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The influence of the gas phase on liquid imbibition in capillary tubes

Published online by Cambridge University Press:  13 May 2011

MARCUS HULTMARK ,
JEFFREY M. ARISTOFF  and
HOWARD A. STONE
MARCUS HULTMARK*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
JEFFREY M. ARISTOFF
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
HOWARD A. STONE
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: hultmark@princeton.edu
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Abstract

The imbibition of liquid into a capillary tube is studied both theoretically and experimentally for sufficiently long tubes where viscous resistance from the gas phase ahead of the moving front is significant. At early times, and as the length of the tube is increased, we observe a systematic deviation from classical theory that cannot be attributed to the inertia of the liquid nor entrance effects. Instead, this behaviour is rationalized by considering the viscous resistance from the gas as it is displaced by the liquid. An explicit analytical solution for a one-dimensional description of the flow is given that accounts for viscous resistance from the displaced fluid. Excellent agreement between experiment and theory is obtained.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 600 - 606
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1990 Theory of Fluid Flows through Natural Rocks. Kluwer.CrossRefGoogle Scholar
Bell, J. M. & Cameron, F. K. 1906 The flow of liquids through capillary spaces. J. Phys. Chem. 10, 658–674.CrossRefGoogle Scholar
Bosanquet, C. H. 1923 On the flow of liquids into capillary tubes. Phil. Mag. Ser. 6 45, 525–531.CrossRefGoogle Scholar
Deutsch, S. 1979 A preliminary study of the fluid mechanics of liquid penetrant testing. J. Res. Natl Bur. Stand. 84, 287–292.CrossRefGoogle ScholarPubMed
Fazio, R. & Iacono, S. 2009 Entrapped gas action for one-dimensional models of capillary dynamics. In Proc. World Congress on Engineering 2009, Vol II. London, UK.Google Scholar
Fisher, L. R. & Lark, P. D. 1979 An experimental study of the Washburn equation for liquid flow in very fine capillaries. J. Colloid Interface Sci. 69, 486–492.CrossRefGoogle Scholar
Gerritsen, M. G. & Durlofsky, L. J. 2005 Modeling fluid flow in oil reservoirs. Annu. Rev. Fluid Mech. 37, 211–238.CrossRefGoogle Scholar
Good, R. J. & Lin, N. J. 1976 Rate of penetration of a fluid into a porous body. J. Colloid Interface Sci. 54, 52–58.CrossRefGoogle Scholar
Kornev, K. G. & Neimark, A. V. 2001 Spontaneous penetration of liquids into capillaries and porous membranes revisited. J. Colloid Interface Sci. 235, 101–113.CrossRefGoogle ScholarPubMed
LeGrand, E. J. & Rense, W. A. 1945 Data on rate of capillary rise. J. Appl. Phys. 16, 843–846.CrossRefGoogle Scholar
Lucas, V. R. 1918 Ueber das zeitgesetz des kapillaren aufstiegs von flssigkeiten. Kolloidn Z. 23, 15–22.CrossRefGoogle Scholar
Parisse, J., Giordano, J., Perrier, P., Burtschell, Y. & Graur, I. 2009 Numerical investigation of micro shock waves generation. Microfluid Nanofluid 6, 699–709.CrossRefGoogle Scholar
Pesse, A. V., Warrier, G. R. & Dhir, V. K. 2005 An experimental study of the gas entrapment process in closed-end microchannels. Intl J. Heat Mass Transfer 48, 5150–5165.CrossRefGoogle Scholar
Quere, D. 1997 Inertial capillarity. Europhys. Lett. 39, 533–538.CrossRefGoogle Scholar
Szekely, J., Neumann, A. W. & Chuang, Y. K. 1971 The rate of capillary penetration and the applicability of the Washburn equation. J. Colloid Interface Sci. 35, 273–278.CrossRefGoogle Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273–283.CrossRefGoogle Scholar
Zhmud, B. V., Tiberg, F. & Hallstensson, K. 2000 Dynamics of capillary rise. J. Colloid Interface Sci. 228, 263–269.CrossRefGoogle ScholarPubMed