On the similarities between the simplified Phan-Thien Tanner (sPTT) and FENE-P models

For many commonly-used single mode viscoelastic constitutive equations of differential type, it is well known that they share many features. For example, in certain parameter limits the Giesekus, Phan-Thien Tanner and FENE-type models approach the Oldroyd-B model. In this short paper we show that for homogeneous flows such as steady simple shear flow or pure extension, the response of the linear form of the simplified Phan-Thien Tanner (the "sPTT") model and the Finitely Extensible Nonlinear Elastic model that follows the Peterlin approximation (the "FENE-P") is identical under certain conditions. In effect this means in viscometric flows, any steady analytical solution derived for one of these models in a particular flow is also a solution for the other model and we demonstrate this equivalence using existing channel flow solutions for the two models from the literature