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{"title":"纳米级润湿性表征--解读纳米孔中液滴的形态演变","authors":"Wenzhen Chu, Kaiqiang Zhang","doi":"10.1002/aic.18623","DOIUrl":null,"url":null,"abstract":"Nanoscale wettability, crucial for various disciplines in science and engineering, challenges traditional theory, particularly the Young's equation. This study proposes and validates a modified format of the Young's equation under nano-confinement and, for the first time, the nano-confined droplet morphological evolution and transition are investigated from thermodynamic theories and molecular dynamics simulation. The morphologies of droplets in nano-silts, identified as double-cap, single-cap, and bridge-shaped, underscore the critical roles of line tension and nano-confinement in characterizing wetting behavior. In hydrophobic nano-slits, droplets transition from the double-cap to the single-cap shape at the critical point of <span data-altimg=\"/cms/asset/8aadb0a1-cdb7-4e0f-a20c-71a72b38c4be/aic18623-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"157\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18623-math-0001.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-role=\"division\" data-semantic-speech=\"r 0 divided by upper H\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0001\" display=\"inline\" location=\"graphic/aic18623-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"2,4\" data-semantic-content=\"3\" data-semantic-role=\"division\" data-semantic-speech=\"r 0 divided by upper H\" data-semantic-type=\"infixop\"><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">r</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\">0</mn></msub><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">H</mi></mrow>$$ {r}_0/H $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> = 0.31 and to bridge shape at the critical point of <span data-altimg=\"/cms/asset/35dfa92b-d451-4a03-9eb7-7b8fa42bb1d9/aic18623-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"158\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18623-math-0002.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-role=\"division\" data-semantic-speech=\"r 0 divided by upper H\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0002\" display=\"inline\" location=\"graphic/aic18623-math-0002.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"2,4\" data-semantic-content=\"3\" data-semantic-role=\"division\" data-semantic-speech=\"r 0 divided by upper H\" data-semantic-type=\"infixop\"><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">r</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\">0</mn></msub><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">H</mi></mrow>$$ {r}_0/H $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> = 0.40. Moreover, the relative width of the neck region in the bridge-shaped droplets is found to stabilize at <span data-altimg=\"/cms/asset/db43126f-f648-40ac-a22e-92de987089a7/aic18623-math-0003.png\"></span><mjx-container ctxtmenu_counter=\"159\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18623-math-0003.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-role=\"division\" data-semantic-speech=\"w divided by r\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"3\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0003\" display=\"inline\" location=\"graphic/aic18623-math-0003.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic-role=\"division\" data-semantic-speech=\"w divided by r\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">w</mi><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"3\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">r</mi></mrow>$$ w/r $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> ratio of 1.8. Particularly, linear relationships have been established between the droplet contact angle and the parameter <span data-altimg=\"/cms/asset/f14413ee-b08c-4f8d-b354-4dabdf8920af/aic18623-math-0004.png\"></span><mjx-container ctxtmenu_counter=\"160\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18623-math-0004.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,4\" data-semantic-content=\"1\" data-semantic- data-semantic-role=\"division\" data-semantic-speech=\"upper H divided by r 0\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0004\" display=\"inline\" location=\"graphic/aic18623-math-0004.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,4\" data-semantic-content=\"1\" data-semantic-role=\"division\" data-semantic-speech=\"upper H divided by r 0\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">H</mi><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><msub data-semantic-=\"\" data-semantic-children=\"2,3\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">r</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\">0</mn></msub></mrow>$$ H/{r}_0 $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, which identify condensation and breakage of droplets within hydrophobic nano-slits. This model effectively characterizes nanoscale wettability, with precise droplet behavior predictions, which could be beneficial to enhance nano-fluid dynamics understanding and its applications in science and engineering.","PeriodicalId":120,"journal":{"name":"AIChE Journal","volume":"87 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nanoscale wettability characterization—Interpreting droplet morphological evolution in nanopores\",\"authors\":\"Wenzhen Chu, Kaiqiang Zhang\",\"doi\":\"10.1002/aic.18623\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Nanoscale wettability, crucial for various disciplines in science and engineering, challenges traditional theory, particularly the Young's equation. This study proposes and validates a modified format of the Young's equation under nano-confinement and, for the first time, the nano-confined droplet morphological evolution and transition are investigated from thermodynamic theories and molecular dynamics simulation. The morphologies of droplets in nano-silts, identified as double-cap, single-cap, and bridge-shaped, underscore the critical roles of line tension and nano-confinement in characterizing wetting behavior. In hydrophobic nano-slits, droplets transition from the double-cap to the single-cap shape at the critical point of <span data-altimg=\\\"/cms/asset/8aadb0a1-cdb7-4e0f-a20c-71a72b38c4be/aic18623-math-0001.png\\\"></span><mjx-container ctxtmenu_counter=\\\"157\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/aic18623-math-0001.