ARR - Annual Report
The attrition and breakage of particles has been examined in a cone cell which permits the clearance between a rotating blade and a wall to be varied between experiments. Breakage is considerable if the clearance between the blade and the wall is just under one particle diameter or about 1% - 2 particle diameters. This effect has been found for a number of absolute initial particle sizes and for two materials of entirely different structure namely a polycrystalline urea and catalyst beads. Breakage is not detectable if the clearance is less than 0.25 particle diameters or greater than 2.5 particle diameters. A pronounced minimum attrition rate is found at about 1.25 particle diameters. An explanation of such effects is offered in terms of the particle packing. The findings are of considerable significance for understanding how attrition occurs in processing equipment.
Studies on well characterised alumina extrudates have been conducted in the annular shear cell used in previous work for IFPRI. The cell has the advantage that the stress, strain and strain rate applied to deforming bodies of particulate solids are known. The extrudates have been made in the different strengths and have known and reproducible structures. A range of normal stresses varying by over three orders of magnitude could be imposed on the deforming bed of particles.
The less strong extrudate showed a progressive decrease in fine attrition product as the normal stress decreased which indicated a shift in dominant mode of breakage from fragmentation to abrasion, but each mechanism remained at every stress. Both photographic evidence and particle size distributions confirmed this behaviour. For the harder particles the photographic evidence was consistent with this behaviour but the particle size distributions were erratic; it is thought that there is some limitation to the use of the cell but this remains to be proved.
It was also found that re-use of broken material in the cell may affect behaviour and further is necessary to establish whether the unification of breakage data may be achieved for the full stress range as it was previously over a more restricted range. The annular shear cell is of most practical use for systems with high ambient stresses.
Work performed on agglomeration of particle systems in fluidized beds at both low temperatures (granulation) and high temperatures (sintering) is The research described in Part I and Part II of this report,. respectively. reported on was performed during the period December 1986 - November 1987. carried out from December 1987 to September 1988 is also included. A special section in Part I (7.2) contains Future work for both projects to be three years program starting in September 1988 for the low temperature granulation project only.
In Part I of this report, containing the description of theoretical and experimental work on granulation in fluidized beds, it is demonstrated that the viscosity of the binder (in addition to other properties such as surface tension, wetting, etc.) is a very important characteristic which in final analysis determines the morphology and strength of the formed granules. After a short review of theoretical and experimental procedures-relating to liquid bridge strength given in section 3, the newly developed "dynamic bridge apparatus" is described (see section 4) and its capabilities are shown. The effects of the Capillary number, viscosity, bridge volume, etc. on the' strength of an axially strained pendular bridge and comparison of theoretical and measured values are given. It was demonstrated that under conditions of low Reynolds and Capillary numbers, large bridge volumes and favorable wetting of the solid surface the theoretical and experimental data are in good agreement. It was also clearly shown (see section 5) that binders which show a high rate of strengthening with time as the solution becomes more concentrated, i.e., the viscosity increases, yield agglomerated granules as a final product from granulation while binders for which the strengthening rate is moderate or low, yield layered granules but no agregates. This result was also predicted from a simple experiment using the dynamic bridge apparatus. Additional experiments with different binders exhibiting a wide range of properties in both the dynamic bridge apparatus and in the fluidized bed granulator are given in the Appendix (see section 10).
In Part II of the report which contains work on agglomeration due to high temperature sintering, it is shown that there is a strong correlation between elongation-contraction behavior of a powder sample in the proposed future work for an additional dilatometer and the agglomeration of the same powder when fluidized. The minimum sintering temperature of m&y different materials as determined in the dilatometer was shown to correspond to the temperature at which the material will defluidize. It was also found however that, although the correlation mentioned above holds for'incipient sintering, there seems to be no direct relation between rates -of deformation in the dilatometer at temperatures beyond sintering and actual sintering rates in the fluid bed. It is therefore often necessary that both dilatometer and fluidized bed tests be performed on the same powder before a final conclusion can be drawn. A detailed description of both experimental methods mentioned above are given in sections 2 and 3 respectively, while results and discussion of different test materials are given in section 4.. This section also contains a case study of a powder undergoing a chemical reaction which induces agglomeration. It was found that if the product of the chemical reaction causes agglomeration the controlling factor in the process is the conversion rate; this type of agglomeration behavior can not be detected in the dilatometer.
