ARR - Annual Report

Summary

This project focuses on the fluid dynamics of vertical gas-solid risers. Its principal objective is to produce data for evaluating theories elaborated by Professors Sundaresan and Jackson at Princeton. Thus in this report, we review Cornell activities in the area of gas-solid suspension flows.

At Cornell, we possess a unique facility with the ability to recycle - rather than discard - fluidization gases of adjustable composition to a vertical riser of 20cm diameter and 7m height. This allows us to simulate the fluid dynamics of industrial units (atmospheric and pressurized coal-burning circulating fluid beds, catalytic crackers) in a cold, atmospheric riser by matching the dimensionless parameters that govern the flow. The facility is equipped with capacitance, optical fiber and pressure instrumentation that records solid concentration profiles in the vertical and radial directions.

In the first year of the award, we have established that, under typical industrial conditions, dense gas-solid flows are nearly independent of gas density in the fully-developed region of the riser. This observation of a viscous flow regime suggests that particle clusters dominate the exchange of momentum between the two phases. It further suggests that extrapolations of flow behavior from atmospheric to pressurized conditions should be more straightforward than previously envisaged.

To inform closure of theories elaborated at Princeton, we have also carried out simultaneous measurements of pressure fluctuations and local wall volume fraction. Here we have shown that, because gas pressure reflects fluctuations originating throughout the vessel, they are not closely correlated with local solid volume fractions.

In addition, we have begun a study of cyclone performance under conditions of high gas density and solid loading, which have not yet received much attention despite their importance for a new generation of high efficiency coal gasifiers and other dense gas-solid processes operating at high pressures.

In 1996, we have also made progress in the area of instrumentation, which is often of interest to industry. In particular, we have designed an uncooled capacitance instrument capable of recording instantaneous solid volume fraction near the wall of an industrial vessel operating up to 950°C and 15 bar. In addition, we have completed a technology review of instrumentation for dense gas-solid suspensions to be presented at an upcoming IFPRI meeting.

This research project aims 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. It is furthermore intended to establish a connection between the results from laboratory tests of the instant/dispersing properties and the large-scale dispersion of the product.

In the first year of the project, laboratory equipment for dispersing powders in stirred vessels was set up, and experiments were performed with agglomerated and milled skim milk powder (Nestle) in 10 1 and 50 1 vessels.

This report contains information required for an experimental set up of an agitated vessel at laboratory scale that enables the engineer to gain data suitable for the design of large-scale-vessels.

Mixing performance of the stirring system was investigated with and without baffles. 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.

The stirred-vessel experiment constructed permits investigation of the combined wetting/dispersing behaviour of powdered products under stirrer action. The results of the experiments indicated that there is an optimal point of operation (regarding specific power and feed rate), at which the total required stirring energy is minimal. The final degree of dispersion for skim milk powder depends upon the volume-specific stirring power.

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. 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 maximal possible feed rate per surface area, short of layer formation, could be determined using the dynamic wetting test. This feed rate was somewhat higher than the rate found in experiments with the agitated 10 1 vessel, the difference being caused by the uneven distribution of the powder across the liquid surface in the stirred vessel.

Use of surfactants improves the combined wetting/dispersing behaviour of powdered products, both in the wetting test and in the stirred vessel. In this case, lower values of specific power and energy are required. It has been shown that, preferably, a premix of surfactant and powder should be used.

The results gained so far enable the design of large-scale agitated vessels for milk powder and similar products.

Introduction

Our research, funded by IFPRI, has concentrated on developing physical models for the rapid flow of particles and gas, and exploring the consequences of these models for fully developed and developing flow of the two phases in both vertical and inclined ducts. Experimental studies have shown that solid particles transported by a gas in vertical pipes, such as those encountered in riser reactors, are distributed non-uniformly over the cross section (Bader et al., 1988). Consequently, neither quantitative nor qualitative features of the overall behavior can be represented correctly by one-dimensional flow models, which take into account the presence of the pipe walls only through empirically introduced friction factors. The origin of this segregation has been investigated by us and others over the last decade.

