Abstract.
We have performed forced drainage experiments on aqueous foams of bubble diameters D varying from 0.18 to 8 mm, and made with different surfactant and protein solutions (providing different surface viscoelastic properties). Changing bubble size or surface properties allows to evolve between two drainage regimes, the respective dimensionless permeabilities also varying with these parameters. We show that the bubble size and surface properties can be incorporated into a single surface mobility parameter that controls the transition between the two drainage regimes. The permeability measurements indicate how do the hydrodynamic resistances of the foam channels and nodes depend on surface mobility. Taking advantage of the large range of experimental conditions, leading to a variation of the mobility parameter over more than 3 decades, a simple and consistent description of both the drainage regimes and the transition in between them is obtained. For the smallest bubbles (D < 0.5 mm) anomalous behaviors are observed and discussed.
Similar content being viewed by others
References
D. Weaire, S. Hutzler, The Physics of Foams (Oxford University Press, 1999).
D. Weaire, N. Pittet, S. Hutzler, D. Pardal, Phys. Rev. Lett. 71, 2670 (1993).
G. Verbist, D. Weaire, Europhys. Lett. 26, 631 (1994).
R. Phelan, D. Weaire, E.A.J.F. Peters, G. Verbist, J. Phys.: Condens. Matter 8, L475 (1996).
G. Verbist, D. Weaire, A. Kraynik, J. Phys.: Condens. Matter 8, 3715 (1996).
D. Weaire, S. Hutzler, G. Verbist, E.A.J. Peters, Adv. Chem. Phys., 102, 315 (1997).
A. Saint-Jalmes, M.U. Vera, D.J. Durian, Eur. Phys. J. B 12, 67 (1999).
S.A. Koehler, S. Hilgenfeldt, H.A. Stone, Phys. Rev. Lett. 82, 4232 (1999)
M. Durand, G. Martinoty, D. Langevin, Phys. Rev. E 60, R6307 (1999).
P.J. Wilde, A.R. Mackie, F.A. Husband, A.P. Gunning, V.J. Morris, A. Fillery-Travis, Proceedings of the international Workshop on Foams and Films, Leuven, Belgium, edited by D. Weaire, J. Banhart (MIT-Verlag, Bremen, 1999) p. 59.
S.A. Koehler, S. Hilgenfeldt, H.A. Stone, Langmuir 16, 6327 (2000).
A. Saint-Jalmes, M.U. Vera, D.J. Durian, Europhys. Lett. 50, 695 (2000).
S.A. Koehler, S. Hilgenfeldt, H.A. Stone, Europhys. Lett. 54, 335 (2000).
S.J. Cox, D. Weaire, S. Hutzler, J. Murphy, R. Phelan, G. Verbist, Proc. R. Soc. London, Ser. A 456, 2441 (2000).
S. Hutzler, D. Weaire, Philos. Mag. Lett. 80, 419 (2000).
P. Grassia, J.J. Cilliers, S.J. Neethling, E. Ventura-Medina, Eur. Phys. J. E 6, 325 (2001).
M. Safouane, M. Durand, A. Saint-Jalmes, D. Langevin, V. Bergeron, J. Phys. IV. 11, 275 (2001) Pr6.
S.J. Cox, G. Bradley, S. Hutzler, D. Weaire, J. Phys.: Condens. Matter 13, 4863 (2001).
S. Hilgenfeldt, S.A. Koehler, H.A. Stone, Phys. Rev.Lett. 86, 4704 (2001).
S.J. Cox, G. Bradley, D. Weaire, Eur. Phys. J., Appl. Phys. 14, 87 (2001).
M. Durand, D. Langevin, Eur. Phys. J. E 7, 35 (2002).
S.A. Koehler, S. Hilgenfeldt, E.R. Weeks, H.A. Stone, Phys. Rev. E 66, 040601(R) (2002).
