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## Characterizing and controlling elastic turbulence in a viscoelastic fluid

Abstract:

The properties of
viscoelastic solutions are exceptionally applicable on the micron
scale. For example, in microfluidic devices mixing and heat transfer
are strongly enhanced. This is due to elastic turbulence [1], which
bears similar qualities as inertial turbulence. The relevant
dimensionless number characterizing viscoelastic fluids is the
Weissenberg number, which compares the polymer relaxation time to the
characteristic time of the flow dynamics.

Numerical solutions of
the Oldroyd-B model in a two-dimensional Taylor-Couette geometry
display a supercritical transition from the laminar Taylor-Couette
flow to the occurrence of a secondary flow [2]. The secondary flow is
turbulent and caused by an elastic instability beyond a critical
Weissenberg number. The order parameter, the time average of the
secondary-flow strength, follows the scaling law Φ ∝ (Wi −
Wi_{c})^{γ} with Wi_{c} = 10 and γ = 0.45
and the power spectrum of the velocity fluctuations shows a power-law
decay with a characteristic exponent. We also present first results on
controlling the elastic instability through an oscillating rotation of
the outer cylinder of the Taylor-Couette cell, with a frequency close
to the characteristic relaxation time of the dissolved polymers.
Finally, we address the three-dimensional geometry of the von Karman
swirling flow between two parallel disks, which was used in Ref.
[1].

[1] A. Groisman and V. Steinberg, Nature
**405**, 53 (2000).

[2] R. Buel, C. Schaaf, H.
Stark, Europhys. Lett. **124**, 14001
(2018).