FRR - Final Report

Executive Summary

The role of short range interparticle forces in controlling the size distribution of submicron particles precipitated from solution has been investigated. The central hypothesis explored is that primary particles formed early in precipitation reactions are subject to short range forces that can be repulsive or attractive depending of the solvent chemical potential and the particle separation.

1. A model system was used to explore the role of short range forces in controlling the colloidal properties of sub-10 nm metal oxide particles. Criteria sought in looking for the particle were i) that it be on the order of the size of primary particles formed in precipitation reactions, ii) be readily available for investigation and iii) have a metal oxide composition. The particle chosen was the silicotungstate anion, SiW12O40,(STA) which is a sphere carrying four negative charges with a diameter of 1.1-1.2 nm. STA is readily soluble in water and is commercially available.
2. The solubility of the acid, lithium and sodium forms of STA was investigated as a function of supporting electrolyte concentration of HCl, LiCl and NaCl, respectively. Second virial coefficients of STA suspensions were measured by static light scattering.
3. The second virial coefficients were converted into an effective temperature, 7, by assuming the particles interact with an attractive pair potential with an extent which is a small fraction of the particle diameter. As T decreases, the strength of the interparticle attraction increases. A comparison was made between predicted and measured phase behavior where *c is plotted as a function particle concentration at the solubility limit. An excellent comparison was found suggesting the adhesive hard sphere model provides an adequate description of STA suspension thermodynamic properties.
4. These results demonstrate that as the supporting electrolyte concentration is increased, interparticle attractions increase. Detailed calculations suggest the attraction is stronger than can be reasonably attributed to van der Waals attractions. The conclusion is drawn that the salting out behavior seen in STA suspensions has an origin in the relative affinity of the solvent for the STA particles and the supporting electrolyte. We hypothesize that as the electrolyte concentration is increased, the water would rather hydrate the supporting ions than the STA particles resulting in a net interparticle attraction. This study clearly shows that the pair potential can be modulated by influencing the chemical potential of the solvent. In addition, these studies indicate that small particles feel weak attractions which will grow in magnitude as the solvent chemical potential is reduced. Note however, that this attraction does not bring particles into contact. Particles remain hydrated in the aggregated state.
5. The interactions of the STA particles were also investigated using osmotic techniques. Here STA crystals were equilibrated with nitrogen streams with different relative humidities of water. The dehydration properties of the STA crystals are very sensitive to the counterion. These studies indicate that the affinity of STA/counterion particles for water is high and that complete dehydration of STA does not occur at 25 C until the relative humidity is less that 0.05 STA crystals dehydrate in steps indicating that the pair potential is oscillatory in nature. If the relative humidity is converted to an osmotic pressure, 'IC (= -kT/vln(RH), where n is the osmotic pressure, v is the molecular volume of the solvent and RH is the relative humidity), one finds that at crystallization, the suspensions must be compressed to a pressure of near 300 atm if they are kept at a constant volume and exposed to pure water. Osmotic pressures of near 1000 atm are required to completely dehydrate the particles.
6. The dehydration experiments indicate that while STA crystals are heavily hydrated, the particle interactions are sensitive to counterion. From this result we conclude that oscillatory interactions arise from counterion hydration rather than particle hydration. Never-the-less, both the dilute solubility experiments and the crystal dehydration experiments indicate that the degree of aggregation (or the separation distance of the particles) can be controlled by alterations in the solvent chemical potential.
7. We conclude that in precipitation reactions, clusters or primary particles grow by molecular addition but do not aggregate because: i) van der Waals forces between small particles are weak, and ii) the hydrated state of the particle surface screens the van der Waals attractions. As the particles grow, the extent and strength of attractive forces increase and aggregation may occur. If the particles remain reactive, such flocculation can result in irreversible agglomerates. In addition, if over the course of the reaction, the solvent chemical potential is decreased, our results suggest that attractions will increase and may lead to aggregation and thus producing a broad particle size distribution.
8. Means of controlling the state of aggregation of sub 50 nm particles suggested by the preceding include control of the solvent chemical potential, and/or the adsorption of small stabilizing agents (such as citrate used in the control of particle size in the precipitation of gold from the reduction of auric acid).

