ARR - Annual Report
SUMMARY
Polymer conformation/orientation plays an important role in polymeric solid-liquid separation processes. However, very little information is available on the mechanisms by which conformation/orientation of polymers determines the flocculation/dispersion of fines, and on the means for controlling polymer configuration to achieve the desired state of colloidal stability. In this study, attempts were made to alter the conformation/orientation of polyacrylic acid by a number of methods, eg.,
- sequential pH-shifting (pH 10 to 4),
- interaction between polyacrylic acid and polydimethylallylarnmonium chloride, and
- complexation of polyacrylic acids with dissolved mineral species.
Changes in the polyacrylic acid conformation/orientation were then correlated with the stability of the suspensions, the charge on the particles and the extent of polymer adsorption on alumina. Results obtained, showed that manipulation of polymer conformation/orientation of polyacrylic acid in-situ or prior to adsorption can significantly improve solid/liquid separation.
EXECUTIVE SUMMARY
This Fall brings to completion the dissertation of Francisco E. Torres on the kinetics and structure of floes grown in shear flows at dilute concentrations. The first phase of the work, reported in its entirety last year and since accepted for publication in the Journal of Colloid and Interface Science, consisted of detailed measurements of floe structure and growth kinetics for rapid, irreversible flocculation in a simple shear flow with minimal effect of Brownian motion. We employed polystyrene latices of 0.1 um diameter in glycerol-water mixtures at 1 .O M NaCl at a volume fraction of 10^-6 with dynamic light scattering detecting the hydrodynamic radius and static light scattering probing the internal structure of the flocs.
Comparison of the results for sheared dispersions with data for Brownian flocculation revealed a similar structure, i.e. flocs having characteristics of fractals with dimension d=l.8+0.1 and an equal number of nearest neighbors. Of course, the kinetics differ substantially with shear accelerating the rate in proportion to the Peclet number gauging the ratio of shear to Brownian collisions. As the floc size approached 1 um, however, the growth rate decreased significantly, suggesting that viscous forces impose a maximum for these tenuous structures. Straightforward calculations -- assuming Smoluchowski kinetics with weak hydrodynamic interactions, adhesion of particles upon contact, and a maximum size estimated by comparing the dispersion attraction to the viscous force -- reproduced the data within the experimental uncertainty.
During the past year we have addressed the evolution of the structure, seeking to understand the similarity between the results for the shear and Brownian modes. This involved hierarchical simulations performed by combining N particles into N/z doublets, colliding those doublets to form quadruplets, etc., until only a single N-particle floe remained. At each step two aggregates at randomly chosen initial positions and orientations were translated along streamlines of the undisturbed velocity field and rotated with the local vorticity until two particles made contact. There the particles were assumed to stick, forming rigid bonds. The structure was characterized statistically through particle-particle correlation functions within the flocs, the variation of the radius of gyration with number of particles, the asymmetry of the shape, and the corresponding light scattering spectrum.
Remarkably, the simulations produce flocs with light scattering spectra indistinguishable from those studied experimentally and no detectable difference between Brownian, shear, and extensional collision processes. Hence, we conclude that irreversible flocculation, with no subsequent rearrangement or breakup, generates fractals of low dimension (d=1.8) essentially independent of the kinematics of the collision process. A corollary is that creating compact, uniform floes with d=3.0 must require substantial rearrangement and/or breakup, processes that probably depend on many collisions. Thus future work along these lines must deal with concentrated dispersions and longer shearing times than examined here.
The attached paper describes the simulations in full and is being submitted to the Journal of Colloid and Interface Science, subject to approval of the members.
This proposal originally addressed the issue of why stagnant zones, such as funnel flows in hoppers, appear in particle flows. To that end, we studied computer simulations of a Couette flow with gravity acting on a system of two-dimensional discs. These were largely described in last year’s report. In those simulations, gravity acted to force a stagnant zone of material to form, so that the conditions that led to the transition from fluid-like to solid-like behavior could be observed and studied. Much to our surprise, the initial motion of the layer occurred in a quasistatic manner with the location of the interface coinciding with a constant value of the ratio of shear to normal stress. We have continued this work in three directions.
- Extension of the model from two to three dimensions. This phase is almost complete.
- Shear cell tests on our simulated material. As we have shown that the yielding appears to follow a Mohr-Coulomb failure criterion, similar to that used in plasticity models, why then, did plasticity models fail in predicting and describing funnel flows in hoppers? One answer is that the plasticity models depended on friction angles measured in Jenike or other, similar, shear cells and, because of the different flow conditions, the observed yielding behavior may be different. To test this hypothesis, we created a simulation of a shear tester to perform the equivalent of a shear test on our simulated material and, indeed, in preliminary results, it appears that the stress ratios measured in the shear cell are larger than those that govern the location of the yield interface in the Couctte flow with gravity simulation.
