Dispersed phase systems

A.S. Kabalnov, A.V. Pertsov and E.D. Shchukin Ostwald Ripening in Two-Component Disperse Phase Systems Application to Emulsion Stability. Colloid Surfaces 24, 19 (1987). 

In principle, interaction in dispersed phase systems may occur in two ways. 

Experiments to measure the interaction rate in a dispersed phase system have been carried out by Madden and Damerell (M2), Miller et al. (M4),... 

A review article by Qiu et al. [212] and references herein [217-226] covers NMCRP in miniemulsions up to 2001. Cunningham wrote a related review in 2002, also covering controlled radical polymerization in dispersed phase systems [227]. Here, the main results reported in the Qiu review will be summarized, and new developments in the field since then will be reviewed. 

Spielman, L. A., and Levenspiel, O., A Monte-Carlo treatment for reacting and coalescing dispersed phase systems. Chem. Eng. Sci. 20, 247 (1965). 

Groothuis and Zuiderweg (GIO) measured coalescence frequencies for continuous-flow dispersed-phase systems by introducing two streams of dispersed phase feed with different densities such that if a drop of one stream coalesces with a drop of the other stream, the new drop will be heavier than the continuous phase. Coalescence frequencies were then estimated by measuring the change in dispersed-phase fraction heavier than water as it passes through the vessel. 

Analysis of Drop Breakage and Coalescence in Dispersed Phase Systems... 

It is evident from these discussions that population balance equations are important in the description of dispersed-phase systems. However, they are still of limited use because of difficulties in obtaining solutions. In addition to the numerical approaches, solution of the scalar problem has been via the generation of moment equations directly from the population balance equation (H2, H17, R6, S23, S24). This approach has limitations. Ramkrishna and co-workers (H2, R2, R6) presented solutions of the population balance equation using the method of weighted residuals. Trial functions used were problem-specific polynomials generated by the Gram-Schmidt orthogonalization process. Their approach shows promise for future applications. 

For Rushton turbines, Chen and Middleman found C2 = 0.053 (Fig. 8) for a broad range of liquid-liquid pairs. Eqs. (1) and (3) show that, at equilibrium, dispersed phase systems created by turbulent flow scale-up by maintaining constant Smax or for practical industrial purposes, by constant Savg. which is equivalent to constant P/Vl- Large Weber numbers result in small drops and vice versa. These expressions are valid for dilute, noncoalescing systems of low pd. at equilibrium. Many stabilized or noncoalescing industrial systems with 0 > 0.05 can also be scaled by the constant P/Vl criterion. 

Valentas KJ, Bilous O, Amundson NR (1966) Analysis of Breakage in Dispersed Phase Systems. I EC Fundamentals 5(2) 271-279... 

Many disperse-phase systems involve collisions between particles, and the archetypical example is hard-sphere collisions. Thus, Chapter 6 is devoted to the topic of hard-sphere collision models in the context of QBMM. In particular, because the moment-transport equations for a GBPE with hard-sphere collisions contain a source term for the rate of change of the NDF during a collision, it is necessary to derive analytical expressions for these source terms (Fox Vedula, 2010). In Chapter 6, the exact source terms are derived... 

Valentas, K. J., Bilous, O. Amundson, N. R. 1966 Analysis of breakage in dispersed phase systems. Industrial and Engineering Chemistry Eundamentals 5, 271-279. 

For any process, the lack of accurate process measurements limits the successful implementation of model identification and control. Crystallizers are dispersed-phase systems, and the shortcomings of on-line measurement techniques for these types of systems are particularly evident. 

The associative mechanism of thickening has been variously described, but is generally thought to result from nonspecific hydrophobic association of water-insoluble groups in water-soluble polymers 34, 35). For associative ASTs, the terminal hydrophobes of the ethoxylated side chains are considered to be the primary interactive components. These hydrophobes can interact with each other via intermolecular association, and can also interact with hydrophobic particle surfaces when present. The specific interaction with dispersed-phase components such as latex particles has been shown to be one of surface adsorption (36). In essence, the associative component of thickening in dispersed-phase systems also has dual character resulting from the building of structure within the aqueous phase and interaction with particle surfaces. 

The overall mass transfer coefficient of QX was obtained by plotting the term on the left-hand side of Eq, (56) versus time, Yang et al, [124] developed a mathematical model concerning mass transfer in a single droplet to describe the dispersed phase system. They measured the distribution coefficient and the mass transfer coefficient of a PT catalytic intermediate between two phases. 

Unique also is the extensive analysis of dispersed phase systems, whether these are gas bubbles in liquids, sprays, a liquid-liquid dispersion or a liquid-solid system. Characteristics of different contactors for such systems are summarized in Tables 1.1 to 1.3 and Figs. 1.1 and 1.2. 

Kabalnov, A. S., Pertzov, A. V., and Shchukin, E. D., Ostwald ripening in two-component disperse phase systems application to emulsion stability. Colloid Surf., 24, 19-32 (1987). 

Garner, F.H. and M. Tayeban, "The Importance of the Wake in Mass Transfer from both Continuous and Dispersed Phase Systems" Anal. 

Engineers encounter particles in an innumerable variety of systems. The particles are either naturally present in these systems or engineered into them. In either case, the particles often significantly affect the behavior of such systems. In many other situations, systems are associated with processes in which particles are formed either as the main product or as a by-product. We will refer to systems containing particles as dispersed phase systems or particulate systems regardless of the precise role of the particles in them. 

Among engineers, population balance concepts are of importance to aeronautical, chemical, civil (environmental), mechanical, and materials engineers. Chemical engineers have put population balances to the most diverse use. Applications have covered a wide range of dispersed phase systems, such as solid-liquid dispersions (although with incidental emphasis on crystallization systems), and gas-liquid, gas-solid, and liquid-liquid dispersions. Analyses of separation equipment such as for liquid-liquid extraction, or solid-liquid leaching and reactor equipment, such as bioreactors (microbial processes) fluidized bed reactors (catalytic reactions), and dispersed phase reactors (transfer across interface and reaction) all involve population balances. 

The number density function, along with the environmental phase variables, completely determines the evolution of all properties of the dispersed phase system. The population balance framework is thus an indispensable tool for dealing with dispersed phase systems. This book seeks to address the various aspects of the methodology of population balance necessary for its successful application. Thus Chapter 2 develops the mathematical framework leading to the population balance equation. It... 

It appears that Valentas and Amundson (1966) were the first to consider a population balance analysis of breakage and coalescence processes in dispersed phase systems in the chemical engineering literature. While at the University of Minnesota, the author recalls, in particular, Oleg Bilous significant contribution to the foregoing effort at the initial stages, although he became uninvolved in subsequent development of the work. 

The foregoing example is interesting because it shows population balance models can account for the occurrence of physicochemical processes in dispersed phase systems simultaneously with the dispersion process itself. Shah and Ramkrishna (1973) also show how the predicted mass transfer rates vary significantly from those obtained by neglecting the dynamics of drop breakage. The model s deficiencies (such as equal binary breakage) are deliberate simplifications because its purpose had been to demonstrate the importance of the dynamics of dispersion processes in the calculation of mass transfer rates rather than to be precise about the details of drop breakup. 

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