Executive Summary

Two kinds of spherical particle materials were manufactured on the demand of IFPRI. One is transparent and the other is opaque. The transparent particles are glass beads made from barium titanate glass or soda-lime-eilicate glass by use of a horizontal flow sintering furnace or a fluidized sintering furnace. The opaque particles are made from phenol-resin spheres and carbonized in vacuum or in nitrogen atmosphere. They are really black. These transparent or black particles are not monodisperse, but they have appropriate size distributions in the respective size range of 1 to 10µm, 3 to 30µm, 10 to 100µm, and 150 to 650µm.

The manufactured transparent particles are here denoted as MBP!-10, MBP3-30, MBP10-100, and LBP150-650, according to their size ranges. Also the corresponding black particles are denoted as GCP1-10, GCP3-30, GCP10-100, and GCP150-650. More than 95% in weight of these particles are respectively within the stated size range. The manufactured amounts of these particles are; MBP1-10:10kg, MBP3-30:10kg, MBP10-100:20Kg, LBP150-650:30kg, GCP1-10:10kg, GCP3-30:10kg, GCP10-100:20kg, GCP150-650:24kg. These particles were sent to AEA Technology, Winfrith Technology Centre, Dorchester Dorset DT2 8DH, England.

Particle density measured by liquid immersion method is about 4.1g/cm3 for MBP particles, about 2.5g/cm3 for LBP particles, and about 1.4g/cm3 for GCP particles. However, the particle density of GCP particles measured by gas compression method was scattered because of the surface open pores. Size distributions of these particles were measured by several methods including the laser scattering and diffraction method and found to be almost logarithmic-normal. Particle shape analysis was also carried out by use of an image analyzer based on photomicrographs. Particles are satisfactorily spherical and average aspect ratio is 1.05 both for the transparent particles and black particles.

These particles may, therefore, be applicable to the calibration of particle-size analysis instruments.

Further characterization of these particles were carried out on the refractive index, particle strength, adhesive characteristics, and contact potential difference (electrostatic property). Refractive indices of transparent MBP and LBP particles were measured by a liquid immersion method with appropriate immersion liquids and found to be 1.93 for MBP particles and 1.52 for LBP particles. On the other hand, the refractive index of GCP black particles was estimated based on the size measurement by use of a laser scattering and diffraction instrument. The particle strength was measured by a micro-compression testing machine and correlated with the particle size. The small black particles have a larger strength than the corresponding transparent particles, but the strength of them depends strongly on the particle size. The strength of the transparent particles is less sensitive to the particle size.

The adhesive force between a particle and stainless-steel surface was measured based on the particle reentrainment by high speed air flow. The black particles are less adhesive than the corresponding transparent particles. For both types of particles it was found that the adhesive force is proportional to the particle size below 30µm, while it increases with the particle size to the 3/2 power for larger sizes.

The contact potential difference between MBP-particles and gold (Au)-electrode is ranged from 0.038V to 0.265V depending on the particle size. It is 0.228V for LBP150-650. On the other hand, the contact potential difference of the black particles is almost constant in this size range. The estimated work function is about 5.0eV for black particles.

The size segregation of particles was also studied. In feeding the particles into a container, smaller particles are concentrated in the periphery of the bottom layer and in the central region of the upper layer. Also in vertical tapping of the container, the smaller particles are gathered in the bottom part and relatively large particles are floating near the surface region. Therefore, the size segregation may cause a problem in handling the standard materials, especially for larger particles such as LBP150-650 or GCP150-650. Complete mixing and careful splitting are very important before distributing them as small samples.

Statistical error caused by sample size has been studied by use of a computer simulation and the theory developed in our previous work has been confirmed. Therefore, the error caused by sample size or numbers of particles required in a measurement can be analytically estimated. Fairly large numbers of particles are required in order to get reliable data.

Executive Summary Theoretical and experimental studies have demonstrated that ac electric fields are effective in suppressing bubbles and promoting expansion of gas fluidized beds of fine powders (< 125 µm). In addition electric fields are effective in controlling elutriation of fines from the bed. A unified theory to explain bubble control and various bed phenomena was proposed and researched. Parametric studies of several variables affecting bubble control (temperature, particle size, particle material, fluidizing gas material, electric field strength, field frequency) were carried out over the last 5 years. A prototype 18 inch cold flow bed was built, tested, and instrumented during the 6th year.

