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

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior of Oldroyd-B model. Here, we compare response simplified linear form Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2, 353–365 (1977)] finitely extensible nonlinear elastic (“FENE”) dumbbell follows Peterlin approximation (“FENE-P”) [Bird et al., “Polymer solution rheology based on a bead—Spring chain model,” 7, 213–235 (1980)]. We show for steady homogeneous flows such as simple shear flow or pure extension, both models identical under precise conditions ([Formula: see text]). The similarity “spring” functions between two shown to help understand this equivalence despite different molecular origin models. then use numerical approach investigate when “complex” in number definitions: first, applied deformation field space but transient time (so-called “start-up” planar extensional flow), then, an intermediate step, start-up channel flow; finally, (through range geometries), which, although being Eulerian steady, are unsteady Lagrangian sense. Although there can be significant differences conditions, especially if extensibility parameter small [Formula: text], limit remain once again observe very close agreement FENE-P sPTT complex geometries.