{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T22:40:52Z","timestamp":1777329652263,"version":"3.51.4"},"reference-count":59,"publisher":"AIP Publishing","issue":"8","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2013,8,1]]},"abstract":"<jats:p>A recently developed microfluidic device, the optimized shape cross-slot extensional rheometer or OSCER [S. J. Haward, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, \u201cOptimized cross-slot flow geometry for microfluidic extensional rheometry,\u201d Phys. Rev. Lett.\u2008109, 128301 (2012)10.1103\/PhysRevLett.109.128301], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluronic acid with various molecular weights and concentrations, are formulated in order to provide fluids with a wide range of rheological properties. Semi-dilute solutions of high molecular weight polymers provide highly viscoelastic fluids with long relaxation times, which achieve a high Weissenberg number (Wi) at flow rates for which the Reynolds number (Re) remains low; hence the elasticity number El = Wi\/Re is high. Lower concentration solutions of moderate molecular weight polymers provide only weakly viscoelastic fluids in which inertia remains important and El is relatively low. Flow birefringence observations are used to visualize the nature of flow instabilities in the fluids as the volumetric flow rate through the OSCER device is steadily incremented. At low Wi and Re, all of the fluids display a steady, symmetric, and uniform \u201cbirefringent strand\u201d of highly oriented polymer molecules aligned along the outflowing symmetry axis of the test geometry, indicating the stability of the flow field under such conditions. In fluids of El &amp;gt; 1, we observe steady elastic flow asymmetries beyond a critical Weissenberg number,Wicrit, that are similar in character to those already reported in standard cross-slot geometries [e.g., P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, \u201cElastic instabilities of polymer solutions in cross-channel flow,\u201d Phys. Rev. Lett.\u200896, 144502 (2006)10.1103\/PhysRevLett.96.144502]. However, in fluids with El &amp;lt; 1 we observe a sequence of time-dependent inertio-elastic instabilities beyond a critical Reynolds number, ${\\mathop{\\rm Re}\\nolimits} _{crit} $ Re crit, characterized by high frequency spatiotemporal oscillations of the birefringent strand. By plotting the critical limits of stability for the various fluids in the Wi-Re operating space, we are able to construct a stability diagram delineating the distinct steady symmetric, steady asymmetric and inertio-elastic flow regimes in this idealized planar elongational flow device.<\/jats:p>","DOI":"10.1063\/1.4818151","type":"journal-article","created":{"date-parts":[[2013,8,28]],"date-time":"2013-08-28T22:32:00Z","timestamp":1377729120000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":45,"title":["Instabilities in stagnation point flows of polymer solutions"],"prefix":"10.1063","volume":"25","author":[{"given":"S. J.","family":"Haward","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology 1 Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, , Cambridge, Massachusetts 02139, USA"},{"name":"Faculdade de Engenharia da Universidade do Porto 2 , Centro de Estudos de Fen\u00f3menos de Transporte, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"given":"G. H.","family":"McKinley","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology 1 Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, , Cambridge, Massachusetts 02139, USA"}]}],"member":"317","published-online":{"date-parts":[[2013,8,28]]},"reference":[{"key":"2023062115361173600_c1","doi-asserted-by":"publisher","first-page":"5030","DOI":"10.1063\/1.1681018","article-title":"Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients","volume":"60","year":"1974","journal-title":"J. Chem. Phys."},{"key":"2023062115361173600_c2","first-page":"241","article-title":"Mechanical models of dilute polymer solutions for strong flows with large polymer deformations","volume":"233","year":"1974","journal-title":"Colloq. Int. C. N. R. S."},{"key":"2023062115361173600_c3","doi-asserted-by":"publisher","first-page":"3004","DOI":"10.1021\/ma00197a022","article-title":"Coil-stretch transitions in mixed shear and extensional flows of dilute polymer solutions","volume":"22","year":"1989","journal-title":"Macromolecules"},{"key":"2023062115361173600_c4","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1017\/S002211207000191X","article-title":"Slender-body theory for particles of arbitrary cross-section in Stokes flow","volume":"44","year":"1970","journal-title":"J. Fluid Mech."},{"key":"2023062115361173600_c5","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1122\/1.550372","article-title":"A filament stretching device for measurement of extensional viscosity","volume":"37","year":"1993","journal-title":"J. Rheol."