{"id":6510,"date":"2021-04-10T20:32:28","date_gmt":"2021-04-10T20:32:28","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=6510"},"modified":"2025-05-05T18:17:55","modified_gmt":"2025-05-05T18:17:55","slug":"18-357-interfacial-phenomena","status":"publish","type":"post","link":"http:\/\/thales.mit.edu\/bush\/index.php\/2021\/04\/10\/18-357-interfacial-phenomena\/","title":{"rendered":"18.357 Interfacial Phenomena"},"content":{"rendered":"\n<div class=\"wp-block-cover alignwide is-light is-style-twentytwentyone-border\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-subtle-background-color has-background-dim-100 has-background-dim\"><\/span><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\"><div class=\"wp-block-image is-resized\">\n<figure class=\"alignright size-full\"><img decoding=\"async\" src=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Poster-2025-1.pdf\" alt=\"\" class=\"wp-image-7349\" title=\"Poster-2021\"\/><\/figure>\n<\/div>\n\n\n<p>We consider fluid systems dominated by the influence of interfacial tension. The roles of curvature pressure and Marangoni stress are elucidated in a variety of situations. Particular attention will be given to the dynamics of drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics. Theoretical developments will be accompanied by classroom demonstrations. The role of surface tension in biology will be highlighted, as will be hydrodynamic quantum analogs.<\/p>\n\n\n\n<p><strong>LINKS<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><a href=\"http:\/\/ocw.mit.edu\/courses\/mathematics\/18-357-interfacial-phenomena-fall-2010\/\">18.357 on MIT\u2019s Open Course Ware, &nbsp;2010 edition<\/a><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><a href=\"http:\/\/math.mit.edu\/~bush\/wordpress\/wp-content\/uploads\/2018\/02\/18.357-LecNotes-2010.pdf\">Lecture notes from 2010<\/a><\/p>\n\n\n\n<p><strong>HANDOUTS<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Poster-2025.pdf\">Course Poster<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-outline-2025-1.pdf\">Course Outline<\/a><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><a href=\"http:\/\/math.mit.edu\/~bush\/wordpress\/wp-content\/uploads\/2016\/02\/Handout-Stone-TensorNotess.pdf\">Handout 1: &nbsp;Howard Stone\u2019s Notes on Vector and Tensor Calculus<\/a><\/p>\n\n\n\n<p><strong>LECTURE NOTES AND SLIDES<\/strong><\/p>\n\n\n\n<p>Lecture 1:   Course Overview,  Song and Dance<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Lecture 2:   <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes-2-3.pdf\">Notes<\/a>  ,   <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-Lec2-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 3:   <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes-2-3.pdf\">Notes<\/a> ,   <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-Lec3-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 4:   <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes4.pdf\">Notes<\/a><\/p>\n\n\n\n<p>Lecture 5:  <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes5.pdf\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes5.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-Lec5-slides-2025.pdf\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-Lec5-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 6:  <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes6.pdf\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/LectureNotes6.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-Lec6-slides-2025.pdf\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/18357-Lec6-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 7: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes7.pdf\">Notes<\/a><\/p>\n\n\n\n<p>Lecture 8: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes8.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec8-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 9: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes9-10.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec9-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 10: Notes (see Lecture.9) , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec10-slides-2025.pdf\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec10-slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 11: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes11.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec11-Slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 12: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes12.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec12-Slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 13: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes13.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec13-Slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 14: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/LectureNotes14.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/18357-Lec14-Slides-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 15: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/LectureNotes15.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/18357-Lec15-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 16: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/LectureNotes16.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/18357-Lec16-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 17: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/LectureNotes17.pdf\">Notes<\/a><\/p>\n\n\n\n<p>Lectures 18-19: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/LectureNotes18.pdf\">Notes<\/a><\/p>\n\n\n\n<p>Lectures 20-21: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/LectureNotes19.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/18357-Lec21-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 22: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/LectureNotes20.pdf\">Notes<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/18357-Lec22-2025.pdf\">Slides<\/a><\/p>\n\n\n\n<p>Lecture 23: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/05\/COVID-2022A.pdf\">SlidesA<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/05\/COVID-2022B.pdf\">SlidesB<\/a><\/p>\n\n\n\n<p>Lecture 24: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/05\/18357-Lec24-2025A.pdf\">SlidesA<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/05\/18357-Lec24-2025B.pdf\">SlidesB<\/a> , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/05\/18357-Lec24-2025C.pdf\">SlidesC<\/a><\/p>\n\n\n\n<p><strong>PROBLEM SET MATERIALS<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/03\/PS1-18357-2025-1.pdf\">Problem Set 1<\/a> (lightly revised!)<\/p>\n\n\n\n<p>Supplements for Problem Set 1: <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/Handout-Rain.jpg\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/Handout-Rain.jpg\">Streaks of Rain<\/a> (for Problem 2c) , <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/Handout-Hele-Shaw.pdf\" data-type=\"link\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/02\/Handout-Hele-Shaw.pdf\">Hele-Shaw Flows<\/a> (for Problem 5b)<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/PS2-18357-2025.pdf\">Problem Set 2<\/a><\/p>\n\n\n\n<p>Supplements for Problem 3:  <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/squeezefilm.pdf\">Squeeze Film Notes<\/a>  ,  <a href=\"https:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2017\/12\/Geri-2017.pdf\">Geri et al. (JFM, 2017)<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2025\/04\/18.355-121-150.pdf\">Supplementary Notes on Lubrication Theory<\/a> (starts on page 133)<\/p>\n<\/div><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-6510","post","type-post","status-publish","format-standard","hentry","category-uncategorized","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v16.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>18.357 Interfacial Phenomena - John W. M. Bush<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/thales.mit.edu\/bush\/index.php\/2021\/04\/10\/18-357-interfacial-phenomena\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"18.357 Interfacial Phenomena - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2021\/04\/10\/18-357-interfacial-phenomena\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. 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