Separating stretching from folding in fluid mixing

Fluid mixing controls many natural and industrial processes, including the spread of air pollution, mass transfer and reactions in microfluidic devices and the detection of odours or other chemical signals. Strongly nonlinear flows enhance mixing by chaotic advection, stretching and folding fluid volumes. Though these processes have been studied in simple models, stretching and folding are difficult to distinguish in real flows with complex spatiotemporal structure. Here we report measurements of these two distinct processes in a two-dimensional laboratory flow. We decouple stretching and folding using tools developed for analysing glassy solids and colloids, breaking fluid deformation into a linear, affine component (primarily stretching) and a nonlinear, non-affine component (primarily folding). Short-time deformation is dominated by stretching, whereas folding occurs only after fluid elements are elongated. The relative strength of the two processes depends strongly on space and time; folding-dominated regions are initially isolated, but later grow to fill space.