{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T20:42:47Z","timestamp":1780519367051,"version":"3.54.1"},"reference-count":15,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:00:00Z","timestamp":1700006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China","award":["12072354"],"award-info":[{"award-number":["12072354"]}]},{"name":"the National Natural Science Foundation of China","award":["12032020"],"award-info":[{"award-number":["12032020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the coupling effect of multiphysical fields of droplet migration is deeply studied by constructing a physical model of droplet migration with multiphysical fields. Digital holographic interferometry and particle image velocimetry are used to simultaneously measure the temperature and velocity fields of the mother liquor in the process of droplet migration for the first time. Due to the advancements of measuring, the zero-velocity region is also in the region where the thermal wake appears, four vortexes appear in the droplet migration and the off-axis behavior of double-droplet migration is found. The aim of this work is to analyze the coupling relationship of multiphysical fields, so as to reveal the physical laws of thermocapillary migration of single droplet and multiple droplets with the same phase and heterophase and to study the driving mechanism of the thermocapillary force and the flow of the mother liquor.<\/jats:p>","DOI":"10.3390\/sym15112069","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T10:51:37Z","timestamp":1700045497000},"page":"2069","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["The Mechanism of Droplet Thermocapillary Migration Coupled with Multi-Physical Fields"],"prefix":"10.3390","volume":"15","author":[{"given":"Zhijun","family":"Ye","sequence":"first","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"College of Engineering Sciences, Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Chen","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Yang","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Di","family":"Wu","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia","family":"Wang","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Hu","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Duan","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"College of Engineering Sciences, Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Kang","sequence":"additional","affiliation":[{"name":"National Microgravity Laboratory (NML), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"College of Engineering Sciences, Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1017\/S0022112059000684","article-title":"The motion of bubbles in a vertical temperature gradient","volume":"6","author":"Young","year":"1959","journal-title":"J. Fluid Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/0021-9797(90)90054-R","article-title":"Thermocapillary migration of a liquid drop normal to a plane surface","volume":"137","author":"Barton","year":"1990","journal-title":"J. Colloid Interface Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/0301-9322(90)90079-X","article-title":"The axisymmetric thermocapillary motion of two fluid droplets","volume":"16","author":"Keh","year":"1990","journal-title":"Int. J. Multiph. Flow"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"022101","DOI":"10.1063\/1.3529442","article-title":"Confined thermocapillary motion of a three-dimensional deformable drop","volume":"23","author":"Brady","year":"2011","journal-title":"Phys. Fluids"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1017\/S0022112093002733","article-title":"Near-contact thermocapillary motion of two non-conducting drops","volume":"256","author":"Loewenberg","year":"1993","journal-title":"J. Fluid Mech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1006\/jcis.2001.7769","article-title":"Interaction of two deformable viscous drops under external temperature gradient","volume":"242","author":"Berejnov","year":"2001","journal-title":"J. Colloid Interface Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"092101","DOI":"10.1063\/1.4752028","article-title":"Numerical simulations on thermocapillary migrations of nondeformable droplets with large Marangoni numbers","volume":"24","author":"Yin","year":"2012","journal-title":"Phys. Fluids"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1017\/jfm.2015.10","article-title":"Thermocapillary migration and interaction of drops: Two non-merging drops in an aligned arrangement","volume":"766","author":"Yin","year":"2015","journal-title":"J. Fluid Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0021-9797(89)90294-4","article-title":"The migration of liquid drops in a vertical temperature gradient","volume":"133","author":"Barton","year":"1989","journal-title":"J. Colloid Interface Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1063\/1.857323","article-title":"The motion of droplets in a vertical temperature gradient","volume":"1","author":"Delitzsch","year":"1989","journal-title":"Phys. Fluids A Fluid Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2636","DOI":"10.1016\/j.ijheatmasstransfer.2005.12.019","article-title":"Experimental investigations on interaction of two drops by thermocapillary-buoyancy migration","volume":"49","author":"Kang","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_12","first-page":"1","article-title":"Experimental research on thermocapillary migration of drops by using digital holographic interferometry. Exp","volume":"57","author":"Zhang","year":"2016","journal-title":"Fluids"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s12217-017-9578-1","article-title":"Experimental Research on Thermocapillary\u2014Buoyancy Migration","volume":"30","author":"Zhang","year":"2018","journal-title":"Microgravity-Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"026310","DOI":"10.1103\/PhysRevE.85.026310","article-title":"Thermocapillary migration in small-scale temperature gradients: Application to optofluidic drop dispensing","volume":"85","author":"Vincent","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.1007\/s10973-022-11906-3","article-title":"Analytical study of a moving boundary problem describing sublimation process of a humid porous body with convective heat and mass transfer. Journal of thermal analysis and calorimetry","volume":"148","author":"Vikas","year":"2023","journal-title":"J. Therm. Anal. Calorim."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/2069\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:23:24Z","timestamp":1760131404000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/2069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,15]]},"references-count":15,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["sym15112069"],"URL":"https:\/\/doi.org\/10.3390\/sym15112069","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,15]]}}}