Using resonances to control chaotic mixing within a translating and rotating droplet

R. Chabreyrie, D. Vainchtein, C. Chandre, P. Singh, N. Aubry

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Enhancing and controlling chaotic advection or chaotic mixing within liquid droplets is crucial for a variety of applications including digital microfluidic devices which use microscopic "discrete" fluid volumes (droplets) as microreactors. In this work, we consider the Stokes flow of a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we have shown in previous work that the rotation not only leads to one or more three-dimensional chaotic mixing regions, in which mixing occurs through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of chaotic mixing within the drop. Such a control was achieved through appropriate tuning of the amplitude and frequency of the rotation in order to use resonances between the natural frequencies of the system and those of the external forcing. In this paper, we study the influence of the orientation of the rotation axis on the chaotic mixing zones as a third parameter, as well as propose an experimental set up to implement the techniques discussed.

Original languageEnglish (US)
Pages (from-to)2124-2132
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number8
StatePublished - Aug 2010

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


  • Chaotic advection
  • Chaotic mixing
  • Control
  • Droplet
  • Microfluidics
  • Resonances
  • Stokes flow


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