A B C D E F
1/f FLUCTUATIONS IN BOILING CRISIS F-FACTOR METHOD FACHINFORMATIONSZENTRUM KARLSRUHE, FIZ FACILITIES WITH A MOVING PISTON FAHRENHEIT TEMPERATURE SCALE FALKNER-SKAN EQUATION FALLING DROPLET EFFECT FALLING FILM EVAPORATORS Falling film flow Falling film heat transfer Falling film mass transfer Falling film, combined heat and mass transfer FALLING RATE PERIOD, DRYING CURVE FANNING EQUATION FANNING FRICTION FACTOR FANNO FLOW FARADAY MHD GENERATOR FARADAY'S LAWS FAST DEFLATION METHODS FAST NEUTRONS FAST REACTORS FATIGUE LIFE PREDICTION FAULT TREES FAXEN FORCES FEEDBACK CONTROL FEEDBACK, DYNAMIC FEEDFORWARD CONTROL FEEDING SYSTEM FOR PLASMA REACTOR FEEDWATER HEATERS FERMI-DIRAC DISTRIBUTION FERROELECTRICITY FERROMAGNETIC FLUID FERTILE ISOTOPES FERTILE MATERIAL FIBER COMPOSITE MATERIALS Fibers FIBRE FILTERS FIBRE OPTICS FIBRE SATURATION POINT FIBROPOROUS MEDIA FIBROUS MEDIA FICK'S LAW FICK'S LAW OF DIFFUSION FICK'S LAW, GENERALIZED FIGURE OF MERIT FOR NUCLEAR REACTOR COOLANTS FILIPPOV EQUATION, FOR THERMAL CONDUCTIVITY OF SOLUTIONS FILM BOILING FILM BOILING COLLAPSE FILM CONDENSATION FILM CONDUCTANCE METHOD, FOR FILM THICKNESS MEASUREMENT FILM COOLING FILM FLOW RATE MEASUREMENT FILM FLOW REGIMES FILM INVERSION FILM METHOD FILM THICKNESS FILM THICKNESS DETERMINATION BY OPTICAL METHODS FILM THICKNESS IN ANNULAR FLOW Film thickness measurements FILMWISE CONDENSATION FILTERING CENTRIFUGES FILTERS FILTRATE FILTRATION FIN EFFICIENCY FIN EFFICIENCY FACTOR FIN TEMPERATURE EFFECTIVENESS FINITE DIFFERENCE METHODS FINITE ELEMENT METHODS FINITE VOLUME FOR SINGLE-PHASE FLOW Finite-element method for radiation diffusion in nonisothermal and nonhomogeneous media FINNED TUBES FINS FINS, CIRCUMFERENTIAL OR HELICAL FIRE BALLS FIRE POINT FIRE SPRINKLERS FIRE TUBE BOILERS FIRES FIRES SUPPRESSANTS First approach engineering models and useful data FIRST LAW OF THERMODYNAMICS FIRST NORMAL STRESS DIFFERENCE COEFFICIENT FISSILE MATERIAL FISSION FISSION PRODUCTS FISSION REACTION FIXED BED REGENERATORS FIXED BEDS FIXED TUBE SHEET EXCHANGERS FIZ FLAME SPEED, OR VELOCITY FLAME TEMPERATURES FLAMEOUT FLAMES FLAMES, TURBULENT FLAMMABILITY FLAMMABILITY LIMIT FLANGES FLASH DISTILLATION FLASH EVAPORATORS FLASH POINT FLASH SMELTING FLASHING FLOW FLAT PLATE COLLECTOR FLAT PLATE, BOUNDARY LAYER ON FLAT PLATE, COMBINED RADIATION AND CONVECTIVE HEAT TRANSFER TO FLIP-FLOP FLOW IN PARALLEL FLOATING HEADER EXCHANGERS FLOCCULATION Flooding and flow reversal FLOTATION FLOW ACROSS CYLINDERS, TUBES FLOW AND SOLUTE TRANSPORT IN SATURATED POROUS MEDIA FLOW BOILING OF ISO-OCTANE FLOW ENHANCEMENT FLOW EXCURSION INSTABILITIES FLOW IN A CURVED POROUS FLOW INSTABILITIES FLOW LAWS IN METALLIC FOAMS FLOW MALDISTRIBUTION Flow Metering FLOW OF FLUIDS FLOW OSCILLATIONS FLOW PATTERN ANALYSIS OF FLOW BOILING IN MICROGRAVITY FLOW PATTERN MAPS IN MINICHANNELS FLOW PATTERNS FLOW REGIME INDUCED INSTABILITIES, TWO-PHASE SYSTEMS FLOW REGIME RELAXATION INSTABILITIES FLOW REGIMES IN BUBBLE FLOW FLOW REVERSAL FLOW SEPARATION FLOW SPLITTING FLOW VISUALIZATION FLUE GASES Fluid FLUID DYNAMICS FLUID FILLED THERMOMETERS FLUID MECHANICS FLUID-SATURATED POROUS MEDIUM FLUIDICS FLUIDIZATION Fluidized bed FLUIDIZED BED GASIFICATION FLUIDS FLUMES FLUORESCEIN FLUORESCENCE FLUORESCENCE METHOD, FOR FILM THICKNESS MEASUREMENT FLUORESCENCE PHOTOGRAPHY FLUORINE FLUTED TUBES FLUX METHODS FLUX PARAMETER FLYING VEHICLES, AERODYNAMICS OF FMEA, FAILURE MODES AND EFFECTS ANALYSIS FOAM FRACTIONATION FOAM METALLIC FOGGING FOGGING IN CONDENSERS FOKKER-PLANK EQUATION FORCED CONVECTION FORCED CONVECTION BOILING FORCED DRAFT AIR COOLED HEAT EXCHANGERS FORCED VORTEX FOREST FIRES FORM DRAG