2 5 10 20 40 60 80 90 95 98 99.5 99.9 Cumulative mass % less than Dp

FIG. 14-91 Particle-size distribution and mist loading from absorption tower in a contact H2SO4 plant. [Gillespie and Johnstone, Chem. Eng. Prog., 51(2), 74 (1955).}

Review of foam rheology is given by Herzhaft [Oil & Gas Sci. & Technol 54, 587 (1999)] and Heller and Kuntamukkula [Ind. Eng. Chem. Res., 26, 318 (1987)]. The influence of surface-active agents on bubbles and foams is summarized in selected passages from Schwartz and Perry, Surface AcUve Agents, vol. 1, Interscience, New York, 1949; and from Schwartz, Perry, and Berch, Surface Active Agents and Detergents, vol. 2, Interscience, New York, 1958. See also Elenkov, Theor. Found Chem. Eng., 1, 1, 117 (1967); and Rubel, Antifoaming and Defoaming Agents, Noyes Data Corp., Park Ridge, NJ, 1972.

A review of foam stability also is given by de Vries, Meded, Rubber Sticht. Delft. No. 328, 1957. Foam-separation methodology is discussed by Aguoyo and Lemlich, Ind. Eng. Chem. Process Des. Dev., 13, 153 (1974); and Lemlich, Ind. Eng Chem., 60, 16 (1968). The following reviews of specific applications of gas-to-liquid dispersions are recommended: Industrial fermentations Aiba, Humphrey, and Millis, Biochemical Engineering, Academic, New York, 1965. Finn, Bacteriol. Rev., 18, 254 (1954). Oldshue, "Fermentation Mixing Scale-Up Techniques," in Biotechnology and Bioengineering, vol. 8, 1966, pp. 3-24. Aerobic oxidation of wastes: Eckenfelder and McCabe, Advances in Biological Waste Treatment, Macmillan, New York, 1963. Eckenfelder and O'Connor, Biological Waste Treatment, Pergamon, New York, 1961. McCabe and Eckenfelder, Biological Treatment oof Sewage and Industrial Wastes, vol. 1, Reinhold, New York, 1955. Proceedings of Industrial Waste Treatment Conference, Purdue University, annually. Zlokarnik, Adv. Biochem. Eng., 11, 158-180 (1979). Cellular elastomers: Fling, Natural Rubber Latex and Its Applications: The Preparation of Latex Foam Products, British Rubber Development Board, London, 1954. Gould, in Symposium on Application oof Synthetic Rubbers, American Society for Testing and Materials, Philadelphia, 1944, pp. 90-103. Firefighting foams: Perri, in Bikerman, op. cit., Chap. 12. Ratzer, Ind. Eng. Chem., 48, 2013 (1956). Froth-flotation methods and equipment: Booth, in Bikerman, op. cit., Chap. 13. Gaudin, Flotation, McGraw-Hill, New York, 1957. Taggart, Handbook oof Mineral Dressing, Wiley, New York, 1945, Sec. 12, pp. 52-81. Tatterson, Fluid Mixing and Gas Dispersion in Agitated Tanks, McGraw-Hill, New York, 1991.

Objectives of Gas Dispersion The dispersion of gas as bubbles in a liquid or in a plastic mass is effected for one of the following purposes: (1) gas-liquid contacting (to promote absorption or stripping, with or without chemical reaction), (2) agitation of the liquid phase, or

(3) foam or froth production. Gas-in-liquid dispersions also may be produced or encountered inadvertently, sometimes undesirably.

Gas-Liquid Contacting Usually this is accomplished with conventional columns or with spray absorbers (see preceding subsection "Liquid-in-Gas Dispersions"). For systems containing solids or tar likely to plug columns, absorptions accomplished by strongly exothermic reactions, or treatments involving a readily soluble gas or a condensable vapor, however, bubble columns or agitated vessels may be used to advantage.

Agitation Agitation by a stream of gas bubbles (often air) rising through a liquid is often employed when the extra expense of mechanical agitation is not justified. Gas spargers may be used for simple blending operations involving a liquid of low volatility or for applications where agitator shaft sealing is difficult.

