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Interaction of foam with a porous medium: Theory and calculations

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Abstract

A new theory of foam drainage in the presence of a porous support was introduced and accordingly, a mathematical model which combines the foam drainage equation with the equation describing imbibition into the porous substrate was developed. Proposed dimensionless equations were solved using finite element method. Boundary conditions were zero liquid flux on the top of the foam and continuity of flux on foam/substrate interface. It was found that the kinetics of foam drainage depends on three dimensionless numbers. The result indicated that there are two possible scenarios for the interaction of foam with a porous substrate: (i) a rapid imbibition, the liquid volume fraction at the bottom of the foam is a decreasing function of time. In this regime the imbibition into the porous substrate dominates and it is faster as compared with the foam drainage; (ii) a slow imbibition, the liquid volume fraction at the interface experiences a peak point and imbibition into the porous substrate is slower for some time as compared with the foam drainage.

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References

  1. D. Exerowa, P.M. Kruglyakov, Foams and foam films: Theory, experiment, application (Elsevier, Amsterdam, 1998)

  2. S. Farrokhpay, Adv. Coll. Interf. Sci. 166, 1 (2011)

    Google Scholar 

  3. A. Arzhavitina, H. Steckel, Int. J. Pharmaceut. 394, 1 (2010)

    Article  Google Scholar 

  4. J.B.M. Hudales, H.N. Stein, J. Coll. Interf. Sci. 140, 307 (1990)

    Article  Google Scholar 

  5. M.V. Ramani, R. Kumar, K.S. Gandhi, Chem. Eng. Sci. 48, 455 (1993)

    Article  Google Scholar 

  6. A.R. Bhakta, K.C. Khilar, Langmuir 7, 1827 (1991)

    Article  Google Scholar 

  7. G. Verbist, D.L. Weaire, EPL (Europhysics Letters) 26, 631 (1994)

    Article  ADS  Google Scholar 

  8. G. Verbist, D.L. Weaire, A.M. Kraynik, J. Phys.: Condens. Mat. 8, 3715 (1996)

    ADS  Google Scholar 

  9. S. Jun, D.D. Pelot, A.L. Yarin, Langmuir 28, 5323 (2012)

    Article  Google Scholar 

  10. D.L. Weaire, N. Pittet, S. Hutzler, D. Pardal, Phys. Rev. Lett. 71, 2670 (1993)

    Article  ADS  Google Scholar 

  11. S. Hutzler, D.L. Weaire, Philosoph. Mag. Lett. 80, 419 (2000)

    Article  ADS  Google Scholar 

  12. P. Stevenson, Colloids and Surfaces A, Physicochem. Eng. Asp. 305, 1 (2007)

    Article  Google Scholar 

  13. S.A. Koehler, S. Hilgenfeldt, H.A. Stone, Langmuir 16, 6327 (2000)

    Article  Google Scholar 

  14. S.A. Koehler, S. Hilgenfeldt, H.A. Stone, EPL (Europhysics Letters) 54, 335 (2001)

    Article  ADS  Google Scholar 

  15. S.A. Koehler, S. Hilgenfeldt, H.A. Stone, in Division of Fluid Dynamics Meeting, New Orleans, LA, USA, 1999

  16. S.A. Koehler, H.A. Stone, M.P. Brenner, J. Eggers, Phys. Rev. E 58, 2097 (1998)

    Article  ADS  Google Scholar 

  17. S.J. Cox, G. Verbist, Microgravity Sci. Technol. 14, 45 (2003)

    Article  Google Scholar 

  18. H. Caps, S.J. Cox, H. Decauwer, D.L. Weaire, N. Vandewalle, Coll. Surf. A: Physicochem. Eng. Asp. 261, 131 (2005)

    Article  Google Scholar 

  19. F. Bolton, D.L. Weaire, Phys. Rev. Lett. 65, 3449 (1990)

    Article  ADS  Google Scholar 

  20. D.L. Weaire, S. Hutzler, The physics of foams (Oxford University Press, Oxford, 1999)

  21. H.P.G. Darcy, Détermination des lois d’écoulement de l’eau à travers le sable (1856)

  22. P. Carman, The J. Agricult. Sci. 29, 262 (1939)

    Article  Google Scholar 

  23. T. Sochi, Polymer 51, 5007 (2010)

    Article  Google Scholar 

  24. M. Van Hecke, J. Phys.: Condens. Mat. 22, 033101 (2010)

    ADS  Google Scholar 

  25. P. Grassia, J. Cilliers, S. Neethling, E. Ventura-Medina, Eur. Phys. J. E 4, 325 (2001)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Procter & Gamble, Cincinnati, Ohio, USA

    A. Bureiko

  2. Department of Chemical Engineering, Loughborough University, Loughborough, LE113TU, UK

    O. Arjmandi-Tash, N. Kovalchuk, A. Trybala & V. Starov

  3. Institute of Biocolloid Chemistry, Kiev, UKraine

    N. Kovalchuk

Authors
  1. A. Bureiko
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  2. O. Arjmandi-Tash
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  3. N. Kovalchuk
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  4. A. Trybala
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  5. V. Starov
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Correspondence to V. Starov.

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Bureiko, A., Arjmandi-Tash, O., Kovalchuk, N. et al. Interaction of foam with a porous medium: Theory and calculations. Eur. Phys. J. Spec. Top. 224, 459–471 (2015). https://doi.org/10.1140/epjst/e2015-02374-2

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  • DOI: https://doi.org/10.1140/epjst/e2015-02374-2

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