Skip to main content
SpringerLink
Log in

Study of Gas–Liquid Interface Displacement in Capillary Driven by Gas Pressurization

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

The main objective of this work is to study the drainage and imbibition in a capillary tube of circular section in a dimensionless form. First, we have presented the configuration of the studied problem. Equations governing physical problems and methods of resolution are displayed. Second, it demonstrates the dimensionless evolution of the interface and gas pressure as a function of non-dimensional time. Finally, the effect of gravity, the effect of inertia and the influence of gas compressibility and capillary radius are also presented and analyzed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

R :

Radius (m)

m :

Mass (kg)

g :

Acceleration due to gravity (m/s2)

Q inj :

Gas volume flow rate (m3/s)

V s :

Gas volume in the Syringe (m3)

S :

Passage section (m2)

x :

Position of the liquid front (m)

x*:

Dimensionless length

T :

Absolute temperature (K)

r :

The specific gas constant (J/K.mol)

u :

Liquid front velocity (m/s)

u*:

Dimensionless velocity

t :

Time (s)

t*:

Dimensionless time

L :

Length variation over time

L :

Length (m)

F :

Force (N)

P w :

Column weight (N)

Ca :

Capillary number, dimensionless

Fr :

Froude number, dimensionless

Bo :

Bond number, dimensionless

Re:

Reynolds number, dimensionless

P :

Pressure (Pa)

ΔP :

Pressure drop (Pa)

P*:

Dimensionless pressure

x ref :

Length characteristic

t ref :

Time characteristic

u ref :

Velocity characteristic

P ref :

Pressure characteristic

l ini :

Initial length (m)

V ini :

Volume of liquid (m3)

ρ :

Density (kg/m3)

μ :

Viscosity of liquid (kg/m s)

θ :

Contact angle (°)

σ :

Surface tension of the silicone oil, (N/m)

α :

Gravitational angle (°)

l :

Liquid

g :

Gas

c :

Capillary

References

  • Barenblatt, G.I., Entov, V.M., Ryzhik, V.M., Kluwer.: Theories of fluid flows through natural rocks. J. Fluid. Mech. 223, 395 (1990)

  • Birkholzer, J.T., Zhou, Q., Tsang, C.-F.: Large-scale impact of CO2 storage in deep saline aquifers: a sensitivity study on pressure response in stratified systems. Int. J. Greenh. Gas Control. 3, 181–194 (2009)

    Article  Google Scholar 

  • Bosanquet, C.H.: On the flow of liquids into capillary tubes. Phil. Mag. Ser. 6(45), 525–531 (1923)

    Article  Google Scholar 

  • Brittin, W.E.: Liquid rise in a capillary tube. J. Appl. Phys. 17, 37–44 (1946)

  • Brody, J.P., Yager, P., Goldstein, R.E., Austin, R.H.: Biotechnology at low Reynolds numbers. Biophys. J. 71, 3430–3441 (1996)

  • Christopher, G.F., Anna, S.L.: Microfluidic methods for generating continuous droplet streams. J. Phys. D Appl. Phys. 40, 319–336 (2007)

    Article  Google Scholar 

  • Coleman, J.W., Garimella, S.: Characterization of two-phase flow patterns in small diameter round and rectangular tubes. Int. J. Heat Mass Transfer. 42, 2869–2881 (1999)

    Article  Google Scholar 

  • Fazio, R., Iacono, S.: Entrapped Gas Action for one-Dimensional Models of Capillary Dynamics. Proc. World Congr. Eng. (2009)

  • Frette, V., Feder, J., Jossang, T., Meakin, P., Maloy, K.J.: Fast immiscible fluid-fluid displacement in three dimensional porous media at finite viscosity contrast. Phys. Rev. E. 50, 2881–2890 (1994)

  • Fries, N., Dreyer, M.: An analytic solution of capillary rise restrained by gravity. J. Colloid Interface Sci. 320, 259–263 (2008)

  • Fu, T.T., Ma, Y.G., Funfschilling, D., Li, H.Z.: Bubble formation and breakup mechanism in a microfluidic flow-focusing device. Chem. Eng. Sci. 64, 2392–2400 (2009)

    Article  Google Scholar 

  • Garstecki, P., Fuerstman, M.J, Stone, H.A, Whitesides, G.M.A.: Formation of droplets and bubbles in a microfluidic T-junction – scaling and mechanism of break-up. Lab Chip. 6, 437–446 (2006)

  • Gerritsen, M., Durlofsky, L.: Modeling fluid flow in oil reservoirs. Annu. Rev. Fluid Mech. 73, 211–238 (2005)

    Article  Google Scholar 

  • Hilpert, M.: Effects of dynamic contact angle on liquid withdrawal from capillary tubes: (semi)-analytical solutions. J. Colloid Interface Sci. 347, 315–323 (2010)

    Article  Google Scholar 

  • Hultmark, M., Aristoff, J.M., Stone, H.A.: The influence of the gas phase on liquid imbibtion in capillary tubes. J. Fluid Mech. 678, 600–606 (2011)

