Mixing by Chaotic Advection (Applied Nonlinear Dynamics)

Mixing is a ubiquitous problem, with applications as diverse as microfluidics, oceanographic flows, mixing in the atmosphere, food engineering, combustion and mixing in the earth's mantle. Fluid mixing frequently appears straightforward: molecular diffusion or turbulence may make the job easy. A third way of mixing, that of mechanically stretching and folding fluid, in order to appeal to ideas of chaos theory, is also possible. A number of ingenious devices have been proposed to implement these ideas, for example the 'blinking vortex', the 'Kenics mixer' and the 'partitioned-pipe mixer'. They typically have the advantage that concepts from dynamical systems and chaos theory can be carried across to quantify or measure how 'chaotic' or 'complex' the resulting mixture might be.

Directions for this project could include: using theoretical tools from ergodic theory of dynamical systems to estimate how quickly a mixed state is reached; developing theoretical and computational tools to address the question of how to characterise the quality of a mixture; using ideas from hyperbolic dynamics to analyse and optimise mixing performance of existing devices; translating techniques from mixing of fluids to the different physical situation of mixing of granular materials.

keywords: applied mathematics, nonlinear dynamics, chaos theory, mixing, ergodic theory, granular materials,

Nonlinear dynamics and its applications at Leeds has for many years enjoyed reputation for a distinctive interdisciplinary approach. The Centre for Nonlinear Studies was established at Leeds in 1984 to enhance existing and foster new research collaborations between mathematicians, scientists and engineers throughout the university and beyond. Twenty five years later, the research group retains its character as an applications driven centre, applying dynamical systems theory to a range of natural phenomena. It has recently expanded with the appointment of several new members of staff, bringing the total to ten permanent members of staff working with five postdocs and postgraduate students.

Applied Nonlinear Dynamics is a vibrant research area lying at the heart of problems of fundamental and practical importance. It employs a wealth of mathematical techniques, from statistical to geometrical, from computational to algebraic, and from qualitative to analytical. The main concern is systems that change with time, where the presence of nonlinearities can produce hugely complicated behaviour. The range of activities in Applied Nonlinear Dynamics is extremely broad. Core areas of investigation include chaos, global bifurcation theory and the role of symmetry, localised solutions (both in spectral and physical space), coupled oscillators and synchronisation, ergodic theory and stochastic dynamics, and pattern formation in fluid mechanics and reaction-diffusion systems. Developments in the basic theory and techniques of Nonlinear Dynamics go hand-in-hand with investigations of particular applications, such as fluid dynamics experiments, dynamics on complex networks and mixing in microfluidics.