{"id":229,"date":"2008-01-22T00:25:03","date_gmt":"2008-01-22T05:25:03","guid":{"rendered":"http:\/\/arxivblog.com\/?p=229"},"modified":"2008-01-22T00:26:50","modified_gmt":"2008-01-22T05:26:50","slug":"fractal-fingers-and-zero-surface-tension","status":"publish","type":"post","link":"http:\/\/arxivblog.com\/?p=229","title":{"rendered":"Fractal fingers and zero surface tension"},"content":{"rendered":"<p><a href=\"http:\/\/arxivblog.com\/wp-content\/uploads\/2008\/01\/zero-surface-tension.jpg\" title=\"Zero surface tension\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/arxivblog.com\/wp-content\/uploads\/2008\/01\/zero-surface-tension.jpg\" alt=\"Zero surface tension\" height=\"225\" width=\"451\" \/><\/a><\/p>\n<p>Ah always thought a fingering instability was what happened after a misunderstanding on a first date.<\/p>\n<p>But apparently it&#8217;s also a hydrodynamic phenomenon, when one fluid displaces another.<\/p>\n<p>This kinda displacement is a complex process; so complex that in most cases it is mathematically intractable. Ya just gotta try it and see.<\/p>\n<p>However, one of the few mathematically tractable examples is the 2-dimensional  case of  a less viscous fluid displacing a more viscous neighbor with zero surface tension.<\/p>\n<p>The math predicts that fractal-like fingers of the less viscous fluid should penetrate the more viscous one.<\/p>\n<p>And that&#8217;s exactly what happens. And here&#8217;s the proof, the picture above taken by Sid Nagel and colleagues at the University of Chicago. The grey area is tiny glass beads that have been sandwiched in a thin layer between two flat plates. The black area is air injected into the plates.<\/p>\n<p>The glass beads behave like a liquid but because there are no forces between them, the surface tension  is zero. And the air indeed displaces its more viscous neighbor forming a fractal pattern, just as the math predicts.<\/p>\n<p>A neat experiment. Next up, those awkward Prom moments.<\/p>\n<p>Ref: <a href=\"http:\/\/arxiv.org\/abs\/0712.2019\">arxiv.org\/abs\/0712.2019<\/a>: Toward the Zero Surface Tension Limit: The Granular Fingering Instability<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ah always thought a fingering instability was what happened after a misunderstanding on a first date. But apparently it&#8217;s also a hydrodynamic phenomenon, when one fluid displaces another. This kinda displacement is a complex process; so complex that in most cases it is mathematically intractable. Ya just gotta try it and see. However, one of [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-229","post","type-post","status-publish","format-standard","hentry","category-booze"],"_links":{"self":[{"href":"http:\/\/arxivblog.com\/index.php?rest_route=\/wp\/v2\/posts\/229","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/arxivblog.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/arxivblog.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/arxivblog.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/arxivblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=229"}],"version-history":[{"count":0,"href":"http:\/\/arxivblog.com\/index.php?rest_route=\/wp\/v2\/posts\/229\/revisions"}],"wp:attachment":[{"href":"http:\/\/arxivblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/arxivblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=229"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/arxivblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}