{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T16:34:37Z","timestamp":1760546077226},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,3,1]],"date-time":"2011-03-01T00:00:00Z","timestamp":1298937600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rheol Acta"],"published-print":{"date-parts":[[2011,3]]},"DOI":"10.1007\/s00397-011-0539-0","type":"journal-article","created":{"date-parts":[[2011,3,31]],"date-time":"2011-03-31T01:03:18Z","timestamp":1301533398000},"page":"277-290","source":"Crossref","is-referenced-by-count":18,"title":["Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: effects of flow geometry"],"prefix":"10.1007","volume":"50","author":[{"given":"Zhuo","family":"Li","sequence":"first","affiliation":[]},{"given":"Xue-Feng","family":"Yuan","sequence":"additional","affiliation":[]},{"given":"Simon J.","family":"Haward","sequence":"additional","affiliation":[]},{"given":"Jeffrey A.","family":"Odell","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Yeates","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,4,1]]},"reference":[{"issue":"1","key":"539_CR1","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/S0377-0257(01)00164-1","volume":"103","author":"M Aboubacar","year":"2002","unstructured":"Aboubacar M, Matallah H, Webster MF (2002) Highly elastic solutions for Oldroyd-B and Phan-Thien\/Tanner fluids with a finite volume\/element method: planar contraction flows. J NonNewtonian Fluid Mech 103(1):65\u2013103","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"2\u20133","key":"539_CR2","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0377-0257(00)00121-X","volume":"93","author":"MA Alves","year":"2000","unstructured":"Alves MA, Pinho FT, Oliveira PJ (2000) Effect of a high-resolution differencing scheme on finite-volume predictions of viscoelastic flows. J NonNewtonian Fluid Mech 93(2\u20133):287\u2013314","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"11","key":"539_CR4","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jnnfm.2004.01.022","volume":"122","author":"MA Alves","year":"2004","unstructured":"Alves MA, Oliveira PJ, Pinho FT (2004) On the effect of contraction ratio in viscoelastic flow through abrupt contractions. J NonNewtonian Fluid Mech 122(11):117\u2013130","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"11","key":"539_CR5","doi-asserted-by":"crossref","first-page":"2908","DOI":"10.1002\/aic.10555","volume":"51","author":"MA Alves","year":"2005","unstructured":"Alves MA, Pinho FT, Oliveira PJ (2005) Visualizations of Boger fluid flows in a 4:1 square-square contraction. AIChE J 51(11):2908\u20132922","journal-title":"AIChE J"},{"issue":"2\u20133","key":"539_CR6","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/0377-0257(96)01470-X","volume":"65","author":"A Baloch","year":"1996","unstructured":"Baloch A, Townsend P, Webster MF (1996) On vortex development in viscoelastic expansion and contraction flows. J NonNewtonian Fluid Mech 65(2\u20133):133\u2013149","journal-title":"J NonNewtonian Fluid Mech"},{"key":"539_CR8","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0377-0257(88)85012-2","volume":"27","author":"DM Binding","year":"1988","unstructured":"Binding DM (1988) An approximate analysis for contraction and converging flows. J NonNewtonian Fluid Mech 27:173\u2013189","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"2\u20133","key":"539_CR10","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0377-0257(88)85026-2","volume":"30","author":"DM Binding","year":"1988","unstructured":"Binding DM, Walters K (1988) On the use of flow through a contraction in estimating the extensional viscosity of mobile polymer solutions. J NonNewton Fluid Mech 30(2\u20133):233\u2013250","journal-title":"J NonNewton Fluid Mech"},{"key":"539_CR12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1146\/annurev.fl.19.010187.001105","volume":"19","author":"DV Boger","year":"1987","unstructured":"Boger DV (1987) Viscoelastic flows through contractions. Ann Rev Fluid Mech 19:157\u2013182","journal-title":"Ann Rev Fluid Mech"},{"issue":"5","key":"539_CR13","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1002\/aic.690240513","volume":"24","author":"PJ Cable","year":"1978","unstructured":"Cable PJ, Boger DV (1978a) A comprehensive experimental investigation of tubular entry flow of viscoelastic fluids. Part I. Vortex characteristics in stable flow. AIChE J 24(5):869\u2013879","journal-title":"AIChE J"},{"issue":"6","key":"539_CR14","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1002\/aic.690240608","volume":"24","author":"PJ Cable","year":"1978","unstructured":"Cable PJ, Boger DV (1978b) A comprehensive experimental investigation of tubular entry flow of viscoelastic fluids. Part II. The velocity