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  • Letter
  • Open Access

Control-based continuation maps out unstable equilibria in laboratory two-phase flow

Sammy Ayoubi1, João V. Fontana1, Anne Juel2, and Alice B. Thompson1

  • 1Department of Mathematics, School of Natural Sciences, University of Manchester, Oxford Road M13 9PL, United Kingdom
  • 2Department of Physics and Astronomy, School of Natural Sciences, University of Manchester, Oxford Road M13 9PL, United Kingdom

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Phys. Rev. Research 7, L032008 – Published 8 July, 2025

DOI: https://doi.org/10.1103/nznz-zc63

Abstract

We apply control-based continuation, an experimental method used to explore the bifurcation structure of nonlinear systems, to a spatially extended system by examining the equilibrium configurations of a bubble placed at the center of a straining flow. Feedback control is delivered by injecting/withdrawing fluid at actuation points and is chosen according to real-time observations of the bubble as viewed from above. The amplitude of actuation is used to locate its unstable equilibria, and thus enable their observation. We map the unstable steady shapes of the bubble as a function of straining flow rate and demonstrate excellent agreement of the resulting experimental bifurcation diagram with numerical predictions.

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References (34)

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Information

Phys. Rev. Research 7, L032008– Published 8 July, 2025
  • Received 10 December 2024
  • Accepted 1 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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