Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation

TL;DR

This paper explores how time-dependent rigid-body rotation can be used to control and enhance mixing inside a spherical droplet, with adjustable parameters enabling complete internal mixing for microfluidic applications.

Contribution

It introduces a novel method of controlling internal droplet mixing through time-periodic rotation, combining chaotic advection with parameter-based control.

Findings

Chaotic mixing regions are generated by imposed rotation.

Adjusting rotation parameters controls the size and location of mixing.

Complete mixing is achievable by increasing the mixing region size.

Abstract

The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to which we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.