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Rates of chaotic mixing in models of fluid devices

Academic lead
Dr Rob Sturman, School of Mathematics
Co-supervisor(s)
Dr Mark Wilson, School of Mechanical Engineering
Project themes
Microflows & heat transfer, Reacting flows, mixing and safety

Recent results of RS, using ergodic theory of dynamical systems, and a study of return time dynamics, determine the rate of fluid mixing in (very abstract) models of chaotic advection. In particular, the exponential mixing rate expected of chaotic dynamics is slowed to an algebraic rate by the nature of the dynamics at the boundaries. This project aims to investigate how these results, and the ideas in the proof, carry over to more accurate models of fluid mixing device.

The fundamental dynamical mechanism here is a fairly universal one – the idea of frequent returns to a hyperbolic mixing region, between excursions to poor mixing regions – and has been shown to underpin a wide variety of industrial mixing device. We will use a combination of mathematical analysis, numerical simulation and, if possible, experimental work, to determine mixing rates in particular designs of mixer, and ideally establish some criteria for optimising mixing under specific conditions.