During the past twelve months, we have focused our efforts on understanding the various routes to formation of clusters in rapid flow of gas-particle mixtures. It was apparent from the reactions of some of the industrial representatives during the annual meeting in Nancy that the connection between this work and riser flow modeling is not entirely obvious. Therefore, we begin this report with a discussion of this connection (section 2), then highlight some of the results (section 3) and finally conclude with a summary of the anticipated course of research for the next year (section 4).

Following the previous work, calculation of gas-solid flow in a vertical duct was made by using LES (Large Eddy Simulation). The same models in LES as the single phase flow is applied to gas-solid flow under the conditions of small particle (50 micron meter) and dilute phase (solid volume fraction = 0.96 X 10^- 4). It was found that the importance of the inter-particle collision was recognized even at such low concentrations of particles, particularly for distributions of particle concentration and velocity fluctuation. As has been observed by many experimental workers, the turbulence modification due to the particles were found in the present simulation. That is, the intensity of gas turbulence is reduced by the presence of particles.

Executive Summary

This is the second Annual Report of the 1994-1997 IFPRI Project on “Reversibly Flocculated Suspensions” at K.U.Leuven. It is an extension of a similar project during the period 1991-1994. The project aims at understanding and predicting the flow properties of colloidal suspensions that are flocculated at rest but can be deflocculated during flow.

Two parts can be distinguished in this project. The first deals with describing the viscosity curves of weakly flocculated suspensions with controlled colloidal stability parameters. Reversibly flocculated suspensions often display time-dependent viscosities or “thixotropy”. It is the purpose of the second part of this project to attempt to identify and possibly quantify the role of the major factors governing thixotropy.

As far as the first part of the project is concerned, this second year was used to study suspensions based on two types of newly provided particles. They differ in particle size and in characteristics of the stabilizer layer. Firstly, stable suspensions of these particles have been studied in order to provide reference data with which to compare the data on reversibly flocculated systems with the same particles. Subsequently, flocculation was very gradually induced by changing the medium as well as the temperature. Gelation temperatures were determined as a function of particle volume fraction, using dynamic moduli. These data were used to determine interaction parameters, which should be useful in relating and predicting viscosity functions. The rheological data are being supplemented with small angle neutron scattering data on flowing systems. This provides information about the structure and the interaction parameters of the suspension. Preliminary results indicate the usefulness of this approach. More systematic data of this nature are being collected.

As for the second part, the available data have been extended in different ways. The scaling relations for sudden decreases in shear rate, i.e. for structure build-up, which had been suggested earlier have been confirmed by data on another system. In addition, the kinetics of structure breakdown after a sudden increase in shear rate have been studied. It is shown that, not surprisingly, breakdown follows somewhat different rules than build-up.

Still, a strain scaling seems to hold here as well and the relation of the characteristic times with the initial stress is in line with that for build-up. Build-up was now also followed after stopping the flow by using dynamic moduli. It has been found that this aspect of behaviour can be quite different in different materials. Some dispersions develop a three-dimensional particulate network nearly immediately after stopping the flow, others remain liquid-like while the moduli increase.

Finally, some thixotropic systems have been investigated by means of a dielectric technique. This should shed some light on the underlying structural behaviour. Transient dielectric data after stopping the flow are being generated. They are still under investigation.

Introduction

It is important to recall that the initial objectives of the research are to develop fundamental understanding and techniques to predict cornmunition behaviour from a universal test based on an experimental rig that reproduces single impact on a target in an air jet mill. The influence of the material properties on breakage in ultra-fine grinding are investigated. In Previous reports gave results for the impact of seven kinds of particles on a target and showed different types of behaviour. A classification was obtained (see report AR 27.03). A second rig has been built to study another impact configuration namely that of the impact between two jets of particles. Experiments are also performed with other types of mill and in particular an Alpine 100 AFG air jet mill. Morphological analysis is developed to study the shape of particles, debris and the action of the mills. In addition progress in the development of a model of an air jet mill is presented.