A. Saint-Jalmes, D. Langevin, J. Phys.: Condens. Matter 14, 9397 (2002).
P. Grassia, S.J. Neethling, J.J Cilliers, Eur. Phys. J. E 8, 517 (2002).
V. Carrier, S. Destouesse, A. Colin, Phys. Rev. E. 65, 1 (2002).
S.J Neethling, H.T. Lee, J.J. Cilliers, J. Phys.: Condens. Matter 14, 331 (2002).
M.U. Vera, D.J. Durian, Phys. Rev. Lett. 88, 088304-1 (2002).
D. Weaire, S. Hutzler, S. Cox, N. Kern, M.A. Alonso, W. Drenckhan, J. Phys.: Condens. Matter 15, S65 (2003).
H.A. Stone, S.A. Koehler, S. Hilgenfeldt, M. Durand, J; Phys. Condens. Matter 15, S283 (2003).
S.A. Koehler, S. Hilgenfeldt, E.R. Weeks, H.A. Stone, to be published in J. Colloid Interface Sci.
O. Pitois, C. Fritz, M. Adler, to be published in J. Colloid Interface Sci.
R.A. Leonard, R. Lemlich, AIChE J. 11, 18 (1965).
A. Kraynik (1983) Sandia Report SAND 83-0844.
I.I. Gol’dfarb, K.B. Kann, I.R. Shreiber, Fluid Dyn. 23, 244 (1988).
D. Desai, R. Kumar, Chem. Eng. Sci. 37, 1361 (1982).
A. Nguyen, J. Colloid Interface Sci. 249, 194 (2002)
S.A. Koehler, S. Hilgenfeldt, H.A. Stone, to be published in J. Colloid Interface Sci.
F.G. Gandolfo, H.L. Rosano, J. Colloid Interface Sci. 194, 31 (1997).
P.A. Lemieux, M.U. Vera, D.J. Durian, Phys. Rev. E 57, 4498 (1998).
M.U Vera, A. Saint-Jalmes, D.J Durian, Appl. Optics 40, 4210 (2001).
S. Cox, private communication.
A. Aradian, E. Raphaël, P-G. de Gennes, Europhys. Lett. 55, 834 (2001).
S. Hutzler, D. Weaire, R. Crawford, Europhys. Lett. 41, 461 (1998).
M.U. Vera, A. Saint-Jalmes, D.J. Durian, Phys. Rev. Lett. 84, 3001 (2001).
N.F. Djabbarah, D.T. Wasan, Chem. Eng. Sci. 37, 175 (1982); J.T. Petkov, K.D. Danov, N.D. Denkov, R. Aust, F. Durst, Langmuir 12, 2650 (1996); C. Barentin, C. Ybert, J.M. DiMeglio, J.F. Joanny, J. Fluid. Mech. 397, 331 (1999).
G. Singh, G.J. Hirasaki, C.A. Miller, J. Colloid Interface Sci. 184, 92 (1996).
S. Stoyanov, N. Denkov, Langmuir 17, 1150 (2001).
O.D. Velev, G.N. Constantinides, D.G. Avraam, A.C. Payatakes, R.P. Borwankar, J. Colloid Interface Sci. 175, 68 (1995).
M. Safouane, A. Saint-Jalmes, V. Bergeron, D. Langevin, submitted to Phys. Fluids.
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 29 April 2004, Published online: 21 September 2004
PACS:
82.70.Rr Aerosols and foams - 47.60. + i Flows in ducts, channels, nozzles, and conduits - 47.55.Mh Flows through porous media
Y. Zhang: Present address: Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, FL, USA.
Rights and permissions
About this article
Cite this article
Saint-Jalmes, A., Zhang, Y. & Langevin, D. Quantitative description of foam drainage: Transitions with surface mobility. Eur. Phys. J. E 15, 53–60 (2004). https://doi.org/10.1140/epje/i2004-10036-x
Issue Date:
DOI: https://doi.org/10.1140/epje/i2004-10036-x