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

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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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