Part A

Part A of this report presents the results of the experiments performed with the single jet apparatus. Eight kinds of alumina particles impacted on a target are studied: three hydrargillites and five calcined hydrargillites. The influences of the material processing, the structure, and the calcination on the behaviour at impact are highlighted.

Part B

Part B presents the methods being developed for morphological analysis and gives results from the experimental impact rig and other methods of particle breakage.

Part C

Part C presents results towards the modelling of an air jet mill. In particular measurements and analysis of pseudo batch grinding experiments leading to the first determination of breakage and selection matrices for an air jet mill.

Executive Summary

We continue working toward a robust and fundamental theory to predict the structure and dynamics of concentrated colloidal dispersions from the interparticle potential, assumed to be pairwise additive, and scalar functions describing the pair hydrodynamics. The former are generally available in approximate form from the colloid science and polymer physics literature. The latter we construct as interpolations between well established limits for the mean-field at large separations and lubrication near contact. Insertion of these into a Smoluchoski equation for the pair distribution function, with an approximate closure to account for couplings with a third particle through the pair potential, provides a basis for determining the non-equilibrium microstructure. From the microstructure we calculate transport propertics (e.g. low shear viscosity qO, frequency dependent shear modulus G’ and dynamic viscosity q’, long-time self-diffusion coefficient Ds”) and optical measures of the structure (eg. static structure factor and stress optical coefficient).

Papers now in press demonstrate the efficacy of the approach via comparison of the predictions without hydrodynamics with results from Brownian dynamics simulations for soft spheres and those with hydrodynamic interactions with experimental data for hard spheres. The theory is at least semi-quantitative with accuracy comparable (but not superior) to other approaches. For hard spheres of diameter d WC find finite d3Gi/kT with the lubrication approximation and --------- (52 = dimensionless frequency) with the discontinuous approximation, in agreement with definitive sets of data, qO/p within 50% of the experimental data and capturing the divergence as the volume fraction ----- c* 0.64, @m/Do conforming with the data for 4 zz 0.45 and qualitatively capturing the zero as ---- 0.64, static structure factors and stress optical coefficients for weak steady shear with the proper qualitative dependence on wave number and volume fraction.

This past year we have pursued a mechanistic study of spheres bearing grafted polymer layers, as studied extensively by Mewis in earlier IFPRI research. We adopt a simple mean field approximation for the interparticle potential between flat plates, apply the Derjaguin approximation to convert it to spheres, and implement Monte Carlo simulations to generate accurate equilibrium pair distribution functions. The high frequency limiting viscosity is calculated at low to moderate volume fractions by incorporating into a conventional effective medium theory the correction proposed by Bedeaux for short range hydrodynamic interactions, which are captured through pair hydrodynamic functions for uniformly permeable spheres in the literature. An asymptotic approach due to Acrivos and Frankel, together with the lubrication force between polymer coated spheres near contact, provides a robust limit at high volume fractions. The viscosity then diverges at a volume fraction that ranges from random close packing to unity, depending on the thickness of the grafted layer. Incorporation into our simple interpolations advanced for hard spheres, these provide sensible approximations for the hydrodynamic functions for polymer coated particles.

Calculations of the high frequency modulus d3GL/kT are now complete, demonstrating clearly the conditions under which one can extract the pair potential from this rheological measurement. Hydrodynamic interactions reduce the modulus significantly up to close packing of effective hard spheres, but when crowding compresses the layers significantly the moduli with and without hydrodynamic interactions differ only modestly. Comparison with the data indicates that the simple approximations for the hydrodynamic interactions appear to capture at least the qualitative features of the phenomena. To remove the error introduced through the approximation for the inter-particle potential, we employed instead measurements reported in the literature from a surface forces apparatus. However, these provided no better agreement, even at sufficiently high volume fractions that the remainder of the theory is demonstrably exact.

Now we are calculating the low shear viscosity, first with the simplified theory of Brady and ultimately with our full theory including the closure approximation. These will yield the low shear viscosity and linear viscoelastic response as a function of volume fraction and ratio of layer thickness to particle radius. To complete the project during the coming year we will assess the relative accuracy of the non-equilibrium theories and close with recommendations for those interested in relatively simple but qualitatively reliable means of calculating the effect of inter-particle potentials on rheology.

