An analysis of the effect of stress diffusion on the dynamics of creeping viscoelastic flow

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−1(x, − y), where Wi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the added viscosity as ν1/2, and is independent of the Weissenberg number. Also, the “expected” maximum extension of the polymer coils remains finite with any stress diffusion and scales as Wi · ν−1/2. These predictions closely match the full simulations. As many investigations of viscoelastic fluids incorporate both finite extension as well as polymer stress diffusion we also investigate the FENE-P model with diffusion to see which effect dominates for various model parameters. With this penalization the percent of maximum extension can be predicted based on Wi, ν, and b, the maximum extensibility length.

► Viscoelastic fluids are studied with the Stokes-Oldroyd-B and FENE-P models.
► A local solution is derived for the polymer stress with a fixed velocity profile.
► The local solution is derived for the polymer stress with a fixed velocity profile.
► The width and extension of polymer stress scale with added diffusion and Wi.
► The local solution is compared with simulations and shows good matching.
► With FENE-P penalization the percent extension can be predicted based on parameters.