field in stable flow. AIChE J 24(6):992\u2013999","journal-title":"AIChE J"},{"issue":"1","key":"539_CR15","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1002\/aic.690250117","volume":"25","author":"PJ Cable","year":"1979","unstructured":"Cable PJ, Boger DV (1979) A comprehensive experiental investigation of tubular entry flow of viscoelastic fluids. Part III. Unstable flow. AIChE J 25(1):152\u2013159","journal-title":"AIChE J"},{"issue":"1","key":"539_CR16","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1002\/pen.760120111","volume":"12","author":"FN Cogswell","year":"1972","unstructured":"Cogswell FN (1972) Converging flow of polymer melts in extrusion dies. Polym Eng Sci 12(1):64\u201373","journal-title":"Polym Eng Sci"},{"issue":"2","key":"539_CR18","doi-asserted-by":"crossref","first-page":"5943","DOI":"10.1021\/ma00022a008","volume":"24","author":"K Devanand","year":"1991","unstructured":"Devanand K, Selser JC (1991) Asymptotic behavior and long-range interactions in aqueous solutions of poly (ethylene oxide). Macromolecules 24(2):5943\u20135947","journal-title":"Macromolecules"},{"issue":"11","key":"539_CR19","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0377-0257(86)80013-1","volume":"20","author":"RE Evans","year":"1986","unstructured":"Evans RE, Walters K (1986) Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquids. J NonNewton Fluid Mech 20(11):11\u201329","journal-title":"J NonNewton Fluid Mech"},{"issue":"1","key":"539_CR20","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0377-0257(89)85043-8","volume":"32","author":"RE Evans","year":"1989","unstructured":"Evans RE, Walters K (1989) Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows. J NonNewtonian Fluid Mech 32(1):95\u2013105","journal-title":"J NonNewtonian Fluid Mech"},{"key":"539_CR21","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1126\/science.1083694","volume":"300","author":"A Groisman","year":"2003","unstructured":"Groisman A, Enzelberger M, Quake SR (2003) Microfluidic memory and control devices. Science 300:955\u2013958","journal-title":"Science"},{"key":"539_CR22","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.jnnfm.2008.05.005","volume":"155","author":"S Gulati","year":"2008","unstructured":"Gulati S, Muller SJ, Liepmann D (2008) Direct measurements of viscoelastic flows of DNA in a 2:1 abrupt planar micro-contraction. J NonNewtonian Fluid Mech 155:51\u201356","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"7","key":"539_CR23","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1007\/s00397-010-0453-x","volume":"49","author":"SJ Haward","year":"2010","unstructured":"Haward SJ, Odell JA, Li Z, Yuan XF (2010a) The rheology of polymer solution elastic strands in extensional flow. Rheol Acta 49(7):781\u2013788","journal-title":"Rheol Acta"},{"issue":"23\u201324","key":"539_CR24","doi-asserted-by":"crossref","first-page":"1654","DOI":"10.1016\/j.jnnfm.2010.09.002","volume":"165","author":"SJ Haward","year":"2010","unstructured":"Haward SJ, Li Z, Lighter D, Thomas B, Odell JA, Yuan XF (2010b) Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro\u2013contraction. J NonNewtonian Fluid Mech 165(23\u201324):1654\u20131669","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"3\u20134","key":"539_CR25","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0377-0257(82)80038-4","volume":"11","author":"DF James","year":"1982","unstructured":"James DF, Saringer JH (1982) Flow of dilute polymer solutions through converging channels. J NonNewtonian Fluid Mech 11(3\u20134):317\u2013339","journal-title":"J NonNewtonian Fluid Mech"},{"key":"539_CR28","doi-asserted-by":"crossref","unstructured":"Li Z, Yuan XF, Haward SF, Odell JA, Yeates S (2011) Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: a study of a benchmark flow problem. J NonNewtonian Fluid Mech (in press)","DOI":"10.1016\/j.jnnfm.2011.04.010"},{"key":"539_CR29","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1017\/S0022112091001489","volume":"223","author":"GH McKinley","year":"1991","unstructured":"McKinley GH, Raiford WP, Brown RA, Armstrong RC (1991) Nonlinear dynamics of viscoelastic flow in axisymmetric abrupt contractions. J Fluid Mech 223:411\u2013456","journal-title":"J Fluid Mech"},{"issue":"2","key":"539_CR31","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0377-0257(01)00186-0","volume":"102","author":"S Nigen","year":"2002","unstructured":"Nigen S, Walters K (2002) Viscoelastic contractions flows: comparison of axisymmetric and planar configurations. J NonNewtonian Fluid Mech 102(2):343\u2013359","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"6","key":"539_CR32","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1007\/s00397-009-0410-8","volume":"49","author":"SC