On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows

M. Davoodi, K. Zografos, P. J. Oliveira, R. J. Poole

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12 Citations (Scopus)
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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 languageEnglish
Article number033110
Number of pages20
JournalPhysics of Fluids
Volume34
Issue number3
Early online date21 Mar 2022
DOIs
Publication statusPublished - 21 Mar 2022

Keywords

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

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