Particle size distribution population

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

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... 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

At the crystallization stage, the rates of generation and growth of particles together with their residence times are all important for the formal accounting of particle numbers in each size range. Use of the mass and population balances facilitates calculation of the particle size distribution and its statistics i.e. mean particle size, etc. 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

If the secondary stream contains emulsifier it can function in three ways. When the emulsion feed is started quickly the added emulsifier can serve to lengthen the particle formation period and hence to broaden the particle size distribution. When the emulsion feed is started later and added in such a manner that the emulsifier is promptly adsorbed on existing particles, one can obtain quite narrow size distributions. If the emulsion feed is started later but added rapidly enough to generate free emulsifier in the reaction mixture a second population of particles can be formed, again yielding a broad size distribution. 

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. 

Particle Size Distribution Determination. To consider the full PSD, a population balance or age distribution analysis on particles must be employed. Table II gives a summary of recent work concerning the determination of PSD s in emulsion systems, using both the "monodispersed" approximation and the population balance approach. More details can be found in the literature sources cited in the Table. 

The importance of chemical-reaction kinetics and the interaction of the latter with transport phenomena is the central theme of the contribution of Fox from Iowa State University. The chapter combines the clarity of a tutorial with the presentation of very recent results. Starting from simple chemistry and singlephase flow the reader is lead towards complex chemistry and two-phase flow. The issue of SGS modeling discussed already in Chapter 2 is now discussed with respect to the concentration fields. A detailed presentation of the joint Probability Density Function (PDF) method is given. The latter allows to account for the interaction between chemistry and physics. Results on impinging jet reactors are shown. When dealing with particulate systems a particle size distribution (PSD) and corresponding population balance equations are intro-... 

Particle size distribution, on a population basis, presented a predominantly unimodal distribution, with a mean size of 26.53 pm for 1 1 ratio microcapsules and 50.29 pm for 2 1 ratio systems. On a population basis the number of aggregates is small, although some of those produced from the 2 1 core wall systems were 200-300 pm. 

Up to this point, the evidence for two particle populations has been based solely on the refractory specific activity. Additional confirmation is based on the observed particle size distribution by mass of an aerial filter sample. A portion of the aerial filter sample designated as 2 in Table I, was separated into size fractions, and the weight distribution of the fraction is shown in Figure 3. The ordinate values are simply ... 

The data, except for the 0-0.1 /x fraction, fall on a straight line. However, the value of f calculated from the intercept is larger by about a factor of 100 than the value of r calculated from the slope. On the basis of this limited trial, the fit of the data to this form of distribution function appears to be quite unsatisfactory. A correct form of distribution function should apply to the entire class of airburst populations, and additional work now underway is devoted largely to resolving the problem of determining an appropriate form of distribution function to apply to airburst particle size distributions. However, there may be no simple function which reflects adequately the over-all behavior of the particle population. Indeed, Johnson (5) was able to demonstrate that his experimental results on isotope distribution with particle size were compatible with theoretical distributions obtained by following a modified version... 

It has been assessed that bimodal particle size distributions consisting of a population of small and large particles may exhibit a better toughening effect than unimodal ones, due to a synergistic effect (Chen and Yan,... 

In precipitation, particle formation is extremely fast due to high supersaturations which in turn lead to fast nucleation. At least in the beginning, size distributions are narrow with particle sizes around one 1 nm. Nanomilling in stirred media mills is characterized by relatively slow particle formation kinetics, particle sizes ranging from several microns down to 10 nm and high sohds volume concentrations of up to 40%. Large particles may scavenge the fine fractions. The evolution of the particle size distribution can be described for both cases by population balance equations (Eq. (7)),... 

Most crystallization processes produce particles whose sizes cover a range of varying breadth. If the particles consist of single crystals, the resulting distribution is a crystal size distribution (CSD) on the other hand, if the particles consist of agglomerates or other combination of multiple crystals, the distribution is a particle size distribution. In either case, the distribution is expressed in terms of either population (number) or mass. The popu-... 

This paper outlines the basic principles and theory of sedimentation field-flow fractionation (FFF) and shows how the method is used for various particle size measurements. For context, we compare sedimentation FFF with other fractionation methods using four criteria to judge effective particle characterization. The application of sedimentation FFF to monodisperse particle samples is then described, followed by a discussion of polydisperse populations and techniques for obtaining particle size distribution curves and particle densities. We then report on preliminary work with complex colloids which have particles of different chemical composition and density. It is shown, with the help of an example, that sedimentation FFF is sufficiently versatile to unscramble complex colloids, which should eventually provide not only particle size distributions, but simultaneous particle density distributions. 

Resolution is without question a key element in accurate and detailed particle characterization. Particle populations that cannot be resolved cannot, in any sense, be distinguished from one another. While deconvolution techniques can provide particle size distribution curves from low resolution systems, the deconvolution must be based on assumptions about instrumental band broadening and band shape. In general, any detailed information lost because of poor resolution cannot be recovered by mathematical manipulation alone. In all cases, the quality of a size distribution curve will increase with the intrinsic resolution exhibited by the system. 

Figure 6 shows a comparison of the particle size distribution curves for samples 68-B and 8-A obtained by SEM, SFFF, and DCP, those methods directly yielding distribution information. For sample 68-B, based on the SEM number distribution, the sample is unimodal with a small shoulder on the large diameter side. The DCP number distribution curve shows the same characteristics. The SFFF number distribution curve appears to be broader and the small population of larger particles is not discernable. The shoulder on the smaller diameter side in the SFFF distribution appears to be an instrument artifact and occured in the distributions of several samples. 

Strawbridge, K.B., Ray, E, Hallett, F.R., Tosh, S.M., Dalgleish, D.G. 1995. Measurement of particle size distributions in milk homogenized by a microfluidizer estimation of populations of particles with radii less than 100 nm.. /. Coll. Interface Sci. 171, 392-398. 

Chapter 5 will be devoted to solid phase synthesis of ceramic powders Chapter 6, to liquid phase synfiiesis and Chapter 7, to gas phase synthesis. Other miscellaneous methods of ceramic powder synthesis are discussed in Chapter 8. All of these ceramic powder synthesis methods have one thing in common, the generation of particles with a particular particle sized distribution. To predict the particle size distribution a population balance is used. The concept of population balances on both the micro and... 

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