Theoretical work included ac and dc interparticle force modeling, application of a perturbation theory for evaluating the bed elasticity modulus, and the utilization of a two-dimensional numerical code (K-Fix) incorporating electric fields to demonstrate real time bubble control. The use of correlations with electric fields represented an alternative approach to quantifying bubble control and bed expansion including the effects of bed voidage, superficial velocity, particle diameter, and electric field strength for glass spheres.

A total of five test facilities were constructed to verify bubble and elutriation control utilizing both rectangular and cylindrical beds. A radiant heater quartz bed with feedback temperature control was used to achieve temperatures up to 530 C for bubble control studies and to 500 C for elutriation control along with computer aided data acquisition. For our elutriation studies a unique electrode-from-below bed was designed to verify our theory of electric fields. A special sampling Faraday cage was designed to measure the charge of fines in the freeboard. A new real time laser monitoring system of particle concentration was developed allowing us to evaluate elutriation constants directly and with high accuracy. Previous researchers have emptied the bed and restarted experiments to achieve time dependent measurements.

For bubble control our studies confirm bed expansions up to 15% while maintaining control of bubbling up to 530 C for FCC Various equations have been developed such as the linear relationship between bed elasticity modulus “and electric field strength and an inverse relationship with field frequency. For elutriation control with fields, our experiments confirm a direct relationship with bubble control. Significant reductions in elutriation of fine particles up to 96 % were measured, The mechanism of retention of fines to parent particles in the bed with electric fields remains speculative.

This research project aimed at working out a method for describing the dispersibility of an agglomerated material in stirred vessels and to apply this method to the improvement of the redispersing properties. Appropriate laboratory tests for describing the instant properties of the powder were also carried out, and a new testing method (dynamic wetting test) was developed. Furthermore a connection between the results from laboratory tests of the instant/dispersing properties and the large-scale dispersion of the product was established. Additional experiments were conducted with an unbaffled, partly or fully baffled vessel to investigate the influence of the flow field in the stirred vessel on the dispersion of powders in liquids.

It is difficult to establish a relation between the laboratory tests (static and dynamic wetting test) and the dispersing experiments in an agitated vessel. Since wetting tests do not take stirring power into account, they can not describe the processes taking place in the liquid. Therefore dynamic wetting tests were developed. It is possible anyway, to derive some trends from these tests. The results of the laboratory tests with lecithin, for example, are in good agreement with the experiments conducted using the stirred vessel.

The dispersion of powder can be divided in two steps: Submersion of powder and destruction of aggregates in the liquid. The wettability of a powder is an important powder property fo the immersion step. Although the specific stirring power that can be achieved in an unbaffled vessel is inferior to the specific stirring power for a baffled one, the improved ability to submerge the powder with help of the vortex formed by the rotating liquid proved to be of decisive importance. The powder can be wetted quickly if the critical height of wetting not exceeded so that lump formation in the liquid is avoided and a high power input is not necessary.

For difficult to disperse powders, however, this may be different. If such a material is to be dispersed, high specific stirring power is necessary and baffles have to be used. The use of smaller baffles close to the bottom of the vessel is a good compromise (partly baffled vessel). Liquid rotation and vortex formation in the upper part of the vessel is possible while the power input is increased by the small baffles compared to an unbaffled vessel.

Powder immersion in an unbaffled or partly baffled vessel is influenced by the vortex depth. At equal vortex depth, the course of a dispersion experiment appears to be independent of the stirrer type and size.

Experiments in a partly baffled and an unbaffled vessel are difficult to compare, but increasing vortex depth improves the immersion step in any case. Along with the vortex depth, the energy input is increased and aggregate dispersion is improved, Partly baffled vessels allow higher maximal energy input before gassing occurs and, for that reason, perform better at dispersing already submerged powder aggregates.

Scale-up experiments were conducted but further experiments are necessary because in stirred vessels scale-up rules cannot be used generally.

