Viscous flow and mixing
Mixing viscous fluids is a challenge because our common-sense mixing strategy, namely creating turbulence, does not work. The solution of this problem is of great practical relevance since viscous fluids need to be mixed in many industrial processes.
Mixing of a fluid in two dimensions maps onto a Hamiltonian system. Such a system can display chaos, and it is precisely this chaos which is used to mix.
Flows on very small scales are completely dominated by viscosity, and also there mixing is a problem, even though the medium may be water. Small-scale flows occur in lab-on-a-chip biosensors, and we do fundamental research to optimize mixing in these micro-devices.