Analysis and Control of Mixing with an Application to Micro and Macro Flow Processes
June 27, 2005 — July 1, 2005
Coordinators:
- Luca Cortelezzi (McGill University, Montreal, Quebec, Canada)
- Igor Mezic (University of California, Santa Barbara, Calif., USA)
The event is part of the program elaborated for the European Atelier for Engineering and Computational Sciences (EUA4X – Marie Curie program). Some of the lectures will be also available on line.
Please check available Marie Curie fellowships under “Admission and Accommodation”
Scope
The study of mixing two or more fluids with or without chemical reactions is of great practical relevance to both engineering applications and natural phenomena. Understanding of mixing in large-scale oceanographic flows and atmospheric flows is crucial for better understanding of climate and processes that shape it. The analysis and control of mixing at macro and micro scales is receiving great attention because of the potential for optimizing the performance of many flow processes. The need to enhance mixing is felt in many industrial applications involving turbulent or laminar flows. Flows in internal combustion engines, gas turbines, industrial burners and broilers, chemical propellants and incinerators, to name a few, are typical turbulent flows of relevance in power generation, the glass industry, public and private transportation and pollution. Flows in stirred tank reactors, partitioned pipe mixers and roller bottles, to name a few, are typical laminar flows of relevance in chemical, petrochemical pharmaceutical, and food industry processes. Flows in micromixers are of relevance in biomedical applications.
In geophysical flows, there are large spatial and temporal scales on which mixing evolves that can be described well by using geometrical dynamical systems theory coupled with statistical analysis of the process. Here, the challenge to traditional dynamical systems theory is typically aperiodic time-dependence of such flows. Small-scale turbulence on the other hand, adds statistical variability to large-scale events. In modern and futuristic industrial applications, the time allowed to find the appropriate mixing action is becoming increasingly shorter while the demands are increasingly more severe. A better understanding of mixing is crucial for improving old and designing new mixing devices that are able to reduce the residence mixing time, improve mixing homogeneity and allow the process of new materials highly sensitive to the presence of concentration and temperature gradients. Mixing of two soluble chemically reacting fluids, even in the simplest case, involves four non-linearly coupled processes: convection, stretching, diffusion, and chemical reaction. A better understanding and control of these processes will minimize partially mixed structures that exhibit strong variability in local composition and, consequently, reduce the spatial dependence of the chemical reaction rates. The control of mixing is a highly relevant, very interesting, and extremely challenging new topic of research for the control theory and dynamical systems community. In particular, control of mixing could be achieved by creating non-equilibrium dynamics in complex nonlinear systems governing the flow phenomena. This non-equilibrium dynamics may be periodic or aperiodic, but should result in a beneficial chaotic motion of the fluid particles with a consequent mixing enhancement.
The aim of the present course is to provide an overview of the physics, mathematics and state-of-the-art theoretical/numerical modeling and experimental investigations of mixing in turbulent and laminar flows at macro and micro scales. In regard to laminar mixing, the course intends to present mathematical and physical underpinnings of this subject that has received much attention recently due to developments in microfluidic flows. Geometrical theory of dynamical systems will be developed, and geometrical properties of stretching and folding of material lines analyzed. Statistical theory of fluid mixing, based on dynamical systems concepts, will be introduced.
In regard to turbulent mixing, the course will characterize the preferred structures in the vorticity and scalar fields and their mutual dynamics and kinematics as they cascade to small scales. Particular attention is given to the characterization of the mixing properties of coherent three-dimensional vortical structures using the dynamical systems concepts. The course intends to present realistic sensors and actuators that can be used in engineering applications in order to control mixing. Finally, the course presents some examples of control of mixing in micro and macro applications, such as micromixers, jets in crossflow, channel flows and oceanographic flows.
WORKSHOP: This course will be complemented by a workshop. The scope of the workshop is to provide a fertile environment for discussions where participants in the course, as well as academic and industry experts from fluids, combustion and control and geophysics disciplines, could present their recent results. This course is addressed to a wide range of scientists and practitioners: postgraduates, postdoctoral researchers, mechanical, chemical and aeronautical engineers, geophysical fluid dynamicists and applied mathematicians in universities and industries.