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14-102 EQUIPMENT FOR DISTILLATION, GAS ABSORPTION, PHASE DISPERSION, AND PHASE SEPARATION
surface of a porous plate was such as to maintain constancy of the
product of bubble specific surface and interfacial tension as the latter
was varied by addition of a surfactant. Konig et al. [Ger. Chem. Eng.,
1, 199 (1978)] produced bubble sizes varying from 0.5 to 4 mm by the
use of two porous-plate spargers and one perforated-plate sparger
with superficial gas velocities from 1 to 8 cm/s. The small bubble sizes
were stabilized by adding up to 0.5 percent of various alcohols to
water.
At high-flow rates through perforated plates such as those that
occur in distillation columns, Calderbank and Rennie [Trans. Instn.
Chem. Engrs., 40, T3 (1962)]; Porter et al. [ibid., 45, T265 (1967)];
Rennie and Evans [Br. Chem. Eng, 7, 498 (1962)]; and Valentin (op.
cit., Chap. 3) have investigated and discussed the effect of the flow
conditions through the multiple orifices on the froths and foams that
occur above perforated plates.
Entrainment and Mechanical Disintegration Gas can be
entrained into a liquid by a solid or a stream of liquid falling from the
gas phase into the liquid, by surface ripples or waves, and by the vertical
swirl of a mass of agitated liquid about the axis of a rotating agitator.
Small bubbles probably form near the surface of the liquid and are
caught into the path of turbulent eddies, whose velocity exceeds the
terminal velocity of the bubbles. The disintegration of a submerged
mass of gas takes place by the turbulent tearing of smaller bubbles
away from the exterior of the larger mass or by the influence of surface
tension on the mass when it is attenuated by inertial or shear forces
into a cylindrical or disk form. A fluid cylinder that is greater in length
than in circumference is unstable and tends to break spontaneously
into two or more spheres. These effects account for the action of fluid
attrition and of an agitator in the disintegration of suspended gas.
Quantitative correlations for gas entrainment by liquid jets and in agitated
vessels will be given later.
Foams Two excellent reviews (Shedlovsky, op. cit.; Lemlich, op.
cit.; Herzhaft, op. cit.; and Heller et al., op. cit) covering the literature
pertinent to foams have been published. A foam is formed when bubbles
rise to the surface of a liquid and persist for a while without coalescence
with one another or without rupture into the vapor space.
The formation of foam, then, consists simply of the formation, rise,
and aggregation of bubbles in a liquid in which foam can exist. The life
of foams varies over many magnitudes—from seconds to years—but
in general is finite. Maintenance of a foam, therefore, is a dynamic
phenomenon.
Gravitational force favors the separation of gas from liquid in a disperse
system, causing the bubbles to rise to the liquid surface and the
liquid contained in the bubble walls to drain downward to the main
body of the liquid. Interfacial tension favors the coalescence and ultimate
disappearance of bubbles; indeed, it is the cause of bubble
destruction upon the rupture of the laminae.
The viscosity of the liquid in a film opposes the drainage of the film
and its displacement by the approach of coalescing bubbles. The
higher the viscosity, the slower will be the film-thinning process; furthermore,
if viscosity increases as the film grows thinner, the process
becomes self-retarding. The viscosity of films appears to be greater
than that of the main body of the parent liquid in many cases. Sometimes
this is a simple temperature effect, the film being cooler
because of evaporation; sometimes it is a concentration effect, with
dissolved or fine suspended solids migrating to the interface and producing
classical or anomalous increases in viscosity; at yet other times,
the effect seems to occur without explanation.
If the liquid laminae of a foam system can be converted to impermeable
solid membranes, the film viscosity can be regarded as having
become infinite, and the resulting solid foam will be permanent.
Likewise, if the laminae are composed of a gingham plastic or a
thixotrope, the foam will be permanently stable for bubbles whose
buoyancy does not permit exceeding the yield stress. For other nonnewtonian
fluids, however, and for all newtonian ones, no matter
how viscous, the viscosity can only delay but never prevent foam
disappearance. The popular theory, held since the days of Plateau,
that foam life is proportional to surface viscosity and inversely proportional
to interfacial tension, is not correct, according to Bikerman
(op. cit., p. 161), who points out that it is contradicted by
experiment.
