Skip to main content
SpringerLink
Log in

Foams as specific gas-liquid technological media

  • Published:
Theoretical Foundations of Chemical Engineering Aims and scope Submit manuscript

Abstract

Basic physicochemical notions of foams as specific gas-liquid technological media are systematized. Structural properties, main parameters, and models of foam are considered. The adsorption-kinetic nature of the skeleton structure-forming phase of foam is discussed. Particular attention is given to the theoretical description of the internal hydrodynamics of foams, the concept of hydroconduction, and the syneresis phenomenon. Basic principles of rheological models of foams are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

radius of equivalent bubble, m

a s :

surface-averaged bubble radius, m

ā :

average radius of bubbles in foam, m

B :

number of edges (Plateau-Gibbs channels) of a foam cell

b :

Plateau-Gibbs channel length, m

C :

partial surfactant density in solution, kg/m3

D :

diffusion coefficient, m2/s

D s :

surface diffusion coefficient, m2/s

E :

modulus of elasticity of an adsorption layer, N/m2

E G :

Gibbs modulus of elasticity, N/m2

E M :

Marangoni modulus of elasticity, N/m2

F :

number of faces (films) of a foam cell

j :

flux of substance toward the surface, kg/(m2 s)

f(a):

bubble size distribution function

G :

shear modulus, N/m2

g:

vector of the acceleration of gravity, m/s2

H :

kinetic hydroconductivity, m2/(Pa s)

h :

film thickness, m

h cr :

critical film thickness, m

K :

foam ratio

k :

Boltzmann constant, J/K

M :

molecular weight of a surfactant

N :

number of nodes of a foam cell; number of moles of surfactant in the system

N s :

number of moles of a surfactant in an adsorption layer

n :

number of characteristic sizes of bubbles in foam

P a :

atmospheric pressure, N/m2

P g :

pressure in the gas phase of foam, N/m2

P 1 :

pressure in the liquid phase of foam, N/m2

Q :

volumetric flow rate of foam through the gap between plates, m3/s

q :

local volumetric liquid content flux density

R b :

Plateau-Gibbs channel radius, m

R n :

radius of curvature of nodal menisci, m

R:

universal gas constant, J/(mol K)

r 1 :

inlet radius of a foam breaker, m

S :

surface area, m2

S b :

cross-sectional area of a Plateau-Gibbs channel, m2

T :

temperature, K

t :

time, s

t a :

adsorption relaxation time, s

U :

translational velocity of foam in a column, m/s

U:

local velocity of foam (or its skeleton phase), m/s

V :

volume, m3

V 1 :

mole fraction of the liquid phase

V 10 :

liquid content of foam at the inlet of a foam breaker

v:

liquid velocity, m/s

vs :

surface liquid velocity, m/s

x :

coordinate along the plate generatrix, normalized to the inlet radius

Z :

vertical coordinate, m

Z 0 :

steady-flow foam-column height, m

z :

coordinate counted from the surface deep into the liquid, m

α:

distribution function parameter

β:

kinetic adsorption coefficient, s-1

β1 :

kinetic desorption coefficient, m/s

Γ:

surfactant adsorption, kg/m2

gG∞ :

surfactant adsorption at the total occupation of an adsorption layer, kg/m2

γ:

angle between the generatrix and axis of rotation, deg

δ:

shear strain

ε:

specific interface area of foam, m-1

κ:

surface curvature, in-1

μ:

dynamic viscosity of the liquid, kg/(m s)

v:

kinematic viscosity of the liquid, m2/s

Ξ:

potential of interaction of a surfactant molecule with the film surface

ξ:

coordinate along the normal to the surface, m

п:

wedging pressure, N/ m2

ρ1 :

liquid density, kg/m3

ρg :

gas density, kg/m3

σ:

surface tension, N/ m2

σ0 :

surface tension of a pure solvent, N/ m2

τ:

shear stress, N/ m2

τ0 :

ultimate shear stress, N/ m2

Φ:

volumetric gas content of foam

Ψ:

free energy, J

ω:

angular velocity of the plates of a foam breaker; frequency, s-1

References

  1. Kruglyakov, P.M. and Ekserova, D.R.,Pena i pennye plenki (Foam and Foam Films), Moscow: Khimiya, 1990.

    Google Scholar 

  2. Rusanov, A.I.,Mitselloobrazovanie vrastvorakh poverkhnostno-aktivnykh veshchestv (Micelle Formation in Surfactant Solutions), St. Petersburg: Khimiya, 1992.

