Many real-life fluids are not Newtonian and have to be modelled with something more complex than a single scalar viscosity. In this talk we will look specifically at dilute polymer solutions. We'll see some simple models that capture the essential features of their behaviour, and then investigate how the properties of these models affect the stability of channel flow.
The story spans my whole research career so far, from an early theoretical prediction which was later observed in experiments, to a more recent realisation that there is still quite a lot we don't understand. If time permits I will also discuss the latest place the research has taken me, which is neither viscoelastic nor unstable.