Viscous interactions in Brownian coagulation
01 Aug 1970-Vol. 33, Iss: 4, pp 562-571
TL;DR: In this article, a modified colloid stability coefficient is obtained and sample calculations are performed to evaluate the influence of the viscous interactions between two spheres and demonstrate that viscous effects can produce a retardation of the coagulation rate by an additional factor of about ten for thin double layers.
Abstract: The assumption of additivity of the single particle Brownian diffusivities to describe relative diffusion during coagulation is replaced by an expression incorporating viscous interactions between two spheres. A modified colloid stability coefficient is thus obtained and sample calculations are performed to evaluate the influence of the viscous interactions. The calculations demonstrate that viscous effects can produce a retardation of the coagulation rate by an additional factor of about ten for thin double layers. The calculations also show that Hamaker constants estimated from measured coagulation rates under negligible repulsion can be greatly in error if viscous interactions are ignored. With values of the relative diffusivity presented here the extra labor required to incorporate the viscous interactions into stability calculations is small.
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TL;DR: In this paper, a review of equations from which Hamaker constants can be calculated theoretically for condensed bodies at short distances is given, and numerical examples obtained from these equations plus Hamaker constant as obtained from colloid chemistry are compared to the optical properties of condensed bodies over a frequency range from visible light to the X-ray region.
790 citations
Book•
01 Jan 1988
TL;DR: In this paper, the authors present a rigorous and fundamental analysis of the production of air pollutants and their control, including the formation of gaseous pollutants in combustion processes, and a thorough treatment of the internal combustion engine, including its principles of operation and the mechanisms of formation of pollutants therein.
Abstract: Analysis and abatement of air pollution involve a variety of technical disciplines. Formation of the most prevalent pollutants occurs during the combustion process, a tightly coupled system involving fluid flow, mass and energy transport, and chemical kinetics. Its complexity is exemplified by the fact that, in many respects, the simplest hydrocarbon combustion, the methane-oxygen flame, has been quantitatively modeled only within the last several years. Nonetheless, the development of combustion modifications aimed at minimizing the formation of the unwanted by-products of burning fuels requires an understanding of the combustion process. Fuel may be available in solid, liquid, or gaseous form; it may be mixed with the air ahead of time or only within the combustion chamber; the chamber itself may vary from the piston and cylinder arrangement in an automobile engine to a 10-story-high boiler in the largest power plant; the unwanted byproducts may remain as gases, or they may, upon cooling, form small particles.
The only effective way to control air pollution is to prevent the release of pollutants at the source. Where pollutants are generated in combustion, modifications to the combustion process itself, for example in the manner in which the fuel and air are mixed, can be quite effective in reducing their formation. Most situations, whether a combustion or an industrial process, however, require some degree of treatment of the exhaust gases before they are released to the atmosphere. Such treatment can involve intimately contacting the effluent gases with liquids or solids capable of selectively removing gaseous pollutants or, in the case of particulate pollutants, directing the effluent flow through a device in which the particles are captured on surfaces.
The study of the generation and control of air pollutants can be termed air pollution engineering and is the subject of this book. Our goal here is to present a rigorous and fundamental analysis of the production of air pollutants and their control. The book is intended for use at the senior or first-year graduate level in chemical, civil, environmental, and mechanical engineering curricula. We assume that the student has had basic first courses in thermodynamics, fluid mechanics, and heat transfer. The material treated in the book can serve as the subject of either a full-year or a one-term course, depending on the choice of topics covered.
In the first chapter we introduce the concept of air pollution engineering and summarize those species classified as air pollutants. Chapter 1 also contains four appendices that present certain basic material that will be called upon later in the book. This material includes chemical kinetics, the basic equations of heat and mass transfer, and some elementary ideas from probability and turbulence.
