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14-100 EQUIPMENT FOR DISTILLATION, GAS ABSORPTION, PHASE DISPERSION, AND PHASE SEPARATION
(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 [AIChE 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 [Ind.
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) singlebubble,
(2) intermediate, and (3) jet.
Single-Bubble Regime Bubbles are produced one at a time,
their size being determined primarily by the orifice diameter d o, the
interfacial tension of the gas-liquid film σ, the densities of the liquid
ρ L and gas ρ G, and the gravitational acceleration g according to the
relation
where d b is the bubble diameter.
d b /d o = [6σ/gd o 2 (ρL −ρ C)] 1/3 (14-206)
f = Q/(πd b 3 /6) = Qg(ρL −ρC)/(πdoσ) (14-207)
where f is the frequency of bubble formation and Q is the volumetric
rate of gas flow in consistent units.
Equations (14-206) and (14-207) result from a balance of bubble
buoyancy against interfacial tension. They include no inertia or viscosity
effects. At low bubbling rates (