Nonlinear evolution of instability in inertialess elasto-viscoplastic Poiseuille flow

Abstract

A widely used constitutive law for elasto-viscoplastic fluids (Saramito's model) predicts linear instability in inertialess pressure-driven channel flow. The instability arises due to the yield stress of the fluid and is strongest at the shortest streamwise wavenumbers, calling into question the physical validity of the constitutive model. Here, we show that the short wavelengths can be controlled by the addition of polymer stress diffusion and conduct two-dimensional numerical simulations to explore the nonlinear dynamics. On reaching finite amplitude, the instability is shown to generate spatio-temporally complicated states. Fluctuations about the final mean state are pronounced near and between the yield surfaces that border an unyielded plug spanning the centre of the channel. The instability and transition arise for Weissenberg numbers of order unity and higher.

22 pages, 12 figures