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STATISTICAL TREATMENT OF PARTICLE PROCESSES A preview o f the Symposium on Characterization o f
Dispersed Systems in Chemical Engineering, sponsored @ the Division of Industrial and Engineering Chemistry of the ACS, to be held at the Massachusetts Institute o f Technology, December 7 7- 72, 7967
articulate materials have always been an important P form of matter in many technologies. Powders, dispersions and emulsions, aerosols, sprays, microbial cultures and large molecules have long had wide application and have consequently received a great deal of study. I n the past there has been, in general, a unit operations compartmentalization of work in such fields as sieving, comminution, crystallization, fluidized reacting beds, mixing, dispersion coalescence, agglomeration, polymerization, and biological cultures. A common denominator has been the statistical description of distributed properties of such systems. It is only relatively recently that efforts have been made to understand and describe the statistical processes involved in the origin of distributed properties of particulate systems. These efforts have, to a large extent, grown simultaneously, but independently, in a variety of disciplines. A scrutiny of these parallel developments reveals that, just as statistical descriptions of properties were common to all disciplines, now statistical descriptions of processes have a common denominator-the multidimensional population balance. It is the purpose of this symposium to bring together workers in a variety of fields who have been using the concepts of population balances in their work in the hope that the resulting cross-fertilization of ideas will lead to
better descriptive, analytical, and experimental tools for future work. One cannot hope to cover completely the full variety of present, much less the possible, applications in a single meeting, but an effort has been made to include representative work from a number of areas. This symposium is offering 18 papers which consist of both reviews and recent studies of: the mathematical foundations for describing particle processes, biological systems, polymers, crystallization, comminution, dispersions, porous media, and fluidized systems. Mathematical Foundations
Throughout this symposium it may be expected that the manipulation of mathematical statements of population balances, and the kinetic terms involved, will be a recurring theme. The general formulation of these “Liouville” equations and some methods of solution will be presented by H. M. Hulburt and T. Akiyama of Northwestern University. I n most cases, these equations are written for presumably large populations of particles. S. Katz and R. Shinnar, City University of New York, will, however, consider the relationship between large and small population descriptions, using Markov-process methods with applications to emulsion polymerization and mineral flotation. Free-radical VOL. 5 9
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polymerization will itself be the subject of a paper by
W. W. Graessley of Northwestern University who will give consideration to the kinetic terms of polymer growth and, especially, to the effects of mixture viscosity in radical termination and related reactions. Microorganisms and Crystals
I t is the power of population balance methods that they apply to “particles” as diverse as bubbles, molecules, and microorganisms. I n the latter area, A. G. Fredrickson, D. Ramkrishna, and H. M. Tsuchiya, University of Minnesota, will demonstrate the use of a multidimensional, or vector, description of the physiological state and the state evolution of cells in biological cultures of bacteria and blue-green algae, which includes the effects of the cellular environment. Crystallization is another process in which particle environment plays a direct role in the evolution of the population. M. A. Larson, Iowa State University, will discuss the work, based on population balances, that has been done in crystallization dynamics and will show how these methods yield an increased understanding of nucleation, growth kinetics, crystallizer stability, and crystal product characteristics. Comminution
Workers in comminution have had considerable success both in analyzing the mechanisms of the grinding process in population terms, and in applying this new understanding to practice. L. G. Austin, North Carolina State University, will review this research area and discuss both the computational and experimental techniques that have been used, while W. J. Whiten and J. A. Lynch, University of Queensland, will show the application of the basic methods to transient comminution in batch and continuous mills, including effects of differential particle movement, mill partitions, and degree of mixing. The subject of comminution will be further elaborated upon by T. S. Mika and D. W. Fuerstenau, who will proceed from a linear model of the breakage process, include particle transport characteristics and material volume changes along a continuous mill to arrive at a model of grinding mills, showing the effects of certain variables. These three papers w7ill complement one another closely but will offer different viewpoints and emphasis on comminution. liquid Dispersions
The largest single category of papers is in the subject of liquid-liquid dispersions, which seem particularly amenable-probably deceptively so-to the analysis of mechanisms and the construction of models. L. Padmanabhan and B. Gal-Or will discuss a generalized cell model for energy and mass transfer in dispersions which have both size and residence time distributions. Experimental work with dispersions will be represented by a paper by J. B. Wijffels and K. Rietema, Technische Hogeschool Eindhoven, on axial dispersion in liquidliquid fluidized systems, in which population classification occurs by drop size, and by a paper of M.M.Young, 54
INDUSTRIAL A N D ENGINEERING CHEMISTRY
University of Waterloo, in which an idealized homogeneous interaction model is used to interpret extended measurements of the rate of dispersed phase coalescence and mass transfer rates. A more complete description of dispersion dynamics requires a knowledge of the distributed-Le., statisticaldrop coalescence and breakage mechanisms. A model for the evolution of drop-size distributions due solely to coalescence during settling, or in a velocity gradient, will be the subject of W. E. Ranz, University of Minnesota. An analytic multivariate model for the general process, including mass transfer, will be presented by C. A. Bayens and R. L. Laurence of Johns Hopkins University with applications to steady-state continuous flow systems with one position variable, and to homogeneous batch reactors. There are many alternative ways of writing the drop, or dispersed phase, population balances, and a variety of these will be considered, with reference to their simplicity and usefulness, by F. H. Verhoff and R. L. Curl of the University of Michigan. Here, a single “mixing” kernel is defined and ways of measuring it are discussed. Reactions and transfer in dispersions represent a class of coupled processes. Another interesting class is twoparticle-type dispersions. The example to be discussed by K. Rietema joins liquid-liquid dispersions and yeastcell populations into a process in which yeast cells adhere to oil drops and consume an alkane dissolved therein. His model couples the yeast population dynamics with the evolution of the alkane concentration distribution among the drops. Particulate Systems
Three papers have been included in this symposium which make less direct use of distributed particle population balances, but which nevertheless concern statistical properties, or processes, in particulate systems. R. C. Hall, Kansas State Vniversity, will describe a probabilistic model for particulate holdup in an N-stage process when the forward and backward split of flow, between stages, is controlled. The application is to such items as horizontal rotary drum driers and kilns. An interesting “particulate” system-porous media-may eventually be amenable to direct statistical analysis of formation, structure, and properties. Structure studies in a porous medium is the subject of a paper by F. A. L. Dullien of The University of Waterloo. Finally, a generalization of previous work on the effects of distributed population characteristics on the light transmission through a coarse dispersion will be given by R. L. Curl of the University of Michigan. This has been a short summary of the topics to be discussed a t the symposium. We hope that this will be a tantalizing glimpse into present-day applications of a viewpoint for modeling processes involving particulate systems and expect that the symposium itself will be extremely fertile for further studies.
R. L . Cull is Associate Professor of Chemical and Metallurgical Engineering at the University of Michigan. He is Program Chairman of the symposium previewed here. AUTHOR
