above about 70 urn and IPFs below about 60 l.t m. Strongly adsorbing gases such as CO2 can increase the IPFs at temperatures below about 1OOC so that even relatively coarse powders may exhibit cohesive behaviour. Dimensional analysis shows that the fluidization behaviour can be characterized by a Cohesion number, and the Galileo and Density numbers. As yet it is not possible to make predictions of the Cohesion number a priori because it depends on the Van der Waals forces which in turn depend on the size of the asperities, and on the Hamaker constant, i.e. on the nature of the material from which the particle is formed. For FCC-FCC contact, particles can be treated as smooth when the asperities are smaller than 0.01 l.trn; however, the interactions between the asperities begin to dominate the IPFs rather than the parent particles when the asperities are larger than 0.1 l,trn. This critical size could be as large as 10 pm for FCC-polymer contacts because the polymer particles are soft and deform easily. For FCC-FCC the theoretical predictions agree well with our experimental results and those of other researchers. Although the Cohesion number cannot readily be predicted for most powders in Group A, other parameters which are relatively easy to measure can be used to characterize their fluidized behaviour, notably the ratio of minimum bubbling to minimum fluidization velocity, and the standardized collapse time. The influence of temperature on these parameters has been measured and has been incorporated into new and existing correlations. Measurements of bubble size confirm that there is an equilibrium size which is sensitive to particle size, but virtually independent of bed level and gas velocity. It appears to change relatively little with increasing temperature.

The presence of small amounts of fine particles influences strongly the behaviour of aerated and fluidized Group A powders, and the percentage present in powders used in any given industrial process may increase due to attrition of coarser components, or may reduce as elutriation occurs. In either case the performance of the process may be affected adversely.

Solid-liquid separation operations leading to the concentration and isolation of fine particles dispersed in liquids are important in the chemical and mineral processing industries. In spite of this, the procedures available for the prediction of equipment performance remain crude. Almost all major mineral and chemical processing companies now have a clear priority in R&D budgets to develop new approaches to waste minimization; a major part of the problem faced by these industries relates to the effect of management of waste slurries. The processes that manage final waste slurries are often classical “end-of-pipe” solutions. One of the key aims of the present broad program is to understand how to manipulate the structure of slurries within the process so that finally it is possible to engineer clear liquor and simultaneously manageable or tractable waste solids. The best way to process such wastes relies on understanding how to control the compressibility and viscosity of these materials.

We have developed a generalized approach to understanding and prediction of solid-liquid separation methods based on the measurement of fundamental material properties. This is of value in designing more efficient methods and ultimately to optimizing the performance of solid-liquid separation methods and the selection of flocculants for any given slurry.

Our model identifies two key parameters, the compressional yield stress P,(Q) and the hindered settling factor r(o) and we have developed laboratory test procedures for the direct measurement of both.

We have demonstrated the application of this model to a variety of thickening and filtration processes and provided a direct relationship between our model parameters and the conventional cake resistance (a) as utilised by current filtration engineers.

We have attempted to compare our model with Terzaghi’s consolidation model with some success but more work is required to perfect this analogy. We also need to investigate the role of a wider particle size distribution and the effects of shear on cake thickening. These remain as future targets in conjunction with the experimental work of Wakeman at al.

Summary

The grinding processes in ball mills are far too complex for an exact mathematical description. The well known, simple Comminu-tion Laws and the phenomenological Population Balance Model provide equations for an estimation of the dependence between feed size, energy consumption and product size distribution. Important parameters like ball size, mill filling or mill speed, however, are not included in these equations. A more detailed quantitative description of the comminution processes seems necessary. For this purpose, the complex grinding process was split into several fundamental processes:

1. Singleparticle fragmentation: the basic process in grinding.
2. Fragmentation under packed bed conditions: packing structure determines the distribution of comminution energy flowing into individual single particles in the bed.
3. Fragmentation by an impacting ball: a packed bed with position-dependent loading intensity is formed during impact.
4. Comminution in a ball mill: if the kinetic energy distribution of the balls in the mill would be known, then the comminution process could be described in terms of a) to c).

