Spatially resolved stretching-rotation-stretching sequence in flow topology as elementary structure of fluid mixing

TL;DR

This paper uses numerical simulations to analyze how elementary flow sequences involving stretching and rotation influence fluid mixing, providing insights into flow topology and stirring protocol design.

Contribution

It introduces a flow topology-based framework to quantify stretching and folding, enhancing understanding of fluid mixing mechanisms.

Findings

Elementary oscillatory sequences induce concentration gradient steepening.

Flow topology measures facilitate stirring protocol design.

Spatial redistribution of concentration is driven by stretching-rotation sequences.

Abstract

We performed two-dimensional numerical simulations of passive stirring of two liquids which generated two spatially distinguishable paradigmatic velocity flows, viz. few large extended vortices and rapid oscillations. Using the Okubo- Weiss criterion, we mapped regions of stretching and rotation in the flow field. We find that an elementary oscillatory sequence of stretching-rotation-stretching induces spatial redistribution and steepening of concentration gradients, and the aggregation of such sequences determines fluid mixing at a downstream position. Furthermore, we quantify the paradigms of 'stretching' and 'folding' by developing measures based on flow topology which would facilitate the design of stirring protocols.