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Mixing by stirring: Optimizing shapes and strategies

Maximilian F. Eggl*

Peter J. Schmid

  • Institute of Physiological Chemistry, University of Mainz Medical Center, 55128 Mainz, Germany

  • Department of Mechanical Engineering, KAUST, Thuwal 23955, Saudi Arabia

  • *maximilian.eggl@uni-mainz.de
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Phys. Rev. Fluids 7, 073904 – Published 27 July, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.073904

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.

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synopsis

Effectively Mixing Two Fluids

Published 27 July, 2022

Want to mix two fluids? Researchers have developed a path to optimize the stirrer shape and velocity to give the best outcome.  

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Phys. Rev. Fluids 7, 073904– Published 27 July, 2022
  • Received 26 August 2021
  • Accepted 16 December 2021
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