Experimental and theoretical investigations as well as evaluation of published experimental data gave following results:

1. Based on fracture mechanics, Weibull flaw size distribution statistics and Hertz-theory of contact forces, simple equations have been derived for the probability of breakage, mass specific comminution energy and fragment size distribution of single particles. The theory contains a few parameters to be determined experimentally and was tested successfully on published experimental data.
2. The contact energy distribution of particle assemblies under packed bed conditions has been determined experimentally using packed beds of polished soft steel balls. Combining this distribution with the single particle fragmentation theory according to a), allows the prediction of the fraction of broken particles in packed bed experiments. The theoretical predictions were verified with experiments carried out on glass spheres.
3. The fragmentation of particle assemblies between a stationary and an impacting ball was studied in detail with simple equipment at the University of Karlsruhe and with the ultra fast load cell of the University of Utah. Both investigations provide evidence that the height of the particle bed is reduced to only 1 to 2 particle layers when comminution begins to be effective. This has to be taken into account in further modeling.
4. The mathematical description of ball mill grinding in terms of processes a) to c) is the final aim of the theoretical development. This, however, was beyond the scope of this research project.

EXECUTIVE SUMMARY

A predictive model of the impact attrition of particulate solids was developed in the previous IFPRI programme (Ghadiri and Zhang, 1992):

where 5 is the fractional loss per impact, a is a proportionality constant, p is the particle density, U is the impact velocity, 1 is the particle size, H is the hardness, KC is the fracture toughness, and 4 is the constraint factor given by the ratio of the hardness to the yield stress. The model describes the chipping process and applies to materials that fail in the semi-brittle mode. The model predictions have been shown to agree reasonably well with the experimental results for ionic crystals that satisfy the semi-brittle failure conditions. In the current programme the work has been extended to glassy polymers, in order to assess the range of application of the model. The glassy polymers represent a category of materials that is completely different from ionic crystals in the material properties as well as structure. Poly-methylmethacrylate (PMMA) was selected as a model material because it is one of the most common glassy polymers and has a wide variety of applications.

Observations of the impact damage by high-speed photography showed that attrition was caused by chipping of comers and/or edges adjacent to the impact site at low impact velocities, and by fragmentation of the particle into relatively large fragments at high impact velocities. Detailed examination of the mother particles as well as debris by scanning electron microscopy and optical microscopy showed that chipping was produced by the propagation of sub-surface lateral cracks, and fragmentation by radial and median cracks. These mechanisms are associated with the semi-brittle failure mode.

A series of impact tests was carried out to quantify the extent of attrition. PMMA extrudates in the size range 2.36-2.80 mm were used. It was shown that these particles failed by chipping in the velocity range lo-30 m s-l and by fragmentation above 30 m s-l. The fractional loss per impact was measured as a function of impact velocity for 20 repeated impacts. In the chipping regime the fractional loss per impact was proportional to the impact velocity raised to the power 2.18, based on the first five impacts, and to the power 2.41, based on all the 20 impacts. The gradual increase in the power index indicates changes in the material properties with repeated impacts. However, these changes have not so far been quantified.

The effect of particle size was investigated on a theoretical basis. The limiting particle size below which fragmentation would not take place was estimated as about 300 urn for PMMA particles. Repeated impacts could reduce the limiting particle size due to fatigue effects or ductile shearing.

The conditions promoting the formation of lateral cracks were investigated by impacting rigid projectiles of various geometries on PMMA targets. It was shown that blunt projectiles were best as they induced a limited plastic deformation to initiate the cracks, and at the same time they could impart a significant amount of elastic strain energy to propagate the cracks. Further work is required to develop a mechanistic model of the fragmentation process.

