Tailoring chaotic mixing within a translating droplet by oscillatory rotation.

ORAL

Abstract

The purpose of this talk is to show how to tailor chaotic mixing within an incompressible three dimensional droplet undergoing a steady translation as well as oscillatory rigid body rotation. We consider a Lagrangian flow which consist of an integrable Hill vortex perturbed by a time-periodic rigid body rotation. The latter is characterized by two parameters, the amplitude and the frequency of the rotation. By using a resonance condition between the frequencies of the integrable flow and the one of the perturbation, we are able to create a chaotic mixing region inside the droplet whose location and size can be tuned precisely. Our results can be viewed as a preliminary step toward the control of mixing for biochemical reactions within individual droplets, also referred to as ``digital microfluidics.''

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Authors

  • Rodolphe Chabreyrie

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

  • Dmitri Vainchtein

    • Georgia Tech
    • School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA

  • Cristel Chandre

    • CPT, CNRS
    • Centre de Physique theorique, Luminy-case 907, F-13288 Marseille cedex 09, France

  • Nadine Aubry

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

  • Pushpendra Singh

    • New Jersey Institute of Technology
    • Mechanical Engineering Department, New Jersey Institute of Technology, Newark, NJ 07102, USA