    Google Scholar 

  3. De Vris, K.,Foam Stability, Amsterdam: Center, 1957.

    Google Scholar 

  4. Tikhomirov, V.K.,Peny (Foams), Moscow: Khimiya, 1983.

    Google Scholar 

  5. Manegold, E.,Schaum, Heidelberg: Strassenbau, Chemie und Technik, 1953.

    Google Scholar 

  6. Kann, K.B.,Kapillyarnaya gidrodinamika pen (Capillary Fluid Dynamics of Foams), Novosibirsk: Nauka, 1989.

    Google Scholar 

  7. Bikerman, J.J.,Foams, New York: Springer, 1973.

    Google Scholar 

  8. Berkman, S. and Egloff, G.,Emulsions and Foams, New York: Reinhold, 1941.

    Google Scholar 

  9. Schwarz, H.W., Rearrangements in Polyhedric Foam,Recl. Trav. Chim. Pays-Bas, 1965, vol. 84, no. 5, p. 771.

    CAS  Google Scholar 

  10. Sheludko, A.D.,Kolloidnaya khimiya (Colloid Chemistry), Moscow: Mir, 1984.

    Google Scholar 

  11. Krotov, V. V., Theory of Syneresis of Foams and Concentrated Emulsions. 1. Local Multiplicity of Polyhedral Disperse Systems,Kolloidn. Zh., 1980, vol. 42, no. 6, p. 1081.

    CAS  Google Scholar 

  12. Foams: Fundamentals and Applications, Prud’homme, R.K. and Khan, S.A., Eds., New York: Marcel Dekker, 1995.

    Google Scholar 

  13. Licinio, P. and Figneizedo, J.M., Steady Foam State,Europhys. Lett., 1996, vol. 36, no. 3, p. 173.

    Article  Google Scholar 

  14. Prigogine, I.,Introduction to Thermodynamics of Irreversible Processes, Springfield (Ill): Thomas, 1955. Translated under the titleVvedenie vtermodinamiku neobratimykh protsessov, Moscow: Inostrannaya Literatura, 1960.

    Google Scholar 

  15. Nicolis, G. and Prigogine, I.,Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations, New York: Wiley, 1977. Translated under the titleSamoorganizatsiya vneravnovesnykh sistemakh, Moscow: Mir, 1979.

    Google Scholar 

  16. Deryagin, B.V., Elastic Properties of Foams,Zh. Fiz. Khim., 1931, vol. 2, no. 6, p. 745.

    Google Scholar 

  17. Princen, H.M., Osmotic Pressure of Foams and Highly Concentrated Emulsions. 1. Theoretical Consideration,Langmuir, 1986, vol. 2, no. 4, p. 519.

    Article  CAS  Google Scholar 

  18. Emelichev, V.A. and Kovalev, M.M.,Mnogogranniki, grafy, optimizatsiya (Polyhedra, Graphs, and Optimization), Moscow: Nauka, 1981.

    Google Scholar 

  19. Gotovtsev, V.M., Viscoelastic Model for the Plug Flow of a Foam in a Cylindrical Channel,Teor. Osn. Khim. Tekhnol., 1996, vol. 30, no. 6, p. 576.

    Google Scholar 

  20. Sedov, L.I.,Mekhanika sploshnoi sredy (Continuum Mechanics), Moscow: Nauka, 1973.

    Google Scholar 

  21. Adamson, A.,The Physical Chemistry of Surfaces, New York: Wiley, 1976. Translated under the titleFizicheskaya khimiya poverkhnostei, Moscow: Mir, 1979.

    Google Scholar 

  22. Ross, S. and Prest, H.F., On the Morphology of Bubble Clusters and Polyhedral Foams,Colloids Surf., 1986, vol. 21, p. 179.

    Article  CAS  Google Scholar 

  23. Princen, H.M. and Levinson, P., The Surface Area of Kelvin’s Minimal Tetrakaidecahedron: The Ideal Foam Cell?,J. Colloid Interface Sci., 1987, vol. 120, no. 1, p. 172.