This program consisted of two major portions: a two-year feasibility study and a three-year investigation into the fundamentals of effervescent atornization. A number of goals were proposed and met during each portion. They are listed in Tables 1 and 2. Those goals are also discussed in the following ten paragraphs.

The primary goal of the feasibility study

The primary goal of the feasibility study was to produce sub-50 µm droplets when spraying highly viscous (up to 100,000 cP) non-Newtonian fluids at process level throughputs (up to 1 kg/s). A secondary goal was to determine the spatial structure of the spray, in terms of how mean drop size and the width of the drop size distribution varied with axial and radial position throughout the spray. Work was conducted using a new type of nozzle developed at Purdue (an effervescent atomizer) because it was the only candidate likely to meet the sub-50 µm criterion. Fluids considered during the feasibility portion of the program consisted of glycerin/water/polymer and coal-water slurry/glycerin/polymer mixtures. Their consistency indices were as high as 41,500 and their flow behavior indices were as low as 0.27, Mean drop sizes as low as 28 µm were achieved when using air-liquid ratio values of less than 0.20, nozzle performance was shown to improve, i.e. mean drop size decreased, with increased throughput (in contrast to the behaviour of conventional atomizers) and polymer addition was demonstrated to have an adverse effect on the atomization of either single-phase or multi-phase feedstocks (although the extent of the increase left the mean drop size below the target value of 50 µm).

The fundamental investigation

The fundamental investigation had a number of goals We first focused on spray behavior in the transition region where the two-phase flow that exits the nozzle as discrete gas bubbles in a continuous liquid is transformed into a continuous gas stream containing discrete liquid drops. Our goal was to determine the mechanism(s) controlling effervescent atomization so that a model could be developed for future design usage. Single-pulse holography was employed to observe the liquid breakup phenomena characteristic of effervescent atomization. A qualitative explanation of the mechanisms responsible for effervescent atomization was provided, based on this data.

Investigation of interactions

We then broadened our efforts to include an investigation of the interactions between the spray and its surroundings. Our goal was to improve the already superior energy efficiency of effervescent atomizers by minimizing the impact of the major energy loss mechanisms. A computational study was performed to identify these major loss mechanisms and suggest methods for reducing their impact. We discovered that turbulent dissipation was the largest loss, followed by transformation of bulk kinetic energy into turbulent kinetic energy, and then entrainment of surrounding air. We concluded it was unlikely that turbulent dissipation and transformation of bulk kinetic energy into turbulent kinetic energy could be reduced, but that entrainment might be minimized.

Entrainment model development

We then focused on entrainment, with our efforts proceeding along two parallel paths. First, an entrainment model was developed for effervescent sprays that is based on the dimensional analysis performed by Ricou and Spalding [ 1961] in their work on entrainment by gas jets. This results in the entrainment number, which is the entrained gas flow rate normalized by jet momentum flux, axial distance, and entrained gas density.

Experimental apparatus

Second, experimental apparatus were built to measure both the entrained mass flow rate and momentum rate for a variety of sprays. The entrainment measurements showed that entrainment increases linearly with axial distance and that it increases with &-liquid-ratio (ALR) and viscosity. By measuring momentum rate, it was possible to calculate the entrainment number directly. Comparison of entrainment numbers showed that it increases with viscosity, nozzle orifice diameter, and the combined effects of surface tension and liquid density. A dimensional scaling by liquid density and orifice diameter collapsed the majority of the entrainment number curves onto a single line. The modified version of the entrainment predictive equation describes the entrainment behavior of effervescent sprays to within 25%.

Fluid rheological properties

Subsequent efforts were focused on the relationship between fluid rheological properties and spray mean drop size. Our goal was to identify the fluid rheological * property that resulted in reduced spray performance upon addition of polymer to a feedstock This work was motivated by our previous study into the influence of polymer addition on nozzle performance.