Chapter 2 is a basic treatment of combustion, including its chemistry and the role of mixing processes and flame structure. Building on the foundation laid in Chapter 2, we present in Chapter 3 a comprehensive analysis of the formation of gaseous pollutants in combustion. Continuing in this vein, Chapter 4 contains a thorough treatment of the internal combustion engine, including its principles of operation and the mechanisms of formation of pollutants therein. Control methods based on combustion modification are discussed in both Chapters 3 and 4.
Particulate matter (aerosols) constitutes the second major category of air pollutants when classified on the basis of physical state. Chapter 5 is devoted to an introduction to aerosols and principles of aerosol behavior, including the mechanics of particles in flowing fluids, the migration of particles in external force fields, Brownian motion of small particles, size distributions, coagulation, and formation of new particles from the vapor by homogeneous nucleation. Chapter 6 then treats the formation of particles in combustion processes.
Chapters 7 and 8 present the basic theories of the removal of particulate and gaseous pollutants, respectively, from effluent streams. We cover all the major air pollution control operations, such as gravitational and centrifugal deposition, electrostatic precipitation, filtration, wet scrubbing, gas absorption and adsorption, and chemical reaction methods. Our goal in these two chapters, above all, is to carefully derive the basic equations governing the design of the control methods. Limited attention is given to actual equipment specification, although with the material in Chapters 7 and 8 serving as a basis, one will be able to proceed to design handbooks for such specifications.
Chapters 2 through 8 treat air pollution engineering from a process-by-process point of view. Chapter 9 views the air pollution control problem for an entire region or airshed. To comply with national ambient air quality standards that prescribe, on the basis of health effects, the maximum atmospheric concentration level to be attained in a region, it is necessary for the relevant governmental authority to specify the degree to which the emissions from each of the sources in the region must be controlled. Thus it is generally necessary to choose among many alternatives that may lead to the same total quantity of emission over the region. Chapter 9 establishes a framework by which an optimal air pollution control plan for an airshed may be determined. In short, we seek the least-cost combination of abatement measures that meets the necessary constraint that the total emissions not exceed those required to meet an ambient air quality standard.
Once pollutants are released into the atmosphere, they are acted on by a variety of chemical and physical phenomena. The atmospheric chemistry and physics of air pollution is indeed a rich arena, encompassing the disciplines of chemistry, meteorology, fluid mechanics, and aerosol science. As noted above, the subject matter of the present book ends at the stack (or the tailpipe); those readers desiring a treatment of the atmospheric behavior of air pollutants are referred to J. H. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution (Wiley-Interscience, New York, 1986).
We wish to gratefully acknowledge David Huang, Carol Jones, Sonya Kreidenweis, Ranajit Sahu, and Ken Wolfenbarger for their assistance with calculations in the book.
Finally, to Christina Conti, our secretary and copy editor, who, more than anyone else, kept safe the beauty and precision of language as an effective means of communication, we owe an enormous debt of gratitude. She nurtured this book as her own; through those times when the task seemed unending, she was always there to make the road a little smoother.
R. C. Flagan
J. H. Seinfeld
749 citations
TL;DR: In this article, the stability of colloidal, iron monosulfide suspensions with ionic strengths typical of marine and lacustrine waters was evaluated using DLVO theory and a term was included to account for the ferrimagnetic properties of greigite.
639 citations
TL;DR: This review is a survey of studies on protein‐stabilized foams and emulsions in relatively simple, well‐defined systems (rather than in food products per se) and the extent of basic understanding developed, particularly in terms of the physicochemical properties involved.
Abstract: This review is a survey of studies on protein-stabilized foams and emulsions in relatively simple, well-defined systems (rather than in food products per se). The emphasis is on the extent of basic understanding developed, particularly in terms of the physicochemical properties involved. The stability of the system, its formation, and its rheology are covered. Unfortunately, much work is of limited fundamental value because of poorly designed experimental approaches and the failure to measure key parameters. Reasonable generalization can be made concerning the effects of a number of variables, particularly protein solubility, pH, protein structure and the presence of small molecule surfactants. However, several possible explanations of these effects in terms of surface properties remain tenable. A number of observations can fairly confidently be ascribed to the influence of rheology on flow processes within foams and emulsions.