},{"key":"2023062115361173600_c6","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1007\/s00397-009-0420-6","article-title":"Extensional rheology of dilute polymer solutions in oscillatory cross-slot flow: the transient behaviour of birefringent strands","volume":"49","year":"2010","journal-title":"Rheol. Acta"},{"key":"2023062115361173600_c7","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/0377-0257(90)85039-2","article-title":"An overview of the project M1","volume":"35","year":"1990","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c8","doi-asserted-by":"publisher","first-page":"128301","DOI":"10.1103\/PhysRevLett.109.128301","article-title":"Optimized cross-slot flow geometry for microfluidic extensional rheometry","volume":"109","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"2023062115361173600_c9","first-page":"240","article-title":"Design of a cross-slot flow channel for extensional viscosity measurements","volume-title":"The XVth International Congress on Rheology, The Society of Rheology 80th Annual Meeting","author":"Co","year":"2008"},{"key":"2023062115361173600_c10","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF01415506","article-title":"The extensibility of macromolecules in solution; A new focus for macromolecular science","volume":"263","year":"1985","journal-title":"Colloid Polym. Sci."},{"key":"2023062115361173600_c11","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1002\/polb.1986.090240901","article-title":"Fracture of isolated linear macromolecules in solution","volume":"24","year":"1986","journal-title":"J. Polym. Sci., Polym. Phys."},{"key":"2023062115361173600_c12","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1007\/s00397-003-0350-7","article-title":"Molecular orientation in non-Newtonian flow of dilute polymer solutions around spheres","volume":"43","year":"2004","journal-title":"Rheol. Acta"},{"key":"2023062115361173600_c13","doi-asserted-by":"publisher","first-page":"2016","DOI":"10.1126\/science.276.5321.2016","article-title":"Single polymer dynamics in an elongational flow","volume":"276","year":"1997","journal-title":"Science"},{"key":"2023062115361173600_c14","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1126\/science.281.5381.1335","article-title":"Response of flexible polymers to a sudden elongational flow","volume":"281","year":"1998","journal-title":"Science"},{"key":"2023062115361173600_c15","doi-asserted-by":"publisher","first-page":"044108","DOI":"10.1063\/1.4816708","article-title":"Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot device","volume":"7","year":"2013","journal-title":"Biomicrofluidics"},{"key":"2023062115361173600_c16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10404-012-1028-1","article-title":"Microdevices for extensional rheometry of low viscosity elastic liquids: a review","volume":"14","year":"2013","journal-title":"Microfluid. Nanofluid."},{"key":"2023062115361173600_c17","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/BF00366504","article-title":"Instabilities in viscoelastic flows","volume":"31","year":"1992","journal-title":"Rheol. Acta"},{"key":"2023062115361173600_c18","first-page":"117","article-title":"Elastically-influenced instabilities in Taylor-Couette and other flows with curved streamlines: a review","volume":"20","year":"2008","journal-title":"Korea-Aust. Rheol. J."},{"key":"2023062115361173600_c19","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1126\/science.1083694","article-title":"Microfluidic memory and control devices","volume":"300","year":"2003","journal-title":"Science"},{"key":"2023062115361173600_c20","doi-asserted-by":"publisher","first-page":"094501","DOI":"10.1103\/PhysRevLett.92.094501","article-title":"A microfluidic rectifier: anisotropic flow resistance at low Reynolds numbers","volume":"92","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2023062115361173600_c21","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1038\/35073524","article-title":"Efficient mixing at low Reynolds numbers using polymer additives","volume":"410","year":"2001","journal-title":"Nature (London)"},{"key":"2023062115361173600_c22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jnnfm.2005.04.006","article-title":"The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries","volume":"129","year":"2005","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c23","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.jnnfm.2007.02.006","article-title":"Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries","volume":"143","year":"2007","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c24","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.jnnfm.2008.05.005","article-title":"Direct measurements of viscoelastic flows of DNA in a 2:1 abrupt planar micro-contraction","volume":"155","year":"2008","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c25","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1016\/j.jnnfm.2010.06.003","article-title":"The