Characterization of Folding and Stretching in Mixing Enhancements

TL;DR

This study models electrokinetic micromixing using stretching and folding theory, revealing that optimal mixing occurs at a specific ratio of these processes and that higher electric fields do not always improve mixing quality.

Contribution

It introduces a novel 2D numerical model of micromixing based on Ottino's theory, with new definitions for stretching and folding compatible with particle tracking.

Findings

Mixing homogeneity varies with electric field strength.

Higher electric fields can decrease mixing efficiency due to flow instability.

Optimal mixing occurs at a specific stretching to folding ratio, m=0.0045.

Abstract

This research paper presents a 2D numerical model of an electrokinetic T-junction micromixer based on the stretching and folding theory presented by Ottino. Particle deformation was considered by simulating 2 $\mu m$ massless particles as 8-point square cells. Furthermore, stretching and folding definitions are proposed, compatible with a Lagrangian particle approach. Moreover, mixing homogeneity and consistency were measured in a 200 $\mu m$ square region of interest neighboring the outlet. Statistical analysis of the exiting mixing homogeneity at four different electric field conditions (93.5 V/cm, 109.8 V/cm, 126 V/cm and 117.9 V/cm, corresponding to a 23V, 27V, 29V and 31V potential difference) show that mixing consistency and homogeneity are not always increased with a higher electric field intensity, even after electrokinetic instabilities are formed, as increasingly unstable flow conditions decrease the ratio of folding to stretching ($m$), hindering the interaction between substances. Finally, an optimal proportion of stretching to folding was found for maximizing mixing efficiency at $m =0.0045$.