Condition for Break-up of Non-Wetting Fluids in Sinusoidally Constricted Capillary Channels

  • 229 Accesses

  • 19 Citations


Analysis of capillary-pressure distribution in single channels with sinusoidal profile shows that surface tension-driven flow in such channels is controlled by the pressure extrema at their “crests” and “troughs”. Formulating the geometric condition for the pressure in the troughs to exceed that in the crests leads to a simple criterion for the spontaneous break-up of the non-wetting fluid in the necks of the constrictions. The criterion reduces to the condition for the Plateau-Rayleigh instability as a limiting case. Similar pressure analysis is applicable to the case of a non-wetting fluid invading an open pore body. Computational-fluid-dynamics experiments have verified the validity of the break-up predicted from the capillary-pressure argument. Although the geometric criterion for the break-up is valid for small capillary numbers, it provides a common framework in which the results of various published studies of a non-wetting phase choke-off in capillary constrictions for a wide range of capillary numbers can be explained and understood.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.


  1. Atherton R.W., Homsy G.M.: On the derivation of evolution equations for interfacial waves. Chem. Eng. Commun. 2, 57–77 (1976). doi:10.1080/00986447608960448

  2. Beresnev I.A.: Theory of vibratory mobilization of nonwetting fluids entrapped in pore constrictions. Geophysics 71, N47–N56 (2006)

  3. Bretherton F.P.: The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188 (1961). doi:10.1017/S0022112061000160

  4. De Gennes P.-G., Brochard-Wyart F., Quéré D.: Capillarity and Wetting Phenomena. Springer, Heidelberg (2004)

  5. Gauglitz P.A., Radke C.J.: An extended evolution equation for liquid film breakup in cylindrical capillaries. Chem. Eng. Sci. 43, 1457–1465 (1988). doi:10.1016/0009-2509(88)85137-6

  6. Gauglitz P.A., Radke C.J.: The dynamics of liquid film breakup in constricted cylindrical capillaries. J. Colloid Interface Sci. 134, 14–40 (1990). doi:10.1016/0021-9797(90)90248-M

  7. Graustein W.C.: Differential Geometry. Dover, New York (2006)

  8. Hammond P.S.: Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe. J. Fluid Mech. 137, 363–384 (1983). doi:10.1017/S0022112083002451

  9. Hemmat M., Borhan A.: Buoyancy-driven motion of drops and bubbles in a periodically constricted capillary. Chem. Eng. Commun. 148-150, 363–384 (1996). doi:10.1080/00986449608936525

  10. Korn G.A., Korn T.K.: Mathematical Handbook for Scientists and Engineers, 2nd edn. McGraw-Hill, New York (1968)

  11. Kovscek A.R., Tang G.-Q., Radke C.J.: Verification of Roof snap off as a foam-generation mechanism in porous media at steady state. Colloids Surf. A Physicochem. Eng. Asp. 302, 251–260 (2007). doi:10.1016/j.colsurfa.2007.02.035

  12. Lamb H.: Hydrodynamics, 6th edn. Cambridge University Press, Cambridge (1997)

  13. Martinez M.J., Udell K.S.: Axisymmetric creeping motion of drops through a periodically constricted tube. In: Wang, T.G. (eds) Drops and Bubbles, AIP Conference Proceedings 197, pp. 222–234. American Institute of Physics, New York (1989)

  14. Melrose, J.C., Brandner, C.F.: Role of capillary forces in determining microscopic displacement efficiency for oil recovery by waterflooding. J. Can. Pet. Technol. October–December, 54–62 (1974)

  15. Middleman S.: Modeling Axisymmetric Flows. Academic Press, New York (1995)

  16. Olbricht W.L., Leal L.G.: The creeping motion of immiscible drops through a converging/diverging tube. J. Fluid Mech. 134, 329–355 (1983). doi:10.1017/S0022112083003390

  17. Roof J.G.: Snap-off of oil droplets in water-wet pores. Soc. Pet. Eng. J. 10, 85–90 (1970). doi:10.2118/2504-PA

  18. Rossen W.R.: A critical review of Roof snap-off as a mechanism of steady-state foam generation in homogeneous porous media. Colloids Surf. A Physicochem. Eng. Asp. 225, 1–24 (2003). doi:10.1016/S0927-7757(03)00309-1

  19. Tsai T.M., Miksis M.J.: Dynamics of a drop in a constricted capillary tube. J. Fluid Mech. 274, 197–217 (1994). doi:10.1017/S0022112094002090

Download references

Author information

Correspondence to Igor A. Beresnev.

Electronic Supplementary Material

The Below is the Electronic Supplementary Material.

ESM 1 (MPG 25.9MB)

ESM 1 (MPG 25.9MB)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Beresnev, I.A., Li, W. & Vigil, R.D. Condition for Break-up of Non-Wetting Fluids in Sinusoidally Constricted Capillary Channels. Transp Porous Med 80, 581 (2009) doi:10.1007/s11242-009-9381-6

Download citation


  • Fluid break-up
  • Instability
  • Capillary flow
  • Porous channels