Section 5 in Part II contains a critical review of existing models of agglomeration; this section also includes some directions for the development of a more realistic theoretical model. The need for some basic knowledge of the magnitude of the break-up forces in a fluidized bed is also discussed. Finally, the Appendix to Part II contains a copy of a paper on high temperature sintering presented at the annual AICHE meeting in November of 1987.
This report consists of an account of work done under IFPRI contract in Cambridge University during the year to December 1987. The principal achievements during that time are:
- Installing pressure transducers on the flow rig and developing the associated software so as to be able to measure the very low pressure differences occurring.
- The performance of a series of experiments on a hopper of half angle 15 degrees; the results confirming the observations tentatively reported in the last IFPRI report.
- The development of a possible theory to explain the observation.
Also included is the programme of work proposed for the rest of the contract.
This report covers research under the auspices cf IFPRI during the period January - December 1987 following the appointment of Hr. M.C. Turner to a Research Assistantship.
The foremost objective of the research is to elucidate the fundamental description and mechanisms of granular flow using both computer simulation and experimental methods. We aim to properly understand and formally describe the diversity of flax behaviour commonly observed in processes such as fluidisation of povters and flow from hoppers.
A generalised three-dimensional computer simulations program has Seen developed, ab initio, specifically designed to integrate the equations-of-motion of colloidal-like interacting spheres under gravitational flow on an inclined plane. The technique uses the general methodology of previous studies of dense suspensions under shear flow but incorporates numerous features essential to granular flow such as boundary friction and an interparticulate coefficier: of restitution to achieve steady-state conditions.
A novel feature of the simulations is the use of "gravitational units" whereby the gravitational constant g sets tie time and energy scales. With this approach we expect to gain s overview of the different regimes of behaviour (e.g. Geldart-types X, B, C, D, etc.) found for different powders on real laboratory of engineering time scales. The basic initial computer program is now 13 'production' and preliminary results are reported.
Laboratory experiments are being carried out alongside the simulations to investigate the flow behaviour of well-characterised (spherical, monodisperse) powders under gravitational: steady-shear flow. An experimental rig comprising a rotating bed, with the provision for a fluidisation flow field, has been constructed E d is operational. Preliminary experiments are reported, for larger particles (> 5~) and no gas field, to resemble the initial simulation conditions as closely as possible.
Both the simulations and the experimental studies are being extended to investigate the effects of a cohesive inter particle potential, which becomes important for fine powder when it is large compared to gmo, the gravitational energy, and t'L2 hydrodynamic flow field where aeration plays an important role.
SUMMARY
The Brownian coagulation (or flocculation) rates of nearly monodispersed particles in aqueous solutions whose diameter goes down to about 5 nm were measured by a low angle light scattering apparatus to clarify the features of the stability of ultrafine particles. It was found that the rapid coagulation rate obeys the modified Smoluchowski theory when the particles size is submicron. But the rate depends on the particle size, the kind of electrolytes, the pH of solvent and the excessive electrolyte concentration, when particles are sufficiently small. The reduction and variation of coagulation rate were explained by the shallow minimum of the inter-particle interaction which is attributed to the layer of water molecules and ions adsorbed on the particle surface.
The flocculation of colloidal particles which were comparable with polymers in size and neutralized by polymer flocculants was also investigated. The flocculation rate was found to increase proportionally with increasing size ratio of polymers to particles if the approximate size of polymers is less than the particle radius.
SUMMARY
Characterisation and prediction of powder flow
D. Geldart, M. C. Turner and L. V. Woodcock
This report covers research under the auspices of IFPRI during the period January-December 1988. Mr. M. C. Turner has continued in the appointment of a Research Studentship for this second year of our IFPRI research.
