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. We propose a PDE-constrained optimization approach to address the problem of mixing enhancement for binary fluids. 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. B INSERT UJRWD OVERLAY B INSERT UPRNT OVERLAY B INSERT SORT OVERLAY A INSERT MODEL4, HSORT OVERLAY A INSERT MODEL 5 OVERLAYA INSERT MODEL 7 OVERLAY A.
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.
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