ARR - Annual Report

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.

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. In this report, we review Cornell activities in the area of gas-solid suspension flows in 1997.

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.

By matching five dimensionless parameters, experiments employing plastic and glass powders fluidized with mixtures of sulfur hexafluoride, carbon dioxide, helium and air near ambient temperature and pressure achieved hydrodynamic similarity with generic high-temperature risers of variable scale operating at pressures of 1 and 8 at-m.

We interpreted our results in the upper riser using steady, fully-developed momentum balances for the gas and solid phases. This analysis showed that, for a wide range of experiments, two parameters capture the dependence of the pressure gradients upon the ratio of the mean gas and solid mass flow rates. The first is the ratio of the mean particle slip and superficial gas velocities. The second represents spatial correlations between the radial profiles of interstitial gas velocity and voidage. Variations of the first with dimensionless parameters indicated that our “atmospheric” and “pressurized” experiments conformed to distinct viscous and inertial regimes.

In 1997, we have also established that the descending velocity of particles clusters at the wall of a riser scales exclusively with the square root of the particle diameter and the gravitational acceleration. This observation showed that the dynamics of wall clusters is chiefly determined by inter-particle contacts. Because these clusters govern heat transfer at the wall, this conclusion has important consequences for modeling.

Zirconia (ZrO,) particles are one of the most important materials for refractory ceramics. However, commercially available ill-defined powders prepared by milling of calcined agglomerates or by gas-phase reaction of ZrCl, and 0, are normally difficult in preparation of crack-free compact for sintering or need high sintering temperatures above 1700 “C. On the other hand, the monosized amorphous powders of a high sinterability prepared by hydrolysis of the alkoxides are not free from the economical problem of their low productivity (< 0.2 mol dmm3 in final concentration).

The objectives of our project are to develop a new method for preparation of unagglomerated ultrafme crystalline spheres of ZrO, of a narrow size distribution with the mean diameter of the order of ten nanometers or less in large quantities on the basis of the gel-sol technique developed in our laboratory, to elucidate the formation mechanism, and to examine the sintering properties. The standard procedure is as follow.

• Zirconium (IV) n-propoxide (ZNP: Zr(OC,H,),) is mixed with triethanolamine (TEOA: N(CH,CH,OH),) at a molar ratio of ZNP:TEOA = 1:3 in a dry box filled with dry air to form a stable compound of Zr”’ against the exceedingly rapid hydrolysis of Zr4’.
• After aging the solution at room temperature for 24 h, doubly distilled water and NH, solution are added to the solution in order to make a solution of 0.5 mol drnm3 in Zr4’ and 1.0 mol dmw3 in ammonia. In this stage no reaction takes place.
• The resulting solution is then aged at 200 “C for 3 days without stirring in a preheated oil bath to nucleate and grow the zirconia particles.

From the UV spectra of the mixed compounds of ZNP and TEOA in n-propanol and FT-IR spectra in chloroform, it was found that the propoxy groups of ZNP were all replaced by ethoxy groups of TEOA. With the elevation of the internal temperature which took ca. 30 min to reach 200 + 1 “C, hydroxide gel was formed and the nucleation occurred on the gel network in 20 min. The nuclei were grown to fairly uniform particles of ca. 15 nm in mean diameter at the expense of the gel until, finally, the gel completely disappeared in 1 h. In this stage the particles were of a rough surface, but as they were further aged, they became spherical with a smooth surface due to the intra-particle recrystallization. When the aging was prolonged to 72 h, the particles were somewhat grown by Ostwald ripening. It is noteworthy that so-prepared particles were tetragonal ZrO, after 30 min as determined by X-ray diffractometry, even at the rather low temperature, 200 “C, while particles prepared at high pH (-13) in the absence of ammonia or those prepared in the presence of acetate ions at neutral pH (-7) were both monoclinic. Also, high-resolution transmission electron microscopy revealed that the produced particles were mostly single crystals.

From the analysis of growth mechanism it is concluded that the fairly uniform unagglomerated ultrafme particles are nucleated on the gel network of the hydroxide, and grown by dissolution of the gel without significant coagulation owing to the gel network holding each particle. In addition, extensive renucleation is inhibited due to the lowered supersaturation by the formation of the gel precursor.

The so-prepared powders (-15nm and -2.5nm) showed an excellent sinterability, as compared to power prepared by gas-phase reaction (-6Onm) or monosized amorphous powder by hydrolysis of zirconium butoxide at 50 “C (-250nm).

In the second year of the project, the laboratory equipment for dispersing powders in stirred vessels described in IFPRI annual report No. ARR 17-04 and the laboratory methods for measuring the wetting properties were used to investigate the dispersing of aspartame (supplied by DSM) and zeolites (supplied by Unilever Research) in the 10 1 scale. For comparing the pitched-blade turbine used so far with the Rushton type turbine, such a turbine was built and tested using wheat flour, instant tlour and other powders. Experiments were conducted with an unbaffled, partly or fully baffled vessel.

The dispersing behaviour of aspartame and zeolite differs considerably from the skim milk powder investigated during the first year of the project and required new methods for controlling dispersion/solution quality. Aspartame was dispersed in small concentrations (0.5 % wt./wt.). The dissolution process was controlled by simultaneous measurement of the size of the undissolved particles (using laser diffraction) and off-line photometric measurement of the aspartame concentration in the solution.

