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An Analytical Model for Flow of Seawater Adjacent to an Igneous Wall

  • K. C. Lewis
  • Marc Nardea
  • Miranda J. Halpern
Article
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Abstract

We develop an analytical model describing the flow of NaCl–\(\hbox {H}_2\hbox {O}\) in a saturated porous medium adjacent to a hot vertical wall and apply the model to flow along a 450-m high dike in a generic, high-temperature seafloor hydrothermal setting. After 0.5–4 days, a steady two-phase layer forms along the wall with a maximum width of approximately 20 cm. The layer consists of rising, low salinity vapor and sinking, high salinity brine; its width increases as height to 1/2 power. The brine salinity is highest at the dike–fluid interface and decreases toward the edge of the layer. Vapor dominates the vertical heat transport, while brine dominates salt transport; the resulting phase separation leads to increasing liquid volume saturation and bulk salinity with increasing depth. The bulk salinity reaches 10% NaCl by weight (wt%) at the lowest height for which the model is valid. The two-phase zone begins to decay from the bottom upward at around 7 days. Phase separation at the top of the system persists for 21 days. The heat required to sustain the layer is derived primarily from the latent heat of magma crystallization.

Keywords

Stefan problem Boundary layer Two-phase flow Seafloor hydrothermal Dike 

Notes

Acknowledgements

We thank R.P. Lowell for much encouragement and many valuable discussions.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • K. C. Lewis
    • 1
  • Marc Nardea
    • 2
  • Miranda J. Halpern
    • 1
  1. 1.Monmouth UniversityWest Long BranchUSA
  2. 2.Rutgers UniversityNew BrunswickUSA

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