{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T16:11:02Z","timestamp":1790784662837,"version":"4.1.0"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Gas\u2013liquid two-phase flow instability is a key issue affecting the safety and efficiency of industrial systems, and the accurate characterization of its multiscale dynamic characteristics remains a challenge. This study proposes a novel approach based on time-shift multiscale equiprobable symbolic sample entropy (TMESE) to characterize flow instability, which is validated using four evaluation metrics on eight typical time series. The TMESE method is applied to analyze the dynamic behaviors of bubble flow, slug flow, and churn flow both qualitatively and quantitatively. Results show that the TMESE distribution effectively captures evolutionary features of different flow patterns, and the joint distribution of average TMESE and complexity index (CI) provides a reliable quantitative measure of multiscale flow instability. Bubble flow exhibits the strongest instability, slug flow the least, and churn flow intermediate. Increasing gas or liquid superficial velocity raises average TMESE and CI values. These findings provide theoretical support for the prediction and control of gas\u2013liquid two-phase flow systems in engineering applications.<\/jats:p>","DOI":"10.3390\/e28020210","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T17:45:36Z","timestamp":1770831936000},"page":"210","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiscale Characterization of Flow Instability for Gas\u2013Liquid Two-Phase Flow"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-5903-0400","authenticated-orcid":false,"given":"Qing-Ming","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical, Qiqihar University, Qiqihar 161000, China"},{"name":"The Engineering Technology Research Center for Precision Manufacturing Equipment and Industrial Perception of Heilongjiang Province, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qing-Chao","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical, Qiqihar University, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Di","family":"Ba","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical, Qiqihar University, Qiqihar 161000, China"},{"name":"The Collaborative Innovation Center for Intelligent Manufacturing Equipment Industrialization, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical, Qiqihar University, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/0301-9322(92)90061-K","article-title":"Structural and interfacial stability of multiple solutions for stratified flow","volume":"18","author":"Barnea","year":"1992","journal-title":"Int. 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