The main problem with aspartame was its low solubility (= 1 % wt./wt.) and slow rate of dissolution in water. For fast dissolution, a fine powder with accordingly large specific surface is required. This in turn requires that the stirrer be designed and operated in a way to immerge and disperse these fine particles as quickly as possible. The results show that using an unbaftled vessel is the best way to achieve this, but that the particle size distribution of the powder is of greater importance. If the powder is too fine, lumping occurs, diminishing the rate of dissolution.

Zeolites, which are insoluble in water, were used for producing slurries with 50 % wt./wt. solids. The main problem here was to immerge the powder during the second half of the mixing process, when the slurry concentration was already high. This problem had already been predicted by the results of wetting time measurements. Powder dispersion and avoidance of sedimentation, on the other hand, were easy to achieve. Again, an unbaffled vessel turned out to be better suited than a baftled one, where floating layers of unwetted or partly wetted powder prevented complete mixing. In the unbaffled vessel, vortex formation occured even at high solids concentration, aiding in immerging the powder. Additional wetting and immersion experiments indicate that a mixture of 20 % zeolite A4 and 80 % A24 may have much better properties than either of the pure powders.

Although the specific stirring power that can be achieved in an unbaffled vessel is inferior to the specific stirring power for a baffled one, the improved ability to submerge the powder with help of the vortex formed by the rotating liquid proved to be of decisive importance. For hard to disperse powders, however, this may be different. If such a material is to be dispersed, a partly baffled vessel might be the best solution.

Comparison of the pitched-blade turbine and the Rushton turbine showed that both perform equally well at immerging powders in unbaffled vessels, which can be seen by plotting the specific stirring power required for immediate immersion over the desired feed rate of the powder. If a fully baffled vessel is used, the Rushton turbine performs better. Further experiments will focus on partly baffled vessels, in which vortex formation occurs as in unbaffled vessels, while higher energy input may allow better dispersion of critical (lump-forming or gelatinizing) products.

While (agglomerated) skim milk powder could be easily dispersed in baffled vessels as well as in unbaffled ones (see annual report No. ARR 17-04), aspartame, zeolite and wheat flour require unbaftled vessels in which the powder is fed to a vortex. Currently, for scale-up from the laboratory scale to large-scale- vessels the concept of constant Froude numbers can be used as a first approach. For baffled vessels, this is not common as it leads to an impracticably high specific stirring power, but for unbaftled vessels, a reasonable design is easily achieved. Vessel operation is constrained regarding the liquid level, since gassing the liquid should usually be avoided. This problem can be solved by using speed-variable stirrers. The fact that unbaffled vessels can be much easier cleaned is an additional incentive to use this kind of design for industrial applications.

The results from the experiments conducted so far indicate, however, that a complete description of the immersion step would also preferably take into account vortex shape and surface flow pattern (surface shear), which depend on the stirrer type and operating variables, and also powder properties like static wetting time or dynamic wettability. Future work will therefore be directed towards characterizing the flow pattern caused by different stirrer types, characterizing the immersion capability and the dispersing efficiency of such vessels, and towards improving the measurement of dynamic powder wetting.

This report summarizes the activities conducted under IFPRI support from November 97 to November 98. The main target of our work is to understand, characterize, and quantify the behavior of powders in the early stages of compaction attendant to the intrinsic properties of the material and the processing conditions. The project involves theoretical, numerical, and experimental components. It is framed within a collaborative effort with concentration on pharmaceutical manufacturing, but the results are relevant to powder compaction in many other industries.

Topics Addressed

• Die pouring (Section 2)
• The reaccomodation process of Region I of the compaction curve (Section 3)
• The mechanics of regular aggregates as they obtain in pre-compaction structures (Section 4)
• The deformation process of Region II of the compaction curve (Section 5)
• An ongoing experimental program aimed at verifying our theoretical and computational results (Section F)

In the Introduction these topics are motivated in the context of the overall goals of the project.

This report summarizes the research activities for the project “Optimal Quality Control of Industrial Crystallizers,” ARR 32 - 01, during the period 1 September 1996 to 31 August 1997. The goal of this project is to develop on-line measurement technology and predictive crystallization models so that advanced on-line crystallizer control can be implemented to enhance precise control of crystal size and shape.

During the current year, we have demonstrated model identification and control strategies to improve filtration of a problematic photochemical of industrial interest. In order to analyze crystal shape as well as size, we have purchased and installed an Olympus BX60 microscope, image capturing hardware, and Image Pro Plus image analysis software. We have further developed our stochastic modelling capabilities so that models with new and complex crystallization mechanisms can be simulated quickly and accurately. We currently can simulate the following mechanisms:

• size dependent nucleation
• size dependent growth
• growth rate and nucleation rate fluctuations
• growth rate dispersion
• size dependent agglomeration

Plans for the next year are to test and commission the new image analysis equipment on a relatively simple system, and identify a model chemical system that is particularly relevant to industrial practice, for which improvements in particle size and shape measurement and control would provide large potential benefit. We will construct a flow cell and circulation loop to monitor the crystal size and shape in real time during crystallization experiments.