{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:15:10Z","timestamp":1761218110304,"version":"3.41.2"},"reference-count":22,"publisher":"AIP Publishing","issue":"11","license":[{"start":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T00:00:00Z","timestamp":1541376000000},"content-version":"vor","delay-in-days":4,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T00:00:00Z","timestamp":1541376000000},"content-version":"tdm","delay-in-days":4,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["17K06173","18K03958"],"award-info":[{"award-number":["17K06173","18K03958"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2018,11,1]]},"abstract":"<jats:p>We experimentally examine the Poiseuille flow of viscoelastic fluids over wavy surfaces. Five precision microfabricated flow channels are utilized, each of depth 2d = 400 \u03bcm, spanwise width w = 10d and with a sinusoidal undulation of amplitude A = d\/20 on one of the spanwise walls. The undulation wavelength \u03bb is varied between each of the channels, providing dimensionless channel depths \u03b1 in the range 0.2\u03c0 \u2264 \u03b1 = 2\u03c0d\/\u03bb \u2264 3.2\u03c0. Nine viscoelastic polymer solutions are formulated, spanning more than four orders in elasticity number El and are tested in the wavy channels over a wide range of Reynolds and Weissenberg numbers. Flow velocimetry is used to observe and measure the resulting flow patterns. Perturbations to the Poiseuille base flow caused by the wavy surfaces are quantified by the depth of their penetration P into the flow domain. Consistent with theoretical predictions made for wavy plane-Couette flow [J. Page and T. A. Zaki, \u201cViscoelastic shear flow over a wavy surface,\u201d J. Fluid Mech. 801, 392\u2013429 (2016)], we observe three distinct flow regimes (\u201cshallow elastic,\u201d \u201cdeep elastic\u201d and \u201ctranscritical\u201d) that can be assembled into a \u201cphase diagram\u201d spanned by two dimensionless parameters: \u03b1 and the depth of the theoretically predicted critical layer\u2008\u03a3\u223cEl. Our results provide the first experimental verification of this phase diagram and thus constitute strong evidence for the existence of the predicted critical layer. In the inertio-elastic transcritical regime, a surprising amplification of the perturbation occurs at the critical layer, strongly influencing P. These effects are of likely importance in widespread inertio-elastic flows in pipes and channels, such as in polymer turbulent drag reduction.<\/jats:p>","DOI":"10.1063\/1.5057392","type":"journal-article","created":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T19:28:28Z","timestamp":1541446108000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":16,"title":["\u201cPhase diagram\u201d for viscoelastic Poiseuille flow over a wavy surface"],"prefix":"10.1063","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1884-4100","authenticated-orcid":false,"given":"Simon J.","family":"Haward","sequence":"first","affiliation":[{"name":"Okinawa Institute of Science and Technology 1 , Onna, Okinawa 904-0495, Japan"}]},{"given":"Jacob","family":"Page","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge 2 , Wilberforce Road, Cambridge CB3 0WA, United Kingdom"}]},{"given":"Tamer A.","family":"Zaki","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Johns Hopkins University 3 , Baltimore, Maryland 21218, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1222-6264","authenticated-orcid":false,"given":"Amy Q.","family":"Shen","sequence":"additional","affiliation":[{"name":"Okinawa Institute of Science and Technology 1 , Onna, Okinawa 904-0495, Japan"}]}],"member":"317","published-online":{"date-parts":[[2018,11,5]]},"reference":[{"key":"2024031600560218200_c1","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.1122\/1.3626584","article-title":"Effects of weak elasticity on the stability of high Reynolds number co-and counter-rotating Taylor-Couette flows","volume":"55","year":"2011","journal-title":"J. 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