- Inclined chute flows: Chute flows have an odd yielding behavior in which they often move largely as a solid block over a thin shearing basal layer. At first glance, this seemed to be in contradiction to the Couette flow results. However, simulations show that the two results arc indeed consistent. But at the same time, they pose other questions. In the Couette flow situation, the location of yielding could be determined more or less on the basis of a frictional criterion. In the chute flow simulation, while the stress ratio at the yield point wus numerically similar to that observed in the Couette flow simulation, one could not determine its location baaed on such a criterion. Consequently, there must be some unexplained connection between the location of the interface and the flow mechanics. As it probably has implications in other flow situations, this is a problem worthy of further study.
At the Teaneck meeting in 1989, Gordon Butters asked me on behalf of the TC, to see if my work could shed some light on the fracture problem. On further consultation with Paul Isherwood, I learned that there was a general lack of information about the forces that are exerted by the flow induced particle collisions. While the simulations have been previously made stress tensor measurements and thus determined averaged forces applied to particles, these are generally irrelevant to the fracture problem as the most damage will be caused by the maximum and not the average forces. Thus, I conducted a series of simulations to determine the maximum collisional impulses that the particles experience in a simple shear flow and their dependence on particle properties and solids concentration. The impulses are divided into their components normal and tangential to the particle surface as it was felt that the two might contribute to different attrition characteristics. The normal impulses - which might lead to large scale particle fracture - was always significantly larger than their tangential counterparts - which would tend to shear off the microroughness that lead to the interparticle surface friction. Along the way, histograms of the distribution of collision impulses as well as their geometric distribution over the surface of the particle were recorded.
Also, at the Teaneck meeting, Hans Buggish, not on behalf of anybody but himself, suggested that I might be able to contribute to his IFPRI sponsoned work on the flow induced mixing of particles in his granular shear cells. Be had observed that the mixing might be modeled as a diffusion process, similar to that of molecules in a gas or liquid. The use of a computer simulation was particularly attractive in such a study as his experimental technique was limited to measuring the diffusion of particles in only the direction parallel to the velocity gradient, while the computer simulation could measure the diffusion in all directions. The results show that the particles do mix by diffusion except at the highest concentrations when the particles become tightly packed in a crystalline microstructure and unable to move relative to their neighbors. However, the diffusion in a shear flow is not isotropic and is only appropriately modeled as a tensor of diffusion coefficients. By far, the largest mixing occurring in the direction of flow. The components of the diffusion tensor were measured both by particle tracking and by a statistical technique developed by Taylor (1922). Furthermore, it showed that the mixing in a granular flow flow was an example of Taylor diffusion by which the diffusion of particles in the direction of the velocity gradient greatly enhanced their mixing.
Finally, this report describes a preliminary attempt to model the flow through pinmills. Like the impulse strength studies mentioned above, this work done pursuant to Gordon Butters’ request that 1 attempt to apply computer simulations to fracture problems. This work was intended to study a situation of more direct interest to industry than a simple shear flow. However, the project has been abandoned due to a general lack of interest in pinmills within the industrial community.
Executive Summary
The overall goal of this feasibility study is to produce sub-50 um droplets when spraying highly viscous (up to 100,000 cP) non-Newtonian fluids at process level throughputs (up to 1 kg/s). Work was conducted using a new type of nozzle, developed during the last three years at Purdue, because it is the only candidate likely to meet the sub-50 um criterion.
Work was carried out using fluids comprised of glycerin/water/polymer and coal-water slurry/glycerine/polymer mixtures. Fluids with consistency indices ns high as 41.500 and flow behavior indices as low as 0.27 were employed. All spray data is reported as mean particle size, in terms of the Sauter mean diameter. Mean drop sizes as low as 28 pm have been achieved with air-liquid ratio values of less than 0.20.
The goal of this feasibility study was achieved. In fact, mean drop sizes as low as 38 um were measured at an air-liquid mass ratio of 0.2 and a nominal throughput of 1 kg/s by using an effervescent atomizer. In addition, nozzle performance was shown to improve with throughput, in contrast to the behavior of conventional twin-fluid injectors. Finally, the addition of polymer to either single- or multiphase fluids was shown to increase mean drop size, although the extent of the increase left SMD below the target value of SO um. An explanation for this increase is being pursued.
Work during the next contract year will be focused in three areas:
- An investigation into how the tightness of the particle size distribution varies with fluid properties and throughput.
- An investigation into why polymer addition increases mean drop size.
- Extension of the mathematical model for effervescent atomization developed by the principal investigator and his colleagues to fluids and conditions of interest to IFPRI members.
The model will then be used to determine the minimum mean drop size achievable with an effervescent nozzle, given a particular fluid, throughput rind nozzle geometry, and to identify the physical mechanisms responsible for performance barriers associated with effervescent atomizer operation.
Executive Summary
This work deals with predicting the flow properties of polymerically (sterically) stabilized colloidal suspensions. In the second year of the present project work has been performed in the three sub-areas which are addressed in the project objectives:
- describing the effect of stabilizer layer deformability (or “softness”) on the rheological properties;
- elucidating the effect of bimodal distributions of particle size;
- predicting the onset of shear thickening.
