## Abstract

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior is that of the Oldroyd-B model. Here, we compare the response of the simplified linear form of the Phan-Thien-Tanner model ("sPTT") [Phan-Thien and Tanner, "A new constitutive equation derived from network theory,"J. Non-Newtonian Fluid Mech. 2, 353-365 (1977)] and the finitely extensible nonlinear elastic ("FENE") dumbbell model that follows the Peterlin approximation ("FENE-P") [Bird et al., "Polymer solution rheology based on a finitely extensible bead - Spring chain model,"J. Non-Newtonian Fluid Mech. 7, 213-235 (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 (ϵ = 1 / L 2). The similarity of the "spring"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 "complex"in a number of different definitions: first, when the applied deformation field is homogeneous in space but transient in time (so-called "start-up"shear and planar extensional flow), then, as an intermediate step, the start-up of the planar channel flow; and finally, "complex"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 L 2 > 100, ϵ < 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.

Original language | English |
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Article number | 033110 |

Number of pages | 20 |

Journal | Physics of Fluids |

Volume | 34 |

Issue number | 3 |

Early online date | 21 Mar 2022 |

DOIs | |

Publication status | Published - 21 Mar 2022 |

## Keywords

- condensed matter physics
- fluid flow and transfer processes
- mechanics of materials
- computational mechanics
- mechanical engineering