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 ...

The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules traveling along the centerline in the wake of the cylinder. With increasing Wi, the coil-stretch transition leads to an unbounded growth in t...

The effect of stress diffusivity is examined in both the Oldroyd-B and FENE-P models of a viscoelastic fluid in the low Reynolds (Stokes) limit for a 2D periodic time-dependent flow. A local analytic solution can be obtained when assuming a flow of the form u =Wi (x, y), whereWi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the ad...

Recently singular solutions have been discovered in purely elongational flows of visco-elastic fluids. We surmise that these solutions are the mathematical structures underlying the so-called birefringent strands seen experimentally. In order to facilitate future experimental studies of these we derive a number of asymptotic results for the scaling of the width and extension of the near-singula...

The finitely extensible nonlinear elastic (FENE) dumbbell model consists of the incompressible Navier–Stokes equation for the solvent and the Fokker–Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit m0 which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in t...

The FENE dumbbell model consists of the incompressible NavierStokes equation for the solvent and the Fokker-Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit √ b which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in terms of the elongation parameter b. Thro...