    Article  CAS  Google Scholar 

  24. Thompson D’Arcy, W.,On Growth and Form, Cambridge: Cambridge Univ. Press, 1961.

    Google Scholar 

  25. Coxeter, H.S.M.,Introduction to Geometry, New York: Wiley, 1961. Translated under the titleVvedenie vgeometriyu, Moscow: Nauka, 1966.

    Google Scholar 

  26. Matzke, E.B., The Three-Dimensional Shape of Bubbles in Foam-An Analysis of the Role of Surface Forces in Three-Dimensional Cell Shape Determination,Am. J. Botany, 1946, vol. 33, no. 1, p. 58.

    Article  Google Scholar 

  27. Hulbary, R.L., Three-Dimensional Cells Shape in the Tuberous Roots of Asparagus and in the Leaf Rhoeo,Amer. J. Botany, 1948, vol. 35, no. 5, p. 558.

    Article  Google Scholar 

  28. Krotov, V.V., Theory of the Syneresis of Foams and Concentrated Emulsions. 2. Local Hydroconductivity of Concentrated Disperse Systems,Kolloidn. Zh., 1980, vol. 42, no. 6, p. 1092.

    CAS  Google Scholar 

  29. Leonard, R.A. and Lemlich, R., A Study of Interstitial Liquid Flow in Foam,AIChE J., 1965, vol. 11, no. 1, p. 18.

    Article  CAS  Google Scholar 

  30. Deryagin, B.V., Churaev, N.V., and Muller, V.M.,Poverkhnostnye sily (Surface Forces), Moscow: Nauka, 1987.

    Google Scholar 

  31. Elimelech, M., Gregory, J., Jia, X., and Willions, R.A.,Particle Deposition and Aggregation, Oxford: Butterworth Heinemann, 1995.

    Google Scholar 

  32. Sebba, F.,Foams and Biliquid Foams-Aphrons, New York: Wiley, 1987.

    Google Scholar 

  33. Krotov, V.V. and Rusanov, A.I., Quasi-Random Processes in Liquid Films, inVoprosy termodinamiki geterogennykh sistem i teorii poverkhnostnykh yavlenii (Problems in the Thermodynamics of Heterogeneous Systems and the Theory of Surface Phenomena), Leningrad: Leningr. Gos. Univ., 1973, issue 2, p. 147.

    Google Scholar 

  34. Krotov, V.V., Rheological Analysis of the Marangoni Effect for an Ideal Interfacial Layer,Kolloidn. Zh., 1986, vol. 48, no. 1, p. 51.

    CAS  Google Scholar 

  35. Krotov, V.V. and Rusanov, A.I., Kinetics of the Adsorption of Surfactants in Liquid Solutions,Kolloidn. Zh., 1977, vol. 39, no. l,p. 48.

    Google Scholar 

  36. De Bœr, J.H.,The Dynamical Character of Adsorption, Oxford: Clarendon, 1953. Translated under the titleDinamicheskii kharakter adsorbtsii, Moscow: Inostrannaya Literatura, 1962.

    Google Scholar 

  37. Rusanov, A.I.,Fazovye ravnovesiya i poverkhnostnye yavleniya (Phase Equilibria and Surface Phenomena), Leningrad: Khimiya, 1967.

    Google Scholar 

  38. Adam, N.K.,Fizika i khimiya poverkhnostei (Surface Physics and Chemistry), Moscow: Gos. Izd. Tekh.-Teor. Literatury, 1947.

    Google Scholar 

  39. Kochurova, N.N. and Rusanov, A.I., On the Nonequilibrium Thermodynamics of Dynamic Surface Tension,Kolloidn. Zh., 1984, vol. 46, no. 1, p. 9.

    CAS  Google Scholar 

  40. Stuke, B., Dynamische Oberflächenspannuny Polarer Flüssigkeiten,Z. Electrochem., 1959, vol. 63, p. 140.

    CAS  Google Scholar 

  41. Krotov, V.V. and Rusanov, A.I., Gibbs Elasticity and Stability of Liquid Objects, inVoprosy termodinamiki geterogennykh sistem i teorii poverkhnostnykh yavlenii (Problems in the Thermodynamics of Heterogeneous Systems and the Theory of Surface Phenomena), Leningrad: Leningr. Gos. Univ., 1971, issue 1, p. 157.