From the present point of view, any large-scale dispersing vessel should be unbaffled if possible or partly baftled if a higher specific stirring power is necessary and be equipped with the impeller type which allows the highest energy input without gas being entrained. If this criterion does not lead to a clear choice, the stirrer with the highest circumferential velocity should be taken since it will probably perform better at aa aregate destruction.

Research in the laboratory of Professor Fuller has centered on applications of techniques in optical rheometry to understand the structure and dynamics of flowing, dense suspensions. This project has involved the design, construction, and implementation of new methods that are thought to be particularly suited to highly turbid systems that are normally difficult to handle using optical methods. The solution to this difficulty has been to develop techniques that can accommodate very thin specimens and still acquire sufficient information to properly access flow-induced anisotropy of a suspension’s structure.

The scattering of light is the dominant optical interaction with most suspensions and this phenomena has been used in the present work. For this reason, scattering dichroism and small angle light scattering have been applied to several systems of concentrated materials through collaborative arrangements. Furthermore, the experiments have been designed so that these optical measurements can be accomplished in combination with more standard, mechanical rheometry measurements. In this way, the coupling of rheological responses to flow-induced structure can be more easily appreciated.

These techniques have been applied to two types of dense suspensions during the past three year funding period. In a collaboration with Professor Jan Mewis of Leuven, Belgium, a complete study of flow-induced structure in dense suspensions of soft spheres has been made. This work examined the consequences of systematic changes in the stabilizing surfactants that were used to control aggregation. These surfactants were demonstrated to also affect the “softness” of the particles. Using scattering dichroism and small angle light scattering, it was found that hydrodynamics forces were able to induce the formation of “stringlike” structures when the shear stress surpassed a critical value. By simultaneously measuring the mechanical properties of the suspensions and their optical properties, it was determined that this structural transition occurred at a stress where the viscosity undergoes a strong shift in its shear thinning behavior.

The second project involved a joint study with the research group of Prof. Piau of Grenoble, France. This collaboration considered dense suspensions of rodlike, sepiolite clay particles. The principal question pursued in these experiments was whether this colloidal system undergoes an isotropic to nematic phase transition as its concentration is increased. Measurements using scattering dichroism and small angle light scattering were demonstrated to produce determinations of the order parameter in flowing suspensions. By subjecting suspensions of varying concentrations to extensional flows, direct evidence of liquid crystalline behavior was obtained.

EXECUTIVE SUMMARY

This report presents a use of an electrical capacitance tomography (ECT) system to study the dynamic behaviour of various modes of fluidization. The results showed that the system can provide instantaneous information on solids distribution for a wide range of gas-solids flow patterns. An application of the ECT system is illustrated here by measurements of the instantaneous behaviour of a fluidised bed. The experimental programme focused on measuring both discrete and continuous parameters which characterise the interaction between the gas and emulsion phases. The first included bubble sizes, their velocities and time scales characterizing a bubble coalescence growth. Solids cross-sectional distribution at various positions in a riser and in a dip leg were measured for a wide range of superficial gas velocities and circulating solids mass fluxes. Instantaneous images showed a flow morphology which is crucial for modelling the heat transfer process. This included details of wall coverage by solids clusters and thickness of the annular layer.

Part of this project was concerned with the development of both hardware and software for capacitance tomography. During the project the software was extended by including a new iterative algorithm and a computer aided procedure for sensor design was developed. As a result the sensors can be designed in different ways to meet differing industrial needs. The data from the ECT system can provide, for the first time, the continuous and on-line information required by the control loop.

The software developed provides the data to the control loop from each individual electrode or from the whole set of electrodes and can be used in in two ways. The first includes images showing solids distribution within a pipe cross-section and the second is based on the statistical analysis of data gathered by a multiplicity of sensor. This can include averaged values, standard deviation and other parameters based on Fourier analysis like spectra or correlation functions. The choice of one of these parameters depends on the particular aim which can be defined by the industrial user.

This final report describes the method and results of discrete particle simulation which we have been developing under the support of IFPRI from 1994 to 1997. Calculations have been performed for dispersed gas-solid flows where particle concentrations are so high that particle-to-particle collision is essential. The method is based on calculation of trajectories of individual particles. In this report the method is described first, and then some results of a preliminary calculation are shown. Main calculations made in three years are classified into three cases.

