Mixing by stirring: Optimizing shapes and strategies

Maximilian F. Eggl, Peter J. Schmid

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.
Original languageEnglish (US)
JournalPhysical Review Fluids
Issue number7
StatePublished - Jul 27 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-12-12
Acknowledgements: We gratefully acknowledge discussions and exchanges with Prof. C. Caulfield, Prof. J.-L. Thiffeault, Prof. K. Schneider, and Dr. F. Marcotte. M.F.E. gratefully acknowledges funding through the Joachim Herz Stiftung.


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