    Google Scholar 

  42. Pushkarev, V.V. and Trofimov, D.I.,Fiziko-khimicheskie osobennosti ochistki stochnykh vod ot PAV (Physicochemical Foundations of the Removal of Surfactants from Waste Water), Moscow: Khimiya, 1975.

    Google Scholar 

  43. Yablonskii, G.S., Bykov, V.l., and Gorban’, A.N.,Kineticheskie modeli kataliticheskikh reaktsii (Kinetic Models of Catalytic Reactions), Novosibirsk: Nauka, 1983.

    Google Scholar 

  44. Rusanov, A.I., Levichev, S.A., and Zharov, V.T.,Poverkhnostnoe razdelenie veshchestv (Surface Separation of Substances), Leningrad: Khimiya, 1981.

    Google Scholar 

  45. Aveyard, R. and Haydon, D.A.,An Introduction to the Principles of Surface Chemistry, Cambridge: Pergamon, 1973.

    Google Scholar 

  46. Chandrasekar, S.,Stochastic Problems in Physics and Astronomy. Translated under the titleStokhasticheskie problemy v fizike i astronomii, Moscow: Inostrannaya Literatura, 1947.

    Google Scholar 

  47. Ruckenstein, E. and Priove, D.C., Rate of Deposition of Brownian Particles Under the Action of London and Double-Layer Forces,J. Chem. Soc, Faraday Trans. 2, 1973, vol. 69, no. 10, p. 1523.

    Google Scholar 

  48. Kazenin, D.A. and Makeyev, A.A., On the Determination of Depth Filter Colloidal Particle Size Separation Properties,Proc. 5th World Congr. Chem. Eng., San Diego, 1996, vol. 5, p. 534.

  49. Kazenin, D.A., Kinetic Parameters of the Deposition of Brownian Particles on a Filter,Khim. Neft. Mashinostr, 1998, no. 2, p. 35.

  50. Lavrent’ev, M.A. and Shabat, B.V.,Metody teorii funktsii kompleksnogo peremennogo (Methods of the Complex Variable Theory), Moscow: Nauka, 1973.

    Google Scholar 

  51. Erdélyi, A.,Asymptotic Expansions, New York: Dover, 1956. Translated under the titleAsimptoticheskie razlozheniya, Moscow: Gos. Izd. Fiz.-Mat. Literatury, 1962.

    Google Scholar 

  52. Izmailova, V.N., Yampol’skaya, G.P., and Summ, B.D.,Poverkhnostnye yavleniya vbelkovykh sistemakh (Surface Phenomena in Protein Systems), Moscow: Khimiya, 1988.

    Google Scholar 

  53. Lin, S.-Y., Chang, H.-Ch., and Chen, E.-M., The Effect of Bulk Concentration on Surfactant Adsorption Processes: The Shift From Diffusion Control to Mixed Kinetic-Diffusion Control with Bulk Concentration,J. Chem. Eng. Jpn., 1996, vol. 29, no. 4, p. 634.

    Article  Google Scholar 

  54. Nigmatulin, R.I.,Dinamika mnogofaznykh sred (Dynamics of Multiphase Media), Moscow: Nauka, 1987, ch. 1.

    Google Scholar 

  55. Nigmatulin, R.I.,Osnovy mekhaniki geterogennykh sred (Fundamentals of the Mechanics of Heterogeneous Media), Moscow: Nauka, 1978.

    Google Scholar 

  56. Pertsov, A.V., Chemin, V.N., Chistyakov, B.E., and Shchukin, E.D., Capillary Effects and Hydrostatic Stability of Foams,Dokl. Akad. Nauk SSSR, 1978, vol. 238, no. 6, p. 1395.

    CAS  Google Scholar 

  57. Kann, K.B., Some Features of Foam Syneresis: Drainage,Kolloidn. Zh., 1978, vol. 40, no. 5, p. 858.

    CAS  Google Scholar 

  58. Ostrovskii, G.M. and Nekrasov, V.A., A Mathematical Model for Outflow of Liquid from Foam,Teor. Osn. Khim. Tekhnol, 1996, vol. 30, no. 6, p. 657.

