Linear stability of a solid–vapour interface

• Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Main Authors: Style, Robert W., Worster, M. Grae
• Format: Article in Journal/Newspaper
• Language: English
• Published: The Royal Society 2009
• Subjects: Sea ice
• Online Access: http://dx.doi.org/10.1098/rspa.2009.0496; https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2009.0496; https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2009.0496

We investigate a system consisting of a condensed phase in contact with its vapour. We derive similarity solutions for vapour and temperature profiles and calculate the condition for the presence of vapour supersaturation adjacent to the condensed phase. We analyse the linear stability of a solid–vapour interface with varying atmospheric conditions. The instability is qualitatively similar to the Mullins–Sekerka instability in binary alloys but the results highlight the important parameters for the solid/vapour problem. We derive the neutral stability condition and results are applied to frost flowers, which are small hoar-frost-like crystals that grow on sea ice, and to physical vapour deposition. The results are applicable to many problems in the wide field of condensed-phase/vapour systems.