Omowunmi","year":"2010","unstructured":"Omowunmi SC, Yuan XF (2010) Modelling the three-dimensional flow of a semi-dilute polymer solution in microfluidics\u2014on the effect of aspect ratio. Rheol Acta 49(6):585\u2013595","journal-title":"Rheol Acta"},{"key":"539_CR33","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0377-0257(96)01446-2","volume":"65","author":"B Purnode","year":"1996","unstructured":"Purnode B, Crochet MJ (1996) Flows of polymer solutions through contractions. Part 1: flows of polyacrylamide solutions through planar contractions. J NonNewtonian Fluid Mech 65:269\u2013289","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"1","key":"539_CR34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0377-0257(94)85056-9","volume":"52","author":"LM Quinzani","year":"1994","unstructured":"Quinzani LM, Armstrong RC, Brown RA (1994) Birefringence and laser-Doppler velocimetry (LDV) studies of viscoelastic flow through a planar contraction. J NonNewtonian Fluid Mech 52(1):1\u201336","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"6","key":"539_CR35","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1122\/1.550725","volume":"39","author":"LM Quinzani","year":"1995","unstructured":"Quinzani LM, Armstrong RC, Brown RA (1995) Use of coupled birefringence and LDV studies of flow through a planar contraction to test constitutive equations for concentrated polymer solutions. J Rheol 39(6):1201\u20131228","journal-title":"J Rheol"},{"key":"539_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jnnfm.2005.04.006","volume":"129","author":"LE Rodd","year":"2005","unstructured":"Rodd LE, Scott TP, Boger DV, Cooper-White JJ, Mckinley GH (2005) The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J NonNewtonian Fluid Mech 129:1\u201322","journal-title":"J NonNewtonian Fluid Mech"},{"key":"539_CR37","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.jnnfm.2007.02.006","volume":"143","author":"LE Rodd","year":"2007","unstructured":"Rodd LE, Boger DV, Cooper-White JJ, Mckinley GH (2007) Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries. J NonNewtonian Fluid Mech 143:170\u2013191","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"1\u20132","key":"539_CR38","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/S0377-0257(98)00202-X","volume":"86","author":"JP Rothstein","year":"1999","unstructured":"Rothstein JP, McKinley GH (1999) Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisymmetric contraction\/expansion. J NonNewtonian Fluid Mech 86(1\u20132):61\u201388","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"1","key":"539_CR39","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0377-0257(01)00094-5","volume":"98","author":"JP Rothstein","year":"2001","unstructured":"Rothstein JP, McKinley GH (2001) The axisymmetric contraction\u2013expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop. J NonNewtonian Fluid Mech 98(1):33\u201363","journal-title":"J NonNewtonian Fluid Mech"},{"key":"539_CR40","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0377-0257(88)85056-0","volume":"29","author":"SA White","year":"1988","unstructured":"White SA, Baird DG (1988) Flow visualization and birefringence studies on planar entry flow behavior of polymer melts. J NonNewtonian Fluid Mech 29:245\u2013267","journal-title":"J NonNewtonian Fluid Mech"},{"key":"539_CR41","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0257(85)87012-9","volume":"19","author":"PR Williams","year":"1985","unstructured":"Williams PR, Williams RW (1985) On the planar extensional viscosity of mobile liquids. J NonNewtonian Fluid Mech 19:53\u201380","journal-title":"J NonNewtonian Fluid Mech"},{"issue":"1\u20133","key":"539_CR42","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0377-0257(97)00072-4","volume":"74","author":"S Xue","year":"1998","unstructured":"Xue S, Phan-Thien N, Tanner RI (1998) Three dimensional numerical simulations of viscoelastic flows through planar contractions. J NonNewtonian Fluid Mech 74(1\u20133):195\u2013245","journal-title":"J NonNewtonian Fluid Mech"}],"container-title":["Rheologica Acta"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00397-011-0539-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00397-011-0539-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00397-011-0539-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,9]],"date-time":"2019-06-09T11:10:07Z","timestamp":1560078607000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00397-011-0539-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["539"],"URL":"https:\/\/doi.org\/10.1007\/s00397-011-0539-0","relation":{},"ISSN":["0035-4511","1435-1528"],"issn-type":[{"value":"0035-4511","type":"print"},{"value":"1435-1528","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}