Research is now advancing on the three interdependent fronts of experimental studies of well-characterised systems, computer simulations of powder rheology, and theoretical work in search of interparticle force models and scaling laws leading to computational fluid mechanics of powders.
The experimental studies have to date concentrated on a rotatine fluidised bed, which is being deployed to examine the behaviour of monodisperse shperical particulates and direct measurements of the coefficient of restitution. Results have been obtained for glass ballatini particles in the size range from 10^-4 m to 10^-3 m. It is planned to extend some of these experimental studies to perfect monodisperse particulates of polystyrene latices, presently under preparation in collaboration with the Polymer Research Unit at Bradford, down to a size range of 10^-6 m. These experimental measurements of the properties of "perfect powders" relate directly to the computer simulations and test the predictive ability and limitations of the early computer models at the particulate dynamics level.
The computer simulation work has developed along two distinct lines. The original approach, as reported previously, was to set up a computer simulation model with boundary conditions closely resembling the simple experimental geometry of chute flow. The early results, reported previously, are now being replaced by more advanced simulations which may include a more sophisticated coefficient of restitution and elementary aeration effects (i.e. Stokes's friction). "Gravitational units" are used in these simulations; the constant g sets the time-scale and hence the energy scale. This approach, once aeration and cohesive forces are incorporated, is expected to give an overview of the different commonly used powder classifications in real engineering time scales.
Since the beginning of 1988 we have embarked upon the determination of the constitutive rheology of the simplest ideal powder, monodisperse frictionless hard-spheres, by the methods of granular dynamics, using homogeneous-shear, non-equilibrium computer simulations. This essential simulation work will eventually lead, for the first-time, to the possibility of complete computational fluid mechanics for a well-defined model in a given geometry. These granular dynamic computations are being designed also to determine and test fundamental scaling laws for rapid granular flow from known thermal equilibrium behaviour.
On the theoretical side, scaling Laws for predicting the rate-of-strain deformation dependence of the pressure tensor in the region of rapid granular flow for slightly inelastic frictionless spheres have been derived. Results are reported for three cases of the form of the coefficient of restitution which may relate to experimental circumstances. Each case gives a quite distinct type of rheological behaviour even though the limiting behaviour in all cases is analytically predictable from the equation-of-state and viscosity data of the hard-sphere fluid at equilibrium. The stress and dilatancy of spheres with a constant (velocity-independent) coefficient of rastitutfon show discrepancies when compared with the kinetic theory predictions of Savage but generally compare favourably with experimental data.
Summary
Flocculation and sedimentation of fine particles are investigated here with emphasis on the correlation of flocculation with adsorbed polymer’s conformation, CAT scan determination of flocculation properties, and theoretical modeling of sedimentation process.
The conformational behavior of polymers and the extent of polymer adsorption are considered critical in flocculation process. Last year, we initiated a study of correlation of polymer conformation with flocculation as measured by the supernatant clarity. This year, we monitor other flocculation properties (settling rate, percent solid settled, and sediment volume) in order to have a complete description of the flocculation behavior: Effects of polymer concentration on both the polymer conformation and the flocculation behavior are also studied. The amount of polymer adsorption is measured by analyzing the residual polymer in the supernatant using carbon analysis technique.
In the CAT scan work, a technique is developed to evaluate flocculation properties from the solid-concentration profiles measured during sedimentation. This new technique is shown to be superior to the traditional methods for measuring flocculation properties. More importantly, the CAT scan provides, for the first time, a method for in-situ determination of effective floe-size distribution.
Computer simulation of sedimentation, based on our discrete model developed last year, is extended to 3D and nonlattice cases. The nonlattice model is shown to simulate sedimentation process more realistically than the original lattice model. 3D simulation generates essentially the same results as 2D simulation for simple sedimentation; its potential for simulating channeling caused by movement of coarser particles or water lenses in real systems is recognized.