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Here, we compare the response of the simplified linear form of the Phan-Thien\u2013Tanner model (\u201csPTT\u201d) [Phan-Thien and Tanner, \u201cA new constitutive equation derived from network theory,\u201d J. Non-Newtonian Fluid Mech. 2, 353\u2013365 (1977)] and the finitely extensible nonlinear elastic (\u201cFENE\u201d) dumbbell model that follows the Peterlin approximation (\u201cFENE-P\u201d) [Bird et al., \u201cPolymer solution rheology based on a finitely extensible bead\u2014Spring chain model,\u201d J. Non-Newtonian Fluid Mech. 7, 213\u2013235 (1980)]. We show that for steady homogeneous flows such as steady simple shear flow or pure extension, the response of both models is identical under precise conditions (\u03b5=1\/L2). The similarity of the \u201cspring\u201d functions between the two models is shown to help understand this equivalence despite a different molecular origin of the two models. We then use a numerical approach to investigate the response of the two models when the flow is \u201ccomplex\u201d in a number of different definitions: first, when the applied deformation field is homogeneous in space but transient in time (so-called \u201cstart-up\u201d shear and planar extensional flow), then, as an intermediate step, the start-up of the planar channel flow; and finally, \u201ccomplex\u201d flows (through a range of geometries), which, although being Eulerian steady, are unsteady in a Lagrangian sense. Although there can be significant differences in transient conditions, especially if the extensibility parameter is small L2&amp;gt;100,\u03b5&amp;lt;0.01, under the limit that the flows remain Eulerian steady, we once again observe very close agreement between the FENE-P dumbbell and sPTT models in complex geometries.<\/jats:p>","DOI":"10.1063\/5.0083717","type":"journal-article","created":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T10:17:47Z","timestamp":1647857867000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":23,"title":["On the similarities between the simplified Phan-Thien\u2013Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1707-6453","authenticated-orcid":false,"given":"M.","family":"Davoodi","sequence":"first","affiliation":[{"name":"Schlumberger Cambridge Research 1 , Madingley Rd., Cambridge CB3 0EL, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5732-7803","authenticated-orcid":false,"given":"K.","family":"Zografos","sequence":"additional","affiliation":[{"name":"James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde 2 , Glasgow G1 1XQ, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9843-7558","authenticated-orcid":false,"given":"P. 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