• Calculations of the first case were made for comparison of our method with those by conventional numerical analysis based on a continuum model.
• The second case was made to investigate structure of gas-solid flows in detail.
• The third case concerns turbulence modification due to particles.

The most important aspect of our work is that the method uses very simple equations of motion and yet it succeeds in producing complicated phenomena in gas-solid flows. It is shown that particle clusters in a riser can be explained by repeated in-elastic collision. Since cluster generation was predicted by another numerical method by another group, their method is based on the model which regards the mixture of gas-solid as being consisted of two fluids. To compare both our method and their method, we performed the discrete particle simulation under the same conditions as their work. In these calculations we clarified similarity and dissimilarity of results between both methods. It is shown in the second case that the existence of such clusters causes large scale turbulent flow. In the third case, we extended our numerical analysis to analysis based on large eddy simulation.

In the first and second cases, the equations of gas motion based on inviscid gas, and thus fluid phase does not have any turbulence in the absence of particles. Thus, as long as we use the method based on inviscid gas, we are not able to predict turbulence phenomena near the wall. We used the large eddy simulation technique to consider the turbulence of gas phase. The empirical constant used in the present LES is the same as has been established in single phase flows. Like the first and second cases, we took into account the particle-particle collision. We found that the effects of particle-particle collision on velocity fluctuation and concentration of particles are significant even in dilute phase flows (volume fraction is the order of O(10^-1)). Most researchers consider that the particle-particle collision can be neglected at such a low concentration. Turbulence suppression due to particles was also observed in the calculation as in experiments.

Finally in this report the future work which should be made as an extension of the present work is briefly described. First, the importance of the work combining the discrete particle model and the continuum model is described. Second, the effects of inter-particle collision on flow structure should be made in more detail.

This report sums up 6 years of work performed for IFPRI involving the development and use of a unique discrete element type simulation for solid fracture. The technique, developed in the first years of this work assembles equivalent solids by “gluing” together discrete polygonal or polyhedral elements. If properly assembled, this results in an approximately homogeneous linearly elastic solid with predictable elastic properties. The “glued” joints can only withstand a specified tensile stress until they break and allow a crack to cross the solid. Both two-dimensional and three-dimensional realizations of this idea have been developed. The three-dimensional simulation has been shown to be able to replicate detailed experiments of particle crushing. In addition, a “hybrid” model has been developed which borrows from finite element techniques on the element level to allow the elements themselves to deform. This permits the simulation of systems that undergo large elastic or plastic deformations. As the simulation was developed from techniques developed to simulate the flow of unbroken particles, it is uniquely adapted to studying situations involving both flow and breakage.

This report will summarize the highlights of the work. As some of the annual reports are nearly as long as this final report, it is impossible to provide much detail here and the reader is referred to the annual reports to fill in the gaps. In addition to the description of the simulation technique, four topics will be discussed in detail.

The first topic

The first topic discussed in detail will be our simulations of single particle impact breakage, which probably revealed the most interesting results from these simulations. These showed that the observed breakage pattern resulted from two mechanisms. The first, “Mechanism I,” breakage results from the stresses that are generated in an unbroken particle. In two-dimensions, this produces a fanlike pattern of cracks issuing from the contact point, while in three-dimensions this results in the breakage into orange-segment fragments. These are the first sets of cracks to appear during the impact. The second, “Mechanism II” cracks are oriented perpendicular to the Mechanism I fragments (and thus cannot be accounted for by the stresses that are generated in an unbroken particle); the cracks appear at the end of the impact and produce the region of finely broken material that surrounds the contact point. Using the power of computer simulation, we were able to determine that the Mechanism II breakage results from the buckling of the Mechanism I fragments. It is clear that these two mechanisms also act in compression breakage (and, in fact, can be seen in some of three-dimensional simulations of compression breakage) and other ways of loading a particle to failure.