FORWARD SWEPT AXIAL COMPRESSOR ROTORS FOSSIL FUEL FIRED BOILERS FOSSIL FUELS FOULING FOULING FACTORS FOULING RESISTANCE FOUR STROKE CYCLE FOURIER ANALYSIS FOURIER EQUATION FOURIER FLUID FOURIER INTEGRAL FOURIER LAW, GENERALIZED FOURIER NUMBER FOURIER SERIES FOURIER SPECTRAL SOLVER Fourier spectroscopy and experimental techniques FOURIER TRANSFORMATION FOURIER'S LAW FOURIER, BARON JEAN BAPTISTE JOSEPH (1768-1830) FOURIER-BESSEL SERIES FRACTAL ATTRACTOR FRACTAL GEOMETRY FRACTIONAL JEFFREY FLUID FRACTIONATION FRACTURE MECHANICS FRACTURE OF SOLID MATERIALS FRACTURE TOUGHNESS FRANCIS TURBINES FRAUNHOFER DIFRACTION FREDHOLM INTEGRAL EQUATIONS FREE BOUNDARY FREE CONVECTION FREE CONVECTION BOUNDARY LAYERS FREE ENERGY FREE JETS Free Molecule Flow FREE SETTLING FREE SURFACE FLOW FREE TURBULENT FLOW FREE VORTEX FREEZE DRYING FREEZING FREEZING FOULING FREEZING POINT DEPRESSION FREONS FRESNEL'S FORMULAS FREYN CHEQUERWORK REFRACTORIES FRICTION COEFFICIENT FRICTION FACTOR Friction factor. Skin- friction coefficient FRICTION FACTORS FOR SINGLE PHASE FLOW IN SMOOTH AND ROUGH TUBES Friction Velocity FRICTIONAL PRESSURE DROP FRIEDEL CORRELATION FRINGE MODEL, FOR LDA FROSSLING MARSHALL EQUATION FROST FORMATION FROSTING FROTH FROTH FLOTATION FROTH FLOW FROUDE NUMBER FROUDE NUMBER, EFFECT ON JET IMPINGEMENT FUEL ASSEMBLIES FUEL CELLS FUEL RODS FUEL TO AIR RATIO FUEL-COOLANT INTERACTION, FCI FUELS FUELS, PROPERTIES OF FUGACITY FUGACITY COEFFICIENT FULLER-SCHETTER-GITTINGS EQUATION, FOR DIFFUSION COEFFICIENT IN GASES Fully developed flow (stabilized flow) FUNCTIONS Fundamental unit of measurement FURNACE FIRED BOILER FURNACE MODELS FURNACES FUSED SILICA OPEN TUBULAR COLUMNS, FSOT FUSION REACTORS FUSION, NUCLEAR FUSION REACTORS
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FOAM FRACTIONATION

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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.)

Continuous foam fractionation.

Figure 1. Continuous foam fractionation.

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

(1)
(2)

AG is the ratio in the foam of bubble surface to bubble volume, cF is the concentration of the component in the feed, cw is the concentration in the bottom product, and cQ is the concentration in the top product. , and are the volumetric flowrates of feed, gas, and top product, respectively. Гw is the solute surface excess (which is effectively the concentration on the bubble surface) in equilibrium with cw.

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)].

(3)

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/D32 ≤ AG ≤ 6.6/D32, where D32 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 AC, 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).

(4)

is the universal gas constant, T is the absolute temperature, Гi is the solute surface excess of the i-th component, ai 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.

(5)

For the major surfactant in a foam, Гi is roughly constant because the bubble surfaces are essentially saturated. Typical values are of the order of 3 × 10−9 kmol/m2 for a molecular weight of several hundred.

If a surfactant is the collector of a trace colligend, Гi 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

  1. Lemlich, R. Ed. (1972) Absorptive Bubble Separation Techniques, Academic Press, New York. DOI: 10.1002/cite.330450427
  2. 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
  3. 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.
  4. 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

Following from:

LIQUID-LIQUID SEPARATION
LIQUID-SOLID SEPARATION

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