Using Resonances to Control Chaotic Mixing within a Translating and Rotating Droplet

TL;DR

This paper investigates how resonant forcing via controlled rotation can manipulate chaotic mixing zones inside a translating droplet, with implications for microfluidic applications.

Contribution

It introduces the effect of rotation axis orientation on chaotic mixing control and proposes an experimental setup for implementation.

Findings

Rotation axis orientation influences chaotic mixing zones.

Resonance tuning controls the size and position of mixing regions.

Proposed experimental setup facilitates practical application.

Abstract

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.