Mixing enhancement for binary fluids using PDE-constrained optimization

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.

In their recently published Physical Review Fluids paper, Maximilian Eggl (Institute of Physiological Chemistry, University of Mainz Medical Center) and Peter J. Schmid (Department of Mechanical Engineering, KAUST) propose a PDE-constrained optimization approach to address the problem of mixing enhancement for binary fluids. Within a gradient-based framework, they targeted 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 produced a significant enhancement in homogeneity in the initially separated fluids, suggesting promising modifications to traditional stirring protocols.

Eggl sat down with the Physical Review Journal Club to discuss the results of their research. After the presentation a live question-and-answer session was moderated by PRFluids Editorial Board Member Viswanathan Kumaran (Indian Institute of Science, Bangalore, India).

[Florreking]

Shapes can have various drag, so if you keep the stirring speed constant for comparison to spheres, the energy put into the system is different so its not apples to apples comparison