The next topic

The next topic, performed at the request of then TC chairman Tom Taylor, was an examination of the attrition shear-cell experiments that John Bridgwater had performed under an IFPRI contract in the 1980’s. These showed some contradictory results that indicated that the efficiency of attrition changed (evidenced as a change in the slope of the Gwyn rate curve) as the prevalent breakage mechanism changed from pervasive fracture to corner chipping. This produced some controversy that we were asked to resolve by simulating those experiments. Using conditions as close to the Bridgwater experiments as we could perform, we were able to replicate his results about the change of breakage mechanism and about the change in slope of the Gwyn rate curve when plotted against a parameter that was equivalent to that used by Bridgwater. This, however, was not a reflection of a change in fracture efficiency or other fracture properties, but was due to transient shear work that was not accounted for in Bridgwater’s parameter. When plotted against the true shear work performed on the system, all the Gwyn rate curves were found to overlap indicating that the efficiency of attrition was unchanged by the change in breakage mechanism.

Ball-drop simulations

Also based on previous IFPRI research performed at the University of Utah, were our ball-drop simulations performed to improve the understanding of ball milling. Like the Utah experiments, these simulated the flow and breakage that resulted from dropping a single grinding ball onto a bed of particles. The first such simulations were performed on randomly assembled beds. These indicated that the strength of the bed was the primary factor in determining the efficiency of breakage. In particular, the stronger the bed, the longer it held together and allowed the grinding ball to do its work. One conclusion that can be drawn from this work is that the breakage occurs more efficiently for shallow particle beds which implies that lightly loaded mills should be more efficient than heavily loaded. We then went on to study regularly assembled beds that should bound the strength of all possible randomly assembled beds. This led to a surprising additional observation that the presence of structures (in this case regular structures) within the bed could supersede simple bed strength as the determining factor for the breakage efficiency.

Preexisting damage on impact breakage

Finally, we studied the effect of preexisting damage on impact breakage. This consisted of three separate but related studies. First of all, in order to fulfill Hans de Jong’s interest in porous particles, we studied the breakage of particles containing regularly spaced circular defects. These defects had two interesting properties. First of all, the holes are isotropic and act as stress concentrators which initiate cracks that follow the local prevailing stress field. Secondly, under large deformation, they developed a local stress field that attracted passing cracks, causing the cracks to close on neighboring holes and produce fragments with sizes on the order of the hole spacing. The resulting size distributions were therefore very steep in that range of fragment sizes. We then studied the effects of linear cracks which are (1) not isotropic and will only initiate larger cracks if the surrounding stress field roughly follows the path of the preexisting crack and (2) possess no mechanism of attracting passing cracks like their circular counterparts. As a result, it was found that linear defects largely affected the energetics of the problem by decreasing the energy required to propagate a crack across a particle and seemed to have no significant other effects on the generated size distributions, unless the cracks were long enough, in which case they interfered with and enhanced the Mechanism II breakage and produced larger quantities of fines.

Other problems were examined that time did not permit to be completed and are not discussed in this report. These included studies on particle shape and impact geometry. Also, we continued to perform unbreakable discrete particle simulations of hopper flows (to fulfill a promise in our first proposal) and developed an efficient technique for the simulation of non-round particles. For information on these, the reader is referred to the various annual reports.

The termination of the IFPRI grant brings these simulation studies to a close, at least for the near future. That’s unfortunate as the simulation technique has a bright future, especially if computers continue their exponential increases in power. Much of the work presented here involves detailed looks at the breakage process that is of scientific interest and, because of the insights they provide into the size distributions that are produced, are of indirect engineering interest. In fact, the work has demonstrated two ways of tightening the size distribution, by using large impact velocity and by inserting holes into the particles before breakage, although it is unlikely that either could be practically implemented. But further insight gained from these simulations might result in just such a practical technique. We would also have liked to study compression breakage in greater detail to see if other breakage mechanisms and other ways of controlling the size distribution would make themselves apparent.

