Tailored mixing inside a translating droplet

Rodolphe Chabreyrie (1) , Dmitri Vainchtein (2) , Cristel Chandre (3, 4) , Pushpendra Singh (5) , Nadine Aubry (1)

1 Department of Mechanical Engineering at Carnegie Mellon
2 CNS-GATECH - Center for Nonlinear Science
3 CPT - Centre de Physique Théorique - UMR 7332
4 CPT - Ex E8 Dynamique non linéaire
5 Department of Mechanical Engineering

Tailored mixing inside individual droplets could be useful to ensure that reactions within microscopic discrete fluid volumes, which are used as microreactors in ''digital microfluidic'' applications, take place in a controlled fashion. In this article we consider a translating spherical liquid drop to which we impose a time periodic rigid-body rotation. Such a rotation not only induces mixing via chaotic advection, which operates through the stretching and folding of material lines, but also offers the possibility of tuning the mixing by controlling the location and size of the mixing region. Tuned mixing is achieved by judiciously adjusting the amplitude and frequency of the rotation, which are determined by using a resonance condition and following the evolution of adiabatic invariants. As the size of the mixing region is increased, complete mixing within the drop is obtained.

Domaines: Dynamique Chaotique [nlin.CD]

Rodolphe Chabreyrie, Dmitri Vainchtein, Cristel Chandre, Pushpendra Singh, Nadine Aubry. Tailored mixing inside a translating droplet. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 77, pp.036314. ⟨10.1103/PhysRevE.77.036314⟩. ⟨hal-00260308⟩