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Fluids with suspended micro-structure -- complex fluids -- arise commonly in micro- and bio-fluidics, and can have fascinating and novel dynamical behaviors. I will give an overview of some interesting problems in complex fluid dynamics at low Reynolds number. This includes how visco-elasticity in a fluid can drive fluid mixing, and how elasticity of the micro-structure can yield random-walk transport across simple closed-streamline flows. I will also discuss recent work on "active suspensions", such as bacterial baths, where the suspended particles are motile and their hydrodynamically mediated interactions lead to large-scale instability, coherent structures, and mixing.

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