ARR - Annual Report
Introduction
In many studies of precipitation, the length of the nucleation period is commonly invoked as the primary control parameter for forming uniform particles in a reaction involving homogeneous nucleation and growth (l-3). In the model originally proposed by LaMer and Dinegar (14) for the mechanism of formation of sulfur sols, uniform size distributions result if all the particles are formed in a short burst of nucleation, and then particle growth occurs by a mechanism where large particles increase in diameter slower than smaller particles (as occurs when growth is limited by diffusion to the particle surface). Despite the influence this model has had on studies of inorganic particle precipitation chemistry, the model has seen little corroboration and indeed has been brought into question for the sulfur sol for which it was developed (15). While the LaMer mechanism would undoubtedly result in uniform particles, finding systems meeting the conditions required for the model to hold has been elusive.
In recent years studies on the formation of polymer latex particles have provided an alternative mechanism whereby uniform particles can result from a homogeneous nucleation, precipitation reaction. In emulsion polymerization, an insoluble monomer is mixed with water and a water soluble free radical initiator added. Final particle size depends on reaction temperature, reagent concentration and parameters controlling the colloidal stability of the growing particles (i.e., ionic strength and pH). The initial locus of the reaction is in the aqueous phase. Oligimers grow to a size where they become insoluble and undergo a sol to gel transition. Due to their relatively low concentration, this transition involves only few polymer molecules and the gel phase grows by aggregation. The charge on the primary particles is small but as the aggregation process proceeds, the charge per particle grows. As a consequence, aggregation rates between particles of equal size decrease but the rate of aggregation of particles of dramatically different size increases. The result is a bimodal particle (or gel phase) size distribution with one peak located at the primary particle size and the second peak containing particles that are stable to mutual coagulation and grow by scavenging smaller particles. Upon aggregation, the gel phase particles coalesce and thus the particles are able to retain a spherical shape. As the reaction proceeds the growing particles reach a constant number density. These colloidally stable particles swell with monomer and the locus of the reaction is transferred from the aqueous phase to the inside of the particle phase. Uniformity is achieved through control of the colloidal stability of the primary particles and aggregates of these particles (6-8).
A second organic analogy to the precipitation of inorganic particles occurs in dispersion polymerization. Here a solvent is chosen where the monomer is soluble but the polymer is not. The reaction is initiated and proceeds through polymerization until the oligimers grow to a size where they undergo a phase transition and precipitate to form polymer and solvent rich phases. Uniform particles are achieved through the addition of steric stabilizers that control the aggregation of the growing gel phase (9).
The major distinction between the model of kMer and that developed for uniform latex particles lies in the incorporation of colloidal stability of small particles. The LaMer model assumes that each nucleus is colloidally stable and survives at the end of the reaction at the center of a particle. The aggregation models argue that while stabilizing such small particles is difficult, aggregation does not necessarily result in a broad particle size distribution. In developing schemes for control of particle size distribution, the result of accepting that colloidal stability can play an important role is that rather than focussing attention on the length of the nucleation period, one becomes very concerned about the colloidal properties of the growing particles.
In this paper we review our studies on the formation of uniform precipitates through the hydrolysis and condensation of titanium and silicon alkoxides. Our work has been aimed at elucidating whether uniformity is the result of the details of the chemistry or if particle size distributions can be controlled by physico-chetnical means. In particular we focus on experiments probing the length of the nucleation period in these systems and the effects of parameters controlling particle interaction potentials. We find that for the systems studied, the nucleation period appears to be a substantial fraction of the entire reaction period and that particle size is largely controlled by parameters related to particle interaction potentials. These results suggest that there are strong links between the physical chemistry underlying the formation of uniform latex particles and that controlling particle size distributions of hydrous metal oxide precipitates (10-14).
Summary
The object of this work is to develop methods for the quantitative prediction of all the major features of flow of a gas, together with solid particulate material, through a duct of arbitrary size and inclination. Flows of this sort are of great technical importance in pneumatic transport of particulate material, and in the circulation of particulate materials within chemical processes. Examples of the latter type include the riser reactors and standpipes which form components of the catalyst circulation loop in catalytic crackers, used in the refining of oil, and the long standpipes used in certain coal liquefaction plants. In all these systems the particles tend to distribute themselves over the cross section of the duct in a markedly non-uniform way, making it very difficult to predict the hold up of solid material and the pressure drop along the duct, or even to extrapolate these quantities from measurements made with the same materials in ducts of other sizes. In addition, the crowding of the particles into limited parts of the cross section can lead to undesirable effects, such as recirculation of the solid material against the direction of the main flow.
