Dynamical systems techniques for enhancing microfluidic mixing

Achieving rapid mixing is often desirable in microfluidic devices, for example in improving reation rates in biotechnological assays. Enhancing mixing within a particular context is often achieved by introducing problem-specific strategies such as grooved or twisted channels, ac electromagnetic fields or oscillatory microsyringe flows. Evaluating the efficiency of these methods is challenging since either experimental fabrication and sensing, or computationally expensive direct numerical simulations with complicated boundary conditions, are required. A review of how mixing can be quantified when velocity fields have been obtained from such situations is presented. A less-known alternative to these methods is offered by dynamical systems, which characterizes the motion of collective fluid parcel trajectories by studying crucial interior flow barriers which move unsteadily, but nevertheless strongly govern mixing possibilities. The methodology behind defining these barriers and quantifying the fluid transport influenced by them is explained. Their application towards several microfluidic situations (e.g. best cross-flow positioning in cross-channel micromixers, usage of channel curvature to enhance mixing within microdroplets traveling in a channel, optimum frequencies of velocity agitations to use) is discussed. (topical review)