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"2,4\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"r 0 divided by upper H\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"1\\\" space=\\\"1\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/aic18623-math-0001.png\\\" overflow=\\\"scroll\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"2,4\\\" data-semantic-content=\\\"3\\\" data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"r 0 divided by upper H\\\" data-semantic-type=\\\"infixop\\\"><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">r</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">0</mn></msub><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">H</mi></mrow>$$ {r}_0/H $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> = 0.31 and to bridge shape at the critical point of <span data-altimg=\\\"/cms/asset/35dfa92b-d451-4a03-9eb7-7b8fa42bb1d9/aic18623-math-0002.png\\\"></span><mjx-container ctxtmenu_counter=\\\"158\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/aic18623-math-0002.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"2,4\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"r 0 divided by upper H\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"1\\\" space=\\\"1\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0002\\\" display=\\\"inline\\\" location=\\\"graphic/aic18623-math-0002.png\\\" overflow=\\\"scroll\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"2,4\\\" data-semantic-content=\\\"3\\\" data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"r 0 divided by upper H\\\" data-semantic-type=\\\"infixop\\\"><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">r</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">0</mn></msub><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">H</mi></mrow>$$ {r}_0/H $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> = 0.40. Moreover, the relative width of the neck region in the bridge-shaped droplets is found to stabilize at <span data-altimg=\\\"/cms/asset/db43126f-f648-40ac-a22e-92de987089a7/aic18623-math-0003.png\\\"></span><mjx-container ctxtmenu_counter=\\\"159\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/aic18623-math-0003.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"w divided by r\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"1\\\" space=\\\"1\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0003\\\" display=\\\"inline\\\" location=\\\"graphic/aic18623-math-0003.png\\\" overflow=\\\"scroll\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"w divided by r\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">w</mi><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">r</mi></mrow>$$ w/r $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> ratio of 1.8. Particularly, linear relationships have been established between the droplet contact angle and the parameter <span data-altimg=\\\"/cms/asset/f14413ee-b08c-4f8d-b354-4dabdf8920af/aic18623-math-0004.png\\\"></span><mjx-container ctxtmenu_counter=\\\"160\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/aic18623-math-0004.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"0,4\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"upper H divided by r 0\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"1\\\" space=\\\"1\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"2,3\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00011541:media:aic18623:aic18623-math-0004\\\" display=\\\"inline\\\" location=\\\"graphic/aic18623-math-0004.png\\\" overflow=\\\"scroll\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"0,4\\\" data-semantic-content=\\\"1\\\" data-semantic-role=\\\"division\\\" data-semantic-speech=\\\"upper H divided by r 0\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">H</mi><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"2,3\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">r</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">0</mn></msub></mrow>$$ H/{r}_0 $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, which identify condensation and breakage of droplets within hydrophobic nano-slits. This model effectively characterizes nanoscale wettability, with precise droplet behavior predictions, which could be beneficial to enhance nano-fluid dynamics understanding and its applications in science and engineering.\",\"PeriodicalId\":120,\"journal\":{\"name\":\"AIChE Journal\",\"volume\":\"87 1\",\"pages\":\"\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIChE Journal\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/aic.18623\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, CHEMICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIChE Journal","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/aic.18623","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
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