Mixing from a switching dynamics perspective

Chaotic advection can significantly improve mixing speed in Stokes flows. Until now, the study of chaotic advection was mostly restricted to time-periodic and spatial-periodic flows, although some examples show that aperiodic flows can mix more efficiently. In this paper a new and general perspective on mixing is presented based on switching dynamical systems that allows the systematic derivation of aperiodic flows that are theoretically guaranteed to yield better mixing than any available periodic flow. Simulations and real-time feedback experiments for mixing control confirm these findings. The application of closed-loop control for mixing is expected to have significant advantages in micro-fluidic and industrial mixing and could enable the creation of desired nonhomogeneous patterns.