Complete Chaotic Mixing in an Electro-osmotic Flow by Destabilization of Key Periodic Pathlines

TL;DR

This paper presents a strategy to achieve complete chaotic mixing in electro-osmotic flows by analyzing the stability of key periodic pathlines and identifying bifurcation points to induce instability and mixing.

Contribution

The study introduces a method to quickly identify parameter values for complete mixing by destabilizing key periodic pathlines in electro-osmotic flows.

Findings

Complete chaotic mixing can be achieved by destabilizing key pathlines.

The stability analysis guides the selection of forcing amplitude and frequency.

Bifurcation points are critical for inducing flow instability and mixing.

Abstract

The ability to generate complete, or almost complete, chaotic mixing is of great interest in numerous applications, particularly for microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter values at which complete mixing occurs. The technique is applied to a time periodic, two-dimensional electro-osmotic flow with spatially and temporally varying Helmoltz-Smoluchowski slip boundary conditions. The strategy consists of following the linear stability of some key periodic pathlines in parameter space (i.e., amplitude and frequency of the forcing), particularly through the bifurcation points at which such pathlines become unstable.