The idea that foam films drain to a critical thickness at which they
spontaneously burst is also rejected by Bikerman. Foam stability, rather,
is keyed to the existence of a surface skin of low interfacial tension
immediately overlying a solution bulk of higher tension, latent until it is
exposed by rupture of the superficial layer [Maragoni, Nuovo Cimento,
2 (5–6), 239 (1871)]. Such a phenomenon of surface elasticity, resulting
from concentration differences between bulk and surface of the liquid,
accounts for the ability of bubbles to be penetrated by missiles without
damage. It is conceivable that films below a certain thickness no longer
carry any bulk of solution and hence have no capacity to close surface
ruptures, thus becoming vulnerable to mechanical damage that will
destroy them. The Maragoni phenomenon is consistent also with the
observation that neither pure liquids nor saturated solutions will sustain
a foam, since neither extreme will allow the necessary differences in
concentration between surface and bulk of solution.
The specific ability of certain finely divided, insoluble solids to stabilize
foam has long been known [Berkman and Egloff, op. cit., p. 133;
and Bikerman, op. cit., Chap. 11]. Bartsch [Kolloidchem. Beih, 20, 1
(1925)] found that the presence of fine galena greatly extended the
life of air foam in aqueous isoamyl alcohol, and the finer the solids, the
greater the stability. Particles on the order of 50 µm length extended
the life from 17 seconds to several hours. This behavior is consistent
with theory, which indicates that a solid particle of medium contact
angle with the liquid will prevent the coalescence of two bubbles with
which it is in simultaneous contact. Quantitative observations of this
phenomenon are scanty.
Berkman and Egloff explain that some additives increase the flexibility
or toughness of bubble walls, rather than their viscosity, to render
them more durable. They cite as illustrations the addition of small
quantities of soap to saponin solutions or of glycerin to soap solution
to yield much more stable foam. The increased stability with ionic
additives is probably due to electrostatic repulsion between charged,
nearly parallel surfaces of the liquid film, which acts to retard draining
and hence rupture.
Characteristics of Dispersion
Properties of Component Phases As discussed in the preceding
subsection, dispersions of gases in liquids are affected by the viscosity
of the liquid, the density of the liquid and of the gas, and the interfacial
tension between the two phases. They also may be affected directly by
the composition of the liquid phase. Both the formation of bubbles and
their behavior during their lifetime are influenced by these quantities
as well as by the mechanical aspects of their environment.
Viscosity and density of the component phases can be measured
with confidence by conventional methods, as can the interfacial
tension between a pure liquid and a gas. The interfacial tension of a
system involving a solution or micellar dispersion becomes less satisfactory,
because the interfacial free energy depends on the concentration
of solute at the interface. Dynamic methods and even
some of the so-called static methods involve the creation of new
surfaces. Since the establishment of equilibrium between this surface
and the solute in the body of the solution requires a finite
amount of time, the value measured will be in error if the measurement
is made more rapidly than the solute can diffuse to the fresh
surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d
national meeting, Repr. 30, Atlanta, 1960) found that measurements
of the surface tension of sodium lauryl sulfate solutions by
maximum bubble pressure were higher than those by DuNuoy tensiometer
by 40 to 90 percent, the larger factor corresponding to a
concentration of about 100 ppm, and the smaller to a concentration
of 2500 ppm of sulfate.
Even if the interfacial tension is measured accurately, there may be
doubt about its applicability to the surface of bubbles being rapidly
formed in a solution of a surface-active agent, for the bubble surface may
not have time to become equilibrated with the solution. Coppock and
Meiklejohn [Trans. Instn. Chem. Engrs., 29, 75 (1951)] reported that
bubbles formed in the single-bubble regime at an orifice in a solution of
a commercial detergent had a diameter larger than that calculated in
terms of the measured surface tension of the solution [Eq. (14-206)].
The disparity is probably a reflection of unequilibrated bubble laminae.