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

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Davoodi, M. and Zografos, K. and Oliveira, P. J. and Poole, R. J. (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. ISSN 1070-6631 (https://doi.org/10.1063/5.0083717)

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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.

ORCID iDs

Davoodi, M., Zografos, K. ORCID logoORCID: https://orcid.org/0000-0001-5732-7803, Oliveira, P. J. and Poole, R. J.;
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