Mixing by stirring: optimizing shapes and strategies

TL;DR

This paper presents a PDE-constrained optimization method to improve mixing efficiency of binary fluids by optimizing stirrer shapes and stirring strategies, leading to more homogeneous mixtures within energy constraints.

Contribution

It introduces a novel gradient-based optimization framework targeting stirrer shape and stirring protocols for enhanced mixing, utilizing unsteady hydrodynamics and vortex-shedding effects.

Findings

Significant improvement in fluid homogeneity achieved

Optimized stirrer shapes and strategies outperform traditional methods

Potential for energy savings and better mixing efficiency

Abstract

The mixing of binary fluids by stirrers is a commonplace procedure in many industrial and natural settings, and mixing efficiency directly translates into more homogeneous final products, more enriched compounds, and often substantial economic savings in energy and input ingredients. Enhancements in mixing efficiency can be accomplished by unorthodox stirring protocols as well as modified stirrer shapes that utilize unsteady hydrodynamics and vortex-shedding features to instigate the formation of fluid filaments which ultimately succumb to diffusion and produce a homogeneous mixture. We propose a PDE-constrained optimization approach to address the problem of mixing enhancement for binary fluids. Within a gradient-based framework, we target the stirring strategy as well as the cross-sectional shape of the stirrers to achieve improved mixedness over a given time horizon and within a prescribed energy budget. The optimization produces a significant enhancement in homogeneity in the initially separated fluids, suggesting promising modifications to traditional stirring protocols.