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. 2017 May 17;7:2036. doi: 10.1038/s41598-017-02163-8

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Bubble departure mechanism. (a) Surrounded by subcooled liquid, the stationary bubble sitting on the hydrophobic surface assumes an elongated slug shape, as the three-phase contact line is pinned at the end of the non-wetting domain. The increasing buoyancy force results in continuous thinning and stretching of the neck section of the bubble, which leads ultimately to its rupture. Dissolved gas in the water is gasified during evaporation, and ends up being entrained into the bubble by the incoming vapour. The accumulation of gas results in a significant temperature difference between the gas-depleted bottom and gas-rich top of the bubble. The surface stress imbalance contributes to strong thermocapillary effect. (b) Plot of the experimentally measured bubble departure diameter, D _b, versus the calculations by equation (4), D _b,cal. The cofactor in the present empirical correlation, D _b,cal = Λ(x _g) $L_{c}^{'}$ , depends on the mole fraction of gas within the bubble, Λ(x _g) = (0.944 ± 7.398 × 10⁻⁴) + (0.0648 ± 2.590 × 10⁻³) × x _g. Here $L_{c}^{'}$ = [6D _pho σ/g(ρ _l − ρ _v)]^1/3 is the modified characteristic capillary length. Error bar: spread of individual measurements over five consecutive bubble growth periods.