Mixing in viscoelastic fluids using elastic turbulence

Abstract

We investigate the influence of elastic turbulence on mixing {of a scalar concentration field} within a viscoelastic fluid in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model. The flow state is determined through the secondary-flow order parameter indicating that the transition at the critical Weissenberg number $\text{Wi}_c$ is subcritical. When {starting in the turbulent state and subsequently} lowering the Weissenberg number, a weakly-chaotic flow occurs below $\text{Wi}_c$. Advection in both {the turbulent and weakly-chaotic} flow states induces mixing, which we illustrate by the time evolution of the standard deviation of the solute concentration from the uniform distribution. In particular, in the elastic turbulent state mixing is strong and we quantify it by the mixing rate, the mixing time, and the mixing efficiency. All three quantities follow scaling laws. Importantly, we show that the order parameter is strongly correlated to the mixing rate and hence is also a good indication of mixing within the fluid.