Targeting Complete Chaotic Mixing by Destabilizing Key Periodic Orbits in an Electro-osmotic Mixer

ORAL

Abstract

The ability to generate complete, or at least well spread, chaotic mixing is of great interest in numerous applications, especially microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter values at which complete mixing occurs. The technique is applied to a time periodic, two-dimensional electro-osmotic flow with spatially and temporally varying Helmoltz-Smoluchowski slip conditions. The strategy consists of following the linear stability of some key periodic orbits in parameter space, particularly identifying bifurcation points at which such orbits become unstable. Poincar\'{e} maps, Lyapunov exponents and a box counting measure are all computed to validate the strategy.

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Authors

  • Rodolphe Chabreyrie

    • Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15215
    • Carnegie Mellon University, Mechanical Engineering Department, Pittsburgh, PA 15213

  • Cristel Chandre

    • Centre de Physique Th\'eorique, CNRS-Aix-Marseille Universit\'e, Campus de Luminy, case 907, F-13288 Marseille cedex 09, France

  • Pushpendra Singh

    • New Jersey Institute of Technology
    • New Jersey Institute of Technology, Mechanical Engineering Department
    • NJIT

  • Nadine Aubry

    • Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15215
    • Carnegie Mellon University, Mechanical Engineering Department, Pittsburgh, PA 15213
    • Carnegie Mellon University