importance of downstream events in microfluidic viscoelastic entry flows: Consequences of increasing the constriction length","volume":"165","year":"2010","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c26","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s00397-011-0539-0","article-title":"Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: effects of flow geometry","volume":"50","year":"2011","journal-title":"Rheol. Acta"},{"key":"2023062115361173600_c27","doi-asserted-by":"publisher","first-page":"951","DOI":"10.1016\/j.jnnfm.2011.04.010","article-title":"Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: A study of a benchmark flow problem","volume":"166","year":"2011","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c28","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1017\/jfm.2011.84","article-title":"Dynamics of high-Deborah-number entry flows: a numerical study","volume":"677","year":"2011","journal-title":"J. Fluid Mech."},{"key":"2023062115361173600_c29","doi-asserted-by":"publisher","first-page":"144502","DOI":"10.1103\/PhysRevLett.96.144502","article-title":"Elastic instabilities of polymer solutions in cross-channel flow","volume":"96","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"2023062115361173600_c30","doi-asserted-by":"publisher","first-page":"8782","DOI":"10.1021\/ma061355r","article-title":"Rheo-optics of equilibrium polymer solutions: Wormlike micelles in elongational flow in a microfluidic cross-slot","volume":"39","year":"2006","journal-title":"Macromolecules"},{"key":"2023062115361173600_c31","doi-asserted-by":"publisher","first-page":"164503","DOI":"10.1103\/PhysRevLett.99.164503","article-title":"Purely elastic flow asymmetries","volume":"99","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"2023062115361173600_c32","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.jnnfm.2008.06.008","article-title":"On extensibility effects in the cross-slot flow bifurcation","volume":"156","year":"2009","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c33","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1017\/S0022112008005119","article-title":"A mechanism for oscillatory instability in viscoelastic cross-slot flow","volume":"622","year":"2009","journal-title":"J. Fluid Mech."},{"key":"2023062115361173600_c34","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1039\/c1sm06494k","article-title":"Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device","volume":"8","year":"2012","journal-title":"Soft Matter"},{"key":"2023062115361173600_c35","doi-asserted-by":"publisher","first-page":"031502","DOI":"10.1103\/PhysRevE.85.031502","article-title":"Stagnation point flow of wormlike micellar solutions in a microfluidic cross-slot device: Effects of surfactant concentration and ionic environment","volume":"85","year":"2012","journal-title":"Phys. Rev. E"},{"key":"2023062115361173600_c36","doi-asserted-by":"publisher","first-page":"5847","DOI":"10.1039\/c2sm25215e","article-title":"Elastic instabilities in a microfluidic cross-slot flow of wormlike micellar solutions","volume":"8","year":"2012","journal-title":"Soft Matter"},{"key":"2023062115361173600_c37","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0377-0257(94)80060-X","article-title":"Instabilities of a stagnation point flow of a dilute polymer solution","volume":"55","year":"1994","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c38","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/0377-0257(90)80027-W","article-title":"High-Deborah-number flows of dilute polymer solutions","volume":"34","year":"1990","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c39","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/0377-0257(92)80052-Y","article-title":"Birefringent pipes: the steady flow of a dilute polymer solution near a stagnation point","volume":"44","year":"1992","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c40","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0377-0257(88)85018-3","article-title":"Elongational flow and rheology of monodisperse polymers in solution","volume":"30","year":"1988","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c41","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/S0377-0257(96)01455-3","article-title":"How do polymers stretch in stagnation point extensional flow-fields?","volume":"67","year":"1996","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2023062115361173600_c42","doi-asserted-by":"publisher","first-page":"4151","DOI":"10.1016\/S0032-3861(96)00999-8","article-title":"Macromolecular dynamics in extensional flows: 1. Birefringence and viscometry","volume":"38","year":"1997","journal-title":"Polymer"},{"key":"2023062115361173600_c43","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1007\/s00397-008-0268-1","article-title":"High shear rate