But soon it should be possible to model entire process systems such as ball mills which are only approximately modeled by the ball-drop simulations described above. While waiting for computers to improve to those levels, it should be possible to use the detailed information obtainable from the simulation to derive “filters,” through which data obtained from large unbreakable simulations might be passed to allow predictions of the breakage rates. For example, there are many unbreakable particle simulations of the flow in a ball mill, which only provide insight into the breakage process at the level of revealing the stress pattern inside the particle bed. A series of simulations of the breakage induced by various loadings on single particles and on particle beds would allow that stress information to be processed into predictions of breakage rates and size distributions; simulations similar to the shear-cell simulations presented herein would be used to ascertain the effects of shear abrasion on the breakage process. (In fact, it should be able to derive preliminary estimates from the data we already have.) That would allow the evaluation of the choice of operating parameters, such as the degree of loading of the ball mill. Knowing the size distribution produced would help in the choice of separation devices. Another possible new direction would be to include interstitial fluid effects in the simulation in an attempt to model wet grinding. (We are in the early days of development of a multiphase flow simulation using a slightly different technique than used in Tsuji’s IFPRI work.) In short, there is still a great deal of information that this simulation technique could reveal about particle breakage and grinding processes that is both of scientific and direct engineering value.

Granulation is a size enlargement process generally involving the agglomeration of particles often with liquid binders using specialised processing equipment. The dried granules in some cases, are further processed into compacts or tablets. Whilst widely used throughout industry the granulation process and related aspects, such as formulation design and scale-up procedures, are in general inadequately described.

With increasing industrial need for directed formulation design linked to prediction, of processing performance and efficient scale-up of granulation, specific project objectives were defined, and several inter-related study areas identified with a view to providing much needed insight to address these issues. The research areas were the physico-chemical interactions between components to aid directed formulation design, the rheology of the wet-mass during granulation for process evaluation knowledge, and scale-up strategies for specific types of processing equipment. Within the project remit of granulation by mechanical agitation, high shear mixer-granulators were selected for the scale-up studies. This project has successfully researched several key aspects in these areas, generated valuable information and knowledge, and developed practically useful guidelines for industrial application.

From an extensive literature review, it was recognised, that the physicochemical interactions between granule components, whilst critically important during granulation, were poorly understood. Through a surface free energy (SFE) approach to derive a group of spreading and interaction coefficients, a model has been developed to predict the nature of material interactions which direct the structure and properties of granules. The model was tested with model systems using both physical evaluation and mixer torque rheometry, then successfully applied to a number of experimental particulate substances of diverse chemical composition granulated with two typical polymeric binders - HPMC and PVP. This procedure thus provides the basis of a rational approach to material selection in granule formulation design.

This research is focussed on the filtration of sub-l urn particles where inter-particle forces start to become significant and affect both the rates of filtration and dewatering and the properties of the filter cakes formed. Existing models for filtration fail to recognise the existence of particle-particle interactions, nor do they account for chemical or physical interactions of the deposited particles with the filter septum. To take these factors into account, existing models rely entirely on empiricisms developed after experiments have been done to quantify the factors. Consequently, the models are unable to describe the effects of changes in basic properties of the feed on the performance of separation equipment.

This work develops a new approach to the analysis of filtration data, taking account of fundamental properties of the suspensions being separated. The background theory is developed in two parts.

Part 1: Initial Deposition

Firstly, the initial deposition of solids onto the filter septum is analysed by taking account of fluctuations in the particle velocity near the septum.

Part 2: Dynamics of Cake Formation

Secondly, the dynamics of cake formation from suspensions of interacting particles is modelled, taking account of:

• (a) changes of the random fluctuations of particle velocities caused by local direction and magnitude changes of the fluid velocity, and
• (b) the skeletal structure stress in the cake by using expressions for the two-particle interactive potential, thereby avoiding the need to introduce empiricism.

The approaches taken to the two stages are wholly consistent with one another.

The simplest theories for constant pressure filtration of non-interacting particles conclude that the filtrate volume produced a PO*‘. This work shows that the filtrate volume produced during the initial stages of cake formation depends on the range of the zeta potential. For soft sphere interactions, the filtrate volume produced is a p2 and for hard sphere interactions filtrate volume a p. During cake formation, it is shown that the two-particle interactive potential lies between the two limiting analytical expressions usually quoted in the colloid science literature. Filtration rates predicted from the model agree well with experimental data for a wide range of feed suspension concentrations; the model also enables calculation of the distributions of skeletal stress, liquid pressures, and fluid and particle velocities through the cake thickness. Effects of fundamental properties such as ionic strength, pH, ion valency and particle size on filtration can be assessed using the model.