The general objective of the work at Surrey has been to elucidate the mechanisms of particle breakage under impact and sliding conditions. Predictive models, describing the chipping under impact and sliding conditions, have been developed based on indentation fracture mechanics. The specific objectives of the current work are to investigate the mechanism of particle fragmentation under impact and to characterise the mechanical properties of porous materials.

The study of fragmentation involved single particle impact tests in a range of impact velocities and feed particle sizes. The test materials covered a wide range of diverse mechanical properties and structures. The effect of impact velocity and feed particle size on breakage was evaluated using the full size distribution of the impact product. The analysis of the experimental results was by recourse to the Gates-Gaudin-Schumann distribution. The cumulative size distribution of the complement, i.e. the size range where fine debris and fragments arc expected, is shown to be a function of the group U’l . This conclusion is qualitatively similar to that applying to the chipping of particulate solids.

In an effort to incorporate the influence of material properties on the extent of fragmentation, the fracture toughness of spherical porous silica particles was measured using quasi-static Vickers indentation. The values of fracture toughness were found to be independent of the applied load and to fit well the expressions proposed in the literature. Fracture toughness is the most appropriate parameter for the characterisation of the resistance of materials to breakage, and the current work aims at establishing a relationship between porosity and fracture toughness by carrying out measurements on a single test material at different levels of porosity. The mechanical characterisation is expected to provide valuable information in the analysis of the effect of material properties on the fragmentation of particulate solids.

The overall objectives of the project are to model and experimentally verify fundamental aspects of the mechanically actuated granulation processes using binders, with focus directed to surface free energy approaches coupled with the experimental technique of mixer torque rheometry (MTR). Further general aims, building on the surface interaction and MTR knowledge, are to develop predictive relationships which can be applied to address scale up in high shear mixer--Granulators and dry granule characteristics. In all sections of the project, MTR is regarded as a pivotal experimental method.

The surface free energy model utilism, spreading coefficients and interaction parameters between substrate and binder components has been shown in previous reported project (J and spreading phenomena during granulation by mechanical agitation. Both model and a range of representative substrates with selected binders have been evaluated and predictions verified experimentally using mean torque granulation profiles from MTR. This knowledge enables formulation components to be selected in a more rational manner than is current practice, based on sound, physicochemical principles. A key requirement, however, is to link the wet mass torque (rheology) with dry granule properties.

Results of studies probing such relationships are presented. A testing method has been developed which defines a friability index, a measure of the relative ease with which dry granules fragment and fracture in a standardized procedure. For three representative granule formulations, similar trends between mean torque and friability index were observed, indicating that data from MTR for wet massed samples provide an indicator of mechanical characteristics of dry granules prepared from the wet mass. These observations have clear practical and industrial relevance, since, together with selection criteria for formulation components mentioned above, procedures which accommodate both granulation component properties and final granule characteristics are being worked to explain wetting, to couple other practically important dry granule properties to wet mass rheology and material properties is indicated.

In considering scale up issues it was considered critically important to test developed relationships at realistic industrial levels and capacity. This has been achieved through extensive collaboration and liaison with mixer-granulator equipment manufacturers as well as by the generous supply of large quantities of experimental materials by Zeneca Pharmaceuticals. Based on a dimensionless number principle linking power number with three other dimensionless groups (Reynolds number, Froude number, and a fill ratio term for the mixer-granulator--bowl) a scale up function was developed. This enables a master curve for a specified formulation to be generated when granulated in geometrically similar equipment. Consistency of wet mass density and rheological characteristics are key parameters in providing linkage between laboratory, pilot and large scale processes.

These studies, combined with those reported previously, show that in a series of fixed bowl high shear mixer-granulators where geometric similarity is respected, scale up to a selected end point can be predicted over the range 25-1800 litre bowl capacity. This is the first time a predictive scale up strategy has been successfully demonstrated to hold over this full range of capacity range for such mixer-granulators.