    Google Scholar 

  59. Krotov, V.V., Structure, Syneresis, and Rupture Kinetics of Polyhedral Disperse Systems, inVoprosy termodinamiki getemgennykh sistem i teorii poverkhnostnykh yavlenii (Problems in the Thermodynamics of Heterogeneous Systems and the Theory of Surface Phenomena), Leningrad: Leningr. Gos. Univ., 1971, issue 6, p. 110.

    Google Scholar 

  60. Krotov, V.V., Generalized Syneresis Equations,Kolloidn. Zh., 1984, vol. 46, no. 1, p. 14.

    Google Scholar 

  61. Krotov, V. V., Theory of Syneresis of Foams and Concentrated Emulsions. 3. Local Syneresis Equation and Presetting of Boundary Conditions,Kolloidn. Zh., 1981, vol. 43, no. 1, p. 43.

    CAS  Google Scholar 

  62. Krotov, V.V., Theory of Syneresis of Foams and Concentrated Emulsions. 4. Some Analytical Solutions of the One-Dimensional Syneresis Equation,Kolloidn. Zh., 1981, vol. 43, no. 2, p. 286.

    Google Scholar 

  63. Vetoshkin, A.G., Hydraulic Conductance of a Foamy Structure: Analysis of Models,Teor. Osn. Khim. Tekhnol., 1995, vol. 29, no. 5, p. 463.

    Google Scholar 

  64. Kuznetsova, L.L. and Kruglyakov, P.M., Flow of Surfactant Solutions in Plateau-Gibbs Channels of Foam,Dokl. Akad. Nauk SSSR, 1981, vol. 260, no. 4, p. 928.

    CAS  Google Scholar 

  65. Tikhomirov, V.K. and Vetoshkin, A.G., Calculation of the Cross-Sectional Area of Plateau-Gibbs Channels in Polyhedral Foams,Kolloidn. Zh., 1992, vol. 54, no. 4, p. 194.

    CAS  Google Scholar 

  66. Vetoshkin, A.G., Kazenin, D.A., and Kutepov, A.M., Fluid Dynamics in a Centrifugal Foam Breaker,Zh. Prikl. Khim. (Leningrad), 1984, vol. 57, no. 1, p. 96.

    CAS  Google Scholar 

  67. Vetoshkin, A.G., Kazenin, D.A., Kutepov, A.M., and Makeev, A.M., On the Theory of Centrifugal Plate Foam Breakers,Teor. Osn. Khim. Tekhnol., 1986, vol. 20, no. 4, p. 503.

    CAS  Google Scholar 

  68. Gol’dfarb, I.I., Kann, K.B., and Shreiber, I.R., Liquid Flow in Foam,Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gazov, 1988, no. 2, p. 102.

  69. Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., and Mikhailov, A.P.,Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii (QuasiLinear Parabolic Equations: Problems with Sharpening), Moscow: Nauka, 1987.

    Google Scholar 

  70. Ibragimov, N.Kh.,Gruppy preobrazovanii vmatematicheskoifizike (Transformation Groups in Mathematical Physics), Moscow: Nauka, 1983.

    Google Scholar 

  71. Zaitsev, V.F. and Polyanin, A.D.,Spravochnik po differentsial’nym uravneniyam s chastnymi proizvodnymi. Tochnye resheniya (Handbook of Differential Equations with Partial Derivatives: Exact Solutions), Moscow: Mezhdunarodnaya Programma Obrazovaniya, 1996.

    Google Scholar 

  72. Reiner, M.,Rheology. Translated under the titleReologiya, Moscow: Mir, 1965.

    Google Scholar 

  73. Astarita, G. and Marrucci, G.,Principles of Non-Newtonian Fluid Mechanics, London: McGraw-Hill, 1974. Translated under the titleOsnovy gidromekhaniki nen’yutonovskikh zhidkostei, Moscow: Mir, 1978.

    Google Scholar 

  74. Wilkinson, W.L.,Non-Newtonian Liquids: Fluid Mechanics, Mixing and Heat Transfer, London: Pergamon, 1960. Translated under the titleNen’yutonovskie zhidkosti, Moscow: Mir, 1964.

