Matthew D Finn | PubMed Health

PubMed2006

Topology, braids and mixing in fluids.

Stirring of fluid with moving rods is necessary in many practical applications to achieve homogeneity. These rods are topological obstacles that force stretching of fluid elements. The resulting stretching and folding is commonly observed as filaments and striations, and is a precursor to mixing. In a space-time diagram, the trajectories of the rods form a braid, and the properties of this braid impose a minimal complexity in the flow. We review the topological viewpoint of fluid mixing, and discuss how braids can be used to diagnose mixing and construct efficient mixing devices. We introduce a new, realizable design for a mixing device, the silver mixer, based on these principles.

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PubMed2006

Topological mixing with ghost rods.

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call "ghost rods", because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.

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