In a practical situation for scale up prediction, the sequence of events would be to define the formulation master curve (i.e. power number correlation) using a small scale mixer-granulator, identify the optimal density and rheological consistency for dry granule properties and performance, use these values and mixer-granulator variables to calculate power requirements on large scale equipment, run the process at defined setting, and check product for density and consistency.

This report also details further scale up studies on high shear removable bowl and low shear planetary mixer-granulators. In the former, geometric similarity was not respected in bowl dimensions for the 75L and 600L equipment and, as expected, parallel power number correlations curves were not found. However, for two bowl sizes of a planetary mixer granulator, although limited in scale up factor, the relationship was verified. Further studies are indicated to probe the breadth of application of these rules, considering additional terms for non-geometric similarity and material and formulation factors.

In the last report, we studied the breakage of particles with regularly spaced circular defects as a way of studying porous particles. Those simulations showed a significant effect on the size distribution which, in particular, showed a nearly vertical portion indicating that the size of a large fraction of the produced fragments was governed by the hole spacing. Most homogeneous solids are assumed to be filled with microcracks and we were curious whether they would demonstrate a similar effect on the final breakage results. Unlike the circular defects studied last year, small linear cracks concentrate more stress at the tip. But at the same time, unlike circular defects, linear cracks have a preferred direction and may only participate in the breakage if that direction coincides with the direction of the induced tensile stresses within the particle. As a result, the breakage behavior was nothing. like that for the circular defects. The major effect of the cracks was to increase the degree of Mechanism II breakage, thus increasing the percentage of fines within the system. No effect was seen on the Mechanism I breakage, which governed the sizes of the largest particles.

We are also continuing our ball drop simulations, in which a single grinding ball is dropped onto a bed of particles, as an approximation to ball milling. In last year’s report, we showed that the stronger the particle bed, the larger the degree of induced breakage. This occurred because the strong beds, held their constituent particles in position long enough, without scattering, for the grinding ball to induce breakage. This year’s results gave a great deal more insight into the manner in which the particle bed affected breakage. We became concerned that the random manner in which the beds were assembled might have a significant effect on the eventual breakage. Thus, we attempted to bound the effect of the bed packing by studying the breakage of the weakest and the strongest regularly packed beds. The strongest and also the densest twodimensional construction is a hexagonal packing in which each particle is in contact with six neighbors. The weakest, and likely the least dense stable bed, is a square packing in which particles are arranged on the corners of a square and each particle is in contact with only four neighbors. We hoped to bound the behavior of randomly packed beds between these two extremes as the strength all such beds must lie between these two. Surprisingly though, we found other effects arising from the regular nature of the packings. In particular, the square bed, which has the weakest packing and in the light of last year’s results, should exhibit the least breakage, actually demonstrated more breakage than the hexagonal packing. This was a result of the square packing presenting internal columnar structures to oppose the descent of the grinding ball; these columns underwent nearly complete breakage. The hexagonal bed, on the other hand, naturally spread the grinding ball’s energy throughout the bed, reducing the energy concentration in any given particle thus reducing the breakage, Further evidence of this can be seen in the fact that there was a small effect of inter-particle friction on the breakage in the square bed, (as least when compared to the hexagonal bed) as friction has little effect on the strength of these columnar structures. As a result, the internal order of the bed as well as the overall bed strength can strongly affect the degree of induced breakage.

Finally, we have developed this year, an algorithm for efficiently studying the mechanics of non-round particles. Most granular simulations study round particles as they are far more efficient to simulate. For example, the polygonal particle simulations that make up the heart of our breakage analyses, are approximately 10 times slower than an equivalent round particle simulation. However, most natural particles are not round and are not as likely to roll as non-round particles. This affects the overall mechanical properties of the system. For example, it is hard to get significant angles of repose for round particles as they simply roll away when the angle becomes marginally steep. This new simulation technique uses particle shapes composed of circular arcs and is only about half the speed of an equivalent round particle simulation. This allows a great variety of shapes to be studied at a relatively inexpensive price.