Mixing by stirring: Optimizing shapes and strategies

Abstract

We present a numerical study of enhanced stirrer shapes and temporal velocity protocols for mixing an initially unmixed incompressible binary fluid in a two-dimensional circular container in a non-turbulent but inertial flow regime. A gradient-based and PDE-constrained optimization approach is combined with modern mixing metrics. The largest efficiency enhancement, by a factor of more than two, comes from simultaneously optimizing stirrer shapes and velocity trajectories, leading to counter-intuitive and complex stirring protocols that benefit from vortex generation, interaction, and collisions. Many challenges remain, but opportunities arise for extending this approach to more realistic configurations.

Topics & Concepts