Capillary pressure overshoot for unstable wetting fronts is explained by Hoffman's velocity-dependent contact-angle relationship

Christine E. Baver, J. Yves Parlange, Cathelijne R. Stoof, David A. Dicarlo, Rony Wallach, Deanna S. Durnford, Tammo S. Steenhuis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Pore velocity-dependent dynamic contact angles provide a mechanism for explaining the formation of fingers/columns in porous media. To study those dynamic contact angles when gravity is present, rectangular capillary tubes were used to facilitate observation of the complete interface without geometric distortion. Results show that the Hoffman (1975) relationship between dynamic contact angle and water velocity applies to gravity-affected flow fields, and that it (when adjusted for nonzero static contact angles) can be used to model dynamic capillary pressures for unstable wettings fronts in porous media by assuming that (1) pressure at the wetting front is discontinuous, (2) the flow field behind the fingertip is highly heterogeneous, and (3) the front line advances one or a few pores at the time. We demonstrate the utility of the Hoffman relationship for porous media with a published infiltration experiment by calculating the capillary pressure successfully at the unstable wetting front as a function of the flux of water in the finger and the grain size diameter. Key Points At the fingertip, pore water velocities are much greater than front velocities Increased pore water velocities result in increased (dynamic) contact angles Dynamic contact angles greater than static values cause overshoot in fingers

Original languageAmerican English
Pages (from-to)5290-5297
Number of pages8
JournalWater Resources Research
Volume50
Issue number6
DOIs
StatePublished - Jun 2014

Keywords

  • dynamic contact angle
  • flow instability
  • gravity

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