The key to making useful predictions for these systems is to understand and quantify the mechanism that determines the distribution of particle concentration over the cross section. In many situations of practical interest the gas flow is highly turbulent, and it is tempting to attribute the observed distribution of the particles to their interaction with turbulent eddies. However, a closer examination shows that this could produce the observed effects only in quite restrictive circumstances, where the particles are almost, but not quite light enough to follow the gas motion exactly. In this work we investigate an alternative mechanism, which attributes the stratification of the concentration distribution to collisions between particles. We have derived a criterion (presented in this report) to judge whether this mechanism is likely to be important in any given system, and have developed a complete mathematical model to predict the distribution of particle concentration and the velocity profiles for both gas and particles in steady flows of this kind. A computer program has been constructed to solve the model equations, and extensive sets of solutions have been found for ducts of different sizes and inclinations.
The solutions obtained appear to simulate most of the characteristic observed properties of flows of this sort, including the undesirable recirculation patterns referred to above. There is a dearth of good quantitative experimental data covering ranges of design and operating conditions broad enough to provide a searching test of the theory, but we intend to seek out what is available for comparison with our predictions. For systems where collisions between particles mediate the pattern of flow our program provides, for the first time, a rational basis for the design of particle-gas transport systems and, perhaps of equal importance, for identifying those circumstances in which their performance is likely to be unsatisfactory. It is not a very large step to extend the method to include developing flows, where the particles are accelerating under the influence of forces exerted on them by the gas stream. To the extent that turbulence can be modelled, it is also possible to introduce into the model some effects of turbulent fluctuations in the gas velocity.
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. The factors that must be taken into account in such models were first explored theoretically. Particles are represented as fractal agglomerates. The mobilities and cross sections of such aggregates were examined, and upper and lower bound estimates of the collision frequency function are developed. Predictions of the dynamics of a coagulating aerosol indicate that aggregates coagulate more rapidly than do dense spheres.
In the initial year of the program we have focussed our experimental program on describing the mobility of agglomerates. Agglomerate particles were classified using electrical mobility techniques. The classified particles were collected on electron microscope grids for image analysis of the photographs taken from those samples to estimate fractal structure parameters. The particles studied include titanium dioxide particles produced by pyrolysis of titanium tetraisopropoxide and elemental silicon particles produced by pyrolysis of silane. The former particles are representative of particles of considerable industrial interest. The latter particles are a convenient model system that has been used for initial studies of coalescence of agglomerate particles.
The mobility equivalent size of the free molecular and transition regime aggregates studied to date has been found to correlate well with the projected area of the particles. During the past year we also had an opportunity to study the mass transfer to agglomerate particles using an instrument which was brought to Caltech by Urs Baltensperger, a visitor from ETH in Zurich. The instrument, called an epiphaniometer, is a device for measuring the mass transfer to particles by attachment of radioactive lead atoms. The experiments have been performed using mobility classified particles and, as expected, we find that the mass transfer rate scales directly with the mobility for drag equivalent diameter of the particles. That is, spherical particles and agglomerate particles with the same migration velocity in an electric field exhibit the same mass transfer rates.
Because electrical mobility measurements play a key role in our studies of the dynamics of agglomerate particles, we have also conducted a series of experiments aimed at measuring the charge uptake by these agglomerate particles. These experiments have been conducted using bipolar chargers, that is, radioactive sources that generate both positive and negative ions in the gas that then attach to the particles. The experiments involve taking a neutral aerosol from which all charge particles have been removed with an electrostatic precipitator and exposing it to bipolar ions. The number of neutral particles remaining after exposure to a fixed ion concentration is measured. The neutral fraction scales, once again, directly with the mobility equivalent diameter.
Thus, from each of our studies to date, we find that the mobility equivalent diameter is a very convenient quantity for characterizing the agglomerate particles. During the past year we have also advanced our efforts somewhat in the modeling of the agglomeration process itself. This requires an understanding not only of the mobility or diffusivities of the particles, but also of their collision cross sections. To date, we do not have direct measurements of the collision cross section, so we have been forced to make estimates to provide upper and lower bounds on those cross sections and, hence, on the coagulation rates. Still, the estimates that we have made do provide some insights into the differences between the agglomeration process and coagulation of rapidly coalescing particles.
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.