ARR - Annual Report
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.
Abstract
Coagulation in a flowing suspension is governed by the colloidal and hydrodynamic interactions between the aggregating particles and flocs. Beyond the initial particle-particle coagulation step, these interactions determine the structure of a floe being formed, and at the same time they depend on the structure of the aggregating floes. To develop a better understanding of the coagulation process, we have examined both the internal structure and growth rate of floes formed by rapid shear coagulation of dilute suspensions. Floe sizes were measured by dynamic light scattering, and structure information was extracted from static light scattering spectra covering the domain 0.18<q.a<1.7, where q is the scattering wavenumber and a is the individual particle radius. Interestingly, comparison of the sheared suspension results with results for floes formed by Brownian coagulation reveals a similar structure for the two modes, indicating similar aggregation mechanisms act in both cases. In contrast, the growth kinetics for these two modes are inherently different, as expected. To model the growth behavior in a shear flow, we treat a porous floe as a body with a hydrodynamic radius which is less than the capture radius corresponding to floc-floc contact, and we compare predicted kinetics based on this model with data at several shear rates.
A theory is presented for the fully-developed flow of gas and particles in a vertical pipe. The relation between gas pressure gradient and the flow rates of the two phases is predicted, over the whole range of cocurrent and countercurrent flows, together with velocity profiles for both phases and the radial concentration profile for the particles. The gas and the particles interact through a drag force depending on their relative velocity, and there are mutual interactions between pairs of particles through inelastic collisions. This model is shown to account for marked segregation of gas and particles in the radial direction, and the predicted relation between the pressure gradient and the flow rates of the two phases is surprisingly complex.
Introduction
There are many important problems on the conduction of heat in granular powder beds, i.e. silo beds, coal beds, high furnace in steel making, compaction of powder in ceramics industry, etc. The mathematical treatise on these problems, however, is not necessarily clear, because the correct physical model is not considered. In this report it is theoretically considered.
Summary
Polymers are used in a number of industries to improve solid-liquid separation. While polymer conformation has been considered to be an important parameter in determining the flocculation/dispersion characteristics of fines, no experimental study that correlates the conformation to flocculation/dispersion in terms of the important flocculation/dispersion responses such as sediment characteristics, sediment volume and supernatant clarity has been reported in the literature. We have developed a multi-pronged approach involving a study of polymer conformation on solids using fluorescence along with adsorption density and zeta potential in order to understand the behavior of various sedimentation characteristics mentioned above. We are currently extending this study to include relevant filtration parameters. Information obtained from these studies should prove useful in identifying conditions under which enhanced solid-liquid separation by either sedimentation or filtration can be achieved using polymer flocculation.