Skip to main content
SpringerLink
Log in

Two-Phase Flow and the Capillarity Phenomenon in Porous Solids – A Continuum Thermomechanical Approach

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Two-phase flow and capillarity phenomenon in porous solids, well known in physics and engineering, are treated from a rigorous continuum thermomechanical point of view for the first time. A ternary model, consisting of a porous solid phase, a liquid phase, and a gas phase, is investigated within the framework of thermodynamics. The main result of the evaluation of the entropy principle turns out to be that the interaction forces between the solid, gas, and liquid phases are dependent on the free Helmholtz energy functions of the corresponding phases and on the gradient of the liquid density. The classical result for the driving volume force for raising a water column in a narrow tube against the force of gravity is contained in the general investigation.

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

Similar content being viewed by others

References

  • Avraam, D. G. and Payatakes, A. C.: 1999, Flow mechanisms, relative permeabilities and coupling effects in steady-state two-phase flows through porous media. The case of strong wettability, Ind. Eng. Chem. Res. 38, 778–786.

    Google Scholar 

  • Davis, H. T.: 1996, Statistical Mechanics of Phases, Interfaces, and Thin Films, VCH, New York, Weinheim, Cambridge.

    Google Scholar 

  • de Boer, R.: 2000, Theory of Porous Media: Highlights in the Historical Development and Current State, Springer, Berlin, Heidelberg, New York.

  • de Boer, R. and Didwania, A. K.: 1997, The effect of uplift in liquid-saturated porous solids - Karl Terzaghi's contributions and recent findings, Géotechnique 47, 289–298.

    Google Scholar 

  • de Boer, R. and Didwania, A. K.: 2001, Saturated elastic porous solids: incompressible, compressible, and hybrid binary models, Transport in Porous Media 45, 425–445.

    Google Scholar 

  • de Boer, R. and Didwania, A. K.: 2002, Capillarity in porous solids: contributions of the Vienna school and recent findings, Acta Mech. 159, 173–188.

    Google Scholar 

  • Didwania, A. K. and de Boer, R.: New governing equations for immiscible two-phase flow through porous media and their special forms for different applications (in preparation).

  • Fillunger, P.: 1934, Der Kapillardruck in Talsperren, Wasserwirtschaft 27, 13/14.

    Google Scholar 

  • Gray, W. G. and Hassanizadeh, S. M.: 1990, Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries, Adv. Water Resour. 13, 169–186.

    Google Scholar 

  • Hassanizadeh, S. M. and Gray, W. G.: 1993, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res. 29, 3389–3405.

    Google Scholar 

  • Kozeny, J.: 1927, Ñber kapillare Leitung des Wassers im Boden (Aufstieg, Versickerung und Anwendung auf die Bewässerung). Sitzungsberichte der Akademie der Wissenschaften in Wien, mathematisch-naturwissenschaftliche Klasse, Abteilung IIa 136, pp. 271–309.

    Google Scholar 

  • Künzel, H. M.: 1994, Verfahren zur ein-und zweidimensionalen Berechnung des gekoppelten Wärme und Feuchtetransports in Bauteilen mit einfachen Kennwerten, Dissertation, Lehrstuhl für Konstruktive Bauphysik, Fakultät Bauingenieur-und Vermessungswesen der Universität Stuttgart.

  • Müller, I.: 1994, Grundzüge der Thermodynamik mit Historischen Anmerkungen, Springer, Berlin, Heidelberg, New York.

  • Muskat, M.: 1937, The Flow of Homogeneous Fluids through Porous Media, McGraw-Hill, New York.

    Google Scholar 

  • Ricken, T.: 2002, Kapillarität in porösen Medien - theoretische Untersuchungen und numerische Simulation, Dissertation, Institut für Mechanik, Fachbereich 10 - Bauwesen, Universität Essen.

  • von Terzaghi, K.: 1925, Erdbaumechanik auf bodenphysikalischer Grundlage, Franz Deuticke, Leipzig/Wien.

  • von Terzaghi, K.: 1933, Auftrieb und Kapillardruck an betonierten Talsperren, Wasserwirtschaft 26, 397–399.

    Google Scholar 

  • Whitaker, S.: 1986, Flow in porous media. 2. The governing equations for immiscible two-phase flow, Transp. Porous Media 1, 105–125.

    Google Scholar 

  • Wooding, R. A. and Morel-Seytoux, H. J.: 1976, Multiphase Fluid flow through porous media, in: M. van Dyke, W. G. Vincenti and J. V. Wehausen (eds), Annual Review of Fluid Mechanics Vol. 8, Annual Reviews Inc., Palo Alto, CA, USA.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mechanik, FB 10, Bauwesen, Universität Essen, 45117, Essen, Germany

    Reint de Boer

  2. University of California at San Diego (UCSD), USA

    Reint de Boer

  3. Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA, 92093-0411, USA

    Anjani Kumar Didwania

Authors
  1. Reint de Boer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anjani Kumar Didwania
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Boer, R., Didwania, A.K. Two-Phase Flow and the Capillarity Phenomenon in Porous Solids – A Continuum Thermomechanical Approach. Transport in Porous Media 56, 137–170 (2004). https://doi.org/10.1023/B:TIPM.0000021731.14083.7f

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:TIPM.0000021731.14083.7f

Search

Navigation