Topological chaos in wide lid-driven channels

Rapid fluid mixing can be produced in laminar flows through a high-aspect-ratio microchannel by means such as pressure-driven flow with staggered surface groove patterns or electro-osmotic flow with potential differences between the upper and lower boundaries. Under certain conditions, passive fluid particles or groups of particles can act as ``rods'' that stir the surrounding fluid and produce exponential stretching. The occurrence of ``topological chaos'' guarantees rapid mixing in these flows, and the Thurston-Nielsen theorem predicts a quantitative lower bound on complexity in the dynamics of the flow. We will present an exact solution for two-dimensional Stokes flow in a lid-driven cavity with periodic side wall boundary conditions and extend this model to approximate three-dimensional channel flow. We will examine the occurrence of topological chaos in these flows and discuss the mixing efficiency.