Abstract
This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille–Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien–Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien–Tanner constitutive equation. This generalised version considers the Mittag–Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification.
Highlights
It is well known that much can be learned about a physical phenomenon if a mathematical model exists that can mimic and predict its behavior
We show that the same happens for the generalised Phan-Thien–Tanner (gPTT) model
The new model allows a better fit for low and high shear rates for the first normal stress difference
Summary
It is well known that much can be learned about a physical phenomenon if a mathematical model exists that can mimic and predict its behavior. We compare the generalised Phan-Thien–Tanner (gPTT), given by Equation (6), with the linear, the exponential and the quadratic versions of the PTT (Equations (2), (4) and (7), respectively) To compare these models, we study the dimensionless material properties in steady shear flow of the three versions of the PTT model and compare them with the new gPTT model, considering different values of α and β. The new model allows a better fit for low and high shear rates for the first normal stress difference (where the errorΨ1 obtained for the exponential PTT model is 20 times higher than the error obtained for the gPTT). This is done by performing a parametric study for the influence of the gPTT parameters
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