Foam Production This is important in froth-flotation separations; in the manufacture of cellular elastomers, plastics, and glass; and in certain special applications (e.g., food products, fire extinguishers). Unwanted foam can occur in process columns, in agitated vessels, and in reactors in which a gaseous product is formed; it must be avoided, destroyed, or controlled. Berkman and Egloff (Emulsions and Foams, Reinhold, New York, 1941, pp. 112-152) have mentioned that foam is produced only in systems possessing the proper combination of interfacial tension, viscosity, volatility, and concentration of solute or suspended solids. From the standpoint of gas comminution, foam production requires the creation of small bubbles in a liquid capable of sustaining foam.

Theory of Bubble and Foam Formation A bubble is a globule of gas or vapor surrounded by a mass or thin film of liquid. By extension, globular voids in a solid are sometimes called bubbles. Foam is a group of bubbles separated from one another by thin films, the aggregation having a finite static life. Although nontechnical dictionaries do not distinguish between foam and froth, a technical distinction is often made. A highly concentrated dispersion of bubbles in a liquid is considered a froth even if its static life is substantially nil (i.e., it must be dynamically maintained). Thus, all foams are also froths, whereas the reverse is not true. The term lather implies a froth that is worked up on a solid surface by mechanical agitation; it is seldom used in technical discussions. The thin walls of bubbles comprising a foam are called laminae or lamellae.

Bubbles in a liquid originate from one of three general sources: (1) They may be formed by desupersaturation of a solution of the gas or by the decomposition of a component in the liquid; (2) They may be introduced directly into the liquid by a bubbler or sparger or by mechanical entrainment; and (3) They may result from the disintegration of larger bubbles already in the liquid.

Generation Spontaneous generation of gas bubbles within a homogeneous liquid is theoretically impossible (Bikerman, Foams: Theory and Industrial Applications, Reinhold, New York, 1953, p. 10). The appearance of a bubble requires a gas nucleus as a void in the liquid. The nucleus may be in the form of a small bubble or of a solid carrying adsorbed gas, examples of the latter being dust particles, boiling chips, and a solid wall. A void can result from cavitation, mechanically or acoustically induced. Basu, Warrier, and Dhir [J. Heat Transfer, 124, 717 (2002)] have reviewed boiling nucleation, and Blander and Katz [AlChE J., 21, 833 (1975)] have thoroughly reviewed bubble nucleation in liquids.

Theory permits the approximation of the maximum size of a bubble that can adhere to a submerged horizontal surface if the contact angle between bubble and solid (angle formed by solid-liquid and liquid-gas interfaces) is known [Wark, J. Phys. Chem., 37, 623 (1933); Jakob, Mech. Eng., 58, 643 (1936)]. Because the bubbles that actually rise from a surface are always considerably smaller than those so calculated and inasmuch as the contact angle is seldom known, the theory is not directly useful.

Formation at a Single Orifice The formation of bubbles at an orifice or capillary immersed in a liquid has been the subject of much study, both experimental and theoretical. Kulkarni and Joshi [lnd. Eng. Chem. Res., 44, 5873 (2005)] have reviewed bubble formation and rise. Bikerman (op. cit., Secs. 3 to 7), Valentin (op. cit., Chap. 2), Jackson (op. cit.), Soo (op. cit., Chap. 3), Fair (op. cit.), Kumer et al. (op. cit.), Clift et al. (op. cit.) and Wilkinson and Van Dierendonck

[Chem. Eng. Sci., 49,1429 (1994)] have presented reviews and analyses of this subject.

There are three regimes of bubble production (Silberman in Proceedings of the Fifth Midwestern Conference on Fluid Mechanics, Univ. of Michigan Press, Ann Arbor, 1957, pp. 263-284): (1) single-bubble, (2) intermediate, and (3) jet.

Single-Bubble Regime Bubbles are produced one at a time, their size being determined primarily by the orifice diameter do, the interfacial tension of the gas-liquid film C, the densities of the liquid pL and gas pG, and the gravitational acceleration g according to the relation db/do = [6c/gd02(pL - pc)]1

where db is the bubble diameter.

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