Measures of mixing quality in open flows with chaotic advection

TL;DR

This paper proposes a new measure for assessing mixing efficiency in open flows with chaotic advection, based on the normalized standard deviation of dye patterns, and explores its theoretical and practical implications.

Contribution

It introduces a novel mixing quality metric suitable for open-flow chaotic mixing experiments, linking pattern analysis to dye mixing behavior.

Findings

Normalized standard deviation effectively quantifies mixing quality.

The measure correlates with dye mixing in continuous injection scenarios.

The approach is validated using an idealized mathematical map.

Abstract

We address the evaluation of mixing efficiency in experiments of chaotic mixing inside an open-flow channel. Since the open flow continuously brings new fluid into the limited mixing region, it is difficult to define relevant mixing indices, as fluid particles experience typically very different stretching and mixing histories. The repeated stretching and folding of a spot of dye leads to a persistent pattern. We propose that the normalized standard deviation of this characteristic pattern is a good measure of the mixing quality of the flow. We discuss the link between this measure and mixing of continuously-injected dye, and investigate it using an idealized map.