Particulate System

For particulate systems, the key characteristics are the surface area per unit volume (as shown in Fig. 1.2), the diameter of the particles (related to a commonly used method called Mesh size), the void volumes for a packed bed of particles and parameters to measure dry particle flowability. 

Void volume between particles. For particulate systems it is useful to know the void space, or interstitial volume, e, in particulate systems. For a loose pack of uniform spheres, e = 0.45 for a tight pack of uniform spheres, = 0.33 for fresh catalyst bed = 0.42 decreasing to 0.38 as the bed ages for uniform tower packing with sphericity of 0.4, e = 0.66. The void volume decreases as the particle distribution deviates from uniformity. For example, for a log normal distribution with a geometric standard deviation of 3, then for a tight pack of spheres = 0.18. 

For the flowability, use the Johanson indices to characterize dry particles (see also related topics conveying solids. Section 2.6, storage bins. Section 10.3, mixing. Section 7.4) These indices are  

Arching index [m], AI, = diameter of the circular exit hole from a hopper that will ensure that an arch collapses in a conical bin or circular mixer, values range 0-1.2 m. 

So far, we have studied the separation of chemical solutions including solutions of macromolecules, e.g. proteins. In macroscopic particulate systems without any Brownian forces of significance, for particles of size tp, mass mp, etc.. 

In the area of chemical engineering there is a big variety of apparatus and reactors in which a stagnant or moving dispersed phase (fluid or solid particles) is surrounded by a moving or nonmoving continuous fluid phase. In Table 3.4-1 some examples are presented. 

All these two-phase systems can be characterized by the following parameter 

nonmoving Gas Fixed beds (adsorber, dryer, reactor) 

moving Liquid Fluidized bed (crystallizer, solid-liquid extractor, reactor) 

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Particulate systems composed of identical particles are extremely rare. It is therefore usefiil to represent a polydispersion of particles as sets of successive size intervals, containing information on the number of particle, length, surface area, or mass. The entire size range, which can span up to several orders of magnitude, can be covered with a relatively small number of intervals. This data set is usually tabulated and transformed into a graphical representation. 

TABLE 20-37 Methods of Characterizing Wetting Dynamics of Particulate Systems ... 

Particulate systems require the addition of the term in order to account for the electrophoretic migration of the particle. The constant... 

Purely physical laws mainly control the behaviour of very large particles. Further down the particle size range, however, specific surface area, i.e. surface area per unit mass, increases rapidly. Chemical effects then become important, as in the nucleation and growth of crystals. Thus, a study of particulate systems within this size range of interest has become very much within the ambit of chemical engineering, physical chemistry and materials science. 

Conservation is a general concept widely used in chemical engineering systems analysis. Normally it relates to accounting for flows of heat, mass or momentum (mainly fluid flow) through control volumes within vessels and pipes. This leads to the formation of conservation equations, which, when coupled with the appropriate rate process (for heat, mass or momentum flux respectively), enables equipment (such as heat exchangers, absorbers and pipes etc.) to be sized and its performance in operation predicted. In analysing crystallization and other particulate systems, however, a further conservation equation is... 

Because the physical characteristics of the particulate solids both affect, and are affected by each unit operation, there exists an interaction between them. The study of particulate systems thus provides methods for synthesizing and evaluating economically optimum process configurations. 

Rossiter and Douglas (1986) state that the first step in process design is to generate a basic structure for the flowsheet i.e. the choice of unit operations and interconnections which can be analysed, refined and costed, and then compared to alternatives. Thus, the generation of an industrial crystallization flowsheet gives rise to a number of optimization problems for which a systematic hierarchical decision process for particulate systems was proposed ... 

Gelbard, F. and Seinfeld, J.H., 1978. Numerical solution of the dynamic equation for particulate systems. Journal of Computational Physics, 28, 357. 

Ramkrishna. D., 2000. Population balances. Theory and applications to particulate systems in engineering. New York Academic Press. 

One advantage with semiconductor particulate systems is that light-induced oxidation/reduction is very often irreversible, unlike homogeneous solutions of... 

Kamat PV, Dimitrijevic NM, Fessenden RW (1988) Photoelectrochemistry in particulate systems. 7. Electron-transfer reactions of indium sulfide semiconductor coUoids. J Phys Chem 92 2324-2329... 

Ashokkumar M (1998) An overview on semiconductor particulate systems for photoproduction of hydrogen. Int J Hydrogen Energy 23 427-438... 

Particulate systems require the addition of the term in order to... 

Polymers in Particulate Systems Properties and Applications, edited by Vincent A. Hackiey, P. Somasundaran, and Jennifer A. Lewis... 

L. Z. Benet, Theories of dissolution Multi-particulate systems, in Dissolution Technology (I. J. Leeson and J. T. Carstensen, eds.), Academy of Pharmaceutical Sciences, American Pharmaceutical Association, Washington, DC, 1974, pp. 29-57. 

A discussion of the population balance approach in modelling particulate systems and the derivation of the general equation are given in Appendix II. 

Barnea E, J Mizrahi. A generalized approach to the fluid dynamics of particulate systems, Part I. Chem Eng J 5 171-189, 1973. 

Feigner, P.L., Particulate systems and polymers for in vitro and in vivo delivery of polynucleotides, Advanced Drug Delivery Reviews, 1990, 5, 163-187. 

There are, however, important differences. For example, in detailed chemistry the source terms do not depend on the flow quantities. In contrast, all of the rate functions for particulate systems can potentially depend on the local flow quantities such as the instantaneous shear rate. 

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-... 

Hills, B.P. and Manning, C.E. 1998. NMR oxygen-17 studies of water dynamics in heterogeneous gel and particulate systems. J. Mol. Liquids 75, 61-76. 

The surfactant is an important component of this process and acts to stabilize the growing polymeric particles by surface adsorption. Phase separation and the formation of solid particles occur before or after termination of the polymerization process [42]. Polymerization can occur in some systems without the presence of surfactants [40]. Various particulate systems have been prepared by this method, including poly(styrene) [43], poly(vinylpyridine) [44, 45], poly(acrolein) [46, 47], and poly(glutaraldehyde) [48-50],... 

The main disadvantage in using poly(acrylamide) systems is that they are not biodegradable and the monomers are toxic. Extensive purification is also required to remove the organic solvents, anionic surfactants, and residual monomers. Edman et al. [74] produced biodegradable poly(acryldextran) particles by incorporating dextran into the poly(acrylamide) chain. These particulate systems were metabolized and eliminated faster, both in vivo and in vitro, than poly(acrylamide) particles. 

I. Aynie, C. Vauthier, E. Fattal, and M. Foulquier, Alginate nanoparticles as a noval carrier for antisense oligonucleotides, in Future Strategies for Drug Delivery with Particulate Systems, Stuttgart, 1997, pp. 11-16. 

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