    Google Scholar 

  75. Kutepov, A.M., Polyanin, A.D., Zapryanov, Z.D.,et al., Khimicheskaya gidrodinamika (Chemical Fluid Dynamics), Moscow: Kvantum, 1996.

    Google Scholar 

  76. Khan, S.A., Foam Rheology: Relation Between Extensional and Shear Deformations in High Gas Fraction Foams,Rheol. Acta, 1987, vol. 26, no. 1, p. 78.

    Article  CAS  Google Scholar 

  77. Princen, H.M. and Kiss, A.D., Rheology of Foams and Highly Concentrated Emulsions,J. Colloid Interface Sci, 1986, vol. 112, no. 2, p. 427.

    Article  CAS  Google Scholar 

  78. Schwartz, L.W. and Princen, H.M., A Theory of Extensional Viscosity for Flowing Foams and Concentrated Emulsions,J. Colloid Interface Sci., 1987, vol. 118, no. l,p. 201.

    Article  CAS  Google Scholar 

  79. Princen, H.M., Rheology of Foams and Highly Concentrated Emulsions. 1. Elastic Properties and Yield Stress of a Cylindrical Model System,J. Colloid Interface Sci., 1983, vol. 91, no. l, p. 60.

    Google Scholar 

  80. Müller, Kh., Vetoshkin, A.G., Kazenin, D.A.,et al., Rheological Properties of Gas-Liquid Foams,Zh. Prikl. Khim. (Leningrad), 1989, vol. 62, no. 3, p. 580.

    Google Scholar 

  81. Gotovtsev, V.M., Viscoelastoplastic Flow of a Foam in a Cylindrical Channel,Teor. Osn. Khim. Tekhnol, 1997, vol. 31, no. 4, p. 346.

    Google Scholar 

  82. Krotov, V.V., Hydrodynamic Stability of Polyhedral Disperse Systems and Kinetics of Their Spontaneous Rupture. 1. Aspects of Hydrodynamic Stability,Kolloidn. Zh., 1986, vol. 48, no. 4, p. 699.

    CAS  Google Scholar 

  83. Ruckenstein, E. and Jain, R.K., Spontaneous Rupture of Thin Liquid Films,J. Chem. Soc, Faraday Trans. 2, 1974, vol. 70, no. l,p. 132.

    Article  CAS  Google Scholar 

  84. Maldarelli, C., Jain, R.K., Ivanov, I.B., and Ruckenstein, E., Stability of Symmetric and Asymmetric Thin Liquid Films to Short and Long Wavelength Perturbations,J. Colloid Interface Sci., 1980, vol. 78, no. 1, p. 118.

    Article  CAS  Google Scholar 

  85. Maldarelli, C. and Jain, R.K., The Hydrodynamic Stability of Thin Films,Thin Liquid Films, Ivanov, I.B., Ed., New York: Marcell Dekker, 1988.

    Google Scholar 

  86. Shugai, G.A. and Yakubenko, P.A., Spatio-Temporal Instability in Free Ultra-Thin Films,Eur. J. Mech. B, 1998, vol. 17, no. 3, p. 371.

    Article  Google Scholar 

  87. Erneux, T. and Davis, S.H., Nonlinear Rupture of Free Films,Phys. Fluids, 1993, vol. 5, p. 1117.

    Article  CAS  Google Scholar 

  88. Sharma, A., Kishore, C.S., Salaniwal, S., and Ruckenstein, E., Nonlinear Stability and Rupture of Ultrathin Free Films,Phys. Fluids, 1995, vol. 7, no. 8, p. 1832.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University of Engineering Ecology, Moscow, Russia

    D. A. Kazenin

  2. Russian State Scientific Center, Karpov Research Institute of Physical Chemistry, ul. Vorontsovo pole 10, 103064, Moscow, Russia

    A. V. Vyaz’min

  3. Institute for Problems of Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, 117526, Moscow, Russia

    A. D. Polyanin

Authors
  1. D. A. Kazenin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Vyaz’min
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. D. Polyanin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kazenin, D.A., Vyaz’min, A.V. & Polyanin, A.D. Foams as specific gas-liquid technological media. Theor Found Chem Eng 34, 211–226 (2000). https://doi.org/10.1007/BF02755969

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02755969

Keywords

Search

Navigation