Mixing in viscoelastic fluids using elastic turbulence

TL;DR

This study explores how elastic turbulence enhances mixing in viscoelastic fluids within a Taylor-Couette setup, revealing that turbulence significantly improves mixing efficiency and follows specific scaling laws.

Contribution

It demonstrates the correlation between elastic turbulence and mixing efficiency, introducing the secondary-flow order parameter as an indicator of mixing performance.

Findings

Elastic turbulence leads to strong mixing in viscoelastic fluids.

Mixing rate, time, and efficiency follow identifiable scaling laws.

The order parameter correlates with mixing rate, indicating its usefulness as an indicator.

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 the regime of elastic turbulence. When starting in the turbulent state and subsequently lowering the Weissenberg number, a weakly-chaotic flow occurs below $\mathrm{Wi_c}$. 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.