Analysis and Control of Mixing with an Application to Micro and Macro Flow Processes pp 35-108 | Cite as

# Lectures on Mixing and Dynamical Systems

## Abstract

The subject of fluid mixing is, from the technological perspective, an old one. It is encountered almost daily when we pour milk into coffee or try to achieve a particular paint color. The yearly output of industrial products for which fluid mixing is a part of the production process is measured in billions of dollars. If two fluids are in contact, mixing can proceed purely by molecular diffusion, but it is most commonly achieved by a combination of stretching of fluid interfaces by the macroscopic velocity field and molecular diffusion. Within the subject of fluid mechanics this process has been studied for 100 years, beginning with a paper of Osborne Reynolds. A lot of work has been devoted to non-diffusive mixing in the applied dynamical systems community in the past 20 years, after a seminal paper by (1984), where he coined the term “chaotic advection” to mean *efficient non-di usive mixing in flows with simple time-dependence*. Since the 1990’s the field of chaotic advection has gained increased attention from (at least) three directions: 1) Scientific investigation of fluid processes at microscale, usually producing flows with simple time-dependence, accompanying the fast technological advances in miniaturization and applications to biology and medicine, 2) Recognition that mixing by large coherent structures can be described using the chaotic advection theory and 3) Increased interest in active control of fluid processes, including control of mixing.

## Keywords

Dimensional Manifold Invariant Torus Chaotic Advection Volume Preservation Dimensional Invariant Manifold## Preview

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