484 citations
TL;DR: In this article, the authors studied the kinetics of coagulation of monodisperse spherical colloids in aqueous suspension at the early stage of pre-coagulation using a fiber-optics-based detection system.
Abstract: In this work we study the kinetics of coagulation of monodisperse spherical colloids in aqueous suspension at the early stage of coagulation. We have performed the measurements on a multiangle static and dynamic light scattering instrument using a fiber-optics-based detection system which permits simultaneous time-resolved measurements at different angles. The absolute coagulation rate constants are determined from the change of the scattering light intensity as well as from the increase of the hydrodynamic radius at different angles. The combined evaluation of static and dynamic light scattering results permits the determination of coagulation rate constants without the explicit use of light scattering form factors for the aggregates. For different electrolytes fast coagulation rate constants were estimated. Stability curves were measured as a function of ionic strength using different particle concentrations.
424 citations
References
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Book•
01 Jan 1965
TL;DR: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, and a host of other disciplines.
Abstract: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, flow through porous media, colloid science, aerosol and hydrosal technology, lubrication theory, blood flow, Brownian motion, geophysics, meteorology, and a host of other disciplines. This text provides a comprehensive and detailed account of the physical and mathematical principles underlying such phenomena, heretofore available only in the original literature.
4,648 citations
TL;DR: Theory of the Stability of Lyophobic Colloids The Interaction of Sol Particles having an Electric Double Layer and the nature of the electrical double layer which exists around them in salt solutions is discovered.
Abstract: MANY of the classical investigations of colloidal chemistry were concerned with the stability of colloidal solutions of insoluble substances, such as gold, arsenic sulphide, silver halides, etc. The well-known phenomenon of coagulation of these sols by comparatively small concentrations of electrolytes suggested that their stability was connected with their electric charges. A considerable amount of research has been made in the past to discover the magnitude and origin of the electric charge on the particles and the nature of the electrical double layer which exists around them in salt solutions. Although qualitative and semi-quantitative explanations have been given of the phenomenon of coagulation and of the rule of Hardy and Schulze, according to which the ionic concentration required for precipitation diminishes rapidly with the charge of the effective ion, yet a complete and satisfactory theory was still lacking. Theory of the Stability of Lyophobic Colloids The Interaction of Sol Particles having an Electric Double Layer. By E. J. W. Verwey and J. Th. G. Overbeek., with the collaboration of K. van Nes. Pp. xi + 205. (New York and Amsterdam : Elsevier Publishing Co., Inc. ; London : Cleaver-Hume Press, Ltd., 1948.) 22s. 6d. net.
3,099 citations
TL;DR: In this article, anwendung der Smoluchowskischen Koagulationstheorie zu aufgeladenen Aerosolen fuhrt zu dem Schlus, das die unipolare Aufladung stark Koagulationshemmend, die bipolare in viel kleinerem Mase koagulationsbeschleunigend wirken mus.
Abstract: Die Anwendung der Smoluchowskischen Koagulationstheorie zu aufgeladenen Aerosolen fuhrt zu dem Schlus, das die unipolare Aufladung stark koagulationshemmend, die bipolare in viel kleinerem Mase koagulationsbeschleunigend wirken mus. Wahlt man aber die Abnahmegeschwindigkeit der Teilchenkonzentration als Kriterium fur die Stabilitat eines Aerosols, so wird die letztere infolge der elektrischen Zerstreuung der Teilchen durch die unipolare Aufladung unbedingt herabgesetzt.
459 citations
TL;DR: In this paper, a liquid drop (phase 1) falling through a lighter liquid (phase 2) onto a Phase 1/Phase 2 interface rests at the interface for a time τ before coalescing with the underlying phase.
314 citations