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Residence time distributions and return time statistics in fluid mixing: understanding and enhancing chaotic mixing

Academic lead
Rob Sturman (Mathematics)
Mark Wilson (Mechanical Engineering)
Project themes
Microflows & heat transfer, Reacting flows, mixing and safety

The importance and relevance of fluid mixing in modern science is clear, both from the range of industrial and environmental situations in which it appears, and from the explosion of research articles connected with mixing by chaotic advection that have appeared in the last thirty years. For fluid mixing devices that operate by chaotic advection (essentially stirring), residence time distributions can reveal important details about the quality of mixing. Chaotic advection is described mathematically using hyperbolic dynamical systems, and rigorous mathematical results can be obtained by applying ergodic theory. For example, rates of mixing for models of chaotic advection can be proven by a careful analysis of return time statistics. This project aims to connect the related notions of residence time distributions and return time statistics. The first step in doing so was completed in CHAOS, 9, 1, p173 (1999), which linked iso-residence time plots and Poincare maps for pipe flows using ergodic theory. The project will combine mathematical analysis (of the kind found in nonlinear dynamics), mathematical modelling (describing simple models of realistic mixing devices), and computation to develop reliable computational tools for mixing studies, enabling improved operation of mixing devices and proposals for new mixing approaches.