Foam fractionation is one of the adsorptive bubble separation techniques (*adsubble techniques*). [See Lemlich (1972)]. It operates through the selective Adsorption of a portion of one or more dissolved (or perhaps finely colloidal) components of a liquid mixture at the surfaces of **Bubbles**, usually of air or nitrogen, that rise through the mixture and then overflow as foam. Adding a surface-active collector may permit the adsorption of an otherwise surface inactive colligend via *chelation, counterionic attraction*, or otherwise. [See Lemlich (1993) and Matis and Mavros (1991)].

The solid lines of Figure 1 illustrate continuous foam fractionation in the simple mode. Alternatively, the stripping mode is obtained by elevating the feed inlet. The enriching mode is obtained by returning some collapsed foam (foamate) to the top of the column as external reflux. Also, spontaneous or deliberate coalescense within the ascending foam can furnish internal reflux. Foam fractionation is analogous to fractional Distillation with entrainment of liquid. (See also Flotation.)

Equations (1) and (2) apply to the continuous simple mode taken as a single theoretical (equilibrium) stage.

A_{G} is the ratio in the foam of bubble surface to bubble volume, c_{F} is the concentration of the component in the feed, c_{w} is the concentration in the bottom product, and c_{Q} is the concentration in the top product.
,
and
are the volumetric flowrates of feed, gas, and top product, respectively. Г_{w} is the solute surface excess (which is effectively the concentration on the bubble surface) in equilibrium with c_{w}.

For stripping, enriching, or combined operation, the ascending stream at any level can be conveniently viewed as consisting of bubble surface plus entrained liquid in mutual equilibrium. Effective operating lines can then be obtained and transfer units or theoretical stages calculated [Lemlich (1972, 1993)].

Since surface capacity is limited, foam fractionation is best suited to low cF. Low superficial gas velocity favors foam drainage and hence enrichment, but limits throughput. The volumetric fraction, e, of liquid in the foam at any predetermined level can be estimated conductimetrically with semi-theoretical Equation (3) [Lemlich (1985)].

K is the electrical conductivity of the foam divided by that of the liquid. Equation (3) has been tested over the entire range of foam and dispersion; that is, for 0 ≤ ε ≤ 1. At extremely low ε, Equation (3) approaches Lemlich's limit of ε= 3K.

Bubble sizes can be roughly estimated visually, or indirectly by light scattering and transmission. From bubble sphericity to polyhedricity, 6/D_{32} ≤ A_{G} ≤ 6.6/D_{32}, where D_{32} is the Sauter mean bubble diameter. For reasonably stable homogenous foam of low ε ascending in plug flow through a column of uniform cross-section A_{C},
is roughly directly proportional to
, and also depends on liquid density, liquid viscosity, surface viscosity, and gravity. D is the bubble diameter, best averaged in some still arguable manner. (See also Optical Particle Characterisation.)

As an alternative to internal sparging, bubbles can be generated through the release of dissolved gas, or by Electrolysis, or by external Venturi action as microbubbles. Also, reactive gases, columns of nonuniform cross-section, plate columns, and individual fractionators connected countercurrently have been investigated.

Adsorption at equilibrium is governed by the classical Gibbs relationship, Eq. (4).

is the universal gas constant, T is the absolute temperature, Г_{i} is the solute surface excess of the i-th component, a_{i} is the activity of i-th component, and σ is the surface tension. Equation (4) simplifies to Equation (5) for a nonionic surfactant in pure water at concentration ci below critical micelle.

For the major surfactant in a foam, Г_{i} is roughly constant because the bubble surfaces are essentially saturated. Typical values are of the order of 3 × 10^{−9} kmol/m^{2} for a molecular weight of several hundred.

If a surfactant is the collector of a trace colligend, Г_{i} for the latter will be directly proportional to its ci at equilibrium if ci is sufficiently low. For collection via counterionic attraction, the coefficient of linearity for adsorption of a trace polyvalent *colligend* ion is generally many times that of a monovalent ion. Too much collector can decrease the separation due to the formation of *micelles* which compete for colligend.

The bursting bubbles from foam fractionation and other adsubble techniques can inject a fine aerosol into the atmosphere. This can be a consideration if toxic, pathogenic, or otherwise noxious substances are involved.

#### REFERENCES

Lemlich, R. Ed. (1972) *Absorptive Bubble Separation Techniques*, Academic Press, New York.

Lemlich, R. (1985) Semitheoretical Equation to Relate Conductivity to Volumetric Foam Density, *Ind. Eng. Chem. Process Des. Dev. 1985*, 24, 686-687.

Lemlich R. (1993) Foam Fractionation, 296-312 in *Encyclopedia of Chemical Processing and Design, Vol. 23*, J.J. McKetta and W.A. Cunningham, Eds., Marcel Dekker, New York (1985) reprinted in *Unit Operations Handbook, Vol. 1*, J.J. McKetta Ed., 523-539, Marcel Dekker, New York, 1993.

Matis, K.A. and Mavros, P. (1991) Recovery of Metals by Ion Flotation from Dilute Aqueous Solutions, *Separ: Purif. Meth. 1991*, 20, 1-418. Foam/ Froth Flotation: Part II. Removal of Particulate Matter, *ibid.*, 163-198.

#### References

- Lemlich, R. Ed. (1972)
*Absorptive Bubble Separation Techniques*, Academic Press, New York. DOI: 10.1002/cite.330450427 - Lemlich, R. (1985) Semitheoretical Equation to Relate Conductivity to Volumetric Foam Density,
*Ind. Eng. Chem. Process Des. Dev. 1985*, 24, 686-687. DOI: 10.1021/i200030a027 - Lemlich R. (1993) Foam Fractionation, 296-312 in
*Encyclopedia of Chemical Processing and Design, Vol. 23*, J.J. McKetta and W.A. Cunningham, Eds., Marcel Dekker, New York (1985) reprinted in*Unit Operations Handbook, Vol. 1*, J.J. McKetta Ed., 523-539, Marcel Dekker, New York, 1993. - Matis, K.A. and Mavros, P. (1991) Recovery of Metals by Ion Flotation from Dilute Aqueous Solutions,
*Separ: Purif. Meth. 1991*, 20, 1-418. Foam/ Froth Flotation: Part II. Removal of Particulate Matter,*ibid.*, 163-198. DOI: 10.1080/03602549108021407