Particle size distribution modeling

Table 5 Parameter Estimates for the Particle Size Distribution Models...

The third and final particle size distribution model assumes that growth is linear as in the first but that breakup results in predominantly small particles (thorough breakage) which are too small to measure by the electronic particle counters used to characterize the suspension. Petenate and Glatz (6) have provided analytical solutions for this model. 

The batch process is similar to the semibatch process except that most or all of the ingredients are added at the beginning of the reaction. Heat generation during a pure batch process makes reactor temperature control difficult, especially for high soHds latices. Seed, usually at 5—10% soHds, is routinely made via a batch process to produce a uniform particle-size distribution. Most kinetic studies and models are based on batch processes (69). 

Aerosol Dynamics. Inclusion of a description of aerosol dynamics within air quaUty models is of primary importance because of the health effects associated with fine particles in the atmosphere, visibiUty deterioration, and the acid deposition problem. Aerosol dynamics differ markedly from gaseous pollutant dynamics in that particles come in a continuous distribution of sizes and can coagulate, evaporate, grow in size by condensation, be formed by nucleation, or be deposited by sedimentation. Furthermore, the species mass concentration alone does not fliUy characterize the aerosol. The particle size distribution, which changes as a function of time, and size-dependent composition determine the fate of particulate air pollutants and their... 

Modeling the pore size in terms of a probability distribution function enables a mathematical description of the pore characteristics. The narrower the pore size distribution, the more likely the absoluteness of retention. The particle-size distribution represented by the rectangular block is the more securely retained, by sieve capture, the narrower the pore-size distribution. 

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. 

The general form of the population balance including aggregation and rupture terms was solved numerically to model the experimental particle size distributions. While excellent agreement was obtained using semi-empirical two-particle aggregation and disruption models (see Figure 6.15), PSD predictions of theoretical models based on laminar and turbulent flow considerations... 

Comparison of the simulations with experimental results (Figure 8.32) showed reasonable agreement prior to the onset of agglomeration. The ultimate aim of the model is to enable particle product design by the ability to relate particle size distribution to equipment design and operating conditions. 

Wachi, S. and Jones, A.G., 1992. Dynamic modelling of particle size distribution and degree of agglomeration during precipitation. Chemical Engineering Science, 47, 3145-3148. 

Mcllvried and Massoth [484] applied essentially the same approach as Hutchinson et al. [483] to both the contracting volume and diffusion-controlled models with normal and log—normal particle size distributions. They produced generalized plots of a against reduced time r (defined by t = kt/p) for various values of the standard deviation of the distribution, a (log—normal distribution) or the dispersion ratio, a/p (normal distribution with mean particle radius, p). 

While the model was in general agreement with the limited experimental data published on bulk PVC particle size distribution, there is still no generally applicable theory describing particle growth and flocculation in the presences of mechanical agitation for precipitation polymerizations. 

A mechanistic model for the kinetics of gas hydrate formation was proposed by Englezos et al. (1987). The model contains one adjustable parameter for each gas hydrate forming substance. The parameters for methane and ethane were determined from experimental data in a semi-batch agitated gas-liquid vessel. During a typical experiment in such a vessel one monitors the rate of methane or ethane gas consumption, the temperature and the pressure. Gas hydrate formation is a crystallization process but the fact that it occurs from a gas-liquid system under pressure makes it difficult to measure and monitor in situ the particle size and particle size distribution as well as the concentration of the methane or ethane in the water phase. 

Leblanc and Fogler developed a population balance model for the dissolution of polydisperse solids that included both reaction controlled and diffusion-controlled dissolution. This model allows for the handling of continuous particle size distributions. The following population balance was used to develop this model. 

JR Crison, GL Amidon. The effect of particle size distribution on drug dissolution A mathematical model for predicting dissolution and absorption of suspensions in the small intestine. Pharm Res 10 S170, 1992. 

Research on the modelling, optimization and control of emulsion polymerization (latex) reactors and processes has been expanding rapidly as the chemistry and physics of these systems become better understood, and as the demand for new and improved latex products increases. The objectives are usually to optimize production rates and/or to control product quality variables such as polymer particle size distribution (PSD), particle morphology, copolymer composition, molecular weights (MW s), long chain branching (LCB), crosslinking frequency and gel content. 

Finally the mean particle size for the model as well as the sphericity and particle size distribution must be determined. The particle size is determined by the need for equal values of u0/umj between the model and the commercial bed. 

Glicksman and Farrell (1995) constructed a scale model of the Tidd 70 MWe pressurized fluidized bed combustor. The scale model was fluidized with air at atmospheric pressure and temperature. They used the simplified set of scaling relationships to construct a one-quarter length scale model of a section of the Tidd combustor shown in Fig. 34. Based on the results of Glicksman and McAndrews (1985), the bubble characteristics within a bank of horizontal tubes should be independent of wall effects at locations at least three to five bubble diameters away from the wall. Low density polyurethane beads were used to obtain a close fit with the solid-to-gas density ratio for the combustor as well as the particle sphericity and particle size distribution (Table 6). 

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