Davoodi, M, Zografos, K, Oliveira, PJ and Poole, RJ 
ORCID: 0000-0001-6686-4301
(2022)
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.
PHYSICS OF FLUIDS, 34 (3).
033110-.
Abstract
<jats:p>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/L2). 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 L2&gt;100,ε&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>
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science and Engineering > School of Engineering |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 08 Jun 2022 08:17 |
| Last Modified: | 15 Mar 2024 07:58 |
| DOI: | 10.1063/5.0083717 |
| Open Access URL: | https://aip.scitation.org/doi/10.1063/5.0083717 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3156044 |
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