The work on the stabiliser layer softness consisted mainly of evaluating scaling principles. Earlier work by Goddard suggested the use of a reduced volume fraction (dividing the effective volume fraction by the maximum packing) to describe soft particles. This procedure does not work very well for really soft particles but is shown here to give reasonable results for polymerically stabilized systems. A similar procedure is found to be useful to reduce the data for the characteristic shear stress that determines the flow conditions at which shear thinning occurs. It also could be shown that these conditions could be characterized more accurately by using shear rate rather than shear stress (i-e replacing the medium viscosity in the Peclet number by the low shear Newtonian viscosity rather than by the viscosity pertaining to the shear rate under consideration). This characteristic shear rate turns out to be quite independent of concentration and is closely related to the long time diffusion coefficient.
For bimodal distributions in particle size, systems are considered in which a relatively coarse fraction is mixed with small particles. A procedure is suggested to predict the limiting Newtonian viscosities. Its suitability is confirmed by comparing predicted and measured values for mixtures with various ratios of particles with 823 and 129 nm diameter.
The onset of shear thickening has been investigated for systems containing particles of a fixed particle size but changing the other parameters. In particular the effect of the medium viscosity has been studied by changing the nature of the medium as well as the temperature. Two types of shear thickening could be identified. The first one is characterized by a gradual increase in viscosity with shear rate while the flow remains smooth. In the second one a sudden change in viscosity can be observed together with the onset of erratic structural changes during flow. A particle Reynolds number does not provide an adequate scaling for the critical shear rate of shear thickening. A scaling related to a kind of Peclet number reduces the data much better.
Executive Summary
The goal of this one year study was to demonstrate that sub-50 pun mcxl drop size sprays can be produced when using an effervescent atomizer to spray high viscosity, non-Newtonian fluids at mass flow rates up to 1 kg/s. That goal was met. 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 within the spray. That objective was also met.
1991- 1992 begins the first year of our three year study into the fundamental mechanisms responsible for effervescent atomization. This year, we will be focusing on the transition region where the two-phase supersonic flow that exits the nozzle as discrete gas bubbles in a continuous liquid is transformed into a continuous gas stream containing discrete liquid drops. Single and multiple-pulse holography will be used to obtain the data necessary to achieve that goal. In particular, single-pulse holography will be used to determine the mechanisms of effervescent atomization while multiple-pulse holography will be used to determine drop size distribution and droplet velocities. A qualitative explanation of the mechanisms responsible for effervescent atomization should be available by the 1992 annual meeting with the first quantitative results available later in 1992.
ABSTRACT
Ball mills, stirred-ball mills, jet mills and vibration mills are commonly used in preparing ultrafine powders in the chemical industries. The comminution behavior of these mills can only be understood by studying the microproces of particle breakage. For many years researchers studied single- particle breakage, but in actual mills beds of particles break between impacting surfaces. Therefore, in this work the break- age of particle layers between a moving ball and a stationary anvil is studied.
In grinding mills ball-to-ball collisions trap and fracture particles. Curved surfaces between balls trap the intervening particles and balls falling on the particles cause breakage. Similarly, particles are also trapped and broken between “curved” and “flat” surfaces (such as liners) within the mill.
Whenever the stress developed within an individual particle exceeds the compressive strength, the particle breaks. The stress applied to the particle depends on the assemblage of particles present in the zone of breakage. Therefore, a systematic study is needed to learn about fracture behavior of assemblage of particles under specific loads and specific geometry of the impacting bodies. Such a study has been carried out at the University of Utah using a device known as the ultrafast load cell.
These studies were conducted in dry systems only. It is found that, regardless of the number of layers of particles present between impacting balls, only the last two or three layers are broken, as long as the mill allows free movement of particles. The distribution of broken fragments gets finer as the energy of impact increases, but the amount of material broken in an assemblage is roughly the same for all energy inputs. The impacting balls consume some energy upon rebounding. For instance, balls falling through larger heights can carry with them 15% of the input energy during rebound. Another important aspect learned in this project, for which direct evidence is not shown in this series of experiments conducted for WPRI, is that the conversion of input energy into particle breakage is higher at low input energy. This means that balls falling through small heights, in the range of 5-20 cm, are very efficient in breaking particles. In the mill, particles break under compressive stress. Shearing stresses only help the particles to escape from the zone of breakage and may somewhat reduce their apparent strength. Therefore, a combination of compressive and shear stresses is ideal for breakage of particle assemblies.
There are two key features to be considered for any comminution device. First, what is the force or stress, produced by impacting surfaces, and second, what is the size distribution of fragments produced by the applied stress? This report details clearly the distribution of fragments produced upon application of a certain energy. What is needed is a study of forces produced by mass of colliding bodies in the mill. In the case of ball mills, the “lifter” lifts the ball, and as a result the falling ball exerts a force on the bed of particles. In the case of attrition mills, the impeller stirs the mass of ball, which in turn generates a distribution of forces within the ball mass, A study of the forces produced within the mills would complement the work reported here.