A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear

John, TP, Poole, RJ ORCID: 0000-0001-6686-4301, Kowalski, AJ and Fonte, CP (2024) A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear. Journal of Fluid Mechanics, 979. a10-.

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Abstract

<jats:p>The finitely extensible nonlinear elastic with Peterlin closure (FENE-P) and simplified Phan-Thien–Tanner (sPTT) viscoelastic models are used widely for modelling of complex fluids. Although they are derived from distinct micro-structural theories, these models can become mathematically identical in steady and homogeneous flows with a particular choice of the values of the model parameters. However, even with this choice of parameter values, the model responses are known to differ from each other in transient flows. In this work, we investigate the responses of the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear (LAOS). In steady shear, the shear stress scales with the non-dimensional group <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline2.png" /> <jats:tex-math>$Wi/(aL)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline3.png" /> <jats:tex-math>$Wi\,\sqrt {\epsilon }$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) for the FENE-P (sPTT) model, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline4.png" /> <jats:tex-math>$Wi$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the Weissenberg number, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline5.png" /> <jats:tex-math>$L^2$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the limit of extensibility in the FENE-P model (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline6.png" /> <jats:tex-math>$a$</jats:tex-math> </jats:alternatives> </jats:inline-formula> being <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline7.png" /> <jats:tex-math>$L^2/(L^2-3)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>), and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline8.png" /> <jats:tex-math>$\epsilon$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the extensibility parameter in the sPTT model. Our numerical and analytical results show that in LAOS, the FENE-P model shows this universality only for large values of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline9.png" /> <jats:tex-math>$L^2$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, whereas the sPTT model shows it for all values of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023009771_inline10.png" /> <jats:tex-math>$\epsilon$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In the strongly nonlinear region, there is a drastic difference between the responses of the two models, with the FENE-P model exhibiting strong shear stress overshoots that manifest as self-intersecting secondary loops in the viscous Lissajous curves. We quantify the nonlinearity exhibited by each constitutive model using the sequence of physical processes framework. Despite the high degree of nonlinearity exhibited by the FENE-P model, we also show using fully nonlinear one-dimensional simulations that it does not shear band in LAOS within the range of conditions studied.</jats:p>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	05 Mar 2024 10:43
Last Modified:	17 Mar 2024 19:39
DOI:	10.1017/jfm.2023.977
Open Access URL:	https://www.cambridge.org/core/journals/journal-of...
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3179132