viscometry","volume":"47","year":"2008","journal-title":"Rheol. Acta"},{"key":"2023062115361173600_c44","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1016\/0032-3861(80)90266-9","article-title":"Polymer chain dimensions and the dependence of viscoelastic properties on concentration, molecular weight and solvent power","volume":"21","year":"1980","journal-title":"Polymer"},{"key":"2023062115361173600_c45","doi-asserted-by":"publisher","first-page":"5943","DOI":"10.1021\/ma00022a008","article-title":"Asymptotic behavior and long-range interactions in aqueous solutions of poly(ethylene oxide)","volume":"24","year":"1991","journal-title":"Macromolecules"},{"key":"2023062115361173600_c46","volume-title":"Structure of Crystalline Polymers","year":"1990"},{"key":"2023062115361173600_c47","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1122\/1.1332389","article-title":"Elasto-capillary thinning and breakup of model elastic liquids","volume":"45","year":"2001","journal-title":"J. Rheol."},{"key":"2023062115361173600_c48","first-page":"427","article-title":"Scaling laws and the effects of concentration polarization on the permeability of hyaluronic acid","volume":"9","year":"1987","journal-title":"Physicochem. Hydrodyn."},{"key":"2023062115361173600_c49","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1122\/1.3122985","article-title":"Determination of the viscoelastic behavior of sodium hyaluronate in phosphate buffered saline with rheo-mechanical and rheo-optical methods","volume":"53","year":"2009","journal-title":"J. Rheol."},{"key":"2023062115361173600_c50","doi-asserted-by":"publisher","first-page":"205","DOI":"10.3233\/BIR-2010-0572","article-title":"Characterization and comparison of shear and extensional flow of sodium hyaluronate and human synovial fluid","volume":"47","year":"2010","journal-title":"Biorheology"},{"key":"2023062115361173600_c51","doi-asserted-by":"publisher","first-page":"3009","DOI":"10.1364\/AO.42.003009","article-title":"Techniques for fast and sensitive measurements of two-dimensional birefringence distributions","volume":"42","year":"2003","journal-title":"Appl. Optics"},{"key":"2023062115361173600_c52","doi-asserted-by":"publisher","first-page":"1314","DOI":"10.1088\/0022-3727\/3\/9\/311","article-title":"Limitations on the measurement of relaxation times using a pulsed Kerr effect method","volume":"3","year":"1970","journal-title":"J. Phys. D: Appl. Phys."},{"key":"2023062115361173600_c53","volume-title":"Optical Rheometry of Complex Fluids","year":"1995"},{"key":"2023062115361173600_c54","doi-asserted-by":"publisher","first-page":"9908","DOI":"10.1039\/c1sm05493g","article-title":"Extensional opto-rheometry with biofluids and ultra-dilute polymer solutions","volume":"7","year":"2011","journal-title":"Soft Matter"},{"key":"2023062115361173600_c55","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.1016\/0032-3861(82)90240-3","article-title":"Photo-correlation velocimetry of polystyrene solutions in extensional flow fields","volume":"23","year":"1982","journal-title":"Polymer"},{"key":"2023062115361173600_c56","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1007\/s00397-010-0453-x","article-title":"The rheology of polymer solutions elastic strands in extensional flow","volume":"49","year":"2010","journal-title":"Rheol. Acta"},{"key":"2023062115361173600_c57","doi-asserted-by":"publisher","first-page":"1928","DOI":"10.1021\/ma035667v","article-title":"Optical polarimetry and mechanical rheometry of poly(ethylene oxide)-silica dispersions","volume":"37","year":"2004","journal-title":"Macromolecules"},{"key":"2023062115361173600_c58","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1143\/JPSJ.24.392","article-title":"Waving motions of flags","volume":"24","year":"1968","journal-title":"J. Phys. Soc. Jpn."},{"key":"2023062115361173600_c59","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1146\/annurev-fluid-121108-145456","article-title":"Flapping and bending bodies interacting with fluid flows","volume":"43","year":"2011","journal-title":"Annu. Rev. Fluid Mech."}],"container-title":["Physics of Fluids"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/pof\/article-pdf\/doi\/10.1063\/1.4818151\/13980578\/083104_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/pof\/article-pdf\/doi\/10.1063\/1.4818151\/13980578\/083104_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T10:42:36Z","timestamp":1687516956000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/pof\/article\/25\/8\/083104\/103108\/Instabilities-in-stagnation-point-flows-of-polymer"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,1]]},"references-count":59,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2013,8,1]]}},"URL":"https:\/\/doi.org\/10.1063\/1.4818151","relation":{},"ISSN":["1070-6631","1089-7666"],"issn-type":[{"value":"1070-6631","type":"print"},{"value":"1089-7666","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2013,8]]},"published":{"date-parts":[[2013,8,1]]},"article-number":"083104"}}