Semi-analytical solutions for the poiseuille-couette flow of a generalised Phan-Thien-Tanner fluid

This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille-Couette flows, described by the recently proposed (Ferras 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.This research was funded by FEDER through COMPETE2020-Programa Operacional Competitividade e Internacionalizacao (POCI) and by national funds through FCT-Fundacao para a Ciencia e a Tecnologia, I. P. through Projects PTDC/EMS-ENE/3362/2014, POCI-01-0145-FEDER-016665, UID-MAT-00013/2013, and UID/MAT/00297/2013 as well as grant number SFRH/BPD/100353/2014. This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes)