Modeling agglomeration

Figure 45(d) shows the determination of the tensile strength of model agglomerates by means of the wall friction method.For this test a cylindrical pellet—sometimes with a central pin—is produced in a press. After removing the specimen from the press, it is stressed directly in the die shell. The tensile force is transmitted by adhesion between the end surfaces and the pistons as well as on the circumference and the die walls. Again, the tensile strength is defined by the quotient rupture force P divided by the cross section of the cylindrical or ring-shaped sample. 

S.G. Thoma, M. Ciftcioglu, D.M. Smith, Determination of agglomerate strength distributions. Part 2. Apphcation to model agglomerates. Powder Technol. 68(1), 63-69 (1991). doi 10.1016/ 0032-5910(91)80064-P... 

To investigate dispersive mixing, 2 mm spheres of fluffy carbon black were moulded into model agglomerates , densities 0.3 and 0.4 gJcrcE and a device ( 2) with 10 mm cavities in both rotor and stator compared with device 1 (deep cavities). Neither were dispersed in 1 (deep cavities), nor was 0.4 in 2 (shallow cavities). However, the 0.3 density agglomerate was dispersed in 2 by tail formation and erosion as described in Chapter 14. 

The Beckstead-Derr-Price model (Fig. 1) considers both the gas-phase and condensed-phase reactions. It assumes heat release from the condensed phase, an oxidizer flame, a primary diffusion flame between the fuel and oxidizer decomposition products, and a final diffusion flame between the fuel decomposition products and the products of the oxidizer flame. Examination of the physical phenomena reveals an irregular surface on top of the unheated bulk of the propellant that consists of the binder undergoing pyrolysis, decomposing oxidizer particles, and an agglomeration of metallic particles. The oxidizer and fuel decomposition products mix and react exothermically in the three-dimensional zone above the surface for a distance that depends on the propellant composition, its microstmcture, and the ambient pressure and gas velocity. If aluminum is present, additional heat is subsequently produced at a comparatively large distance from the surface. Only small aluminum particles ignite and bum close enough to the surface to influence the propellant bum rate. The temperature of the surface is ca 500 to 1000°C compared to ca 300°C for double-base propellants. 

The rest of the less volatile fission products along with constituents of zircalloy, stainless steel, and the control rods are assumed to be in condensed form as inert aerosols that are treated together in TRAPMELT as "other aerosols." The aerosols are modeled as agglomerating and depositing on surfaces by several mechanisms (e.g., gravitational settling). 

It calculates one-dimensional heat conduction through walls and structure no solid or liquid ciMiibustion models are available. The energy and mass for burning solids or liquids must be input. It has no agglomeration model nor ability to represent log-normal particle-size distribution. 

Consider the erystal size distribution in a model MSMPR erystallizer arising beeause of simultaneous nueleation, growth and agglomeration of erystalline partieles. Let the number of partieles with a eharaeteristie size in the range L to L + dL be n L)dL. It is assumed that the frequeney of sueeessful binary eollisions between partieles (understood to inelude both single erystals and previously formed agglomerates) of size V to V + dV and L to Ll +dL" is equal to j3n L )n L")dL dL". The number density n L) and the eollision frequeney faetor (3 are related to some eonvenient volumetrie basis, e.g. unit volume of suspension. 

The final modelling equation proposed for the agglomeration kernel is... 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Several reported chemical systems of gas-liquid precipitation are first reviewed from the viewpoints of both experimental study and industrial application. The characteristic feature of gas-liquid mass transfer in terms of its effects on the crystallization process is then discussed theoretically together with a summary of experimental results. The secondary processes of particle agglomeration and disruption are then modelled and discussed in respect of the effect of reactor fluid dynamics. Finally, different types of gas-liquid contacting reactor and their respective design considerations are overviewed for application to controlled precipitate particle formation. 

An alternative theory has been developed to model precipitation with agglomeration where, beside the overall particle size, an additional co-ordinate of crystal number within an agglomerate is introduced (Wachi and Jones, 1992). Figure 8.22 shows the concept of agglomeration and disruption respectively. 

In this model, the size of the primary partieles is proportional to their individual residenee time within the erystallizer and this, together with the identifiea-tion number of the agglomerate to whieh the partiele is attaehed, forms a state matrix eontaining detailed information about eaeh partiele. In the ealeulation, within a unit volume of suspension during any time interval At ... 

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