Study of viscoelasticity

One result of that study was the conclusion that spray mean drop size was independent of changes in either consistency index or flow behavior index for a power law fluid - it is fluid viscoelasticity that degrades nozzle performance. We then focused our efforts on a study of viscolelastic liquid effervescent atomization. Fluids were formulated using a Newtonian solvent into which were dissolved varying amounts of Poly(ethylene oxide). Six different polymer molecular weights were investigated between 12,000 and 900,000. Qualitative and quantitative drop size measurements were made for a range of fluid operating conditions. Liquid mass flow rate was held constant at 10 g/s while the air-liquid mass flow rate ratio varied from 2 to 10%.

Data analysis

Data show that the spray mean drop size decreases with increasing air-liquid ratio, that the addition of polymer increases mean drop size, and that spray mean drop size increases with polymer molecular weight and polymer concentration beyond a molecular weight of 35,000. Below 35,000 no significant variations in mean drop size were measured regardless of polymer concentration.

Holograms and ligament formation

Holograms of the near nozzle structure indicated that the presence of polymer in the fluid serves to delay the formation of ligaments from an annular sheet as the fluid exits the nozzle. Also the breakup length and diameter of the ligaments increases with the addition of polymer. These two phenomena explain the increase in mean drop size with the addition of polymer to a pure Newtonian solvent.

Modeling of spray formation

Modeling of the spray formation process was carried out in the spirit of previous effervescent spray models. The analysis correctly predicts an increase in mean drop size with increases in polymer molecular weight or polymer concentration. The model predicts excellent qualitative behavior of Sauter mean diameter (SMD) versus ALR. In addition the error between the experimental data and the model predictions was as low as 10%. The maximum disagreement was never more than 50%.

Theoretical analysis

Finally, a theoretical analysis was performed to describe the combined longitudinal- circumferential breakup of the annular liquid sheet present at the nozzle exit plane. The analysis considered only linear terms in the governing equations for momentum and mass conservation.

Conclusion of analysis

This analysis provided the correct scaling for ligament breakup length and number of ligaments formed from the annular sheet at the exit plane versus fluid viscosity, air-liquid ratio, and mass flow rate. However, the analysis did not provide the correct ligament breakup length and ligament number scaling versus surface tension, and predicted too few ligaments formed in the viscous case, as well as a fastest growing circumferential mode of order zero. Neutral stability plots indicated that the model was able to predict the combined circumferential-longitudinal breakup observed experimentally, thereby justifying a more sophisticated study that included the influence of non-linear effects. Finally, the neutral stability plots indicated that the present analysis can be used as a basis for derivation of drop size distribution functions from first principles. Such an analysis would couple classic instability theory, as presented here, with the discrete probability function (DPP) approach to incorporate contributions to the drop spectrum from all unstable modes. Fluctuations in fluid properties, such as viscosity, density and surface tension, due to inhomogeneities, as well as velocity variations due to turbulence could be incorporated. Consequently, the influence of these variations on the width of the drop size distribution could be evaluated.

CONCLUSIONS

Nine different test devices have been discussed in this report and beside them other designs are possible. Now the question arises which particular device should be selected? Obviously this depends on the objectives of the planned investigations. For this reason the following aspects have to be considered for a decision:

• Are the investigations focussed on the particle breakage behaviour and the primary breakage or on the secondary breakage?
• What kind of material should be tested: brittle materials as minerals and the like or ductile deforming materials such as polymers?
• Is it of interest to vary widely the particle size and what size range is to be investigated?

Each researcher has to decide what contribution to the comminution science or what improvement to the technology he wishes to perform. Nevertheless it seems reasonable to suggest two test devices for measuring the data for secondary breakage (fraction of broken particles, breakage function, increase of the specific surface and the liberation grade) for wide applicability.

1. A piston press with different working units for testing brittle particles in the single particle situation above 1 mm and for interparticle stressing above 10 pm. Special working units for different temperatures are possible, therefore also polymer particles could be stressed at low temperatures. The piston force should be at least 200 kN, but the hydraulic system has to be sufficiently sensitive that a force of only a couple of kN could be applied accurately. The advantages of such a device are the following: