Rotating arc mixer

The picture shows industrial mixers used to mix viscous fluids.  The stainless tube, held in hand, is the Kenix mixer.  Another variant is the rotating arc mixer.  It consists of a pipe with slots in its wall, where the fluid is driven tangentially by a rotating sleeve. The fluid flows along the axis of the tube.

Mapping the mixing problem to Hamiltonian dynamics

This problem can be mapped onto a Hamiltonian one, namely the famous circle map.  Then, time flows with the axial fluid flow, and the tangential velocities provide the kicks.  In the circle map, chaos mixes phase space.  In the rotating arc mixer, chaos mixes the viscous fluids. 

Experiment: mixing heat in 2D

Not only is it difficult to mix two fluids, but it is also difficult to mix a tracer into a vicous fluids.  In this experiment, the tracer is heat.  It is mixed from the circumference into the interiour of the device, by moving fluid at the boundary.