{"id":11521,"date":"2015-10-14T14:55:13","date_gmt":"2015-10-14T19:55:13","guid":{"rendered":"https:\/\/college.unc.edu\/?p=11521"},"modified":"2024-07-02T16:08:09","modified_gmt":"2024-07-02T16:08:09","slug":"pipe-fluid-flow","status":"publish","type":"post","link":"https:\/\/collegearchive.unc.edu\/?p=11521","title":{"rendered":"Mathematics research reveals that the shape of a pipe dramatically affects how pollutants and other chemicals will spread"},"content":{"rendered":"
\"UNC<\/a>
UNC researchers find that the shape of a pipe dramatically affects how a pollutant will spread in the moments after it is introduced into a fluid flow.<\/figcaption><\/figure>\n

Researchers have long known and well-documented how dye disperses when injected into a fluid flowing through a pipe.<\/p>\n

But a team of mathematicians at the University of North Carolina at Chapel Hill has discovered that the size and shape of the pipe dramatically affects how the dye will disperse in the early moments after injection.<\/p>\n

Their results have major implications for drug delivery, chemical manufacturing, managing pollutants spilled in waterways or any application that involves mixing substances into fluids that are flowing.<\/p>\n

\u201cSpecifically, we found that flows in rectangular ducts instantaneously distribute pollutants asymmetrically as opposed to the even spreading observed in circular or elliptical pipe flows,\u201d said Richard M. McLaughlin, professor and chair of the department of mathematics in UNC-Chapel Hill\u2019s College of Arts and Sciences. \u201cWe also found that whether the duct is skinny or fat makes a huge difference.\u201d<\/p>\n

McLaughlin, co-author with Kenan Distinguished Professor Roberto Camassa, both experts in fluid dynamics, and graduate students Manuchehr Aminian and Francesca Bernardi, report their results in \u201cSquaring the Circle: Geometric Skewness and Symmetry Breaking for Passive Scalar Transport in Ducts and Pipes,\u201d published in the Oct. 5 issue of Physical Review Letters.<\/p>\n

In skinny ducts, dye disperses with a sharp front followed by a long tapering tail, Camassa said. In fat ducts, the dispersion is reversed, with a gradual spread building to a sharp front.<\/p>\n

\u201cThe area of the two rectangles may be the same, but the shape makes a significant difference in how the dye disperses,\u201d he said.<\/p>\n

Knowing that could enable drug device makers, for instance, to produce rectangular devices of varying shapes that would allow some treatments to be delivered with a sharp punch and others dispensed gradually, based on what works best.<\/p>\n

\u201cThe most surprising finding,\u201d Camassa said, \u201cis that the rectangle that best mimics the spread that occurs in a round pipe is not a square, as one would expect, but a flatter rectangle with an aspect ratio of 1.82, meaning its width is approximately twice its height.\u201d<\/p>\n

The study may be found online: http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.115.154503<\/a><\/p>\n

The research was funded with grants from the National Science Foundation.<\/p>\n

By Cyndy Falgout
\n<\/strong><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Results from mathematicians in the College of Arts and Sciences have major implications for drug delivery and managing pollutants spilled in waterways.<\/p>\n","protected":false},"author":4,"featured_media":11522,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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