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DY: Fachverband Dynamik und Statistische Physik

DY 42: Delay and Feedback Dynamics

DY 42.3: Talk

Thursday, March 19, 2015, 10:15–10:30, BH-N 128

Feedback control of flow vorticity at low Reynolds numbers — •Maria Zeitz, Jenny Triptow, Peter Kalle, and Holger Stark — Institut für Theoretische Physik, Technische Universitat Berlin, D-10623 Berlin

Our goal is to explore feedback control strategies to stabilize novel dynamic flow patterns in microfluidic model systems. As a first example, we investigate a Newtonian fluid in a circular geometry realizable by a long rotating cylinder. The fluid vorticity satisfies a diffusion equation. We control fluid flow via the angular velocity of the circular boundary, which we determine from the mean vorticity in the sensing area using two control strategies: feedback with hysteretic switching or with time delay.

Hysteretic feedback control generates self-regulated stable oscillations in time the frequency of which can be adjusted over several orders of magnitude by tuning the feedback parameters.

Historically time-delayed feedback was developed in order to stabilize orbits in a chaotic system. Here, we show that it can be used as well to destabilize an inherently stable system such as vortex diffusion. For large values of feedback gain we find that vorticity diverges exponentially in time. Adjusting the parameters accurately, the vorticity oscillates with a stable amplitude. Large delay times promote oscillation pulses of vorticity, resulting in a complex time periodic pattern.

In a next step we apply these control strategies to more complex fluids. We present first results on the viscoelastic two-fluid system.