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.
One contribution of 23 to a Triennial Issue ‘Mathematics and physics’.
↵We are leaving out the crucial role of molecular diffusion in ultimately achieving this homogenization.
↵As for the Golden ratio, there is a geometrical construction of the silver means: start with a rectangle with one side of unit length, and remove m unit squares. The ratio of the sides of the remaining rectangle is given by the mth silver mean if it is the same ratio as the original rectangle.
- © 2006 The Royal Society