Tailored mixing inside a translating droplet

TL;DR

This paper investigates how to control and optimize mixing inside a translating spherical droplet by applying a periodic rotation, enabling tailored and complete mixing through resonance tuning and adiabatic invariants.

Contribution

It introduces a method to achieve controlled, tunable mixing inside droplets by adjusting rotation parameters based on resonance conditions and adiabatic invariants.

Findings

Controlled mixing regions can be tuned by adjusting rotation amplitude and frequency.

Complete mixing is achievable by increasing the size of the mixing region.

Resonance conditions guide the optimization of mixing within the droplet.

Abstract

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.