  • Ichikawa, N., Hosokawa, K., Maeda, R.: Interface motion of capillary-driven flow in rectangular microchannel. J. Colloid Interface Sci. 280, 155–164 (2004)

    Article  Google Scholar 

  • Ichikawa, N., Satoda, Y.: Interface dynamics of capillary flow in a tube under negligible gravity condition. J. Colloid Interface Sci. 162, 350–355 (1994)

  • Jagan, V., Satheesh, A.: Experimental studies on two phase flow patterns of air-water mixture in a pipe with different orientations. Flow Meas. Instrum. 52, 170–179 (2016)

  • Khemili, F., Bahrini, I., Najjari, M.: Oil Drainage in a capillary Tube: Experimental and Numerical Study. Microgravity Sci. Technol. 33, 2–8 (2021)

    Article  Google Scholar 

  • Lavi, B., Marmur, A., Bachmann, J.: Capillary Extraction. Langmuir 24(5), 1918–1923 (2008)

    Article  Google Scholar 

  • Lenormand, R., Touboul, E., Zarcone, C.: Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165–187 (1988)

  • Liou, W.W., Peng, Y., Parker, P.E.: Analytical modeling of capillary flow in tubes of non-uniform cross section. J. Colloid Interface Sci. 333, 292–397 (2009)

  • Louriou, C.: Modélisation instationnaire des transferts de masse et de chaleur au sein des évaporateurs capillaires. PhD thesis (in French), INPT (2010)

  • Louriou, C., Ouerfelli, H., Prat, M., Najjari, M., Bennasrallah, S.: Gas injection in a liquid saturated porous medium. Influence of pressurization effects and liquid films. Transp. Porous. Media. 91, 153–171 (2012)

  • Marmur, A., Cohen, R.D.: Characterization of Porous Media by the kinetics of liquid penetration: The vertical capillalries Model. J. Colloid Interface Sci. 189, 299–304 (1997)

    Article  Google Scholar 

  • Pesse, A.V., Warrier, G.R., Dhir, V.K.: An experimental study of the gas entrapement process in closed microchannels. Int. J. Heat Mass Transfer. 48, 5150–5165 (2005)

    Article  Google Scholar 

  • Schoelkopf, J., Gane, P., Ridgway, C., Mattehews, G.: Practical observation of deviation from Lucas-Washburn scaling in porous media. J. Colloids Surf. 206, 445–454 (2002)

  • Serizawa, A., Fenz, Z., Kawara, Z.: Two-phase flow in micro-channels. Exp. Therm. Fluid Sci. 26, 703–714 (2002)

    Article  Google Scholar 

  • Szekely, J., Neumann, A.W., Chuang, Y.K.: The rate of capillary penetration and the applicability of the Washburn equation. J. Colloid Interface Sci. 35, 273–278 (1971)

  • Tan, J., Li, S.W., Wang, K., Luo, G.S.: Gas-liquid flow in T-junction microfluidic devices with a new perpendicular rupturing flow route. J. Chem. Eng. 146, 428–433 (2009)

  • Teh, S.Y., Lin, R., Hung, L.H., Lee, A.P.: Droplet microfluidics. Lab Chip. 8, 198–220 (2008)

  • Van der Graaf, S., Steegmans, M.L.J., Van der Sman, R.G.M., Schroen, C.G.P.H., Boom, R.M.: Droplet formation in a T-shaped microchannel junction: a model system for membrane emulsification. J. Colloids Surf. A Physicochem. Eng. Asp. 266, 106–116 (2005)

  • Washburn, E.W.: The dynamics of capillary flow. Phys. Rev. 17, 273–283 (1921)

    Article  Google Scholar 

  • Wilmarth, T., Ishii, M.: Two-phase flow regimes in narrow rectangular vertical and horizontal channels. Int. J. Heat Mass Transfer. 37, 1749–1758 (1994)

    Article  Google Scholar 

  • Zeguai, S., Chikh, S., Tadrist, L.: Experimental study of air- water two-phase flow pattern evolution in a mini tube: Influence of tube orientation with respect to gravity. Int. J. Multiphase Flow. 132, 103–413 (2020)

  • Zhumud, B.V., Tiberg, F., Hallstensson, K.: Dynamics of capillary rise. J. Colloid Interface Sci. 228, 263–269 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Monastir, National Engineering School of Monastir, LESTE, 5019, Monasir, Tunisia

    Imen Bahrini, Faycel Khemili, Samia Abdi Ben Nasrallah & Jemni Abdelmajid

  2. University of Hafar Al Batin, College of Science, 39524, Hafar Al Batin, Kingdom of Saudi Arabia

    Faycel Khemili

Authors
  1. Imen Bahrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Faycel Khemili
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Samia Abdi Ben Nasrallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jemni Abdelmajid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Imen Bahrini.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bahrini, I., Khemili, F., Abdi Ben Nasrallah, S. et al. Study of Gas–Liquid Interface Displacement in Capillary Driven by Gas Pressurization. Microgravity Sci. Technol. 34, 56 (2022). https://doi.org/10.1007/s12217-022-09967-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12217-022-09967-y

Keywords

Search

Navigation