{"id":1686,"date":"2008-01-16T17:33:25","date_gmt":"2008-01-16T22:33:25","guid":{"rendered":"https:\/\/engineering.jhu.edu\/magazine-archive\/?p=1686"},"modified":"2014-12-16T17:34:06","modified_gmt":"2014-12-16T22:34:06","slug":"fixing-ficks-law","status":"publish","type":"post","link":"https:\/\/engineering.jhu.edu\/magazine-archive\/2008\/01\/fixing-ficks-law\/","title":{"rendered":"Fixing Fick\u2019s Law"},"content":{"rendered":"<p><strong>Marc Donohue<\/strong>, the Whiting School\u2019s vice dean of research, places a cup of water on a table in his office. A cherry-flavored Life Saver rests at the bottom. \u201cThat\u2019s diffusion,\u201d he says, pointing at the cup.<\/p>\n<p>Donohue has been working to better understand diffusion for nearly a decade. Recently, he and a team of colleagues shed new light on a classic diffusion equation\u2014known as Fick\u2019s Law\u2014that has caused questions among mathematicians and researchers for nearly a century.<\/p>\n<p>\u201cEinstein gave a lot of credence to the idea that Fick\u2019s Law is correct,\u201d says Donohue, a professor in the Department of Chemical and Biomolecular Engineering. \u201cBut,\u201d he concludes, \u201chis analysis of it was overly simplistic.\u201d<\/p>\n<p>First described by physiologist Adolf Fick in 1855, Fick\u2019s Law provides a mathematical explanation for diffusion. Specifically, it holds that during diffusion (the process by which molecules randomly and gradually spread from a high concentration to a low), the flux\u2014or rate\u2014at which the molecules spread is proportional to the concentration gradient.<br \/>\n<a href=\"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/Ficks-Law.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1687\" src=\"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/Ficks-Law.jpg\" alt=\"Fick's Law\" width=\"244\" height=\"291\" \/><\/a><\/p>\n<p>To illustrate, Donohue uses the submerged Life Saver and the ring of reddish-pink that slowly colors the water at the cup\u2019s bottom. Left to sit for a week, the red coloring slowly creeps toward the top, until finally all the water in the cup is an even shade of pale red.<\/p>\n<p>Classical Fick\u2019s Law holds that the time it takes for the red to reach the top of the cup depends on the concentration gradient. \u201cBut, for the past century, everyone has known that concentration is not really the right variable to use in the equation,\u201d says Donohue. \u201cInstead, everyone believed that the flux is proportional to the gradient of the chemical potential.\u201d In other words, the amount by which the free energy of the system (i.e., cup\u2019s water) would change if another particle (i.e., Life Saver) was introduced.<\/p>\n<p>So, Donohue, along with Gregory Aranovich, a fellow professor in the department, and a cadre of graduate students, set out to determine whether the chemical potential is the true driving force for the equation.<\/p>\n<p>They concluded that it isn\u2019t. At the same time, they discovered an even bigger problem. \u201cWe knew that concentration is not the driving force for diffusion,\u201d Donohue says. \u201cWe soon learned that chemical potential is not, either. But then we determined that the equation itself is wrong.\u201d<\/p>\n<p>To develop a more robust and accurate theory, the team began to look at instances in which Fick\u2019s Law doesn\u2019t work. \u201cOne of the things we then predicted is that while diffusion is a dissipative process in which molecules move from high to low concentration, it also includes a wave phenomenon.\u201d Previously, it was thought that during diffusion the random movement of molecules occurs on an infinitesimally small scale; that each molecule moves in one direction a tiny bit and then in another a tiny bit, and so forth. Donohue found that those distances can be large and, in some instances, density waves are created that lead to a layered buildup of molecules.<\/p>\n<p>Profiled across a graph, classical Fick\u2019s Law looks like a loaf of bread: an even distribution of molecules over time. Donohue\u2019s theory, on the same graph, looks like a frontal silhouette of Batman\u2019s head. It\u2019s generally round, but the density waves create two spiky ears. \u201cWe call it the Batman Profile,\u201d Donohue explains with a hint of a smile.<\/p>\n<p>The team found that density waves manifest in a variety of conditions. For example, in low pressure gases, or when diffusion occurs on a really small scale, such as in nanoporous materials, or on a really large scale, such as in outer space where molecules travel long distances before colliding with anything. Ultimately, it means that the definition of Fick\u2019s Law as Einstein derived it is flawed, and that there is a better explanation to be found.<\/p>\n<p>\u201cBut, this is not going to be solved completely in my lifetime,\u201d Donohue says. \u201cOur biggest contribution is that we\u2019ve shown people that the current theory is limited in its applicability, and we\u2019re pointing them in the direction of a more complete theory.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Marc Donohue, the Whiting School\u2019s vice dean of research, places a cup of water on a table in his office. A cherry-flavored Life Saver rests at the bottom. \u201cThat\u2019s diffusion,\u201d he says, pointing at the cup. Donohue has been working to better understand diffusion for nearly a decade. Recently, he and a team of colleagues&#8230;<\/p>\n","protected":false},"author":4,"featured_media":1687,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[75],"tags":[],"class_list":["post-1686","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-research-development","issue-winter-2008"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fixing Fick\u2019s Law - JHU Engineering Magazine<\/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:\/\/engineering.jhu.edu\/magazine-archive\/2008\/01\/fixing-ficks-law\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fixing Fick\u2019s Law - JHU Engineering Magazine\" \/>\n<meta property=\"og:description\" content=\"Marc Donohue, the Whiting School\u2019s vice dean of research, places a cup of water on a table in his office. A cherry-flavored Life Saver rests at the bottom. \u201cThat\u2019s diffusion,\u201d he says, pointing at the cup. Donohue has been working to better understand diffusion for nearly a decade. 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