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).