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. 2021 Apr 26;11:8940. doi: 10.1038/s41598-021-88334-0

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© The Author(s) 2021

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Bubble detection and mask extraction results for various gas–liquid two-phase flow experiments: (a) bubble plume (J_G = 0.033 × 10^–3 m/s, d_e = 1.8 mm) (unpublished data); (b) bubbly flow in a rod-bundle of nuclear power plant (J_G = 0.008 m/s, J_L = 0, 0.68 m/s, d_e = 2.8 and 2.0 mm) (unpublished data); (c) pool boiling bubble (T_w = 104 ℃, T_l = 98 ℃, d_e = 3.1 mm) (unpublished data); (d) bubble-swarm flow⁹ (α = 0.021, d_e = 4.2 mm); (e) upward bubbly flow in an expansion pipe⁸ (α = 0.0072, d_e = 3.0 mm). J_G: gas flow rate, J_L: liquid flow rate, d_e: mean bubble equivalent diameter, T_w: wall temperature, T_l: liquid temperature, α: volume void fraction.